Videos and presentation materials from other INI events are also available.
Event  When  Speaker  Title  Presentation Material 

DNMW01 
14th January 2019 09:45 to 10:30 
Peter PalffyMuhoray  Attractive and Repulse Interactions in Dense Nematics  
DNMW01 
14th January 2019 11:00 to 11:45 
Jonathan Robbins 
Asymptotics of Landaude Gennes theory
We consider the Landaude Gennes model for nematic liquid crystals in a twodimensional domain subject to integerdegree boundary conditions, consistent with the absence of defects, in the physically relevant regime of weak elasticity. At leading order, the minimumenergy configuration is described by the simpler OseenFrank theory. We obtain the nextorder corrections using a Gammaconvergence 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 wellknown problem in the GinzburgLandau 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 structureseeker energy landscape. Third, while efficient algorithms for cluster detection and data completion in highdimensional 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 lowdimensional dynamical transition networks from highdimensional 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 socalled "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 nematicisotropic transition temperature. In this talk, we consider a Landaude 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 Landaude 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, nonspherical, 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 socalled 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 nonunique. While only providing results in the simpler twodimensional 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
Coauthors: 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 SelfOrganization, 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 pointlike. 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 liquidlike 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 manmade 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 
Highthroughput search for new phase transformation materials with low hysteresis
Coauthors: Monika Løberg (University of Oslo), Nicholas Pike (University of Oslo) Phase transformation materials (PTMs) can be used for energy harvesting of heat from lowtemperature 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 highthroughput 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 stressinduced 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.: Ultralowfatigue shape memory alloy films, Science 348 (2015), 10041007.
(2) Gu, H.; Bumke, L.; Chluba, C.; Quandt, E.; James, R.D.: Phase engineering and supercompatibility of shape memory alloys, Materials Today 21 (2018), 265277.


DNMW01 
15th January 2019 14:30 to 15:15 
Angkana Ruland 
Microstructures in SMA: Rigidity, NonRigidity and Simulations
Coauthors: 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 shapememory 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 twodimensional 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 manmade selfpropelled colloids
have shown that active particles present interesting
emergent collective properties [4–6], such as motilityinduced
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. selfpropelled 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 selfassembly 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], micelleinducing potential [12])
or anisotropic (Januslike) 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. FournierBidoz 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. 219244 (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. AngiolettiUberti, 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)
COAUTHORS: 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 nonconvex vectorvalued 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 needlelike 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 selfpropelled 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
Lowdensity 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 scalefree (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 lowdensity networks the slow relaxation proceeds through the formation of an intermediate nonequilibrium 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 Landaude 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 testparticle 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
Coauthors: 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 nonconvex, vectorial, topologically constrained, multiscale variational problems. Yet despite the daunting complexity inherent in the problem arising from the 21st century technological applications, rigorous variational analysis can still elucidate energydriven 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 onedimensional 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 onedimensional 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 onedimensional 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 GinzburgLandau 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 divergencefree maps in R^N (similar to the theory of entropies for the AvilesGiga 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 Landaude Gennes Qtensor theory
We study a Laudaude 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) nonminimizing rotationally symmetric critical points. Joint work with Radu Ignat, Valeriy Slastikov and Arghir Zarnescu.


DNMW01 
17th January 2019 14:30 to 15:15 
Rodrigo LedesmaAguilar 
Manipulating droplets on lubricant impregnated surfaces
Lubricant impregnated surfaces are bioinspired 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 
Pressuredriven active nematics systems: possible optimisation and design methods
Active nematic fluids combine the flowmolecular 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 noneqiuilibrium 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  pressuredriven flow in a channel  in which multiple nontrivial 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. Coauthors: 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 [35]. 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 GayBerne beads [11]. [1] H. Iino, T. Usui and JI. Hanna, Nature Comm. 6, 6828 (2015) [2] O.M. Roscioni, C. Zannoni, Molecular Dynamics Simulation and its Applications to ThinFilm 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 nematictoisotropic 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 GinzburgLandautype 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 wedgeshaped molecules with large electric dipole moments. CoAuthors: 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
CaffarelliKohnNirenberg inequalities are
radial. Further, they are used to obtain sharp aprioribounds 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
infinitedimensional, possibly damped and driven, Hamiltonian systems. The
approximate solutions are typically characterised by a small number of
timedependent 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 highfield regime, beyond the
wellknown 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 twistbend:the heliconical phase of nonchiral liquid crystals
The (onedimensional modulated) nematic twistbend 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 (bentcore, 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 longrange 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 bentcore 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. 34643467]. Here, within generalized LandaudeGennes theory and molecular simulations we present theoretical studies concerning stability of NTB relative to other homogeneous and inhomogeneous structures [69]. We use a systematic bifurcation and numerical analyses to identify absolutely stable onedimensional 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. DEC2013/11/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 bentshaped molecules”, Rev. Mod. Phys., 90, 045004 (2018). [2]R. B. Meyer, “Structural Problems in Liquid Crystal Physics”, pp. 273373 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 bananashaped molecules”, Europhys. Lett. 56, 247 (2001). [4]S. M. Shamid, S. Dhakal and J. V. Selinger, ‚“Statistical mechanics of bend flexoelectricity and the twistbend phase in bentcore 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 twistbend 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 (selfpropelling)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 gravitylike 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 selffolding Kirigami
Threedimensional shells can be synthesized from the spontaneous selffolding of twodimensional templates of interconnected panels, called nets. However, some nets are more likely to selffold 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 selfassembly 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 nitestrain setting in the Kelvin`sVoigt`s rheology where the viscosity stress tensor complies with the principle of timecontinuous frameindierence. We identify weak solutions in the nonlinear framework as limits of timeincremental 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 timediscrete approximations and we provide a corresponding commutativity result. This is a joint work with M. Friedrich (Munster). 

