# Seminars (DNM)

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Event When Speaker Title Presentation Material
DNMW01 14th January 2019
09:45 to 10:30
Peter Palffy-Muhoray Attractive and Repulse Interactions in Dense Nematics
DNMW01 14th January 2019
11:00 to 11:45
Jonathan Robbins Asymptotics of Landau-de Gennes theory
We consider the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain subject to integer-degree boundary conditions, consistent with the absence of defects, in the physically relevant regime of weak elasticity. At leading order, the minimum-energy configuration is described by the simpler Oseen-Frank theory. We obtain the next-order corrections using a Gamma-convergence approach. These turn out to be determined by an algebraic rather than a differential equation. The most important qualitative feature is the appearance of biaxiality, with strength and orientation determined by the gradient of the Frank director. The results are applied to the variational problem in which only the degree of the boundary conditions is fixed. In contrast to an analogous and well-known problem in the Ginzburg-Landau model of vortices, it is found that the energy is only partially degenerate at leading order, with a family of conformal boundary conditions, parameterised by the positions of escape points (the analogues of vortices), achieving the minimum possible energy. This partial degeneracy is lifted at the next order.

This is joint work with G di Fratta, V Slastikov and A Zarnescu.
DNMW01 14th January 2019
11:45 to 12:30
Halim Kusumaatmaja Surveying Energy Landscapes: From Protein Folding to Bistable Liquid Crystal Device and Cylindrical Buckling
Given a Hamiltonian or energy functional, I will describe a suite of numerical methods designed to efficiently characterise its energy landscape. The methods allow systematic study of not only the most relevant minimum energy configurations, but also the transition pathways between any two minima, as well as their corresponding energy barriers and transition state configurations. I will then illustrate the versatility of the methods by studying three very distinct problems. First, using a multistable liquid crystal square well as an example, I will provide insights into how optimal transition pathways can be qualitatively different even though the minimum energy configurations remain similar, and how certain minima can lose stability. Second, I will study how thin cylindrical shells buckle. In particular, I will discuss the large number of minima we observe and whether we have a glassy or a structure-seeker energy landscape. Third, while efficient algorithms for cluster detection and data completion in high-dimensional spaces are well developed, considerably less is known about the reliable inference of state transition dynamics in such settings. Here I will show how we can reconstruct low-dimensional dynamical transition networks from high-dimensional static samples, and demonstrate the practical potential of our scheme for several protein folding transitions.
DNMW01 14th January 2019
14:30 to 15:15
Giacomo Canevari Design of effective bulk potentials for nematic liquid crystals via homogenisation
The material properties of a given nematic liquid crystal may be altered by dopants, i.e. suspended micro- to nano- particles in the nematic host. Even under weak anchoring conditions at the surface of the inclusions, and in the so-called "dilute regime" (i.e., when the total volume occupied by the inclusions is small), dopants can still have a significant effect; for instance, they can modify the nematic-isotropic transition temperature. In this talk, we consider a Landau-de Gennes model for a periodic suspension of small colloidal inclusions in a nematic host. By studying the homogenised limit, and proving rigorous convergence results for local minimisers, we compute the effective free energy for the doped material. In particular, we show that not only the phase transition temperature, but any coefficient of the quartic Landau-de Gennes bulk potential can be tuned. The talk is based on a joint work with Arghir D. Zarnescu (BCAM, Bilbao, Spain).
DNMW01 14th January 2019
15:15 to 16:00
Jamie Taylor Construction of two dimensional convex shapes from their excluded volumes
In a dilute system of spatially homogeneous system of hard, non-spherical, particles, Onsager tells us that all phase behaviour can (in principle) be derived by explained by understanding how much volume is excluded to one particle by the presence of another, given their relative orientations. In this talk, we will consider the case of two dimensional convex bodies, and describe forward and inverse problems related to evaluating their so-called excluded volume function, which depends entirely on the particle shape. In particular, we propose and analyse an algorithm which can reconstruct a convex body from an excluded volume function, although such solutions can be shown generally to be non-unique. While only providing results in the simpler two-dimensional setting, these results pave the way for design of particle shape based on desired phase behaviour properties.
DNMW01 14th January 2019
16:15 to 17:00
Daniel Beller Defect loops in 3D active nematics
Co-authors: Guillaume Duclos, Minu Varghese, Matthew Peterson, Arvind Baskaran, Aparna Baskaran, Michael Hagan (Martin A. Fisher School of Physics, Brandeis University ), Debarghya Banerjee (Max Planck Institute for Dynamics and Self-Organization, Göttingen), Federico Toschi (Department of Applied Physics, Eindhoven University of Technology), Sebastian Streichan, Zvonimir Dogic (Department of Physics, University of California, Santa Barbara), Vincenzo Vitelli (James Franck Institute and Department of Physics, University of Chicago), Robert Pelcovits (Department of Physics, Brown University), Thomas Powers (School of Engineering and Department of Physics, Brown University). Abstract: In 2D active nematics, internally driven chaotic flows are characterized by the continual production, motion, and annihilation of point defect pairs. We investigate the behavior of active nematics in 3D, for which we have developed an experimental model system of microtubules and molecular motors, as well as numerical modeling approaches. The defects characterizing chaotic flow are here curvilinear rather than point-like. We present a theoretical model predicting a certain class of closed disclination loops to be the system’s generic singularities. Through detailed analysis of experimental and numerically generated configurations, we show how our predictions of defect topology, geometry, and dynamics provide important insights into this highly complex 3D system.
DNMW01 15th January 2019
09:00 to 09:45
Richard James Materials from Mathematics
We present some recent examples of new materials whose synthesis was guided by some essentially mathematical ideas. They are materials that undergo phase transformations from one crystal structure to another, with a change of shape but without diffusion. They are hard materials, but nevertheless show liquid-like changes of microstructure under a fraction of a degree change of temperature. The underlying mathematical theory was designed to identify alloys that show low hysteresis and exceptional reversibility. The new alloys, of which Zn_45Au_30Cu_25 and Ti_54.7Ni_30.7Cu_12.3Co_2.3 are currently the best examples, do show unprecedented levels of these properties, but also raise fundamental questions for mathematical theory. Magnetoelectric properties of solids are often sensitive to lattice parameters, so they can be switched on and off at a phase transformation: briefly, multiferroism by reversible phase transformation. This switching can be combined with induction in the ferromagnetic case, or capacitance in the ferroelectric case, to yield devices that convert heat directly to electricity, without a separate electrical generator. We describe briefly the associated mathematical theory. The resulting multiferroics provide interesting possible ways to recover the vast amounts of energy stored on earth at small temperature difference. They move heat produced by natural and man-made sources from higher to lower temperature and therefore contribute negatively to global warming.
DNMW01 15th January 2019
09:45 to 10:30
Francesco Della Porta A moving mask hypothesis to select physically relevant microstructures
In this talk I present a moving mask hypotheses that can be used as a selection mechanism for physically relevant microstructures in thermally induced martensitic phase transitions. The moving mask hypotheses allows to better understand the importance of the cofactor conditions, particular conditions of supercompatibility between phases, which are believed to influence reversibility.
DNMW01 15th January 2019
11:00 to 11:45
Ole Martin Lovvik High-throughput search for new phase transformation materials with low hysteresis
Co-authors: Monika Løberg (University of Oslo), Nicholas Pike (University of Oslo)
Phase transformation materials (PTMs) can be used for energy harvesting of heat from low-temperature heat sources if the phase transformation is accompanied by an abrupt jump in a physical property like magnetization or polarization. In addition, the temperature hysteresis should be low in order to prevent losses. The criteria for this supercompatibility can be described in terms of the crystal structure of the phases. We are exploiting this in a new project where we are using various experimental and theoretical high-throughput techniques to search for unknown PTMs with very low hysteresis and a large change in potential energy. Some preliminary results are shown and discussed in light of the recent international progress in the field.
DNMW01 15th January 2019
11:45 to 12:30
Eckhard Quandt Supercompatibility and its role on fatigue in shape memory materials
Functional shape memory alloys need to operate reversibly and repeatedly. This is especially crucial for many future applications such e.g. elastocaloric cooling, where more than ten million transformation cycles will be required. In recent years examples of unprecedented functional and structural fatigue resistance and lowered hysteresis in shape memory alloys have been achieved by combining conditions of supercompatibility between phases with suitable grain size and a favorable array of fine precipitates (1). The relative roles of these factors, especially in the case of the more demanding stress-induced phase transformations, will be discussed (2) also in view of elastocaloric applications. (1) Chluba, C.; Ge, W.; Lima de Miranda, R.; Strobel, J.; Kienle, L.; Quandt, E.; Wuttig, M.: Ultralow-fatigue shape memory alloy films, Science 348 (2015), 1004-1007. (2) Gu, H.; Bumke, L.; Chluba, C.; Quandt, E.; James, R.D.: Phase engineering and supercompatibility of shape memory alloys, Materials Today 21 (2018), 265-277.
DNMW01 15th January 2019
14:30 to 15:15
Angkana Ruland Microstructures in SMA: Rigidity, Non-Rigidity and Simulations
Co-authors: Jamie M Taylor (BCAM), Christian Zillinger (USC), Barbara Zwicknagl (TU Berlin)In this talk I will discuss a striking dichotomy which occurs in the mathematical analysis of microstructures in shape-memory alloys: On the one hand, some models for these materials display a very rigid structure with only very specific microstructures, if one assumes that surface energies are penalised. On the other hand, without this penalisation, for the same models a plethora of very wild solutions exists. Motivated by this observation, we seek to further understand and analyse the underlying mechanisms. By discussing a two-dimensional toy model and by constructing explicit solutions, we show that adding only little regularity to the model does not suffice to exclude the wild solutions. We illustrate these constructions by presenting numerical simulations of them. The talk is based on joint work with J. M. Taylor, Ch. Zillinger and B. Zwicknagl.
DNMW01 15th January 2019
15:15 to 16:00
Chantal Valeriani Designing novel functional materials made of active colloids: the role played by interactions
Active matter systems are composed of constituents that consume energy in order to move or exert mechanical forces, constantly driving themselves away from equilibrium [1]. Examples of active particles at the mesoscopic scale are living, such as bacteria, or artificial, such as active colloids [2,3] Experiments on spherical man-made self-propelled colloids have shown that active particles present interesting emergent collective properties [4–6], such as motility-induced phase separation (MIPS), involving spontaneous assembly of particles due to the persistence of their direction of motion [7]. An example of colloids undergoing MIPS under suitable conditions are Active Brownian Particles (ABP), i.e. self-propelled Brownian particles interacting with each other via a purely repulsive potential [8]. In order to design novel functional materials, one might need to gain control on the self-assembly process of active colloids. With this goal in mind, we have explored the competition between activity and a broad range of interactions in a suspension of active colloids, considering either isotropic (strongly repulsive [9], attractive [10,11], micelle-inducing potential [12]) or anisotropic (Janus-like) potential[13], unravelling the relevance of hydrodynamics [11,14] and investigating mixtures of active/passive particles [15,16,17]. REFERENCES: [1] C. Bechinger et al. Rev. Mod. Phys. 88, 045006 (2016). [2] W.F. Paxton et al. Chem. Commun. 441, 3 (2005). [3] S. Fournier-Bidoz et al. J. Am. Chem. Soc. 126, 13424 (2004). [4] S. Thutupalli, R. Seemann, S. Herminghaus New J. Phys. 13, 073021 (2011). [5] D. Nishiguchi, Masaki S. Phys. Rev. E 92, 052309 (2015). [6] I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, T. Speck. Phys.Rev. Lett. 110, 238301 (2013). [7] M.E. Cates, J. Tailleur. Annu. Rev. of Condens. Matt. Phys. 6, pp. 219-244 (2015). [8] S.Mallory, C.Valeriani and A.Cacciuto Annual review of Physical Chemistry, 69 59 (2018) [9] Diego Rogel Rodriguez, Francisco Alarcon, Raul Martinez, Jorge Ramirez, and Chantal Valeriani, in preparation (2018) [10] B. Mognetti, A. Saric, S. Angioletti-Uberti, A. Cacciuto, C. Valeriani and D. Frenkel Phys.Rev.Lett., 111 245702 (2013) [11] F.Alarcon, C.Valeriani and I.Pagonabarraga Soft Matter 10.1039/C6SM01752E (2017) [12] C.Tung, J.Harder, C.Valeriani and A.Cacciuto, Soft Matter 12 555 (2016) [13] S.Mallory, F.Alarcon, A.Cacciuto and C.Valeriani New Journal of Physics (2017) [14] F.Alarcon, E.Navarro, C.Valeriani and I.Pagonabarraga, PRE submitted (2018) [15] J.Harder, S.Mallory, C.Tung, C.Valeriani and A.Cacciuto, J.Chem.Phys. 141 194901 (2014) [16] R.Martinez, F.Alarcon, D.R.Rodiguez, J.L.Aragones and C.Valeriani, EPJE 41 91 (2018) [17] Diego Rogel Rodriguez, Francisco Alarcon, Raul Martinez, Jorge Ramirez, and Chantal Valeriani, under review JCP (2018) CO-AUTHORS: Francisco Alarcon, Raul Martinez, Juan Luis Aragones, Jorge Ramirez, Stewart Mallory, Ignacio Pagobanarraga, Angelo Cacciuto
DNMW01 15th January 2019
16:15 to 17:00
Barbara Zwicknagl Microstructures in martensites: Scaling regimes and optimal domain shapes
Microstructures in martensites are often modeled variationally by singularly perturbed multiwell elastic energies. In this talk, I shall disusss recent analytical progress on the associated non-convex vector-valued energy minimisation problems. The focus will lie on scaling regimes for geometrically linear models for martensitic nuclei with small volume fraction of one martensitic variant, and on needle-like microstructures.
This talk is based on joint works with S. Conti, J. Diermeier, N. Lüthen, D. Melching, and M. Rumpf.
DNMW01 15th January 2019
17:00 to 18:00
Mike Cates Reverse Engineering of Design Principles using Biased Dynamics
Suppose we want to create a material with a certain unusual property. One strategy is to start with a model of an existing material without that property, and bias its dynamics to sample unlikely trajectories for which the atypical property is pres ent. Looking at the biased trajectories, it may be possible to spot some choice of local interactions that would achieve the required effect. I will describe an instance of this in the realm of self-propelled spherical colloids. Here, biasing the ensemble to reduce colloidal collisions creates states in which the propulsion directions have polar order: accordingly, collisions can be reduced by introducing polar interactions. While this particular outcome is relatively obvious, the method is generalizable in principle to more complex cases where genuinely new design principles might emerge.

Coauthors: Takahiro Nemoto, Étienne Fodor, Robert L. Jack, Julien Tailleur

Reference: Optimizing active work: dynamical phase transitions, collective motion and jamming. T. Nemoto et al, arXiv 1805.02887
DNMW01 16th January 2019
09:00 to 09:45
Margarida Telo da Gama Designing colloidal structures: fast and slow dynamics
Low-density networks of molecules or colloids form at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim’s theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid–gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), in low-density networks the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition. We show that the low temperature slow dynamics is universal, being observed also in the single phase region.

C. S. Dias, J. M. Tavares, N. A. M. Araujo and M. M. Telo da Gama, Soft Matter 14, 2744 (2018).
DNMW01 16th January 2019
09:45 to 10:30
Pingwen Zhang Defects of Liquid Crystals
Defects are local breakings of symmetry in an ordered medium, which can be found in various fields of physics such as solids, liquid crystals, astrophysics and high energy physics. Defects in liquid crystals are of great practical importance in material science and theoretical interest in physics and mathematics. In this talk, I will review the representation, modeling and computation of defects in liquid crystals. Within the Landau-de Gennes tensor model, we found a rich variety of defect patterns in topologically confined nematic liquid crystals, and the profiles of point defect and disclination line are obtained. The connection and difference between defect patterns under the tensor model and the vector model will be discussed. Finally, some conjectures and challenges are proposed to summarize the common characteristics of defects, in the hope of providing a deeper understanding of the defect pattern in nematic liquid crystals.
DNMW01 16th January 2019
11:00 to 11:45
Randall Kamien Knitogami
Knitting is not knotting, but minimal manifolds make modeling fabrics fun and facile.  Tying these templates together produces a plethora of patterns.
DNMW01 16th January 2019
11:45 to 12:30
Dirk Aarts Measuring g(r) by test-particle insertion
The pair distribution function g(r) plays a central role in liquid state theory, linking structure and thermodynamics. It is typically measured by constructing a histogram of the distances between all pairs of particles, which is used in simulations and experiments where single particle coordinates can be obtained. Here, we present a novel method based on Henderson’s method [1] for measuring the cavity distribution function, going beyond our recent work on particles with hard interactions [2]. The method measures g(r) in a highly efficient way; moreover, it allows us to obtain an effective pair potential between colloidal particles in experiment.
DNMW01 17th January 2019
09:00 to 09:45
Antonio DeSimone Morphing and shape control: some lessons from the motility of unicellular organisms
Locomotion strategies employed by unicellular organism are a rich source of inspiration for studying mechanisms for shape control. In fact, in an overwhelming majority of cases, biological locomotion can be described as the result of the body pushing against the world, by using shape change. Motion is then a result Newton’s third and second law: the world reacts with a force that can be exploited by the body as a propulsive force, which puts the body into motion following the laws of mechanics. Strategies employed by unicellular organisms are particularly interesting because they are invisible to the naked eye, and offer surprising new solutions to the question of how shape can be controlled.

