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# Seminars (GFS)

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Event When Speaker Title Presentation Material
GFS 29th August 2017
11:00 to 12:00
Thomas Powers Shapes of Colloidal Membranes
GFS 30th August 2017
15:00 to 16:00
Emmanuel Villermaux Morphodynamics of cohesive objects
GFS 5th September 2017
11:00 to 12:00
Nicholas Hill Gyrotactic focussing by swimming micro-organisms in three-dimensional flows
GFS 7th September 2017
15:00 to 16:00
Jacques Dumais Deconstructing Tip Growth Morphogenesis
Growth and form in plant, fungal, and bacterial cells is achieved with two complementary processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by forces developed within the cell.  To understand how these two processes contribute to cell growth, we have undertaken a biophysical analysis of one major mode of cell morphogenesis called tip growth; whichrevealed that a few basic biophysical principles can explain all essential features of tip growth.  We first showed that the seemingly obscure surface expansion in these cells can be accounted for by the dissipation of elastic energy in the wall.  We also showed that a simple force balance at the cell surface explains the striking ability of these cells to penetrate stiff environments.  Finally, recent experiments suggest that tip-growing cells regulate their shape by controlling the spatial distribution of wall deposition.

GFS 14th September 2017
14:00 to 15:00
Yves Couder About the wave-particle duality observed with a classical particle driven by its memory-endowed wave-field
Yves Couder Laboratory MSC University Paris-Diderot     Self-organization is usually studied in systems with many interacting entities. In this talk I will describe self-organization in the dynamics of a single entity in interaction with its own past. It is observed with a wave-particle association, called a walker, in which a droplet bouncing on the surface of a vibrated fluid is self propelled and piloted by the surface waves it generates. It is a “symbiotic” entity: the drop generates the wave and the wave determines where the drop goes. ­­A specificity of this system is that, owing to the parametric forcing by substrate vibration, the generated waves are Faraday standing waves that can be sustained for some time. In the regimes where the waves have a long lifetime the global field that drives the motion thus contains information on the previous trajectory of the drop. Surprisingly, in these long-memory regimes, several behaviours characteristic of wave-particle duality can be observed. I will discuss more specifically recent experiments in which a walker, confined in a potential well, has an orbiting motion. In spite of the classical nature of this system, several quantum-like characteristics emerge with a form of double quantization (1) of the orbits as well as probabilistic behaviours (2).   (1)     S. Perrard, M. Labousse, M. Miskin, E. Fort, & Y. Couder, Nature Com. 5, 3219, (2014) (2)     S. Perrard, M. Labousse, E. Fort, Y. Couder, Phys Rev Lett, 113, 104101, (2014).

GFSW01 18th September 2017
09:40 to 10:20
Arezki Boudaoud On the robustness of morphogenesis
What sets the size and shape of an organism? How can robust shapes emerge from stochastic cells? We are addressing these questions by combining experimental and theoretical approches. Plants appear as active viscoelastoplastic materials with spatiotemporally variable mechanical properties.
GFSW01 18th September 2017
10:20 to 11:00
Jose Bico Elastocapillarity: When surface tension deforms elastic solids
Surface tension is usually associated with the spherical shape of small droplets and bubbles, wetting phenomena or the motion of insects at the surface of water. Beyond liquid interfaces, may capillary forces also affect solid bodies?
We propose review recent experiments where soft solids or slender structures are deformed by surface tension. We will focus in the following “elastocapillarity” configurations:
- 3D, deformations induced in bulk solids
- 1D, bending and bundling of rod-like structures
- 2D, bending and stretching of thin sheets