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 cellcell interactions, which grow more relevant as the density in the patches increases. By addressing the combined effects of motility, cellcell interaction and turbulent flow conditions, we uncover a general mechanism: the coupling of cellcell 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 tanktreading 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. PyckhoutHintzen, 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 pcapacitary 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 20052007 Burdzy, Caffarelli and Lin, Van den Berg conjectured in different contexts that the sum (or the maximum) of the first eigenvalues of the DirichletLaplacian 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 RobinLaplacian 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 semicontinuity 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 doubleintegral 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 PhysicsCondensed Matter, 23(5), 053201 (2011) [2] Released under the GPL2 license: http://www.mtg.msm.cam.ac.uk/Codes/AIRSS [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 (20092015), and Reader in Physics, University of St Andrews (20062008). 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 multicomponent fractured media
Multicomponent 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 twocomponent 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 blowup method, are determined by a delicate interplay between the optimization of sharp interfaces and the diffusion of microcracks. This model has the farreaching 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 criticalcontrast PDEs: microresonances, 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  Domesticscale 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  Bioinspired Soft Robotics: Turning Soft Materials into Intelligent Machines  
OFBW43 
27th February 2019 16:15 to 16:40 
Stoyan Smoukov  Bottomup 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 EricksenLeslie's hyperbolic model for liquid crystals
The original EricksenLeslie's model for liquid crystals includes the inertia effect, the corresponding balance laws includes second material derivatives. This system includes a coupling of NavierStokes equations with a S^2 valued hyperbolic system. In this talk, we review our recent work on the wellposedness of this hyperbolic EricksenLeslie'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 metamaterials with microresonators 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 metamaterials with microresonators: Arrays of small Helmholtz resonators in acoustics, plasmonic wave induced perfect transmission, and Maxwells equations in negative index metamaterials. 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 selfsimilarity and disclinations in martensite
The austenitetomartensite phasetransformation is a firstorder 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 interconnected phenomena observed in martensite, which are selfsimilarity (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, highenergy 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 (nonlinear) elastic model that describes disclinations as solutions of some differential inclusion. Secondly an atomistic model of nearestneighbor 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 longrange forces that favor drop fragmentation. More generally, these problems present a prime example of problems of energy driven pattern formation via a competition of longrange attraction and longrange 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. nonexistence, 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, microrobotics, 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 particlelike solitary waves [2]. By using a newly developed technique of nanophotonic 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 electroosmosis [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 outofequilibrium active matter, in which the levels of activity and degree of orientational order can be controlled separately.The work is supported by NSF DMREF DMS1729509 and by Office of Science, U.S. Department of Energy, grant DESC0019105.[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, 13511354 (2013).[2] B. X. Li, V. Borshch, R. L. Xiao, S. Paladugu, T. Turiv, S. V. Shiyanovskii, and O. D. Lavrentovich, Electricallydriven threedimensional 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, HighResolution and HighThroughput Plasmonic Photopatterning of Complex Molecular Orientations in Liquid Crystals Advanced Materials 28, 23532358 (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, 947950 (2010).[5] I. Lazo, C. H. Peng, J. Xiang, S. V. Shiyanovskii, and O. D. Lavrentovich, Liquid crystalenabled electroosmosis 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, 882885 (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 PalffyMuhoray  Heliconical cholesteric liquid crystals: selfassembled 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 PalffyMuhoray  Heliconical cholesteric liquid crystals: selfassembled tunable photonic bandgap materials  2  
DNMW05 
28th March 2019 16:00 to 17:00 
Peter PalffyMuhoray  Heliconical cholesteric liquid crystals: selfassembled 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 PalffyMuhoray  Heliconical cholesteric liquid crystals: selfassembled 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 onedimensional particle systems with
nonconvex 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 nonconvex interaction potentials. This is joint work with L.~Lauerbach, S.~Neukamm and M.~Schäffner. 