In recent years, we have studied locomotion and shape control in Euglena gracilis using a broad range of tools ranging from theoretical and computational mechanics, to experiment and observations at the microscope, to manufacturing of prototypes. This unicellular protist is particularly intriguing because it can adopt different motility strategies: swimming by flagellar propulsion, or crawling thanks to large amplitude shape changes of the whole body (a behavior known as metaboly). We will survey our most recent findings within this stream of research.

References:

1. Rossi, M., Cicconofri, G., Beran, A., Noselli, G., DeSimone, A.:
Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes.
PNAS 2017

2.
Noselli, G., Beran, A., Arroyo, M., DeSimone, A.:
Swimming Euglena respond to confinement with a behavioral change enabling effective crawling.
Nature Physics (to appear, 2019)
DNMW01 17th January 2019
09:45 to 10:30
Cyrill Muratov Analysis of Novel Domain Wall Types in Ferromagnetic Nanostructures
Co-authors: Valeriy Slastikov (University of Bristol), Ross Lund (NJIT). Recent advances in nanofabrication allow an unprecedented degree of control of ferromagnetic materials down to the atomic scale, resulting in novel nanostructures whose properties are often dominated by material interfaces. Mathematically, these systems give rise to challenging problems in the calculus of variations that feature non-convex, vectorial, topologically constrained, multi-scale variational problems. Yet despite the daunting complexity inherent in the problem arising from the 21st century technological applications, rigorous variational analysis can still elucidate energy-driven pattern formation in these systems. In this talk, I will discuss several examples of variational problems emerging from models of current ferromagnetic nanostructures under development. With the help of asymptotic techniques and explicit solutions, I will give three examples in which the energy minimizing configurations may be characterized in terms of optimal one-dimensional transition lay er profiles separating magnetic domains with different magnetization orientation.
DNMW01 17th January 2019
11:00 to 11:45
Radu Ignat Symmetry in materials science models under the divergence constraint
The symmetry of the order parameter is one of the most important features in materials science.
In this talk we will focus on the one-dimensional symmetry of transition layers u in some variational
models (such as smectic liquid crystals, thin film blisters, micromagnetics...)
where the divergence div(u) vanishes.
Namely, we determine a class of nonlinear potentials such that the minimal transition layers are
one-dimensional symmetric. In particular, this class includes in dimension N=2 the nonlinearities w^2
with w being an harmonic function or a solution to the wave equation,
while in dimensions N>2, this class contains a perturbation of the standard Ginzburg-Landau potential
as well as potentials having N+1 wells with prescribed transition cost between the wells.
For that, we develop a theory of calibrations for divergence-free maps in R^N (similar to the theory of entropies
for the Aviles-Giga model when N=2).
This is a joint work with Antonin Monteil (Louvain, Belgium).
DNMW01 17th January 2019
11:45 to 12:30
Luc Nguyen Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory
We study a Laudau-de Gennes model for liquid crystals where both the energy functional and the boundary data are invariant under the orthogonal group. In three dimensional settings, it is conjectured that minimizers break the rotational symmetry. We show however that in two dimensional settings, this no longer holds when the boundary data have no topological obstruction: the minimizers are unique and rotationally symmetric'. As an application, we obtain existence of (multiple) non-minimizing rotationally symmetric critical points. Joint work with Radu Ignat, Valeriy Slastikov and Arghir Zarnescu.
DNMW01 17th January 2019
14:30 to 15:15
Rodrigo Ledesma-Aguilar Manipulating droplets on lubricant impregnated surfaces
Lubricant impregnated surfaces are bio-inspired surfaces that offer virtually no static friction to the motion of droplets. In this talk I will present experimental, theoretical and simulation results that demonstrate how droplets can be manipulated on such surfaces.
DNMW01 17th January 2019
15:15 to 16:00
Nigel Mottram Pressure-driven active nematics systems: possible optimisation and design methods
Active nematic fluids combine the flow-molecular orientation coupling phenomena seen in liquid crystals and the presence of internal energy generation that lead to spontaneous flow. These two effects combine to produce a fascinating non-eqiuilibrium system, in which enhanced mixing, defect creation and anihilation and active turbulence have all been observed. In this presentation we will consider a relatively simple system - pressure-driven flow in a channel - in which multiple non-trivial equilibria can be found. The interaction between the strength of activity, the applied pressure gradient and other parameters such as boundary anchoring constraints will be explored, with the aim of allowing optimisation of, for instance, the observed fluid flux. Using similar methodologies to those commonly used in the design of liquid crystal display devices, we are able to affect the fluid flux of each possible stable state and to even change the number of possible equilibria.

Co-authors: Dr Geoff McKay and Josh Walton (Strathclyde)
DNMW01 17th January 2019
16:15 to 17:00
Claudio Zannoni Realistic prediction of molecular organizations in thin organic films
The molecular organization of organic semiconductors (OSC), and in particular of those that present liquid crystal (LC) phases [1], has a strong influence on charge and energy transport, particularly at interfaces [2]. Predicting realistic morphologies and molecular organizations from chemical structure is, however, far from easy and has only recently proved doable by atomistic molecular dynamics [3-5]. The issue is further complicated in thin films, where the material is strongly affected by surface interactions, even if obtaining information on alignment and anchoring is essential to optimize the specific interfacial orientations required for different applications (e.g. for Field Effect Transistors, rather than Organic Solar Cells).
Here we show examples of the prediction of alignment and anchoring of organic functional materials (cyanobiphenyls in particular) at the interface with different substrates giving alignment parallel to the support surface e.g. for crystalline and glassy silica with different roughness [5] or polymers like PMMA or polystyrene [6]. We also show how hometropic orientations can be obtained coating the silica surface with suitable self assembled monolayers (SAM) of alkysilanes [7,8]. The importance of the film fabrication process on molecular alignment is also briefly discussed taking as an example the vapour deposition of sexithiophene (T6) on C60 [9] or pentacene on silica [10] While detailed atomistic simulations are on the way to providing reliable results for samples of the order of a few thousand molecules, going to significantly larger sizes comparable to those of real devices (e.g. 100nm thick) demands samples of the order of, say 106 molecules, which in turns requires giving up some details, using some form of coarse graining (CG). Ideally this CG procedure should provide reliable morphologies, albeit at molecular, rather than fully atomistic resolution, but also be capable of returning on demand the atomistic details needed for further charge transport calculations. Some examples will be presented of such a reversible CG approach based on modelling organic functional materials with collections of anisotropic Gay-Berne beads [11].

[1] H. Iino, T. Usui and J-I. Hanna, Nature Comm. 6, 6828 (2015)
[2] O.M. Roscioni, C. Zannoni, Molecular Dynamics Simulation and its Applications to Thin-Film Devices, in Unconventional Thin Film Photovoltaics, edited by E. Da Como, F. De Angelis, H. Snaith, A. B Walker, RSC (2016)
[3] J. Idé, R. Méreau, L. Ducasse, F. Castet, H. Bock, Y. Olivier, J. Cornil, D. Beljonne, G. D’Avino, O. M. Roscioni, L. Muccioli, C. Zannoni, JACS, 136, 2911 (2014)
[4] M. F. Palermo, L. Muccioli, C. Zannoni, PCCP, 17, 26149 (2015)
[5] O. M. Roscioni, L. Muccioli, R. G. Della Valle, A. Pizzirusso, M. Ricci, C. Zannoni, Langmuir, 29, 8950 (2013).
[6] M.F. Palermo, F. Bazzanini, L. Muccioli, C. Zannoni, Liq. Cryst. 44, 1764 (2017)
[7] A. Mityashin, O.M. Roscioni, L. Muccioli, C. Zannoni, V. Geskin, J. Cornil, D. Janssen, S. Steudel, J. Genoe, P. Heremans, ACS Applied Materials & Interfaces, 17, 15372 (2014)
[8] O. M. Roscioni, L. Muccioli, C. Zannoni, ACS Applied Materials & Interfaces 9, 11993 (2017).
[9] G. D'Avino, L. Muccioli and C. Zannoni, Adv. Funct. Mater. 25, 1985 (2015).
[10] O. M. Roscioni, G. D'Avino, L. Muccioli and C. Zannoni, J. Phys. Chem. Lett. 9, 6900 (2018).
[11] M. Ricci, O. M. Roscioni, L Querciagrossa, C. Zannoni. to be published (2019)
DNMW01 18th January 2019
09:00 to 09:45
John Ball Remarks on polycrystalline microstructure
The talk will discuss some questions related to the understanding of microstructures arising from martensitic phase transformations, and the role of compatibility across grain boundaries, drawing on joint work with Carsten Carstensen (Humboldt University, Berlin).
DNMW01 18th January 2019
09:45 to 10:30
Dmitry Golovaty Interfaces with singularities: understanding phase transitions in nematic liquid crystals
Experimental data indicates that the nematic-to-isotropic phase transition in liquid crystals may proceed via evolution of interfaces that are not smooth. In this talk, our goal is to provide a possible explanation for the observed singularities of the phase boundaries.

In order to develop an initial understanding of transitions between the ordered and disordered states, we formulate a simple toy model based on the modified Ginzburg-Landau-type energy defined over vector fields on the plane. The corresponding variational model consists of anisotropic gradient terms and a potential that vanishes on two disconnected sets.

The principal observation from the study of the simplified model is that the phase boundary singularities can be explained by large disparity between the elastic constants in the gradient contribution to the energy. In the talk we will present a combination of rigorous analysis and numerics that leads to this conclusion. This is a joint work with Michael Novack, Peter Sternberg, and Raghavendra Venkatraman.
DNMW01 18th January 2019
11:00 to 11:45
Alenka Mertelj Polar order in liquids
Polar order, i.e., ferromagnetic or ferroelectric, in 3D liquids is experimentally rarely observed. In this talk I will discuss the reason for this and show two examples of how shape of constituents can promote polar order. The first example is a ferromagnetic liquid phase, which emerges in a suspension of magnetic nanoplatelets in isotropic solvent as a result of platelets’ shape. The second example is antiferroelectric splay nematic phase, which appears in materials made of wedge-shaped molecules with large electric dipole moments.
Co-Authors: Darja Lisjak1, Patricija Hribar Boštjančič1, Borut Lampret1, Luka Cmok1, Žiga Gregorin1, Natan Osterman1, Nerea Sebastian1, Martin Čopič1, Joachim Kohlbrecher2, Juergen Klepp3, Richard J. Mandle4, Rachel R. Parker4, Adrian C. Whitwood4, John W. Goodby4
1J. Stefan Institute, Slovenia; 2PSI Villigen, Switzerland; 3University of Vienna, Austria; 4University of York, UK
DNMW01 18th January 2019
11:45 to 12:30
Mark Warner Microstructure for continuous and localised intrinsic curvature creation
DNM 23rd January 2019
15:00 to 16:00
Friedemann Brock Isoperimetric inequalities on RN with respect to homogeneous weights
We solve a class of isoperimetric problems in the whole spacewith respect to monomial weights.  Our results imply that the optimizers  in some Caffarelli-Kohn-Nirenberg inequalities are radial. Further, they are used to obtain sharp apriori-bounds for solutions to some weighted elliptic BVPs.  \\ This is joint work with A. Alvino, F. Chiacchio and M.R. Posteraro (Napoli).

DNM 30th January 2019
17:00 to 18:00
Jonathan Robbins Collective coordinates, asymptotics and domain wall dynamics in ferromagnets
The method of collective coordinates is a simple and widely used variational procedure for finding approximate solutions to many- or infinite-dimensional, possibly damped and driven, Hamiltonian systems. The approximate solutions are typically characterised by a small number of time-dependent parameters, which are understood to describe a small number of activated modes. The simplicity of the method comes at a price, however, as it does not allow a determination of how good (or bad) the approximation is. In certain regimes, asymptotic expansions can provide the requisite estimates, though they require more work.   This is illustrated for the problem of the motion of domain walls in ferromagnets. Domain walls are interfaces between differently oriented magnetic domains, and the dynamics of these interfaces under applied magnetic fields and currents is a problem of current physical and technological interest.   We also describe behaviour in a high-field regime, beyond the well-known Walker breakdown, where one of the domains becomes unstable. A new type of dynamics emerges that appears to be beyond the reach of a collective coordinate description. It can be described using front propagation theory, but rigorous results (akin to a KPP analysis) appear to be challenging.   This is joint work with Arseni Goussev, Valeriy Slastikov, and Sergiy Vasylkevych.