In each case, we will present the relevant characteristic lengths and scaling parameters.
GFSW01 18th September 2017
11:30 to 12:10
Daniel Goldman Some surprises in self-propulsion via self-deformation: snake scattering & supersmarticles
I will discuss two examples from our recent work in animal and robot locomotion (i.e. self-propulsion via self-deformation). First, our studies of snake locomotion in heterogeneous environments have revealed  new collisional dynamics; we have used these dynamics to infer neuromechanical control templates in desert specialist snakes. That is, we have discovered that when transiting a linear array of posts, certain snakes and snake-like robots passively “scatter” into preferred directions, the extent of which is inversely related to the post spacing; these systems thus mimic diffraction dynamics of subatomic particles. A minimal model predicts that the animal operates in an open-loop scheme, whereby perturbation rejection via hypothesized fixed muscle activation patterns and passive body properties can generate the observed scattering patterns. Second, I will discuss how, inspired by the fact that all metazoans are composed of hierarchically organized living systems (cells), we have begun to construct a robot which is made of other robots. We developed a phototaxing stochastic locomotor composed of simple non-motile robots called “smarticles”. Although no single smarticle can locomote, when confined into a ring, the collective (the “supersmarticle”) diffuses randomly through collisions among continuously self-deforming smarticles and the ring; directed self-propulsion can be effected if a smarticle at the edge becomes inactive via light or sound cues.
GFSW01 18th September 2017
12:10 to 12:30
Sungyon Lee Capturing gas in soft granular media
Bubble migration through a soft granular material involves a strong coupling between the bubble dynamics and the deformation of the material. This is relevant to a variety of natural processes such as gas venting from sediments and gas exsolution from magma. Here, we study this process experimentally by injecting air into a quasi-2D packing of soft hydrogel beads and measuring the morphology of the bubbles as they rise due to buoyancy. We systematically modulate the overall elasticity of the packing by confining it to different degrees with a rigid but fluid-permeable upper boundary. We find that this new combination of buoyancy, capillarity, and elasticity under confinement leads to complex morphologies of air migration, as well as nontrivial dynamics in the amount of trapped air in the system. Surprisingly, more confined packings are able to capture larger volumes of air, with a sharp transition between the so-called “small” and “large” air-capture regimes. This result alludes to the possibility of utilizing soft particles to enable control of the gas migration in practical applications, such as carbon capture and storage.
GFSW01 18th September 2017
13:30 to 14:10
Shreyas Mandre The transverse arch of human foot
Fossil record indicates that the emergence of arches in human ancestral feet coincided with a transition from an arboreal to a terrestrial lifestyle. Propulsive forces exerted during walking and running load the foot under bending, which is distinct from those experienced during arboreal locomotion. I will present mathematical models with varying levels of detail, accompanied by data from human subject experiments and fossilized human ancestral feet, to illustrate a simple function of the transverse arch. Just as we curve a dollar bill in the transverse direction to stiffen it while inserting it in a vending machine, the transverse arch of the human foot stiffens it for bending
deformations. A fundamental interplay of geometry and mechanics underlies this stiffening -- curvature couples the soft out-of-plane bending mode to the stiff in-plane stretching deformation.

GFS 18th September 2017
14:00 to 16:30
Goldman D
GFSW01 18th September 2017
14:10 to 14:30
Cathal Cummins The Stokes-flow parachute of the dandelion fruit
Cathal Cummins1, 2, 3 ,a)
Ignazio Maria Viola1, b)
Maddy Seale2,3,4
Daniele Certini1
Alice Macente2
Enrico Mastropaolo4
Naomi Nakayama2, 3, 5, c)

1)
Institute for Energy Systems
School of Engineering
University of Edinburgh, EH9 3DW

2)
Institute of Molecular Plant Sciences
School of Biological Sciences
University of Edinburgh, EH9 3BF

3)
SynthSys Centre for Systems and Synthetic Biology
School of Biological Sciences
University of Edinburgh, EH9 3BF

4)
Institute for Integrated Micro and Nano Systems
Scottish Microelectronics Centre
School of Engineering
University of Edinburgh, EH9 3FF

5)
Centre for Science at Extreme Conditions
School of Biological Sciences
University of Edinburgh, EH9 3BF

a) Electronic mail: Cathal.Cummins[at]ed.ac[dot]uk
b) Electronic mail: I.M.Viola[at]ed.ac[dot]uk
c)Electronic mail: Naomi.Nakayama[at]ed.ac[dot]uk