DNM 
3rd April 2019 15:10 to 15:50 
Junichi 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 secondrank 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, vortexlike 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]. 

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 MaierSaupe 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 offlattice 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 fluidfluid 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 particleshape 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 selfassembly into ordered structures [1], but also on how the interaction of a charged colloidal particle with an oilwater 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 nontrivial topology including tori, multitori and knots can be realised in charged colloids with complexshaped particles, using numerical modelling. We show that the topology of double layers can be defined via a cutoff 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 spinorbit coupling mechanism, in the guise of DzyaloshinskiiMoriya interaction (DMI), is considered. The evidence of these states sheds light on the role of the geometry in magnetism: chiral spintextures 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 Poincarétype inequality that allows for a precise characterization of the global minimizers of the micromagnetic energy functional on the 2sphere. 

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 sheardominant, lattice distortive and diffusionless
solidsolid 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 powerlaw 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 Landaude Gennes Energy with a Subquadratic Elastic Energy
I will present a modiified Landaude 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, ITALYEmail 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 imageprocessing operators that provides a unified approach to the standard regularizers and PDEbased approaches to image denoising.


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 nonvanishing 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 
Selforganization of patchy colloidal particles: 2 & 3D We investigate the selforganization 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 largescale 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 KardarParisiZhang (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 magnetoviscoelastic materials
In this talk I will survey our recent approach
to the modeling of magnetoviscoelastic materials. Our system of partial
differential equations consists of the NavierStokes equations, the
LandauLifshitzGilbert 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 shapeshifting 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 shapeshifting path.


DNMW03 
13th May 2019 14:10 to 14:50 
Ard Louis 
Simplicity bias in random design
The
design of a softmatter system can be recast as an inputoutput map, where the
inputs are the parameters that fix the components and their interactions, and
the outputs describe the outcome of a selfassembly 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 selfassembled structure. We provide evidence for
these trends for selfassembled 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 twistbend nematic phase.


DNMW03 
13th May 2019 16:00 to 16:40 
Alex Travesset 
Soft Skyrmions and Programmable SelfAssembly 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
selfassembly. 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 quasiFrankKasper 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 nonlinear 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 3.3V5V
cellphone battery) and close in less than 100 ms. They operate within a power
range of 140160 mW generated by the specifically designed resistive heating
element (inhouse 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 selforganization 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 largescale 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 bioinspired active materials based on colloidal and microbial suspensions or internally actuated gels. These nonequilibrium 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 networkbased 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
CoAuthors: 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 failureresistant 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 selfconsistent field theory for networks [2], I will discuss how entropy counterintuitively leads to spatial clustering of reversible crosslinks around permanent crosslinks in the polymer gel. This entropyinduced 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: OrliczSobolev 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 mid1970’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 planklike 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 planklike molecular shapes. Part of the presentation will focus on the experiments performed by ProfessorLavrentovich’s group on materials such as food dyessunset yellowand antiasthmatic 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 OseenFrank 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: selfmotile 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 workextraction 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 quasistatic cycles of elastic deformations. Such materials can be designed based on active mechanical components that include sensors and actuators. Inside the material, workextraction 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 activityinduced 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 
Qtensor model of twistbend and splay nematic phases
The twistbend 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 bendsplay 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 Qtensor 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 Qtensor 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 selforganisation 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 [13] 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 NI phase transition, the nematic order parameter and consider the formation of chains of polar nanoparticle [47]. 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 meanfield 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 threedimensional 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 nonlinearity: 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 “activematter” systems render it a promising
candidate in a discussion on the optimal design of soft matter.
While many activematter 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 ~0.1mm100cm) 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 selfassembly 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 defectbased nematic profiles, including exhibiting highelastic multipoles. In active nematics, we show defect profiles in threedimensional active nematic droplet, also highlighting the role of different surface coupling regimes.


DNMW03 
15th May 2019 11:50 to 12:30 
Davide Marenduzzo 
Selfassembly of liquid crystal mixtures: cubic fluid cylinders, elastic emulsions and colloidactive 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 phaseseparating 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 redisperse the aggregates observed in passive
colloidliquid 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 KibbleZurek mechanism (KZM) describes the formation of topological defects during the rapid crossing of a secondorder 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 latestage 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 isotropicnematic 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 microconfinement for controlled structure formation in nonequilibrium 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 nonequilibrium 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 fieldinduced 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, Crosstalk 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
BallandSpring
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 zeroenergy surface modes and nonlinear elastic
GuestHutchinson 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 MaierSaupe interaction are radially symmetric. Second, a description will be given of joint work with Lu Liu on exterior problems in the 2D oneconstant OseenFrank 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. PhBTBTC10 [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 
Flowinduced states in channelconfined nematics
Anisotropy of liquid crystals couples their orientational order to velocity shear, and consequently, induces different regimes in flows with different strengths. A flowaligning nematic liquid crystal, confined to a channel with homeotropic surface alignment, is known to undergo a transition from a homeotropic to a flowaligned state. I will present a more detailed view of this behaviour, including a hidden pretransitional state with broken chiral symmetry and dynamics of flowaligned 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 BentCore 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 bowshaped 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 opticallycreated 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. DalleFerrier, M.C. Jenkins1, I. Ladadwa, A. Heuer, R. CastañedaPriego and S.U. Egelhaaf, European Physical Journal Special Topics, 2012, 222, 2995–3009