DNM 6th February 2019
16:00 to 16:40
Lech Longa Nematic twist-bend:the heliconical phase of nonchiral liquid crystals
The (one-dimensional modulated) nematic twist-bend phase (NTB), a fifth member of the nematic family, formed through spontaneous chiral symmetry breaking in the isotropic and nematic phases of a large class of liquid crystalline systems of achiral molecules (bent-core-, dimeric-, trimeric, etc.) is one of the most spectacular recent discoveries in soft matter physics. It has become a major field of activity in liquid crystal research across the world [1]. Its unique property is a heliconical structure of nanoscale pitch , where the director rotates on the cone like in the smectic C*, but without long-range positional order of molecules.
Initially, the theoretical concept of this phase has been presented by R. B. Meyer [2]. Subsequently Dozov [3] suggested that the formation of the NTB phase can be facilitated by the shape of bent–core molecules. In 2014 Shamid et. al. [4,5] showed that polar order induced by bend flexopolarization in liquid crystals of bent-core molecules can be responsible for the stabilization of NTB and of the novel class of blue phases. Their analysis was consistent with predictions of the mesoscopic theory of flexopolarization that we introduced as early as in 1990 [6, pp. 3464-3467].
Here, within generalized Landau-deGennes theory and molecular simulations we present theoretical studies concerning stability of NTB relative to other homogeneous and inhomogeneous structures [6-9]. We use a systematic bifurcation and numerical analyses to identify absolutely stable one-dimensional modulated structures that can condense from the isotropic phase. In addition, the behavior of NTB subjected to an external field is discussed in detail. We show that by controlling field’s strength and sign of anisotropy of permittivity a web of new structures can be identified.
Acknowledgments
This work is supported by the Grant No. DEC-2013/11/B/ST3/04247 of the National Science Centre in Poland.
[1]For a recent review see A. Jákli, O. D. Lavrentovich, and J. V. Selinger, “Physics of liquid crystals of bent-shaped molecules”, Rev. Mod. Phys., 90, 045004 (2018).
[2]R. B. Meyer, “Structural Problems in Liquid Crystal Physics”, pp. 273-373 in Les Houches
Summer School in Theoretical Physics, 1973 (Gordon and Breach, New York, 1976); Phys. Rev. Lett. 22, 918 (1969).
[3]I. Dozov, “On the spontaneous symmetry breaking in the mesophases of achiral banana-shaped molecules”, Europhys. Lett. 56, 247 (2001).
[4]S. M. Shamid, S. Dhakal and J. V. Selinger, ‚“Statistical mechanics of bend flexoelectricity and the twist-bend phase in bent-core liquid crystals”, Phys. Rev. E 87, 052503 (2013).
[5]S. M. Shamid, D. W. Allender and J. V. Selinger, “Predicting a Polar Analog of Chiral Blue Phases
in Liquid Crystals”, Phys. Rev. Lett. 113, 237801 (2014).
[6]L. Longa and H.-R. Trebin, “Spontaneous polarization in chiral biaxial liquid crystals”, Phys. Rev. A 42, 3453 (1990).
[7]Longa L, Pajak G., “Modulated nematic structures induced by chirality and steric polarization”.
Phys Rev E. Rapid 93, 040701 (2016).
[8]Trojanowski K, Cieśla M, and Longa L., “Modulated nematic structures and chiral symmetry
breaking in 2D”, Liquid Crystals, DOI: 10.1080/02678292.2016.1261192 (2016).
[9] Pajak G., Longa L, Chrzanowska A., “Nematic twist--bend phase in an external field”, www.pnas.org/cgi/doi/10.1073/pnas.1721786115, PNAS, 115, E10303–E10312 (2018).
DNM 6th February 2019
16:40 to 17:20
Juho Lintuvuori Hydrodynamic assembly of out of equilibrium colloids
In this talk, I will describe our recent and ongoing simulation efforts of hydrodynamic stabilisation of coherent structures formed by out of equilibrium spherical (colloidal) particles suspended in a fluid. I will provide examples of both internally and externally driven systems. In the first case we will consider active (self-propelling)particles, while in the second case a system of driven colloidal spinners is created by energising passive particles by an external rotational drive. In both of these systems, there exists an unexpected coupling between translational and rotational motion: Spherical active particles, modelled as squirmers, can form small hydrodynamically bound chiral spinners consisting of two or three particles, when exposed to gravity-like aligning field near a surface. Passive but rotationally driven particles show a spontaneous formation of a large scale vortex at low but finite Reynolds numbers. Finally, I will discuss mixtures of the driven spinners, where the other component can be either passive particles or particles with an opposite spin giving a rise to a racemic mixture.
DNM 6th February 2019
17:20 to 18:40
Nuno Araujo Finding the optimal nets for self-folding Kirigami
Three-dimensional shells can be synthesized from the spontaneous self-folding of twodimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements. The optimal nets are the ones that maximize the number of vertex connections, i.e., vertices that have only two of its faces cut away from each other in the net. Previous methods for finding such nets are based on random search and thus do not guarantee the optimal solution. We proposed a deterministic procedure [1]. Our method allows not only to design the self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of the nets with the maximum number of vertex connections is obtained.
[1] N. A. M. Araújo, R. A. da Costa, S. N. Dorogovtsev, J. F. F. Mendes, Physical Review Letters
120, 188001 (2018).
DNM 13th February 2019
16:00 to 16:40
Martin Kruzik On the passage from nonlinear to linearized viscoelasticity
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a nite-strain setting in the Kelvins-Voigt`s rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indierence. We identify weak solutions in the nonlinear framework as limits of time-incremental problems for vanishing time increment. Moreover, we show that linearization around the identity leads to the standard system for linearized viscoelasticity and that solutions of the nonlinear system converge in a suitable sense to solutions of the linear one. The same property holds for time-discrete approximations and we provide a corresponding commutativity result. This is a joint work with M. Friedrich (Munster).
DNM 13th February 2019
16:40 to 17:20
Marco Mazza Emergence of phytoplankton patchiness at small scales in mild turbulence
Sailors have known for millennia that periodically the seas appear of unusual color and can even turn red. These large swaths of colors stretching for tens or hundreds of km are caused by countless microscopic organisms called phytoplankton. These are microscopic algae that use sunlight to produce energy. They are the base of the marine food chain, and produce 50% or more of the oxygen in the atmosphere. Phytoplankton often encounter turbulence in their habitat. The spatial distribution of motile phytoplankton cells exhibits patchiness at distances of decimeter to millimeter scale for numerous species with different motility strategies. The explanation of this general phenomenon remains challenging. We combine particle simulations and continuum theory to study the emergence of patchiness in motile microorganisms in three
dimensions, by including hydrodynamic cell-cell interactions, which grow more relevant as the density in the patches increases. By addressing the combined effects of motility, cell-cell interaction and turbulent flow conditions, we uncover a general mechanism: the coupling of cell-cell interactions to the turbulent dynamics favors the formation of dense patches.
[R. E. Breier, et al., Proc. Natl. Acad. Sci. USA 115, 12112 (2018)]
DNM 13th February 2019
17:20 to 18:00
Christos Likos Polymer flow and polymer topology: linear chains, rings and knots flow differently
Modifications of the topological state of polymers are extremely interesting and relevant operations for a vast domain of scientific inquiry ranging from knot theory and polymer science all the way to materials science and biophysics, where cyclic and knotted DNA plays a key role in biological processes. Recent work has demonstrated that joining the two ends of a linear chain to form a cyclic (ring) polymer has a number of significant consequences in the structural [1,2] and rheological [3] properties of concentrated or semidilute solutions of the same. Accordingly, a number of questions arise regarding the behavior of linear, cyclic and knotted ring polymers under flow: how does the topology of the dissolved polymer affect its orientational resistance, as well as its rotation-, tumbling- or tank-treading motion under Couette flow? What consequences does shear flow have for knot localization along a sheared polymer? Can one make use of the different flow properties of various polymer topologies to build microfluidic devices that
act as filters/separators of topologically different polymers? By applying hybrid act as filters/separators of topologically different polymers? By applying hybrid (MPCD/MD) simulation techniques that take into account the hydrodynamics, we address the questions above for polymers of varying topologies, knotedness and the questions above for polymers of varying topologies, knotedness and stiffness and we analyze quantitatively the influence of polymer topology on singlepolymer properties under flow [4]. Polymer properties under Poiseuille flow will also be analyzed and on this basis concrete suggestions for the construction of topologyseparating microfluidic devices will be presented [5].
[References
[1] M. Z. Slimani, P. Bacova, M. Bernabei, A. Narros, C. N. Likos, and A. J. Moreno, ACS Macro
Letters {\bf 3}, 611 (2014).
[2] P. Poier, S. A. Egorov, C. N. Likos and R. Blaak, Soft Matter {\bf 12}, 7983 (2016).
[3] M. Kapnistos, M. Lang, D. Vlassopoulos, W. Pyckhout-Hintzen, D. Richter,
D. Cho, T. Chang, and M. Rubinstein, Nature Materials {\bf 7}, 997 (2008).
[4] M. Liebetreu and C. N. Likos, in preparation (2017).
[5] L. Weiß, A. Nikoubashman, and C. N. Likos, in preparation (2017).

DNM 20th February 2019
16:00 to 17:00
Virginia Agostiniani Monotonicity formulas in linear and nonlinear potential theory
In this talk, we rst recall how some monotonicity formulas can be derived along the level set ow of the capacitary potential associated with a given bounded domain. A careful analysis is required in order to preserve the monotonicity across the singular times, leading in turn to a new quantitative version of the Willmore inequality. Remarkably, such analysis can be carried out without any a priori knowledge of the size of the singular set. Hence, the same order of ideas applies to the p-capacitary potential of whose critical set, for p 6= 2, is not necessarily negligible. In this context, a generalised version of the Minkowski inequality is deduced.
Joint works with M. Fogagnolo and L. Mazzieri.

DNM 20th February 2019
17:00 to 18:00
Dorin Bucur Optimal honeycomb structures
In 2005-2007 Burdzy, Caffarelli and Lin, Van den Berg conjectured in different contexts that the sum (or the maximum) of the first eigenvalues of the Dirichlet-Laplacian associated to arbitrary cells partitioning a given domain of the plane, is asymptomatically minimal on honeycomb structures, when the number of cells goes to infinity. I will discuss the history of this conjecture, giving the arguments of Toth and Hales on the classical honeycomb problem, and I will prove the conjecture (of the maximum) for the Robin-Laplacian eigenvalues and Cheeger constants. The results have been obtained in joint works with I. Fragala, G. Verzini and B. Velichkov
DNM 21st February 2019
15:00 to 16:00
Elvira Zappale Lower semicontinuity and relaxation of nonlocal $L^\infty$ functionals.

We consider variational problems involving nonlocal supremal functionals, i.e.
L1(;Rm) 3 u 7! esssup(x;y)2  W(u(x); u(y)); with Rn a bounded, open set and a suitable function W : Rm Rm ! R.
Using the direct methods of the Calculus of Variations it is shown for m = 1 that weak lower semi-continuity holds if and only if the level sets of a symmetrized and suitably diagonalized version of W are
separately convex. Moreover the supremal structure of the functionals is preserved in the process of relaxation, a question which is still open in the related context of double-integral functionals. In our proofs we
strongly exploit the connection between supremal and indicator functionals, thus reformulating the relaxation problem into studying weak closures of a class of nonlocal inclusions. Some special assumptions on
W allow us to generalize the results to the vectorial setting m > 1.
Joint work with Carolin Kreisbeck (Utrecht University)

DNM 26th February 2019
15:00 to 15:45
Chris Pickard New directions for random search
Genuinely new knowledge and scientific insight can be obtained about matter by combining random numbers with reliable and efficient first principles methods. Diverse ensembles of initial structures can be generated, and structurally optimised. The resulting low energy structures are candidates for stable, and metastable, phases and/or defects that might be experimentally realised. This, of course, depends on a sufficiently broad and thorough sampling of configuration space. Algorithms which attempt to learn from (computational) experience are necessarily sequential, and correlated. A purely random strategy, as employed by Ab Initio Random Structure Searching (AIRSS),[1,2] is entirely parallel, and a natural fit to the high throughput computation (HTC) paradigm. The absence of correlation between the independent random samples ensures that it is possible to estimate when a sufficiently dense sampling has been achieved (or at least, has not been achieved). Challenging cases can be tackled by designing the initial random structures so that they focus the search in regions of configuration space that are anticipated to yield success. The design of these random “sensible” structures will be explored, along with some new directions which promise to accelerate random search,[3] and recent applications to materials.
[1] C. J. Pickard, and R. J. Needs, Phys. Rev. Lett., 97 (4), 045504 (2006) & Journal of Physics-Condensed
Matter, 23(5), 053201 (2011)
[3] C. J. Pickard, “Hyperspatial optimization of structures”, Phys. Rev. B, 99, 054102 (2019)
*C.J.P. is supported by the Royal Society through a Royal Society Wolfson Research Merit award
and the EPSRC through Grants No. EP/P022596/1.
Biography:
Chris Pickard is the Sir Alan Cottrell Professor of Materials Science in the Department of Materials
Science and Metallurgy, University of Cambridge. Previously he was Professor of Physics, University
College London (2009-2015), and Reader in Physics, University of St Andrews (2006-2008). He
has held both EPSRC Advanced and Leadership Research Fellowships, and is currently a Royal
Society Wolfson Research Merit Award holder (2015). He is a lead developer of the widely used
CASTEP code, and introduced both the GIPAW approach to the prediction of magnetic resonance
parameters and Ab Initio Random Structure Searching (AIRSS). In 2015 he won the Rayleigh Medal
and Prize of the Institute of Physics, awarded for distinguished research in theoretical, mathematical
or computational physics.
http://www.msm.cam.ac.uk/department/profiles/portrait/Pickard.jpg
Web page:
http://www.mtg.msm.cam.ac.uk/
DNM 26th February 2019
15:45 to 16:30
Marco Morandotti Optimal design of multi-component fractured media
Multi-component materials are fundamental in many applications: the different mechanical, physical, and chemical properties of each component can be exploited to design a composite with tailored properties. The presence of sharp interfaces between different component leaves room for the formation of microcracks and therefore the generation of a multiscale geometry of the material. In this seminar, we will discuss an optimal design problem for two-component fractured media for which a macroscopic strain is prescribed. The presence of fractures motivates setting the problem in the framework of structured deformations. In this context, we start from an energy functional accounting for bulk and surface contributions coming from both constituents of the material and we derive an integral representation for the relaxed energy functional. The  relaxed energy densities, obtained via a blow-up method, are determined by a delicate interplay between the optimization of sharp interfaces and the diffusion of microcracks. This model has the far-reaching perspective to incorporate elements of plasticity in optimal design of composite media.
These results have been obtained jointly with José Matias and Elvira Zappale.
DNM 26th February 2019
16:30 to 17:15
Kirill Cherednichenko Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties.
OFBW43 27th February 2019
10:00 to 10:10
Jane Leeks, David Abrahams Welcome and Introduction
OFBW43 27th February 2019
10:10 to 10:20
Xian Chen Outline and Summary of INI Research Programme 'The Mathematics of New Matierals'
OFBW43 27th February 2019
10:20 to 10:55
Eckhard Quandt Shape Memory Thin Films for Medical Applications
OFBW43 27th February 2019
10:55 to 11:25
Chris Wagner Opportunities for Novel Actuators in Surgical Robotics
OFBW43 27th February 2019
11:45 to 12:15
Ruth Cameron Materials for Regenerative Medicine
OFBW43 27th February 2019
12:15 to 12:50
Richard James New Concepts for the Direct Conversion of Heat to Electricity
OFBW43 27th February 2019
13:50 to 14:20
Andrew Bissell Domestic-scale Thermal Storage Using Phase Change Materials and Heat Pumps
OFBW43 27th February 2019
14:20 to 14:50
Xavier Moya Mechanocaloric Materials for Environmentally Friendly Refrigeration
OFBW43 27th February 2019
14:50 to 15:25
Pietro Valdastri Lifesaving Capsule Robots
OFBW43 27th February 2019
15:45 to 16:15
Fumiya Iida Bio-inspired Soft Robotics: Turning Soft Materials into Intelligent Machines
OFBW43 27th February 2019
16:15 to 16:40
Stoyan Smoukov Bottom-up Robotics - Emerging Intelligence in Materials
OFBW43 27th February 2019
16:40 to 17:00
Discussion & Questions
DNM 6th March 2019
15:00 to 16:00
Ning Jiang On the Ericksen-Leslie's hyperbolic model for liquid crystals
The original Ericksen-Leslie's model for liquid crystals includes the inertia effect, the corresponding balance laws includes second material derivatives. This system includes a coupling of Navier-Stokes equations with a S^2 valued hyperbolic system. In this talk, we review our recent work on the well-posedness of this hyperbolic Ericksen-Leslie's liquid crystal model and the justification of the zero inertia limit to the parabolic model which has been extensively studied in the past three decades. This is a series work joint with Luo, Tang, Zarnescu, and Huang, Zhao, respectively.
DNM 6th March 2019
16:00 to 17:00
Ben Schweizer On some meta-materials with micro-resonators and their effective equations

In order to explore common research interests with other participants, I sketch various results on the derivation of effective limit models for meta-materials with micro-resonators: Arrays of small Helmholtz resonators in acoustics, plasmonic wave induced perfect transmission, and Maxwells equations in negative index meta-materials. I conclude with some comments on cloaking by localized resonance near negative index materials.