The fluid mechanical principles that allow a passenger jet to lift off the ground are not applicable to the flight of small plant fruit (the seed-bearing structure in flowering plants). The reason for this is scaling: human flight requires very large Reynolds numbers, while plant fruit have comparatively small Reynolds numbers. At this small scale, there are a variety of modes of flight available to fruit: from parachuting to gliding and autorotation. In this talk, I will focus on the aerodynamics of small plumed fruit (dandelions) that utilise the parachuting mode of flight. If a parachute-type fruit is picked up by the breeze, it can be carried over formidable distances.

Incredibly, these parachutes are mostly empty space, yet they are effectively impervious to the airflow as they descend. In addition, the fruit can become more or less streamlined depending on the environmental conditions. In this talk, I will present results from our numerical and physical modelling that demonstrate how these parachutes achieve such impermeability despite their high porosity. We explore the form and function of the filamentous building blocks of this parachute, which confer the fruit's incredible flight capacity.
GFSW01 18th September 2017
14:30 to 14:50
Marina Ferreira The dynamics of a packed cell tissue
In a packed tissue neighboring cells exert high pressure on each other at all times. Such mechanical interactions are believed to play an important role on the dynamics of the tissue. However, their contribution to the tissue shape is not yet fully understood. In this talk I will first present a framework to model this type of systems based on a geometric representation of individual cells. The cells interact with each other aiming at minimizing a local potential energy, subjected to non-overlapping constraints. Mathematically, the problem is formulated as a non-convex minimization problem, which will be tackled with the recently proposed damped Arrow-Hurwicz algorithm. I will then apply this framework to the study of a pseudo-stratified epithelial tissue. Finally, I will present some numerical results showing how the tissue may be deformed when simple defects on individual cells are introduced.
GFSW01 18th September 2017
14:50 to 15:10
Sharon Lubkin Form, flow, deformation, and transport in the embryonic lung
The mammalian airway branches prenatally in a limited number of stereotyped modes. It is well established that various experimental interventions can change the nature of the branching. We have developed several  hypotheses for the mechanisms governing this mode selection, including the potential roles of geometry, mechanics, and transport, and interactions between the three. We developed a suite of models testing the implications of these hypotheses. Our models rule out some hypotheses and support others.
GFSW01 18th September 2017
15:10 to 15:30
Simon Pearce Microtubule Rings
Microtubules are a filamenteous protein found inside cells, where they are the stiffest cytoskeletal polymer with a persistence length of several millimetres. In axons, the thin projections of nerve cells which wire the brain, well-organised parallel bundles of microtubules function as structural backbones and highways for intracellular transport by motor proteins.
However, in areas of neurodegeneration, highly curved microtubules are found, with radius of curvature on the order of 1µm. Similarly curved microtubules are sometimes seen in gliding assays, where microtubules are moved by the motor protein kinesin, rotating in a stable circular orbit amongst other microtubules translocating as rigid rods.
Recent evidence suggests that some microtubule-associated proteins such as kinesin are able to sense and alter MT curvature, and so we model MTs moving on gliding assays as inextensible rods with a preferred curvature, which is controlled by the differential binding of the kinesin. We find that there exist parameter regimes wherein metastable rings can form, and hence offer this differential binding as an explanation for these highly curved microtubules seen in vitro and in vivo.
GFSW01 19th September 2017
09:00 to 09:40
Neil Balmforth Indentations of plastic layers
The indentation of a layer of plastic material by a solid object is a classical problem in plasticity theory. Using the method of sliplines (characteristics) Prandtl provided two key solutions suitable for the indentation of either a relatively shallow or deep layer by a flat plate. In this talk I will summarize how both solutions, and their generalizations, apply in three rather different problems:
1) locomotion through a yield-stress fluid (the viscoplastic version of Taylor's 1951 viscous problem),
2) the formation of footprints, and
3) the washboarding instability of a towed plate above a deformable layer
GFSW01 19th September 2017
09:40 to 10:20
Pasquale Ciarletta Turing revisited: the chemo-mechanical bases of morphogenesis in soft living matter
Life phenomena result from the mutual equilibrium between the living matter and the surrounding media. A network of servo-mechanisms physiologically restores the stable equilibrium between the interior matter of a living entity in the face of external perturbative agents. In particular, living cells can balance exogenous and endogenous forces using an iterative process, also known as mechano-reciprocity. Hence, not only living matter can adapt through epigenetic remodelling to the external physical cues, but it can also respond by activating gene regulatory processes, which may also drive the onset of pathologies, e.g. solid tumours. Moreover, living materials have the striking ability to change actively their micro-structural organization in order to adjust their functions to the surrounding media, developing a state of internal tension, which even persists after the removal of any external loading. This complex mechanical and biochemical interaction can finally control morphogenesis during growth and remodelling, leading to shape instabilities characterized by a complex morphological phase diagram