DNMW03 
17th May 2019 09:00 to 09:40 
Ivan Smalyukh 
Nematic colloidal micromotors powered by light
Manmade nano and micromotors are key to many future applications. I will describe highly reconfigurable selfassembly of colloidal micromotors that exhibit a repetitive rotation when immersed in a liquid crystal and powered by a continuous exposure to unstructured ~1nW light. A monolayer of selfassembled 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 optomechanical 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 selfassembled 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 [14] 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 340685MicroMotility. 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), 1308513090 (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, 234246 (2019). [4] Caruso, N., Cvetkovic, A., Lucantonio, A., Noselli, G., DeSimone, A.: “Spontaneous morphing of equibiaxially prestretched elastic bilayers: The role of sample geometry”, Int J Mech Sci 149, 481486 (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 inversedesign 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 preprogrammed 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 networkbased 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 selfassembly 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 
Antonio Prados 
Building and optimising finitetime adiabatic processes in stochastic thermodynamics
In this talk, we address the building of finitetime 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 finitetime 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 GuéryOdelin 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 [14]. Programming selfassembly of colloidal particles
into open crystals has proved a longstanding challenge due both to the
mechanical instability and lack of kinetic accessibility that colloidal open
crystals typically suffer from. Building on our recent work [57], I will
here introduce a hierarchical selfassembly scheme for triblock patchy
particles to address the challenges met with programming selfassembly into
colloidal open crystals [8]. The
presentation will demonstrate in silico the hierarchical selfassembly 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 selflimiting [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 soughafter 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 [14] and selfassemble 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 selfassembly
paradigms can emerge as an exciting scientific frontier of condensed matter.
1. P. J. Ackerman and I. I. Smalyukh. Nature Mater 16, 426432 (2017). 2. J.S.B. Tai, P.J. Ackerman and I.I. Smalyukh. PNAS. 115, 921926 (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 spacetime 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 3d printed materials
We address the grand question of identifying the set of possible elasticity tensors (including anisotropic ones) of 3dprinted 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 3delasticity tensors live in an 18dimensional 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 CamarEddine, 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 NeumannLaplacian 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 nontrivial one is maximized by the ball, the result being due to Szego
and Weinberger in the fifties. Concerning the second nontrivial 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 splitrings 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 splitrings 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 cellproblem. 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 splitring 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 levelset 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 
AncaMaria 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 socalled branched
transport and the socalled 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 costoptimal 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 singlescale interpretations of optimal designs in the context of extremal stiffness
It is wellknown that rankN laminates can reach the
theoretical bounds on strain energy in the context of linear elasticity. The
theory of homogenizationbased topology optimization using this class of
composite materials is welldeveloped, and can therefore be used to find an
overall optimal material distribution at low computational cost. A downside of
these optimal multiscale designs is that features exist at several
lengthscales 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 highresolution 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 singlescale 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 singlescale, resulting in a
performance that is close (e.g. 1015%) 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 nearoptimal performance in the high
porosity limit. The performance difference between closed and openwalled
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 2d and in 3d
The work presented here is motivated by the optimization of socalled 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 2d 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 3d case is more involved and requires new ingredients. In particular, the full rotation matrix is regularized (instead of just one angle in 2d) and the projection map which deforms the periodic lattice is computed component by component. 

DNMW04 
12th June 2019 10:00 to 11:00 
Jesus MartinezFrutos 
Levelset topology optimization for robust design of structures under internal porosity constraints
Porosity is a wellknown 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 threedimensional 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 posttreatment 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 microstructure. 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 GinzburgLandau 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 GL 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 
MultiScale 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 finitedimensional 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 twoscale 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 
Gradientfree perimeter approximation for topology optimization and domain partitioning
I will present a Gammaconvergence 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 consumerlevel 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 worstcase load. Our coarsescale design optimization can then automatically assign these metamaterials to an input geometry so that the printed object undergoes a userspecified 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 largescale
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 nonlocal 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 nonlinear dependence on jumps, the present approach to relaxation of nonlocal 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 nonlocal 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), 37103. [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
infinitedimensional, possibly damped and driven, Hamiltonian systems. The
approximate solutions are typically characterised by a small number of
timedependent 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.