DNM 20th March 2019
15:00 to 16:00
Pierluigi Cesana Models for self-similarity and disclinations in martensite
The austenite-to-martensite phase-transformation is a first-order diffusionless transition occurring in elastic
crystals and characterized by an abrupt change of shape of the underlying crystal lattice. It manifests itself
to what in materials science is called a martensitic microstructure, an intricate highly inhomogeneous
pattern populated by sharp interfaces that separate thin plates composed of mixtures of different martensitic
phases (i.e., rotated copies of a low symmetry lattice) possibly rich in defects and lattice mismatches. In
this talk we review a series of separate results on the modeling of inter-connected phenomena observed in
martensite, which are self-similarity (criticality) and disclinations.
Inspired by Bak’s cellular automaton model for sand piles, we introduce a conceptual model for a
martensitic phase transition and analyze the properties of the patterns obtained. Nucleation and evolution
of martensitic variants is modeled as a fragmentation process in which the microstructure evolves via
formation of thin plates of martensite embedded in a medium representing the austenite. While the
orientation and direction of propagation of the interfaces separating the plates is determined by kinematic
compatibility of the crystal phases, their nucleation sites are inevitably influenced by defects and disorder,
which are encoded in the model by means of random variables. We investigate distribution of the lengths
of the interfaces in the pattern and establish limit theorems for some of the asymptotics of the interface
profile. We also discuss numerical aspects of determining the behavior of the density profile and power
laws from simulations of the model and present comparisons with experimental data.
Turning our attention on defects, we investigate wedge disclinations, high-energy rotational defects caused
by an angular lattice mismatch that were predicted by Volterra in his celebrated 1907 paper. Unlike
dislocations, which have received considerable attention since the 1930s, disclinations have received
disproportionally less interest. However, disclinations are not uncommon as they accompany, as a relevant
example, rotated and nested interfaces separating (almost) kinematically compatible variants as in
martensitic avalanche experiments. Here we follow two modeling approaches. First, we introduce a few
recent results on the modeling of planar wedge disclinations in a continuum, purely (non-linear) elastic
model that describes disclinations as solutions of some differential inclusion. Secondly an atomistic model
of nearest-neighbor interactions over a triangular lattice inspired by the literature on discrete models for
dislocations.
Some of these results are from a collaboration with J.M. Ball and B. Hambly (Oxford) and P. Van Meurs
(Kanazawa).
DNM 20th March 2019
16:00 to 17:00
Cyrill Muratov The mathematics of charged liquid drops
In this talk, I will present an overview of recent analytical developments in the studies of equilibrium configurations of liquid drops in the presence of repulsive Coulombic forces. Due to the fundamental nature of Coulombic interaction, these problems arise in systems of very different physical nature and on vastly different scales: from femtometer scale of a single atomic nucleus to micrometer scale of droplets in electrosprays to kilometer scale of neutron stars. Mathematically, these problems all share a common feature that the equilibrium shape of a charged drop is determined by an interplay of the cohesive action of surface tension and the repulsive effect of long-range forces that favor drop fragmentation. More generally, these problems present a prime example of problems of energy driven pattern formation via a competition of long-range attraction and long-range repulsion. In the talk, I will focus on two classical models - Gamow's liquid drop model of an atomic nucleus and Rayleigh's model of perfectly conducting liquid drops. Surprisingly, despite a very similar physical background these two models exhibit drastically different mathematical properties. I will discuss the basic questions of existence vs. non-existence, as well as some qualitative properties of global energy minimizers in these models, and present the current state of the art for this class of geometric problems of calculus of variations.
DNMW05 25th March 2019
13:30 to 14:30
Kathleen J Stebe Geometry and assembly at fluid boundaries - 1
DNMW05 25th March 2019
14:45 to 15:45
Kathleen J Stebe Geometry and assembly at fluid boundaries - 2
DNMW05 25th March 2019
16:00 to 17:00
Mitchell Luskin Mathematical Modeling and Numerical Analysis for Incommensurate 2D Materials - 1
DNMW05 26th March 2019
09:00 to 10:00
Mitchell Luskin Mathematical Modeling and Numerical Analysis for Incommensurate 2D Materials - 2
DNMW05 26th March 2019
10:15 to 11:15
Oleg Lavrentovich Design of Liquid Crystals for Microscale Dynamics - 1

Dynamics of small particles in fluids has fascinated scientists for centuries, since van Leeuwenhoek observed in 1674 tiny creatures, nowadays known as “bacteria”, swimming chaotically in a droplet of water. Much later, Brown found that even inanimate small particles, when placed in water, engage in a similar chaotic dynamics. If one could learn how to control and streamline the chaotic motion of particles such as bacteria and colloids at the microscale, that would open technological opportunities in areas such as transformation of stored or environmental energy into systematic motion, micro-robotics, transport of matter at microscale, etc. Remarkably, bacteria and colloids driven by an external field do not obey the laws of thermodynamics and can be used to extract a useful work. This set of lecture presents an approach to command microscale dynamics by replacing an isotropic medium such as water with an anisotropic fluid, a liquid crystal. The liquid crystals are formed by elongated molecules that tend to align parallel to each other along a common direction called the director. As a result, physical properties, such as electric conductivity or viscosity depend on the direction of measurement, whether it is parallel or perpendicular to the director. Orientational order of the medium leads to new dynamic effects, such as anomalous diffusion [1] and formation of particle-like solitary waves [2]. By using a newly developed technique of nano-photonic photoalignment, the liquid crystal director can be patterned into any predesigned structure [3]. We demonstrate that the patterned liquid crystals can control microscale dynamics of inanimate particles such as solid colloids, fluid droplets, through the effects of nonlinear electrophoresis [4] and electro-osmosis [5]. Moreover, plasmonic patterning of liquid crystals allows one to command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming and concentration in space [6]. The patterned director design can also be extended to liquid crystal elastomers, in which case the director field controls the thickness of elastomer coatings [7]. Some of these systems form an experimental playground for the exploration of out-of-equilibrium active matter, in which the levels of activity and degree of orientational order can be controlled separately.The work is supported by NSF DMREF DMS-1729509 and by Office of Science, U.S. Department of Energy, grant DE-SC0019105.[1] T. Turiv, I. Lazo, A. Brodin, B. I. Lev, V. Reiffenrath, V. G. Nazarenko, and O. D. Lavrentovich, Effect of Collective Molecular Reorientations on Brownian Motion of Colloids in Nematic Liquid Crystal, Science 342, 1351-1354 (2013).[2] B. X. Li, V. Borshch, R. L. Xiao, S. Paladugu, T. Turiv, S. V. Shiyanovskii, and O. D. Lavrentovich, Electrically-driven three-dimensional solitary waves as director bullets in nematic liquid crystals, Nature Communications 9, 2912 (2018).[3] Y. Guo, M. Jiang, C. Peng, K. Sun, O. D. Lavrentovich, and Q.-H. Wei, High-Resolution and High-Throughput Plasmonic Photopatterning of Complex Molecular Orientations in Liquid Crystals Advanced Materials 28, 2353-2358 (2016).[4] O. D. Lavrentovich, I. Lazo, and O. P. Pishnyak, Nonlinear electrophoresis of dielectric and metal spheres in a nematic liquid crystal, Nature 467, 947-950 (2010).[5] I. Lazo, C. H. Peng, J. Xiang, S. V. Shiyanovskii, and O. D. Lavrentovich, Liquid crystal-enabled electro-osmosis through spatial charge separation in distorted regions as a novel mechanism of electrokinetics, Nature Communications 5, 5033 (2014).[6] C. Peng, T. Turiv, Y. Guo, Q.-H. Wei, and O. D. Lavrentovich, Command of active matter by topological defects and patterns, Science 354, 882-885 (2016).[7] G. Babakhanova, T. Turiv, Y. B. Guo, M. Hendrikx, Q. H. Wei, A. Schenning, D. J. Broer, and O. D. Lavrentovich, Liquid crystal elastomer coatings with programmed response of surface profile, Nature Communications 9, 456, 456 (2018).

DNMW05 26th March 2019
11:30 to 12:30
Oleg Lavrentovich Design of Liquid Crystals for Microscale Dynamics - 2
DNMW05 26th March 2019
13:30 to 14:30
Kathleen J Stebe Geometry and assembly at fluid boundaries - 3
DNMW05 26th March 2019
14:45 to 15:45
Kathleen J Stebe Geometry and assembly at fluid boundaries - 4
DNMW05 26th March 2019
16:00 to 17:00
Mitchell Luskin Mathematical Modeling and Numerical Analysis for Incommensurate 2D Materials - 3
DNMW05 27th March 2019
09:00 to 10:00
Mitchell Luskin Mathematical Modeling and Numerical Analysis for Incommensurate 2D Materials - 4
DNMW05 27th March 2019
10:15 to 11:15
Oleg Lavrentovich Design of Liquid Crystals for Microscale Dynamics - 3
DNMW05 27th March 2019
11:30 to 12:30
Oleg Lavrentovich Design of Liquid Crystals for Microscale Dynamics - 4
DNMW05 28th March 2019
09:00 to 10:00
Richard James Supercompatibility and the direct conversion of heat to electricity - 1
DNMW05 28th March 2019
10:15 to 11:15
Richard James Supercompatibility and the direct conversion of heat to electricity - 2
DNMW05 28th March 2019
11:30 to 12:30
Peter Palffy-Muhoray Heliconical cholesteric liquid crystals: self-assembled tunable photonic bandgap materials - 1
DNMW05 28th March 2019
13:30 to 14:30
Richard James Supercompatibility and the direct conversion of heat to electricity - 3
DNMW05 28th March 2019
14:45 to 15:45
Peter Palffy-Muhoray Heliconical cholesteric liquid crystals: self-assembled tunable photonic bandgap materials - 2
DNMW05 28th March 2019
16:00 to 17:00
Peter Palffy-Muhoray Heliconical cholesteric liquid crystals: self-assembled tunable photonic bandgap materials - 3
DNMW05 29th March 2019
09:00 to 10:00
Richard James Supercompatibility and the direct conversion of heat to electricity - 4
DNMW05 29th March 2019
10:15 to 11:15
Peter Palffy-Muhoray Heliconical cholesteric liquid crystals: self-assembled tunable photonic bandgap materials - 4
DNM 3rd April 2019
14:30 to 15:10
Anja Schlömerkemper Passages from discrete to continuous systems allowing for fracture, external forces and heterogeneities
Passages from discrete to continuous systems of particles have been the subject of research with various approaches for many years. Here we focus on one-dimensional particle systems with non-convex interaction potentials, which allow for the formation of cracks. We consider variational models and their continuum limits by means of $\Gamma$-convergence techniques.

Firstly, I will present the main ideas of a recent work with M.~Carioni and J.~Fischer which allows for external forces that may depend on the material points or on the deformed configuration, i.e.~on Lagrangian or Eulerian coordinates, and thus may be related to dead as well as live loads. Secondly, I will show homogenization results for composite materials that are modelled by either periodically or stochastically distributed non-convex interaction potentials. This is joint work with
L.~Lauerbach, S.~Neukamm and M.~Schäffner.

DNM 3rd April 2019
15:10 to 15:50
Jun-ichi Fukuda Exotic ordered structures of a thin film of a chiral liquid crystal

Liquid crystals fascinated scientists because they exhibit ordered structures in diverse length scales. Here we focus on structures formed in a thin film of a chiral liquid crystal that allows spontaneous local twist of orientational order. By numerical calculations based on a continuum theory describing the orientational order by a second-rank tensor, we show that a thin film of a chiral liquid crystal exhibit a variety of exotic mesoscale structures depending on temperature, film thickness and surface anchoring that dictates the orientational order at the film surfaces [1,2]. These structures are understood as a result of frustrations between the bulk ordering and the surface anchoring, and include a hexagonal lattice of Skyrmions, vortex-like topological entities that have been shown to emerge in various condensed matter systems. We also briefly mention the optical properties of these structures [2,3].

[1] J. Fukuda and S. Žumer, Phys. Rev. Lett. 104, 017801 (2010); Phys.
Rev. Lett. 106, 097801 (2011); Nature Commun. 2, 246 (2011).

[2] A. Nych, J. Fukuda, et al., Nature Phys. 13, 1215 (2017).

[3] J. Fukuda et al., Sci. Rep. 8, 17234 (2018).

DNM 3rd April 2019
15:50 to 16:30
Claudio Zannoni Hard and soft packing in the molecular organization of liquid crystals
The first generation of theories and computer simulations of liquid crystals have made drastic and often contrasting assumptions on the model representation of constituent mesogens and on the type of intermolecular interactions (e.g purely attractive in Maier-Saupe type and purely hard repulsive in Onsager models). Computer simulations of liquid crystals, that started with simple lattice models, have upgraded over the years to off-lattice models where molecules are replaced by relatively simple objects endowed with purely steric or attractive and repulsive type interactions of various softness and, more recently, to very realistic fully atomistic models. In the talk we shall briefly summarize the main features of these models and show various examples for the prediction of liquid crystal phase behavior starting from microscopic models. The contribution of different interactions to the phase morphologies obtained as well as open problems will be discussed.

DNM 17th April 2019
15:30 to 16:30
Irene Fonseca A homogenization result in the gradient theory of phase transitions
A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In particular, the case where the scale $\varepsilon$ of the small homogeneities is of the same order of the scale governing the phase transition is considered.  Here the interaction between homogenization and the phase transitions process will lead, in the limit as $\varepsilon \to 0$, to an anisotropic interfacial energy.
DNM 24th April 2019
15:00 to 17:00
Jeffrey Everts Medium- and particle-shape effects on electric double layers
Charged surfaces in contact with liquids containing ions are accompanied in equilibrium by an
electric double layer consisting of a layer of electric charge on the surface that is screened by a diffuse ion
cloud in the bulk fluid. This screening cloud determines not only the interactions between charged
colloidal particles or poly- electrolytes and their self-assembly into ordered structures [1], but also on how
the interaction of a charged colloidal particle with an oil-water interface can be tuned from attractive to
repulsive by varying the salt concentration, as we will discuss in this talk [2]. In the second part of this
talk we will discuss to what spatial complexity the electric double layers can be designed. We show that
electric double layers of non-trivial topology -including tori, multi-tori and knots- can be realised in
charged colloids with complex-shaped particles, using numerical modelling. We show that the topology
of double layers can be defined via a cut-off in the ion concentration without any loss of generality, and
demonstrate that the double layer topology can be tuned by changing the Debye screening length of the
medium, or by changing the shape and topology of the (colloidal) particle [3]. If time permits, we will
finally discuss the coupling of electric double layers to a nematic texture, and show the effects of salt on
the anchoring strength of a charged wall.
[1] J.C. Everts, M.N. van der Linden, A. van Blaaderen and R. van Roij, Soft Matter 12 (2016) 6610-
6620.
[2] J.C. Everts, S. Samin and R. van Roij, Phys. Rev. Lett. 117 (2016) 098002.
[3] J.C. Everts and M. Ravnik, Sci. Rep. 8 (2018) 14119.
DNM 1st May 2019
15:00 to 16:00
Giovanni Di Fratta Magnetic skyrmions in spherical thin films
Curved thin films are currently of great interest due to their capability to support spontaneous skyrmion solutions, i.e., chiral spin textures observable in a stable state even when no spin-orbit coupling mechanism, in the guise of Dzyaloshinskii-Moriya interaction (DMI), is considered. The evidence of these states sheds light on the role of the geometry in magnetism: chiral spin-textures can be stabilized by curvature effects only, in contrast to the planar case for which the DMI is required. In addition to fundamental reasons, the interest in these geometries is triggered by recent advances in the fabrication of magnetic spherical hollow nanoparticles, which lead to artificial materials with unexpected characteristics and numerous applications ranging from logic devices to biomedicine.
In this talk, after a brief overview of the existing literature on the micromagnetics of curved thin films, we will focus on the investigation of magnetic skyrmions in spherical thin films. The question will lead to a sharp Poincaré-type inequality that allows for a precise characterization of the global minimizers of the micromagnetic energy functional on the 2-sphere.
DNM 1st May 2019
16:00 to 17:00
Tomonari Inamura Emergence of power law in martensite microstructure of shape memory alloy
Martensitic transformation is a shear-dominant, lattice distortive and diffusionless solid-solid transformation occurring by nucleation and growth. Shape memory alloy exhibits a martensite microstructure, which is a complex pattern of martensitic domains.  In this study, the character of the interfaces between the martensite domains, dynamics of the formation of the microstructure and the emergence of power-law in the domain size distribution are investigated by various recent microscopy techniques in shape memory alloys. The experimental results are analyzed in the framework of the nonlinear elasticity theory of the microstructure which was founded by Ball and James, to bridge the theory and experiment and to elucidate underlying problems to be solved.

DNM 8th May 2019
15:00 to 15:40
Bianca Stroffolini Minimizers of a Landau-de Gennes Energy with a Subquadratic Elastic Energy
I will present a modiified Landau-de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. In fact, there is little experimental evidence to conjecture thatthe elastic energy density may be subquadratic near defects matched by a quadratic growth away from defects. The analysis of the behaviour of global minimizers in two and three dimensional domains, subject to uniaxial boundary conditions, in the asymptotic regime, is performed using tools of the regularity theory for functionals with general growth. The results presented in this talk have been obtained in collaboration with Giacomo Canevari (Verona) and Apala Majumdar ( Bath). B Stroffolini, Dipartimento di Ingegneria Elettrica e delle Tecnologie dell' Informazione, Via Claudio, 80125 - Napoli, ITALYE-mail address: bstroffo[at]unina[dot]it
DNM 8th May 2019
15:40 to 16:20
Xavier Lamy On solutions to the eikonal equation with finite entropy production
Solutions with finite entropy productions arise in the sharp interface
limit of a gradient phase field model that was proposed by Aviles and
Giga as a simplified model for smectic liquid crystals, and is also
related to thin film elasticity, micromagnetics and pattern formation
models. I will present recent results on their regularity, based on
joint work with Francesco Ghiraldin.

DNM 8th May 2019
16:20 to 17:00
Davit Harutyunyan Recent progress in the geometric rigidity of thin domains
We will discuss the celebrated geometric rigidity estimate of Friesecke,
James and Mueller. While It is known to be asymptotically sharp for plates in
the thickness vanishing limit, the question for general thin domains is still open.
We will discuss the analogous Korn inequality (the linear version of the rigidity
estimate) and the resolution of it for vector fields under Dirichlet boundary
condition on the domain thin face. We will also present the so called novel Korn
and Geometric Rigidity interpolation inequalities, which solve the question of
best constant in Korn’s second inequality in thin domains; the last had been
unknown since 1908. This is partially joint work with Yury Grabovsky.
DNM 10th May 2019
16:00 to 17:00
Irene Fonseca Kirk Distinguished Visiting Fellow Lecture: Variational Methods in Image Processing and in the Mathematical Analysis of Novel Advanced Materials

In this talk we will use variational models involving density measures of different dimensionality to study training/learning schemes for a novel class of image-processing operators that provides a unified approach to the standard regularizers and PDE-based approaches to image denoising.
To illustrate the relevance of similar bulk-surface energy models in the study of novel materials, we will analyze the onset of man-made nanocrystals of semiconducting materials (quantum dots). Their formation and assembly patterns play a central role in nanotechnology, and in particular in the optoelectronic properties of semiconductors. Changing the dots' size and shape gives rise to many applications that permeate our daily lives. As the creation of quantum dots evolves with time, materials defects appear and these may strongly influence material properties, including rigidity and conductivity. The regularity and evolution of the quantum dots shapes, and the nucleation and motion of dislocations will be addressed.