In this lecture, I will introduce few mathematical modelling approaches to mechanobiology and morphogenesis in living materials [1], with several applications concerning solid tumours [2,3], gastro-intestinal organogenesis [4], bacterial colonies [5] and nerve fibers [6].

[1] Ciarletta P, Preziosi L, Maugin GA.Mechanobiology of interfacial growth. JOURNAL OF
THE MECHANICS AND PHYSICS OF SOLIDS, 2013, vol. 61, p. 852-872;
[2] Giverso, C.,  Ciarletta, P. (2016). Tumour angiogenesis as a chemo-mechanical surface instability. SCIENTIFIC REPORTS, 6.
[3] Ciarletta P. Buckling instability in growing tumour spheroids. PHYSICAL REVIEW LETTERS, 2013, vol. 110.
[4] Ciarletta P., Balbi V., Kuhl, E. Pattern selection in growing tubular tissues. PHYSICAL
REVIEW LETTERS, 2014, 113, 248101.
[5] Giverso, C., Verani M., Ciarletta P. Branching instability in expanding bacterial colonies.
JOURNAL OF THE ROYAL SOCIETY INTERFACE, 2015, 12, 20141290
[6] Taffetani M., Ciarletta P. Elastocapillarity can control the formation and the morphology
of beads-on-string structures in solid fibers, PHYSICAL REVIEW E, 2015, 91, 032413
GFSW01 19th September 2017
10:20 to 11:00
Eva Kanso Flow-mediated synchronization of swimmers and rotors at the micron scale
Dynamic order is observed in natural systems at all length scales, from the schooling of fish to the coordinated beating of cilia and flagella. These systems, including flagella and cilia from the same organism and cell type, often transition between different modes of coordinated motions. For example, Chlamydomonas biflagellates switch from in-phase to anti-phase beating and ependymal cilia periodically change their collective beat orientation. While there is a substantial body of evidence supporting the hypothesis that hydrodynamic interactions provide a robust mechanism for synchrony, little is known about the mechanisms responsible for the transition between multiple synchronization modes. Here, I will present a series of models of increasing level of complexity that examine the emergence of collective coordination in microfluidic systems of swimmers and rotors. I will report new findings on flow-mediated synchrony in chains of swimmers and rotors and I will focus on the existence of bi-stable synchronization modes in systems of rotors. These results could have important implications on understanding the biophysical mechanisms underlying transitions between multiple synchronization modes, as well as on the design and self-assembly of active materials.
GFSW01 19th September 2017
11:30 to 12:10
David Hu How the elephant grabs with its trunk
Elephants feed on food items using a flexible yet heavy trunk.  In this talk, we report experiments from Zoo Atlanta showing how the trunk can be used to manipulate both small to large food items.  For smallest items, the elephant creates kinks in its trunk which enables the elephant to the trunk's weight to jam piles of particles together. Larger items can be grabbed using air suction, whereby the elephant generates air flows rivaling the speed of the human sneeze.  The heaviest items are grabbed by wrapping the trunk and lifting with the elephant's head, using the trunk as a lever.  A series of simple robots demonstrate how elephant-inspired principles can aid in picking up objects.
GFSW01 19th September 2017
12:10 to 12:30
Ido Regev Motility induced elongation of the vertebrate embryo
While the genotype provides an instruction set for morphogenesis, how those instructions are converted to shape involves physical patterning as cells change their relative number, size, shape and position in space and time, in conjunction with chemical gradients that they are driven by and in turn drive. We study one of the simplest geometrical motifs in morphogenesis, the elongation of the vertebrate embryo, and show how spatially modulated expression of a specific signaling molecule Fgf8 leads to variations in motility and density. Our experiments and theory show how just a few cellular parameters that control activity and mechanics allow us to quantify the characteristic scale over which elongation occurs and also determines a typical velocity of the elongation of the body.