DNMW03 13th May 2019
09:40 to 10:20
Randall Kamien Packing Liquid Crystal Domains
Focal conic domains are complex, geometric configurations found in cholesteric and smectic liquid crystals: they are not topologically protected but are very low energy states. How do they pack on finite geometries? Come and listen!
DNMW03 13th May 2019
10:20 to 10:40
Thomas Machon Contact Topology and the Cholesteric Landscape
Cholesterics, chiral liquid crystals, typically exhibit a large number of metastable states for a given geometry. This is both a blessing and a curse, it affords great potential for the creation of new devices but can also mean that tight control of a structure can be difficult to achieve. In this talk we will discuss why it is that the tendency of cholesterics to twist means that they have a complex energy landscape. Our principle tools will be drawn from the field of contact topology. By describing cholesterics as contact structures we will show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This characterises the morphological richness of these systems, leads to a number of additional topological invariants for cholesteric textures that are not captured by traditional descriptions, and gives a geometric characterisation of cholesteric dynamics in any context, including active systems, those in confined geometries or under the influence of an external field.
DNMW03 13th May 2019
11:10 to 11:50
Margarida Telo da Gama Self-organization of patchy colloidal particles: 2 & 3D

We investigate the self-organization of patchy colloidal particles deposited on flat substrates in three (2+1) and two (1+1) spatial dimensions. We propose and use a simple stochastic model for the interaction between the particles, which allows the simulation of very large systems, to probe the long time and large-scale structure of the deposited films. The latter exhibit well defined surface, liquid and interfacial regions except when the growth is dominated by the formation of chains, which occurs for systems with an effective valence close to two. We also investigate the interfacial roughening in (1+1) systems and compare our results with those obtained experimentally for evaporating droplets. We find, in line with the experiments, that when the film growth is dominated by chains the generic Kardar-Parisi-Zhang (KPZ) interfacial roughening is replaced by quenched KPZ. We discuss this somewhat surprising result.

DNMW03 13th May 2019
11:50 to 12:30
Anja Schlömerkemper Evolution of magneto-viscoelastic materials
In this talk I will survey our recent approach to the modeling of magneto-viscoelastic materials. Our system of partial differential equations consists of the Navier-Stokes equations, the Landau-Lifshitz-Gilbert equation and an evolution equation for the deformation gradient. I will address modeling aspects, analytical results and potential applications.
DNMW03 13th May 2019
13:30 to 14:10
Hillel Aharoni Making Faces: Universal Inverse Design of Thin Nematic Elastomer Surfaces
Thin nematic elastomer sheets can be programmed, via the nematic director field embedded into them, to take different shapes in different environments. Recent experiments from various groups demonstrate excellent control over the director field, thus opening a door for achieving accurate and versatile designs of shape-shifting surfaces. At the crux of any effort to implement this design mechanism lies the inverse design problem -- given an arbitrary surface geometry, constructing the director field that would induce it. In this talk I describe several aspects of this inverse problem. I present a numerical algorithm for finding global approximate solutions for any 2D geometry. I also show that many exact solutions always exist locally and can be readily integrated, and classify the set of all director fields that deform into an arbitrary given geometry. These results allow optimizing the resultant director fields for different purposes, e.g. maximizing the domain of a global solution, increasing its robustness, reducing residual stresses, or controlling the entire shape-shifting path.
DNMW03 13th May 2019
14:10 to 14:50
Ard Louis Simplicity bias in random design
The design of a soft-matter system can be recast as an input-output map, where the inputs are the parameters that fix the components and their interactions, and the outputs describe the outcome of a self-assembly process. By extending the coding theory from algorithmic information theory, we have recently shown [K Dingle, C. Camargo and AAL, Nat Comm. 9, 761 (2018)] that for many computable maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity $\tilde{K}(x)$ of that output. While Kolmogorov complexity is technically uncomputable, we show how to make approximations that work in practice, allowing for a tight upper bound on P(x). For soft matter systems, simplicity bias implies that randomly sampling design inputs will naturally lead to outputs that have low descriptional complexity. Since high symmetry structures typically have low descriptional complexity, simplicity bias implies that randomly picking design patterns can lead to the spontaneous emergence of highly symmetric self-assembled structure. We provide evidence for these trends for self-assembled RNA and protein structures.
DNMW03 13th May 2019
15:20 to 16:00
Gareth Alexander Geometric Topology of Liquid Crystal Textures: Chirality and Bend
The textures and phases of liquid crystals are replete with geometric motifs, and the geometric approach to elasticity underpins a large portion of nonlinear theories. Despite this, the basic characterisation of topology comes from the homotopy theory without particular attention to geometric features. I will describe our recent work developing geometric approaches to liquid crystal topology, describing cholesteric point defects and topological chirality, and the geometric features of bend distortions, illustrated by applications to the twist-bend nematic phase.
DNMW03 13th May 2019
16:00 to 16:40
Alex Travesset Soft Skyrmions and Programmable Self-Assembly of Superlattices
Materials whose fundamental units are nanocrystals (NC)s, instead of atoms or molecules, are gradually emerging as major candidates to solve many of the technological challenges of our century. Those materials display unique structural, dynamical and thermodynamical properties, often reflecting deep underlying geometric, packing and topological constraints. In this talk, I will discuss the rational design of NC materials by programmable self-assembly. I will present the Orbifold Topological Model (OTM), which successfully describes the structure of crystal or quasicrystal arrangements of NCs (superlattices) by considering capping ligands as Skyrmion textures, which determine the bonding very much like atomic orbitals in lattices of simple atoms. I will show that the OTM describes “atomic orbitals” as consisting of vortices, which enable the generation of a spontaneous valence and reveal the universal tendency of these systems towards icosahedral order, allowing to describe them as quasi-Frank-Kasper phases.  These results will be confirmed by numerical simulations. I will elaborate on the success of the OTM in describing all existing experimental structural data on single component and binary superlattices obtained by solvent evaporation and present new candidate phases.
DNMW03 13th May 2019
16:40 to 17:00
Shayandev Sinha Thermally actuated portable microvalves using elastomeric focusing
Thermally actuated controlled shape changes in soft materials is a challenge as the material shows non-linear expansion characteristics. CTE of many materials is not properly available. In order to focus the expansion of the soft solid into large displacements a confined geometry is created to amplify the shape changes. Here we use an elastomer (PDMS sheet) confined between two rigid layers, which when locally heated using resistive heating expands into the micromolded channels, resulting into a massive relative displacement compared to the case of an unconfined geometry. This principle is used to make microfluidic valves which are electrically controlled (using a 3.3V-5V cellphone battery) and close in less than 100 ms. They operate within a power range of 140-160 mW generated by the specifically designed resistive heating element (in-house made ink) screen printed on the chip. We investigate the parameters of the heating element design, height dimensions and flow conditions through the valves. This technique helps us to make multiple valves along the fluidic pathway with arbitrary positioning. The size of these really help to make the devices portable as one does not need a separate controller for the actuating the valves.
DNMW03 14th May 2019
09:00 to 09:40
Daniel Joseph Needleman Structure, Mechanics, and Thermodynamics of Mixtures of Microtubules and Molecular Motors
The self-organization of the microtubule cytoskeleton underlies diverse cell biological processes, ranging from chromosome segregation to neuronal morphogenesis. In order to gain insight into these biological processes, and the properties of active matter more generally, we are studying the large-scale structure, mechanics, and thermodynamics of collections of microtubules and molecular motors in cell extracts and reconstituted systems of purified components. I will present our recent work characterizing spontaneous contractions, ordering, instabilities, and heat production in these systems.
DNMW03 14th May 2019
09:40 to 10:20
Jorn Dunkel Towards rationally designed active metamaterials
Recent advances in 3D printing and lithography have spurred rapid progress in the development of passive metamaterials. By interweaving simple subunits in intricate geometric arrangements, metamaterials can be custom designed to have many remarkable response features, from acoustic and photonic band gaps to auxetic behavior and topological robustness. In parallel, the last few years have seen the introduction of new classes of artificial and bio-inspired active materials based on colloidal and microbial suspensions or internally actuated gels. These non-equilibrium systems show great promise as components in autonomous soft robotic and microfluidic devices, and have reached a level of understanding where these applications can now be fruitfully developed. In this talk, I will discuss our recent work that aims to implement a computational framework for the inverse design of discrete active metamaterials. Building a network-based description, we will illustrate how optimized material structures can be used to harvest energy from correlated fluctuations [1,2], and outline basic design principles for active topolectrical circuits [3]. [1] Woodhouse et al, Phys Rev Lett 121: 178001, 2018 [2] Ronellenfitsch et al, Phys Rev Lett 121: 208301, 2018 [3] Kotwal et al, arXiv:1903.10130
DNMW03 14th May 2019
10:20 to 10:40
Nicholas Tito Exploiting entropy to enhance toughness in polymer gels with reversible crosslinks
Co-Authors: Costantino Creton, Cornelis Storm, Wouter Ellenbroek

Entropy is the daunting "second half" of thermodynamics, universally encountered yet often overlooked when designing molecular recipes for new soft materials and structures. This talk seeks to inspire a line of thought on how entropy can be harnessed as a central design element in soft polymeric materials, for imbuing adaptability, robustness, and functional uniqueness.

Highly elastic yet failure-resistant polymer gels with reversible crosslinks [1] will be showcased as a recent example where entropy provides unexpected functionality. Using a combination of theory, molecular simulation, and polymer self-consistent field theory for networks [2], I will discuss how entropy counter-intuitively leads to spatial clustering of reversible crosslinks around permanent crosslinks in the polymer gel. This entropy-induced order leads the gel to be less prone to failure, while maintaining its high degree of extensibility [3]. Practical guidelines will be outlined to optimise this design in experiment, along with a discussion of key kinetic and timescale considerations.

[1] Kean, Z. S.; et al. Adv. Mat. 2014, 26, 6013.
[2] Tito, N. B.; Storm, C.; Ellenbroek, W. G. Macromolecules 2017, 50, 9788.
[3] Tito, N. B.; Creton, C.; Storm, C; Ellenbroek, W. G. Soft Matter 2019, 15, 2190.
DNMW03 14th May 2019
11:10 to 11:50
Bianca Stroffolini Function spaces meet material science: Orlicz-Sobolev nematic elastomers
In the last decade, models for nematic elastomers and magnetoelasticity has been extensively studied. These models consider both an elastic term where a polyconvex energy density is composed with an unknown state variable defined in the deformed configuration, and a functional corresponding to the nematic energy (or the exchange and magnetostatic energies in magnetoelasticity) where the energy density is integrated over the deformed configuration. In order to obtain the desired compactness and lower semicontinuity, one has to face the regularity requirement that maps create no new surface. I'll discuss that this in fact the case for maps whose gradients are in an Orlicz class with an integrability just above the space dimension minus one. The results presented in this talk have been obtained in collaboration with Duvan Henao (Pontificia Universidad Cat\'olica de Chile).
DNMW03 14th May 2019
11:50 to 12:30
Carme Calderer Modeling and analysis of chromonic liquid crystal condensates
The discovery of the liquid crystal phases of DNA and their study has attracted the attention of many scientists, for several decades. These include the contributions by soft matter physicists such as Professor F. Livolant, that began in the mid-1970’s. On the other hand, the observation of clustering phenomena in lyotropic liquid crystals, analogous to that formed by DNA condensates and bacteriophage viral genome in a capsid domain, led John Lyndon to coin the chromonic denomination of the liquid crystals formed by plank-like molecules (2013). All these liquid crystals are found to form hexagonal columnar chromonic phases, although they differ in order of magnitude by a factor of 106. This presentation addresses modeling and analysis of bacteriophage viruses, the toroidal structures formed by condensed DNA in free solutions, and the analogous phenomena observed in lyotropic chromonic liquid crystals phases of materials with plank-like molecular shapes. Part of the presentation will focus on the experiments performed by ProfessorLavrentovich’s group on materials such as food dyes--sunset yellow--and anti-asthmatic drugs. A special feature determining the arrangement of DNA in a capsid is the dominant contribution of the elastic energy penalizing distortion of the cross sections perpendicular to the column axis. The central mathematical problem is formulated as a free boundary problem for the Oseen-Frank and Ericksen’s energies, where the domain and the vector (or tensor) field are unknown. The admissible set includes volume constraints as well as those expressing the high resistance of the chromonic structures to splay and twist deformation. The first part of the presentation will involve general geometries of the domain, resorting to earlier analyses of liquid crystal droplets. We will subsequently show that minimizers of the bending dominated constrained energy have toroidal shapes. Moreover, we will show that axisymmetric configurations lead to families of polyconvex energies for which minimization can be established by standard methods of calculus of variations. Moreover, in the case of bacteriophage viruses, we will identify the absolute minimizer as the coiling DNA configuration. We will conclude the presentation with the discussion of a numerical algorithm aimed at the design of viruses for applications to drug delivery and nanotransport.
DNMW03 14th May 2019
13:30 to 14:10
Julia Yeomans Bacteria: self-motile liquid crystals?
We discuss recent work showing that the concepts of liquid crystal physics can give insight into the behaviour of colonies of bacteria. Dense bacterial layers show local nematic order and the appearance of associated topological defects can act as preferential sites for biofilm formation. Moreover less dense swimming bacterial suspensions can be focused by an underlying passive nematic, a step towards exploiting their energy for microfluidic transport.

Women in Materials Science

DNMW03 14th May 2019
14:10 to 14:50
Elisabetta Matsumoto Twisted topological tangles: or the knot theory of knitting
Shashank Markande, Michael Dimitriyev, Krishman Singal and Elisabetta Matsumoto Imagine a 1D curve, then use it to fill a 2D manifold that covers an arbitrary 3D object – this computationally intensive materials challenge has been realized in the ancient technology known as knitting. This process for making functional materials 2D materials from 1D portable cloth dates back to prehistory, with the oldest known examples dating from the 11th century BCE. Knitted textiles are ubiquitous as they are easy and cheap to create, lightweight, portable, flexible and stretchy. As with many functional materials, the key to knitting’s extraordinary properties lies in its microstructure. At the 1D level, knits are composed of an interlocking series of slip knots. At the most basic level there is only one manipulation that creates a knitted stitch – pulling a loop of yarn through another loop. However, there exist hundreds of books with thousands of patterns of stitches with seemingly unbounded complexity. The topology of knitted stitches has a profound impact on the geometry and elasticity of the resulting fabric. This puts a new spin on additive manufacturing – not only can stitch pattern control the local and global geometry of a textile, but the creation process encodes mechanical properties within the material itself. Unlike standard additive manufacturing techniques, the innate properties of the yarn and the stitch microstructure has a direct effect on the global geometric and mechanical outcome of knitted fabrics.
DNMW03 14th May 2019
15:20 to 16:00
Anton Souslov Odd elasticity in soft active solids
An active material is either a solid or a fluid in which microscopic constituents convert energy into motion. These microscopic engines can be organised to output collective macroscopic work. For active solids, we show that the theory of elasticity can be modified to describe this work-extraction process. This talk focuses on the specific example of how an antisymmetric (or odd) component of the elastic tensor leads to the extraction (or injection) of work during quasi-static cycles of elastic deformations. Such materials can be designed based on active mechanical components that include sensors and actuators. Inside the material, work-extraction cycles manifest themselves in signal propagation: in an overdamped active solid, elastic waves propagate via a balance between energy injection and dissipation. In addition, activity can be measured via static deformations, including activity-induced auxetic behaviour. This theory of odd elasticity suggests design principles for emergent autonomous materials in which work is locally injected, transported, and then extracted.
DNMW03 14th May 2019
16:00 to 16:40
Martin Copic Q-tensor model of twist-bend and splay nematic phases
The twist-bend nematic phase is characterized by a conically twisting director and by a dramatic softening of the bend elastic constant. The instability towards bend can theoretically also induce a splay -bend phase with a bend-splay modulation along the director. Recently we found another modulated nematic phase  where the splay elastic constant tends to zero, resulting in a splay modulation perpendicular to the director. These phases can be modeled by a single Q-tensor free energy with a  term that breaks the degeneracy between the splay and bend elastic constant and with a flexoelectric coupling of the divergence of the Q-tensor with polarization.

Martin Čopič and Alenka Mertelj - Insitute J. Stephan, Ljubljana, Slovenia
DNMW03 14th May 2019
16:40 to 17:00
Mikhail Osipov Orientational ordering and self-organisation of nanoparticles in liquid crystal and polymer nanocomposites
Nematic liquid crystals (LCs) and block copolymers doped with nanoparticles possess a number of interesting properties. In particular, anisotropic nanoparticles are orientationally ordered in the boundary region between the blocks [1-3] and a small concentration of nanoparticles can shift the transition temperatures between different phases, orientational ordering of nanoparticles is responsible for the enhanced dielectric anisotropy of the composite lamellae and hexagonal phases which opens a possibility to align block copolymers by external fields. This may enable one to solve various application problems. We first summarise the results of a molecular theory of nematic LCs doped with anisotropic nanoparticles and describe the effect of nanoparticles on the N-I phase transition, the nematic order parameter and consider the formation of chains of polar nanoparticle [4-7]. We then present the results of a molecular theory of the induced orientational order of anisotropic nanoparticles in the lamellae and in the hexagonal phase of a diblock copolymer taking into anisotropic interaction between nanoparticles and the polymer chains. Numerical concentration and orientational order parameter profiles are presented for different values of the model parameters including the strength of the anisotropic interaction. We also present the results of the general mean-field theory which enables one to describe both the effect of segregation of monomers between different blocks on the orientational order of nanoparticles and the effect of nanoparticles on the stability of different phases..
Finally we present the results of the computer simulations of the lamellae and hexagonal copolymer nanocomposites doped with nanoparticles of different length and affinity, and the simulated concentration and order parameter profiles are compared with theoretical results [1,3]. We also discuss the corresponding phase diagrams which illustrate how the nanoparticles may effect the phase behaviour of block copolymers.
References
[1] Osipov, M. A., Gorkunov, M. V., Berezkin, A. V., Kudryavtsev, Y. V., Phys. Rev. E, 97, 042706 (2018)
[2] M.A. Osipov and M.V. Gorkunov, Eur.Phys.J., 39, 126 (2016)
[3] A.V. Berezkin, Y.V. Kudryavtsev, M.V. Gorkunov, and M.A. Osipov, J. Chem. Phys., 146, 144902 (2017) [4] M.V. Gorkunov and M.A. Osipov, Soft Matter, 7, 4348 (2011)
[5] M.A. Osipov and M.V. Gorkunov, ChemPhys.Chem. 15, 1496 (2014)
[6] M.A. Osipov and M.V. Gorkunov, Phys. Rev. E , 92, 032501 (2015)
[7] Osipov, M. A. and Gorkounov, M. V. in Liquid Crystals with Nano and Microparticles. Lagerwall, J. P. F. and Scalia, G. (eds.). Singapore: World Scientific Publishing Company, 2016.

DNMW03 15th May 2019
09:00 to 09:40
Monica Olvera de la Cruz Control of Magnetoelastic Matter
Magnetic materials hold tremendous potential for precision control of matter due to their tunable interactions in dynamic magnetic fields. Flexible superparamagnetic filaments and membranes under the influence of precessing magnetic fields, for example, can exert controllable forces to generate microscopic actuation. We characterize the resulting changes of shapes in terms of their material parameters, as well as of the strength of the magnetic field. In particular, we show how by controlling the magnetic field, open membranes may form either rippled or helicoidal surfaces, whereas closed membranes can buckle into convex and concave shapes with specific symmetries. Shape control via magnetic fields is also discussed in three-dimensional gels reinforced with ferromagnetic matter. These systems might be suitable for constructing devices with controllable conformational changes such as artificial muscles.
DNMW03 15th May 2019
09:40 to 10:20
Daphne Klotsa A touch of non-linearity: mesoscale swimmers and active matter in fluids
Living matter, such as biological tissue, can be seen as a nonequilibrium hierarchical assembly of assemblies of smaller and smaller active components, where energy is consumed at many scales. The functionality and versatility of such living or “active-matter” systems render it a promising candidate in a discussion on the optimal design of soft matter. While many active-matter systems reside in fluids (solution, blood, ocean, air), so far, studies that include hydrodynamic interactions have focussed on microscopic scales in Stokes flows, where the active particles are <100μm and the Reynolds number, Re <<1. At those microscopic scales viscosity dominates and inertia can be neglected. However, what happens as swimmers slightly increase in size (say ~0.1mm-100cm) or as they form larger aggregates and swarms? The system then enters the intermediate Reynolds regime where both inertia and viscosity play a role, and where nonlinearities in the fluid are introduced. In this talk, I will present a simple model swimmer used to understand the transition from Stokes to intermediate Reynolds numbers, first for a single swimmer, then for pairwise interactions and finally for collective behavior. We show that, even for a simple model, inertia can induce hydrodynamic interactions that generate novel phase behavior, steady states and transitions.
DNMW03 15th May 2019
10:20 to 10:40
Anja Pusovnik Liquid crystal metamaterials from nematic colloidal platelets
Metamaterials are artificial materials with properties otherwise not existing in nature. This is achieved through the design of its constituent building blocks, which are generally several times smaller than the operating wavelength. An interesting route for the fabrication of photonic metamaterials is their self-assembly in liquid crystals. Here, we firstly determine the optimal geometrical parameters of a single split ring resonator (SRR) colloidal particle in order to achieve the stability of the 2D and 3D SRR structures in liquid crystals using free energy calculations. Then we focus on the optical response of such a composed material, notably the resonances in the transmissivity spectra, and tunability of optical properties of the SRR colloidal crystal with external fields.
DNMW03 15th May 2019
11:10 to 11:50
Miha Ravnik Design of passive and active passive nematic defects
Complex –passive or active- nematic fluids are characterised by internal orientational order, which upon tuning or frustration, can exhibit topological defects. The type of defects and their role naturally depend on dimensionality of the system, but importantly also on the geometry, confinement, flow, driving or even activity. Here, we present design of topological defects in passive and active nematic complex fluids – forming umbilic defects, singular loops, point defects and disclinations. Specifically, we show in passive nematics how confinement in the form of complex geometry and fractal surfaces can lead to formation of various defect-based nematic profiles, including exhibiting high-elastic multipoles. In active nematics, we show defect profiles in three-dimensional active nematic droplet, also highlighting the role of different surface coupling regimes.
DNMW03 15th May 2019
11:50 to 12:30
Davide Marenduzzo Self-assembly of liquid crystal mixtures: cubic fluid cylinders, elastic emulsions and colloid-active gels composites
In this talk we will show results from lattice Boltzmann simulations probing the behaviour of soft matter mixtures based on a liquid crystalline host (which can be either passive or active).   In the first part of the talk we will investigate the behaviour of a phase-separating mixture of a blue phase I liquid crystal with an isotropic fluid. The resulting morphology is primarily controlled by an inverse capillary number, setting the balance between interfacial and elastic forces. When this dimensionless number and the concentration of the isotropic component are both low, the blue phase disclination lattice templates a novel cubic array of fluid cylinders. In different regions of parameter space, we find elastic emulsions which coarsen very slowly, rewiring the blue phase disclination lines as they do so.   In the second part of the talk, we will study the dynamics of a dispersion of passive colloidal particles in an active nematic host. We find that activity induces a dynamic clustering of colloids even in the absence of any preferential anchoring of the active nematic director at the particle surface. When such an anchoring is present, active stresses instead compete with elastic forces and re-disperse the aggregates observed in passive colloid-liquid crystal composites.
DNMW03 15th May 2019
13:30 to 14:30
Tom Lubensky Colloquium: Review of the 2019 NAS Decadal Survey on Materials Research
At the request of the US National Science Foundation (NSF) and the Department of Energy (DOE), the National Academies of Sciences, Engineering and Medicine undertook a broad study of the current status and promising future directions of materials research in the United States.  This talk will present an overview of this report.
DNMW03 16th May 2019
09:00 to 09:40
Igor Musevic Topological defect formation in a nematic undergoing an extreme temperature quench
The Kibble-Zurek mechanism (KZM) describes the formation of topological defects during the rapid crossing of a second-order phase transition. Several experiments have been performed using nematic liquid crystals, with the aim being to observe the KZM. Most of the experiments report on the late-stage coarsening dynamics of the defect tangle, whereas the mechanism of defect formation in the early stage is still not convincingly demonstrated and lacks solid evidence. We have designed an experiment that can generate an extremely rapid crossing of the isotropic-nematic phase transition which currently achieves cooling rates in excess of 40,000 K/s, with cooling rates as fast as 1,000,000 K/s being achievable in principle. We have developed a novel illumination technique that can take instantaneous images of the quenched sample area with an exposure time of 20 nanoseconds. We have also developed a technique to measure the time dependence of the temperature during the quench. This makes it possible to study defect formation with very accurate timing and an accurate measurement of the local temperature during the quench. The robustness of the experiment allows for several thousand repetitions, which can greatly improve the statistics of the measurements. The current status of the experiments is reported. Coauthored by Uros Jagodic and Anna V. Ryzhkova.
DNMW03 16th May 2019
09:40 to 10:20
Sriram Ramaswamy Fluid flocks with inertia
I will show that inertia can stabilise flocks in bulk fluid provided their order is vectorial, not nematic, and their active stresses are extensile. Among our results is a flocking transition driven by inertia, and two kinds of turbulent states, one of which is ordered "phase turbulence". This work was done with Rayan Chatterjee, Aditi Simha and Prasad Perlekar.
DNMW03 16th May 2019
10:20 to 10:40
Ziga Kos Design of micro-confinement for controlled structure formation in non-equilibrium nematic fluids
Nematic fluids can be designed for a specific purpose by changing their chemical structure, or also by changing the properties of the confinement. I will discuss how the interface between orientational structures in non-equilibrium nematic fluids in microfluidic confinement is affected by the viscoelastic properties of the nematic, flow rate, and shape of the channels [1]. Furthermore, by combining multiple channels into junctions, we were able to create an advanced platform for generation of various topological states, where the strength of the topological singularity in the nematic orientational field is related to the strength of the stagnation point in the junction [2]. The position and strength of the nematic defect can be tuned by the number of channels meeting in a junction and the flow rates through the channels. Flow of confined nematics is of further interest as the nematic structure can allow for the control of the transport properties in porous materials, or the external field-induced modulation of the nematic structure can be designed as a local flow pump, which is a contribution towards using the internal structure of fluids for advanced microfluidic techniques. [1] T. Emeršič, R. Zhang, Ž. Kos, S. Čopar, N. Osterman, J. J. de Pablo, and U. Tkalec, Sculpting stable structures in pure liquids, Sci. Adv. 5, eaav4283 (2019). [2] L. Giomi, Ž. Kos, M. Ravnik, and A. Sengupta, Cross-talk between topological defects in different fields revealed by nematic microfluidics, Proc. Natl. Acad. Sci. 114, E5771 (2017).
DNMW03 16th May 2019
11:10 to 11:50
Tom Lubensky Elasticity and Response in Mechanical Topological Lattices
Ball-and-Spring lattices that have a perfect balance between the number of degrees of freedom and the number of constraining springs under periodic boundary conditions have topologically protected zero-energy surface modes and nonlinear elastic Guest-Hutchinson modes. This talk will provide an overview of these modes in various model systems, including one whose excitation spectrum matches that of a quantum model on a honeycomb lattice introduced by Kitaev. It will also discuss bulk and surface excitation in systems in which the number constraining springs exceeds the number of degrees of freedom.
DNMW03 16th May 2019
11:50 to 12:30
John Ball Some remarks on mathematical theories of liquid crystals
The talk will concern two different topics. First a quick new proof will be given of a result of Fatkullin & Slastikov (2005), Liu, Zhang & Zhang (2005) (see also Zhou et al (2005)), to the effect that stationary solutions to the Onsager equation with the Maier-Saupe interaction are radially symmetric. Second, a description will be given of joint work with Lu Liu on exterior problems in the 2D one-constant Oseen-Frank theory.
DNMW03 16th May 2019
13:30 to 14:10
Claudio Zannoni Bottom Up Modelling of Liquid Crystals and Device Applications
Liquid crystals (LC), with their unique combination of physical properties, offer an increasing number of novel fascinating applications ranging from optical and haptic displays to organic electronics devices, waveguides etc... The variety of observables of interest, and the complexity of LC mesogens require their bottom up modelling and computer simulations to be performed at different (micro-, nano- and Angstrom) length scales, that can be tackled respectively with lattice, molecular and atomistic approaches. In the talk we plan to present some recent examples of application of these different simulations. In particular, we show that Monte Carlo simulations of lattice models [1] can help investigating the structure of defects in photopatterned hybrid nematic films with different in plane surface order [2]. A much more detailed, atomistic level description is instead required to try and understand the role of liquid crystal ordering, if present, in rationalizing charge mobility in organic semiconductors and, possibly in designing better organic electronic materials. We shall discuss, in particular, the proposed hypothesis [3] that a smectic E organization is key to the unusually high performance of certain organic seminconductors, e.g. Ph-BTBT-C10 [4].
[1] C. Chiccoli, L. R. Evangelista, P. Pasini, G. Skačej, R. Teixeira de Souza and C. Zannoni, Scientific Reports, 2018, 8, 2130.
[2] C. Chiccoli, P. Pasini, , C. Zannoni, G. Skačej, H. Yoshida,T. Hiroshima, K. Sunami, T. Ouchi, and M. Ozaki, submitted (2018)
[3] H. Iino, T. Usui and J.-i. Hanna, Nature Comm. 6, 6828 (2015).
[4] A. Baggioli, M. Casalegno, G. Raos, L. Muccioli, S. Orlandi, and C. Zannoni submitted (2019).
DNMW03 16th May 2019
14:10 to 14:50
Simon Copar Flow-induced states in channel-confined nematics
Anisotropy of liquid crystals couples their orientational order to velocity shear, and consequently, induces different regimes in flows with different strengths. A flow-aligning nematic liquid crystal, confined to a channel with homeotropic surface alignment, is known to undergo a transition from a homeotropic to a flow-aligned state. I will present a more detailed view of this behaviour, including a hidden pre-transitional state with broken chiral symmetry and dynamics of flow-aligned domain under uniform or alternating flow. Additionally, I will present a Landau model that captures the stability of different states with respect to material parameters.
DNMW03 16th May 2019
15:20 to 16:00
Apala Majumdar Nematic Pattern Formation on 2D Polygons - a Landau de Gennes study
DNMW03 16th May 2019
16:00 to 16:40
Lidia Mrad Constrained Energy Minimization for Bent-Core Liquid Crystals
One of the important applications of liquid crystal materials is their use in optical and display devices. There are several phases of liquid crystals, some of which promise more efficient and less expensive optical devices than others. A recently discovered phase is made up of bow-shaped molecules, a characteristic that endows them with spontaneous ferroelectricity. Under the effect of an applied electric field, two competing mechanisms of switching can be detected in the tilted structure of these materials. An important question in this setup is how the dominant mechanism - switching here - is affected by specific system parameters. We formulate the model as an energy minimization problem allowing us to use several variational tools in its analysis. We emphasize how we can deal with challenges that arise from constraints and nonlinearities peculiar to this problem. Our results address existence and uniqueness of solutions to the ensuing partial differential equations, which in turn shed light on the physical mechanisms observed.
DNMW03 16th May 2019
16:40 to 17:00
Katherine Macmillan Materials from Colloidal Particles using Optical Fields
Katherine A. Macmillan, Erick Sarmiento and Stefan U. Egelhaaf The interaction of light with colloidal particles has been widely exploited in optical tweezers [1]. In addition, multiple traps or extended potential energy landscapes (optical fields) have been applied using periodic interference patterns, speckle patterns created using ground glass and freely configurable patterns created using spatial light modulators [1, 2]. The capability of these optical potential energy landscapes to trap multiple colloidal particles in a designed structure has yet to be fully explored. In order to pursue this goal, here we study a two dimensional colloidal glass in a periodic potential. We find that a periodic potential with a periodicity commensurate with the lattice spacing for a hexagonally close packed array can induce the particles to crystallise. We have investigated the influence of parameters describing the potential on the formation of crystals from disordered structures. Upon the removal of the periodic potential, the colloidal particles can return to a more disordered state rendering the crystal structures only transient. The possibility of fixing this transient state by attaching the particles together has begun to be investigated. In the future, we aim to use optically-created potential energy landscapes to imprint a structure on a dispersion of colloidal particles that can be fixed by covalently bonding the particles together. [1] Richard D. L. Hanes, Matthew C. Jenkins and Stefan U. Egelhaaf, Review of Scientific Instruments, 2009, 80, 083703 [2] F. Evers, R.D.L. Hanes, C. Zunke, R.F. Capellmann, J. Bewerunge, C. Dalle-Ferrier, M.C. Jenkins1, I. Ladadwa, A. Heuer, R. Castañeda-Priego and S.U. Egelhaaf, European Physical Journal Special Topics, 2012, 222, 2995–3009
DNMW03 17th May 2019
09:00 to 09:40
Man-made nano- and micro-motors are key to many future applications. I will describe highly reconfigurable self-assembly of colloidal micro-motors that exhibit a repetitive rotation when immersed in a liquid crystal and powered by a continuous exposure to unstructured ~1nW light. A monolayer of self-assembled azobenzene molecules defines how the liquid crystal’s optical axis mechanically couples to the colloidal particle’s surface, as well as how they jointly rotate as the light’s polarization changes. The rotating particle twists the liquid crystal, which, in turn changes polarization of the light traversing it. The resulting feedback mechanism spontaneously yields a continuous opto-mechanical cycle and drives the unidirectional particle spinning, with handedness and frequency robustly controlled by polarization and intensity of light. I will discuss how this may enable new forms of active matter and self-assembled machines.
DNMW03 17th May 2019
09:40 to 10:20
Antonio DeSimone Reconfigurable surfaces with controlled stretching and shearing: from biological templates to engineering devices
In recent years, we have studied locomotion and shape control in Euglena gracilis using a broad range of tools ranging from theoretical and computational mechanics, to experiment and observations at the microscope, to manufacturing of prototypes.