This work was done in collaboration with Karine Guevorkian, Olivier Pourqui'e and L. Mahadevan.
GFSW01 19th September 2017
13:30 to 14:10
Shilpa Khatri Simulations of Pulsating Soft Corals
Soft corals of the family Xeniidae have a pulsating motion, a behavior not observed in many other sessile organisms. We are studying how this behavior may give these coral a competitive advantage. We will present direct numerical simulations of the pulsations of the coral and the resulting fluid flow by solving the Navier-Stokes equations coupled with the immersed boundary method. Furthermore, parameter sweeps studying the resulting fluid flow will be discussed.
GFSW01 19th September 2017
14:10 to 14:30
Amir Gat Fluid Mechanics of Soft Robots and Actuators
Soft robotics is an emerging field of research and development. Its goal is to design robots with flexible structure that can deform and change their shape and dimensions continuously. The structure and actuation of soft robotics is greatly inspired by biology, where living creatures across a wide span of scales use soft appendages or a flexible body for manipulation or locomotion - from elephant's trunk and octopus' arm to jellyfish and caterpillar. While the mechanism of biological motion is based on muscle actuation, artificial soft robots require some sort of flexible actuation. A promising approach of soft robotics is actuation by pressurization of embedded fluidic networks. While common, currently, the effects of viscosity are not examined in such configurations, thus limiting the available deformation patterns possible by such actuation.