As a concrete example, the behavior of Euglena gracilis is particularly interesting.This unicellular protist is particularly intriguing because it can adopt different motility strategies: swimming by flagellar propulsion, or crawling thanks to large amplitude shape changes of the whole body (a behavior known as metaboly).

We will survey our most recent findings [1-4] within this stream of research.

This is joint work with M. Arroyo, G. Cicconofri, A. Lucantonio, and G. Noselli, and is supported by ERC Advanced Grant 340685-MicroMotility.

References
[1] Rossi, M., Cicconofri, G., Beran, A., Noselli, G., DeSimone, A.: “Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes”, Proceedings of the National Academy of Sciences USA 114(50), 13085-13090 (2017).
[2] Noselli, G., Beran, A., Arroyo, M., DeSimone, A.: “Swimming Euglena respond to confinement with a behavioral change enabling effective crawling”, Nature Physics, 2019.
[3] Noselli, G., Arroyo, M., DeSimone, A.: “Smart helical structures inspired by the pellicles of euglenids”, J. Mech Phys Solids 123, 234-246 (2019).
[4] Caruso, N., Cvetkovic, A., Lucantonio, A., Noselli, G., DeSimone, A.: “Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry”, Int J Mech Sci 149, 481-486 (2018).
DNMW03 17th May 2019
10:20 to 10:40
Henrik Ronellenfitsch Inverse design of discrete mechanical metamaterials
Mechanical and phononic metamaterials exhibiting negative elastic moduli, gapped vibrational spectra or topologically protected modes enable precise control of structural and acoustic functionalities. While much progress has been made in their experimental and theoretical characterization, the inverse design of mechanical metamaterials with arbitrarily programmable spectral properties and mode localization still poses an unsolved problem. Here, we present a flexible computational inverse-design framework that allows the efficient tuning of one or more gaps at nearly arbitrary positions in the spectrum of discrete phononic metamaterial structures. The underlying algorithm optimizes the linear response of elastic networks directly, is applicable to ordered and disordered structures, scales efficiently in 2D and 3D, and can be combined with a wide range of numerical optimization schemes. We illustrate the broad practical potential of this approach by designing mechanical bandgap switches that open and close pre-programmed spectral gaps in response to an externally applied stimulus such as shear or compression. We further show that the designed structures can host topologically protected edge modes, and validate the numerical predictions through explicit 3D finite element simulations of continuum elastica with experimentally relevant material parameters. Generally, this network-based inverse design paradigm offers a direct pathway towards manufacturing phononic metamaterials, DNA origami structures and topolectric circuits that can realize a wide range of static and dynamic target functionalities. Joint work with Norbert Stoop, Josephine Yu, Aden Forrow, Joern Dunkel
DNMW03 17th May 2019
11:10 to 11:50
Douwe Jan Bonthuis Charging of neutral solutes in water
Owing to the small length scales involved, aqueous interfaces dominate the properties of colloidal materials suspended in water. Surface charges, in particular, control the stability of colloidal suspensions and the self-assembly and organization of nanoparticles. Apart from charging by surface groups, ions and protons adsorb at the surfaces of colloids, lipid membranes and biological molecules, affecting their electrostatic and hydrodynamic interactions.

We study the interfacial structure of the aqueous interfaces of oil droplets, air bubbles and solid surfaces. A combination of analytical work, molecular dynamics simulations and continuum theory allows for direct comparison to experimental results for surface tensions, conductivities and electrokinetic mobilities.
DNMW03 17th May 2019
11:50 to 12:10
In this talk, we address the building of finite-time adiabatic processes at the mesoscale, i.e. processes in which the average heat exchange between the system and its surroundings vanishes. Specifically, we consider a Brownian particle trapped by a harmonic potential and immersed in a fluid. Therein, we analyse some general properties and, in particular, we show that there emerges a minimum time for connecting two equilibrium states with such a finite-time adiabatic process. Also, we look into a different optimisation problem, namely that of the final temperature for a given connection time. Interestingly, we find out that this second problem is closely related to the first one: both of them are controlled by the same function. Finally, we discuss some perspectives for future work.

(In collaboration with Carlos A. Plata, David Guéry-Odelin and Emmanuel Trizac)
DNMW03 17th May 2019
12:10 to 12:30
Dwaipayan Chakrabarti Colloids Get Creative: Key to Open Crystals
Open crystals are sparsely populated periodic structures, which, when composed of colloidal particles, are appealing for their variety of applications, for example, as photonic materials, phononic and mechanical metamaterials, as well as porous media [1-4]. Programming self-assembly of colloidal particles into open crystals has proved a long-standing challenge due both to the mechanical instability and lack of kinetic accessibility that colloidal open crystals typically suffer from. Building on our recent work [5-7], I will here introduce a hierarchical self-assembly scheme for triblock patchy particles to address the challenges met with programming self-assembly into colloidal open crystals [8].  The presentation will demonstrate in silico the hierarchical self-assembly of colloidal open crystals via what we call closed clusters, which stop to grow beyond a certain size in the first stage and are thus self-limiting [8].  Our designer patchy particles are spherical in shape, having two attractive patches at the poles across a charged middle band – a close variant of those synthesised recently [9]. By employing a variety of computer simulation techniques, I will show that the design space supports different closed clusters (e.g. tetrahedra or octahedra with variable valences) en route to distinct open crystals. Our design rules thus open up the prospects of realising a number of colloidal open crystals from designer triblock patchy particles, including, most remarkably, a diamond crystal [8], much sough-after for is attractive photonic applications. The relevant photonic band structure will be presented.

References
[1] J. D. Joannopoulos, P. R. Villeneuve and S. Fan, Nature 1997, 386, 143.
[2] K. Aryana and M. B. Zanjani, J. Appl. Phys. 2018, 123, 185103.
[3] X. Mao and T. C. Lubensky, Annu. Rev. Condens. Matter Phys. 2018, 9, 413.
[4] X. Mao, Q. Chen and S. Granick, Nature Mater. 2013, 12, 217.
[5] D. Morphew and D. Chakrabarti, Nanoscale 2015, 7, 8343.
[6] D. Morphew and D. Chakrabarti, Soft Matter 2016, 12, 9633.
[7] D. Morphew and D. Chakrabarti, Nanoscale 2018, 10, 13875.
[8] D. Morphew, J. Shaw, C. Avins and D. Chakrabarti, ACS Nano 2018, 12, 2355.
[9] Q. Chen, S. C. Bae and S. Granick, J. Am. Chem. Soc. 2012, 134, 11080.
DNM 21st May 2019
15:00 to 16:00
Ibrahim Fatkullin Gibbs Ensembles of Partitions: from limit shapes to hydrodynamic limits
Distributions of aggregate sizes in various polymerization processes may be described by measures on partitions of integers and sets. We explicitly compute limit shapes for several grand canonical Gibbs ensembles and prove that all possible limit shapes for these ensembles fall into distinct classes determined by the asymptotics of the internal energies of aggregates. Further on, we establish hydrodynamic limits for a class of stochastic processes on the associated Young diagrams and deriving PDEs governing the evolution of limit shapes in suitable asymptotic regimes.

DNM 29th May 2019
16:00 to 17:00
Ivan Smalyukh Hopf and Skyrme Solitons
Topologically nontrivial fields and vortices frequently arise in classical and quantum field theories, plasmas, optics, cosmology and atomic systems. On the other hand, condensed matter systems, such as colloids, magnets and liquid crystals, offer the complexity in degrees of freedom and symmetries that allow for probing topologically analogous phenomena on experimentally accessible scales. In my lecture, I will discuss Hopf and Skyrme solitons, continuous but topologically nontrivial knotted field configurations localized in three or two spatial dimensions. They emerge as static structures within the chiral condensed matter systems [1-4] and self-assemble into crystals, but can also exhibit emergent collective motions when powered by external stimuli [5]. I will show how such a synergistic interplay of topology and self-assembly paradigms can emerge as an exciting scientific frontier of condensed matter.
1. P. J. Ackerman and I. I. Smalyukh. Nature Mater 16, 426-432 (2017).
2. J.-S.B. Tai, P.J. Ackerman and I.I. Smalyukh. PNAS. 115, 921-926 (2018).
3. P. J. Ackerman and I. I. Smalyukh. Phys Rev X 7, 011006 (2017).
4. J.-S. B. Tai and I. I. Smalyukh. Phys Rev Lett 121, 187201 (2018). 5. H.R.O. Sohn, C.D. Liu and I.I. Smalyukh. (2019).

DNM 3rd June 2019
16:00 to 17:00
Graeme Milton Rothschild Distinguished Visiting Fellow Lecture: Metamaterials: composite materials with striking properties
Sometimes the properties of a composite are completely unlike those of the constituent materials, even when the structure is small compared to the wavelength: these composites are called metamaterials. Classic examples include bubbly fluids and stained glass windows made from suspensions of metal particles in glass. Other examples include metamaterials with negative thermal expansion made from materials all having positive thermal expansion; metamaterials with negative and/or possibly anisotropic mass density over a range of frequencies; metamaterials that get fatter as they are stretched (having a negative Poisson's ratio); materials with artificial and possibly negative magnetic permeability. The list goes on. Recent attention has been directed to space-time microstructures where the material moduli vary in both space and time. We will review some of the progress that has been made. One particular class of elastic metamaterials, known as pentamodes, has proved useful for guiding stress. Cable networks can also guide stress. It turns out that essentially any cable network under tension, and supporting a given loading, can be replaced by one in which at most four cables meet at any junction. Like pentamodes, these can support, up to a constant factor, only one stress field. Thus by tightening just one cable one gets the desired forces at all the terminal nodes. This last work is joint with Guy Bouchitte, Ornella Mattei and Pierre Seppecher.
DNM 5th June 2019
14:00 to 15:00
Robert Kohn A variational perspective on wrinkling due to geometric incompatibility
DNM 5th June 2019
15:00 to 16:00
Marta Lewicka Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models
DNM 5th June 2019
16:00 to 17:00
Gregoire Allaire Topology optimization of structures: a review of manufacturing constraints
DNMW04 10th June 2019
10:00 to 11:00
Graeme Milton Optimizing the elastic response of 3-d printed materials
We address the grand question of identifying the set of possible elasticity tensors (including anisotropic ones) of 3d-printed materials constructed from a given elastic material with known elastic constants. We identify many almost optimal geometries with elasticity tensors arbitrarily near the boundary of what one can achieve. We characterize many parts of the surface of the set of possible elasticity tensors. This is no easy task as completely anisotropic 3d-elasticity tensors live in an 18-dimensional space of invariants, much more than the two invariants (bulk and shear moduli) that characterize isotropic elasticity tensors. We completely characterize the set of possible (average stress, average strain) pairs that can exist in these porous materials. Unfortunately, the geometries we find are rather extreme but this should motivate the search for more realistic ones that come close to having the desired elasticity tensors. Also, not all parts of the surface are characterized for elastically isotropic composites. Further progress will require new ideas. This is joint work with Marc Briane, Mohamed Camar-Eddine, and Davit Harutyunyan.
DNMW04 10th June 2019
11:30 to 12:30
Dorin Bucur Spectral shape optimization problems with Neumann conditions on the free boundary
In this talk I will discuss the question of the maximization of the $k$-th eigenvalue of the Neumann-Laplacian under a volume constraint. After an introduction to the topic I will discuss the existence of optimal geometries. For now, there is no a general existence result, but one can prove existence of an optimal {\it (over) relaxed domain}, view as a density function. In the second part of the talk,  I will focus on the low eigenvalues. The first non-trivial one is maximized by the ball, the result being due to Szego and Weinberger in the fifties. Concerning the second non-trivial eigenvalue, Girouard, Nadirashvili and  Polterovich proved that the supremum in the family of planar simply connected domains of $R^2$ is attained by the union of two disjoint, equal discs. I will show that a similar statement holds in any dimension and without topological restrictions.
DNMW04 10th June 2019
14:30 to 15:30
Agnes Lamacz Effective Maxwell's equations in a geometry with flat split-rings and wires
Propagation of light in heterogeneous media is a complex subject of research. Key research areas are photonic crystals, negative index metamaterials, perfect imaging, and cloaking.   The mathematical analysis of negative index materials, which we want to focus on in this talk, is connected to a study of singular limits in Maxwell's equations. We present a result on homogenization of the time harmonic Maxwell's equations in a complex geometry. The homogenization process is performed in the case that  many (order $\eta^{-3}$) small (order $\eta^1$), flat (order $\eta^2$) and highly conductive (order $\eta^{-3}$) metallic split-rings are distributed in a domain $\Omega\subset \mathbb{R}^3$. We determine the effective behavior of this metamaterial in the limit $\eta\searrow 0$. For $\eta>0$, each single conductor occupies a simply connected domain, but the conductor closes to a ring in the limit $\eta\searrow 0$. This change of topology allows for an extra dimension in the solution space of the corresponding cell-problem. Even though both original materials (metal and void) have the same positive magnetic permeability $\mu_0>0$, we show that the effective Maxwell system exhibits, depending on the frequency, a negative magnetic response. Furthermore, we demonstrate that combining the split-ring array with thin, highly conducting wires can effectively provide a negative index metamaterial.
DNMW04 10th June 2019
16:00 to 17:00
Beniamin Bogosel Optimization of support structures in additive manufacturing
Support structures are often necessary in additive manufacturing in order to ensure the quality of the final built part. These additional structures are removed at the end of the fabrication process, therefore their size should be reduced to a minimum in order to reduce the material consumption and impression time, while still preserving their requested properties.   The optimization of support structures is formulated as a shape and topology optimization problem. Support structures need to hold all overhanging parts in order to assure their manufacturability, they should be as rigid as possible in order to prevent the deformations of the structure part/support and they should not contain overhanging parts themselves. In processes where melting metal powder is involved, high temperature gradients are present and support structures need to prevent eventual deformations which are a consequence of these thermal stresses.   We show how to enforce the support of overhanging parts and to maximize the rigidity of the supports using linearized elasticity systems. In a second step we show how a functional depending on the gradient of the signed distance function allows us to efficiently prevent overhang regions in the support structures. The optimization is done by computing the corresponding shape derivatives with the Hadamard method. In order to simulate the build process we also consider models in which multiple layers of the part and of the support are taken into account.   The models presented are illustrated with numerical simulations in dimension two and three. The goal is to obtain algorithms which are computationally cheap, while still being physically relevant. The numerical framework used is the level-set method and the numerical results are obtained with the freeware software FreeFem++ and other freely available software like Advect and Mshdist from the ISCD Toolbox.This work was done in the project SOFIA in collaboration with Grégoire Allaire.
DNMW04 11th June 2019
10:00 to 11:00
Anca-Maria Toader Optimization of bodies with locally periodic microstructure by varying the shape, the topology and the periodicity pattern
Mimicking nature, an optimization method that makes the link between microstructure and macrostructure is considered. Homogenization theory is used to describe the macroscopic (effective) elastic properties of the body.   The already known alternate optimization of shape and topology of the model cell is a procedure that gives a limited flexibility to the microstructure for adapting to the macroscopic loads. Beyond that, one may vary the periodicity cell itself during the optimization process, thus allowing the microstructure to adapt more freely to the given loads.   What we propose is a method that combines the three optimization techniques : the shape, the topology and the periodicity pattern. By combining variations of these three ingredients, the obtained optimal design approaches the homogenized structure of the body, giving one the possibility to obtain a manufacturable design with smooth transition of material properties as in functionally graded materials.   Numerical examples will be presented. The problem is numerically heavy, since the optimization of the macroscopic problem is performed by optimizing in simultaneous hundreds or even thousands of periodic structures, each one using its own finite element mesh on the periodicity cell. Parallel computation is used in order to alleviate the computational burden.
DNMW04 11th June 2019
11:30 to 12:30
Benedikt Wirth Variational models for transportation networks: old and new formulations
A small number of models for transportation networks (modelling street, river, or vessel networks, for instance) has been studied intensely during the past decade, in particular the so-called branched transport and the so-called urban planning. They assign to each network the total cost for transporting material from a given initial to a prescribed final distribution and seek the cost-optimal network. Typically, the considered transportation cost per mass is smaller the more mass is transported together, which leads to highly patterned and ramified optimal networks. I will present novel formulations of these models which allow a better interpretation as an optimal design problem.
DNMW04 11th June 2019
13:30 to 14:30
Jeroen Peter Groen Simple single-scale interpretations of optimal designs in the context of extremal stiffness
It is well-known that rank-N laminates can reach the theoretical bounds on strain energy in the context of linear elasticity. The theory of homogenization-based topology optimization using this class of composite materials is well-developed, and can therefore be used to find an overall optimal material distribution at low computational cost. A downside of these optimal multi-scale designs is that features exist at several length-scales limiting the manufacturability. The main contribution of the presented work is to develop and extend on new methods, to interpret these designs on a single scale, while still being close to what is theoretically possible. Using these methods high-resolution near optimal designs can be achieved on a standard PC at low computational cost. Several modifications are given, such as a method to locally adapt microstructure spacing and a method to interpret the single-scale designs as a frame structure.   Furthermore, simple microstructures are presented that are optimized for multiple anisotropic loading conditions. This is done by approximating optimal microstructures on a single-scale, resulting in a performance that is close (e.g. 10-15%) to the theoretical bounds. When used as starting guess for topology optimization these proposed microstructures can be further improved, outperforming topology optimized designs using classical starting guesses both in performance and simplicity.   Finally, a class of simple periodic truss lattice structures is presented that exhibits near-optimal performance in the high porosity limit. The performance difference between closed and open-walled microstructures is presented for anisotropic loading situations, where it is demonstrated that the maximum difference occurs when isotropic microstructures are considered.
DNMW04 11th June 2019
14:30 to 15:30
Perle Geoffroy Topology optimization of modulated and oriented periodic microstructures by the homogenization method in 2-d and in 3-d
The work presented here is motivated by the optimization of so-called lattice materials which are becoming increasingly popular in the context of additive manufacturing. We propose a method for topology optimization of structures made of periodically perforated material, where the microscopic periodic cell can be macroscopically modulated and oriented in the working domain.
This method is made of three steps. The first step amounts to compute the homogenized properties of an adequately chosen parametrized microstructure (here, a cubic lattice with varying bar thicknesses). The second step optimizes the homogenized formulation of the problem, which is a classical problem of parametric optimization. The third, and most delicate, step projects the optimal oriented microstructure at
a desired length scale. In 2-d case, rotations are parametrized by a single angle, to which a conformality constraint can be applied. A conformal diffeomorphism is then computed from the orientation field, thanks which each periodic cell is well oriented in the final structure. The 3-d case is more involved and requires new ingredients. In particular, the full rotation matrix is regularized (instead of just one angle in 2-d) and the projection map which deforms the periodic lattice is computed component by component.
DNMW04 12th June 2019
10:00 to 11:00
Jesus Martinez-Frutos Level-set topology optimization for robust design of structures under internal porosity constraints
Porosity is a well-known phenomenon occurring during various manufacturing processes (casting, welding, additive manufacturing) of solid structures, which undermines their reliability and mechanical performance. The main purpose of this talk is to introduce a new constraint functional of the domain which controls the negative impact of porosity on elastic structures in the framework of shape and topology optimization. The main ingredient of our modeling is the notion of topological derivative, which is used in a slightly unusual way: instead of being an indicator of where to nucleate holes in the course of the optimization process, it is a component of a new constraint functional which assesses the influence of pores on the mechanical performance of structures. The shape derivative of this constraint is calculated and incorporated into a level set based shape optimization algorithm. This approach will be illustrated by several two- and three-dimensional numerical experiments of topology optimization problems constrained by a control on the porosity effect. These works have been conducted together with Grégoire Allaire, Charles Dapogny and Francisco Periago.
DNMW04 12th June 2019
11:30 to 12:30
Olivier Pantz Singular lattices, regularization and dehomogenization method
The deshomogenization method consists in reconstructing a minimization sequence of genuine shapes converging toward the optimal composite.
We introduced this method a few years ago. Since, it has gain some interest -- see the works of JP. Groen and O. Sigmund -- thanks to the rise of additive manufacturing. Bascillay, it can be considered as a post-treatment of the classical homogenization method.
The output of the (periodic) homogenization method is :
- An orientation field of the periodic cells
- Geometric parameters describing the local micro-structure.
From this output, the deshomogenization method allows to construct a sequence of genuine shapes, converging toward the optimal, (almost) suitable for 3D printers.