The aim of the presented work is to analytically and experimentally examine steady and transient deformation of soft actuators by internal viscous flow. We specifically focus on interaction between elastic deflection of a slender beam and viscous flow in a long serpentine channel, embedded within the beam. The embedded network is positioned asymmetrically with regard to the neutral plane, and thus pressure within the channel creates a local moment deforming the beam. We show that by setting appropriate time-varying inlet pressure signal, viscosity enables to increase the possible deformation patterns available to a given actuator geometry and limit the deformation to a section of the actuator. This work connects fluid dynamics to soft robotics research.
GFSW01 19th September 2017
14:30 to 14:50
James Hanna The planar elastica, stress, and material stress
We revisit the classical problem of the planar Euler \emph{elastica} with applied forces and moments, and present a classification of the shapes in terms of tangentially conserved quantities associated with spatial and material symmetries.  We compare commonly used director, variational, and dynamical systems representations, and present several illustrative physical examples.
We remark that an approach that employs only the shape equation for the tangential angle obscures physical information about the tension in the body.
GFSW01 19th September 2017
14:50 to 15:10
Douglas Holmes Swelling and Shaping of Soft Structures
Swelling-induced deformations of slender structures occur in many biological and industrial environments, and the shapes and patterns that emerge can vary across many length scales. The dynamics of fluid movement within elastic networks, and the interplay between a structure's geometry and its boundary conditions, play a crucial role in the morphology of growing tissues, the shrinkage of mud and moss, and the curling of cartilage, leaves, and pine cones. We aim to utilize swelling-induced deformations of soft mechanical structures to dynamically shape materials. Adaptive structures that can bend and fold in an origami-like manner provide advanced engineering opportunities for deployable structures, soft robotic arms, mechanical sensors, and rapid-prototyping of 3D elastomers. Swelling is a robust approach to structural change as it occurs naturally in humid environments and can easily be adapted into industrial design. Small volumes of fluid that interact favorably with a material can induce large, dramatic, and geometrically nonlinear deformations. This talk will examine the geometric nonlinearities that occur as slender structures are swollen – surfaces will crease, beams will bend and snap, circular plates will warp and twist, and fibers will coalesce and detach. I will describe the intricate connection between materials and geometry, and present a straightforward means to permanently morph 2D sheets into 3D shapes.
GFSW01 19th September 2017
15:10 to 15:30
Scott Waitukaitis Coupling the Leidenfrost Effect and Elastic Deformations to Power Sustained Bouncing
The Leidenfrost effect occurs when an object near a hot surface vaporizes rapidly enough to lift itself up and hover. Although well-understood for liquids and stiff sublimable solids, nothing is known about the effect with materials whose stiffness lies between these extremes. Here we introduce a new phenomenon that occurs with vaporizable soft solids: the elastic Leidenfrost effect. By dropping hydrogel spheres onto hot surfaces we find that, rather than hovering, they energetically bounce several times their diameter for minutes at a time. With high-speed video during a single impact, we uncover high-frequency microscopic gap dynamics at the sphere-substrate interface. We show how these otherwise-hidden agitations constitute work cycles that harvest mechanical energy from the vapour and sustain the bouncing. Our findings unleash a widely applicable strategy for injecting mechanical energy into soft materials, with potential relevance to fields ranging from soft robotics and metamaterials to microfluidics and active matter.
GFSW01 20th September 2017
09:00 to 09:40
François Gay-Balmaz Flexible tubes conveying fluid: geometric modeling, stability, and variational integrators
Co-author: Vakhtang PUTKARADZE (University of Alberta)

We derive a geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. We consider both compressible and incompressible fluids. We proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results. Based on this theory, we derive a variational discretization of the dynamics based on the appropriate discretization of the fluid’s back-to-labels map, coupled with a variational discretization of the elastic part of the Lagrangian.
GFSW01 20th September 2017
09:40 to 10:20
Adil Mughal, Denis Weaire Packing problems, phyllotaxis and Fibonacci numbers
We study the optimal packing of hard spheres in an infinitely long cylinder. Our simulations have yielded dozens of periodic, mechanically stable, structures as the ratio of the cylinder (D) to sphere (d) diameter is varied [1, 2, 3, 4]. Up to D/d=2.715 the densest structures are composed entirely of spheres which are in contact with the cylinder. The density reaches a maximum at discrete values of D/d when a maximum number of contacts are established. These maximal contact packings are of the classic "phyllotactic" type, familiar in biology. However, between these points we observe another type of packing, termed line-slip. We review some relevant experiments with small bubbles and show that such line-slip arrangements can also be found in soft sphere packings under pressure. This allows us to compute the phase diagram of columnar structures of soft spheres under pressure, of which the main feature is the appearance and disappearance of line slips, the shearing of adjacent spirals, as pressure is increased [5].