The sequence of shapes is defined via a so called "grid map", which aim is to ensure the correct alignment of the cells with respect to the orientation. field.
It also enforce the connectivity of the structure between neighboring cells. If the orientation field is regular and the optimization domain $D$ is simply connect, the grid map can be defined as local diffeomorphism from $D$ into $R^n$ (with n=2 or 3). If those requirements are not met, the definition of the grid map is much more intricate.

Moreover, a minimal kind of regularity is needed to be able to ensure the convergence of the sequence of shapes toward the optimal composite : it is necessary to regularize the orientation field but still allow for the presence of singularities. This is done by a penalization of the cost function based on the Ginzburg-Landau theory.

In this talk, we will present
1/ A general definition of the grid map based on the introdcution of an abstract manifold.
2/ A regularization of the orientation field based on G-L theory.
3/ Numerical applications in 2D and 3D.

This talk is based on a joint work by G. Allaire, P. Geoffroy and K. Trabelsi.

DNMW04 13th June 2019
10:00 to 11:00
Martin Rumpf Multi-Scale and Risc Averse Stochastic Shape Optimization
This talk discusses the optimization for elastic materials and elastic microstructures under different and in particular stochastic loading scenarios.
To this end, on the one hand we transfers concepts from finite-dimensional stochastic programming to elastic shape optimization.
Thereby, the paradigm of stochastic dominance allows for flexible risk aversion via comparison with benchmark random variables,
Rather than handling risk aversion in the objective, this enables
risk aversion by including dominance constraints that single out subsets of
nonanticipative shapes which compare favorably to a chosen stochastic benchmark.

On the other hand, we investigate multiscale shape optimization using mechanically simple, parametrized microscopic
supporting structure those parameters have to be optimized.
An posteriori analysis of the discretization error and the modeling error is investigated
for a compliance cost functional in the context of the optimization of composite elastic materials
and a two-scale linearized elasticity model. This error analysis includes a control of the
modeling error caused when replacing an optimal nested laminate microstructure by this considerably simpler microstructure.

Furthermore, an elastic shape optimization problem with simultaneous and competitive optimization of domain and complement
is discussed. Such a problem arises in biomechanics where a bioresorbable polymer scaffold is implanted in
place of lost bone tissue and in a regeneration phase new bone tissue grows in the scaffold complement via osteogenesis.
In fact, the polymer scaffold should be mechanically stable to bear loading in the early stage regeneration phase
and at the same time the new bone tissue grown in the complement of this scaffold should as well bear the loading.

The talk is based on joint work with Sergio Conti, Patrick Dondl, Benedikt Geihe, Harald Held, Rüdiger Schultz,
Stefan Simon, and Sascha Tölkes.
DNMW04 13th June 2019
11:30 to 12:30
Samuel Amstutz Gradient-free perimeter approximation for topology optimization and domain partitioning
I will present a Gamma-convergence approximation of the perimeter of a set built upon the solution of an elliptic PDE. I will discuss the advantages and drawbacks of this approach compared with other functionals, at first to address topology optimization problems with perimeter control. I will emphasize the specific mathematical properties and algorithmic issues, showing in particular how the variational formulation of the PDE can be exploited to design alternating minimizations schemes. Then I will explain how those results and methods, through combinatorial and duality techniques, can be adapted to multiphase optimal partitioning problems with an energy term consisting of a weighted sum of measures of interfaces. Problems of hydrostatics with surface tensions will be shown as examples.
DNMW04 13th June 2019
13:30 to 14:30
Julian Panetta Computational Design of Robust Elastic Metamaterials and Deployable Structures
My talk will present some computational design tools targeting various classes of structures and fabrication technologies. In the first half, I will present a method for designing elastic metamaterials that can be fabricated with consumer-level single material 3D printers to achieve custom deformation behaviors. These metamaterials cover a wide range of elastic properties and are optimized for robustness in generic use, experiencing minimal stresses under the worst-case load. Our coarse-scale design optimization can then automatically assign these metamaterials to an input geometry so that the printed object undergoes a user-specified deformation under applied loads. In the second half, I will introduce a new class of deployable elastic gridshell structures. These structures consist of flat, conveniently assembled layouts of elastic beams coupled by rotational joints that can be deployed to programmed 3D curved shapes by a simple expansive actuation. During deployment, the coupling imposed by the joints forces the beams to twist and buckle out of plane, allowing interesting 3D forms to emerge. However the simulation and optimization of these structures is challenging, especially due to the frequent unstable equilibria encountered in the deployment path; I will discuss the efficient algorithms we have developed to assist the design of these structures. This talk is based on joint work with Denis Zorin, Mark Pauly, and Florin Isvoranu.
DNMW04 13th June 2019
14:30 to 15:30
Charles Dapogny About new constraints induced by additive manufacturing technologies on the shape optimization process
However they allow, in principle, to assemble arbitrarily complex structures - thereby arousing much enthusiasm within the engineering community - modern additive manufacturing technologies (also referred to as 3d printing) raise new difficulties which have to be taken into account from the early stages of the construction, and notably at the level of the design optimization. In this presentation, we shall deal with the modeling and the understanding of two such major challenges related to additive construction methodologies. The first one of these is to avoid the emergence of overhanging regions during the shape optimization process, that is, of large, nearly horizontal regions hanging over void, without sufficient support from the lower structure. The second difficulty addressed in this presentation is related to the fact that the use of an additive technique to realize a structure entails a significant alteration of the mechanical performance of the constituent material of the assembled shape: this material turns out to be inhomogeneous, and it presents anisotropic properties, possibly depending on the global shape itself.
These works have be conducted together with Grégoire Allaire, Rafael Estevez, Alexis Faure and Georgios Michailidis.
DNMW04 14th June 2019
10:00 to 11:00
Antonin Chambolle Remarks on the discretizations of the perimeter
I will discuss some results on finite differences and finite element approximations of the total variation for possibly discontinuous functions.
In particular the talk will focus on the differences between various types of approximations, both qualitatively and quantitatively. This is based on
joint works with Thomas Pock (TU Graz) and Corentin Caillaud (CMAP, Ecole Polytechnique & CNRS, Palaiseau)
DNMW04 14th June 2019
11:30 to 12:30
H Alicia Kim Optimization for Multiscale Material Design
Topology optimization is able to provide unintuitive and innovative design solutions and a performance improvement (e.g. weight savings) in excess of 50% is not uncommonly demonstrated in a wide range of engineering design problems. With the rise of advance materials and additive manufacturing, topology optimization is attracting much attention in the recent years. This presentation will introduce topology optimization in structural design, fiber composites and architected material. It will also include more recent advances topology optimization, multiscale design optimization breaking down the barrier between material and structural designs. Another direction of interests in large-scale topology optimization using the latest sparse data structures tailored to novel level set method. We have demonstrated an order of magnitude improvements on both the memory footage and the computation time. These efforts represent a pathway to applying topology optimization for complex multiphysics multifunctional structures, which may be too complex to rely on designers’ intuition.
DNM 19th June 2019
14:30 to 15:10
Dimitrios Tsagkarogiannis Virial inversion and microscopic derivation of density functionals
We present a rigorous derivation of the free energy functional for
inhomogeneous systems, i.e. with a density that depends on the position,
orientation or other internal degrees of freedom. It can be viewed as an
extension of the virial inversion (developed for homogeneous systems) to
uncountably many species. The key technical tool is a combinatorial identity for
a special type of trees which allows us to implement the inversion step as well
as to prove its convergence. Applications include classical density functional
theory, Onsager's functional for liquid crystals, hard spheres of different sizes
and shapes. Furthermore, the method can be generalized in order to provide
convergence for other expansions commonly used in the liquid state theory.
The validity is always in the gas regime, but with the new method we improve
the original radius of convergence for the hard spheres as proved by Lebowitz
and Penrose and subsequent works. This is joint work with Sabine Jansen and
Tobias Kuna.
DNM 19th June 2019
15:10 to 15:50
Jose Matias Explicit integral representations of the relaxation of non-local energies for structured deformations
The theory of structured deformations in the SBV setting developed by Chocki & Fonseca [1]
only takes into account the linear dependance on jumps along the approximating sequences. Following a
model from Del Piero & Owen [2] that captures the non-linear dependence on jumps, the present approach
to relaxation of non-local energies rests on two limiting processes: start from a submacroscopical level
where we have a weighted average of disarrangements within neighborhoods of fixed size r > 0 and pass to
the macrolevel, permitting disarrangements to diffuse through such a neighborhood. This limiting process
determines a structured deformation as well as the non-local dependence of the energy density of such a
structured deformation. Pass to the limit as r ! 0, to obtain purely local bulk and interfacial energy
densities for the structured deformation identified in the first step.
This is a joint work with
Marco Morandotti, Dipartimento di Scienze Matematiche “G. L. Lagrange”, Politecnico di Torino,
David R. Owen, Department of Mathematical Sciences, Carnegie Mellon University,
Elvira Zappale, Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno.
References
[1] R. Choksi and I. Fonseca: Bulk and interfacial energy densities for structured deformations of continua. Arch. Rational
Mech. Anal. 138 (1997), 37-103.
[2] G. Del Piero and D. R. Owen: Structured Deformations: Part Two. Quaderni

DNM 19th June 2019
15:50 to 16:10
Jorn Dunkel Wrinkles, spaghetti & knots
Buckling, twisting and fracture are ubiquitous phenomena that, despite
having been studied for centuries, still pose many interesting conceptual and
practical challenges. In this talk, I will summarize our recent theoretical and
experimental work that aims to understand the role of curvature and torsion
in wrinkle pattern selection, fragmentation cascades and knots. First, we will
show how changes in curvature can induce phase transitions and topological
defects in the wrinkling patterns on curved elastic surfaces. Thereafter, we will
revisit an observation by Feynman who noted that dry spaghetti appears to
fragment into at least three (but hardly ever two) pieces when placed under
large bending stresses. Using a combination of experiments, simulations and
analytical scaling arguments, we will demonstrate how twist can be used to
control binary fracture of brittle elastic rods. Finally, in the last part, we will try to
shed some light on how topology and torsion affect the stability of commonly
used knots.

DNM 26th June 2019
15:30 to 16:30
Elvira Zappale Optimal design problems
Results devoted to obtain a measure representation for  functionals arising in the context of optimal design problems will be presented. Aiming at the description of several applications, different sets of assumptions  will be considered.

DNM 15th October 2019
17:00 to 18:00
Jonathan Robbins Collective coordinates, asymptotics and domain wall dynamics in ferromagnets
The method of collective coordinates is a simple and widely used variational procedure for finding approximate solutions to many- or infinite-dimensional, possibly damped and driven, Hamiltonian systems. The approximate solutions are typically characterised by a small number of time-dependent parameters, which are understood to describe a small number of activated modes. The simplicity of the method comes at a price, however, as it does not allow a determination of how good (or bad) the approximation is. In certain regimes, asymptotic expansions can provide the requisite estimates, though they require more work.   This is illustrated for the problem of the motion of domain walls in ferromagnets. Domain walls are interfaces between differently oriented magnetic domains, and the dynamics of these interfaces under applied magnetic fields and currents is a problem of current physical and technological interest.