We provide an analytical understanding of these helical structures by recourse to a yet simpler problem: the packing of disks on a cylinder [1, 2, 4]. We show that maximal contact packings correspond to the perfect wrapping of a honeycomb arrangement of disks around a cylindrical tube. While line-slip packings are inhomogeneous deformations of the honeycomb lattice modified to wrap around the cylinder (and have fewer contacts per sphere). Finally, we note that such disk packings are of relevance to the spiral arrangements found in stems and flowers, when labelled in a natural way, which are generally represented by some triplet of successive numbers from the Fibonacci series (1,1,2,3,5,8,13...). This has been an object of wonder for more than a century. We review some of this history and offer yet another straw in the wind to the never-ending debate [6].
GFSW01 20th September 2017
10:20 to 11:00
Jean-Luc Thiffeault Unraveling hagfish slime
GFSW01 20th September 2017
11:30 to 12:10
Michael Shelley Fluid and solid mechanics in active cellular processes
Many fundamental phenomena in eukaryotic cells -- nuclear migration, spindle positioning, chromosome segregation -- involve the interaction of often transitory structures with boundaries and fluids. I will discuss the interaction of theory and simulation with experimental measurements of active processes within the cell. This includes understanding the force transduction mechanisms underlying nuclear migration, spindle positioning and oscillations, as well as how active displacement domains of chromatin might be forming in the interphase nucleus.
GFSW01 20th September 2017
12:10 to 12:50
Saverio Spagnolie Deformable bodies in anisotropic fluids
Liquid crystals (LCs) are anisotropic, viscoelastic fluids that can be used to direct colloids into organized assemblies with unusual optical, mechanical, and electrical properties. In past studies, the colloids have been sufficiently rigid that their individual shapes and properties have not been strongly coupled to elastic stresses imposed by the LCs. We will discuss how soft colloids (micrometer-sized shells) behave in LCs. We reveal a sharing of strain between the LC and shells, resulting in formation of spindle-like shells and other complex shapes. These results hint at previously unidentified designs of reconfigurable soft materials with applications in sensing and biology. Also to be discussed: related efforts relevant to biolocomotion and an immersed boundary method for computing fluid-structure interactions in a nematic liquid crystal.
GFSW01 21st September 2017
09:00 to 09:40
Laura Miller Flight of the smallest insects
A vast body of re-search has described the complexity of flight in insects ranging from the fruit fly, Drosophila melanogaster, to the hawk moth, Manduca sexta. Over this range of scales, flight aerodynamics as well as the relative lift and drag forces generated are surprisingly similar. The smallest flying insects (Re~10) have received far less attention, although previous work has shown that flight kinematics and aerodynamics can be significantly different. In this presentation, we have used a multi-pronged approach that consists of measurements of flight kinematics in the tiny insect Thysanoptera (thrips), quantification of wing morphology, measurements of flow velocities and forces using physical models, and direct numerical simulations to compute flow and lift and drag forces. The lift to drag ratio during hovering flight decreases significantly as the Re decreases below 10. The clap and fling mechanism of lift generation does augment lift forces ~30%, however, peak drag can increase almost an order of magnitude due to viscous effects from wing-wing interaction. Bristles can reduce these peak forces, and may aid in passive flight behavior.
GFSW01 21st September 2017
09:40 to 10:20
Yves Couder Fibonacci phyllotaxis in plants and algae, a biological convergence with a physical origin
Plants and brown algae do not belong to the same lineage. Phylogenetic analysis demonstrates that the divergence between these two clades occurred approximately 1800 million years ago. Their most recent common ancestors were unicellular eukaryotic organisms and the transition to multi-cellularity occurred independently in the two lineages. It is therefore remarkable that similar global morphologies can be observed in both clades. The role of physical laws and evolution in these convergences will be discussed using the Fibonacci spiral organization as a test case.
GFSW01 21st September 2017
10:20 to 11:00
Pierre Degond Coarse-graining of collective dynamics models
In this talk, we will report on some new individual-based models of collective dynamics and their coarse-graining into continuum models. The applications span from collective cell dynamics (such as social bacteria or sperm) to flocking of birds or fish. Models of social behavior are best set up at the individual scale where behavioral rules can be easily introduced and tested. However, the complexity of individual-based models increases rapidly with the number of individuals and their calibration or control can hardly be implemented at this level. To overcome this limitation, one often uses continuum model that describe the system through average quantities such as densities or mean orientation. But the downside of most models in the literature is that the link between the rules at the individual behavior and the coefficients in the macroscopic model are not known exactly and are at best extrapolated from heuristic consideration. Here, we propose a systematic and mathematical rigorous way to derive continuum models from collective dynamics models. It relies on the introduction of a new concept, the ‘generalized collision invariants’, which permit to overcome the lack of physical invariance in most systems undergoing collective dynamics. In this talk, we will review some recent developments of these concepts and how they can be used to model systems of practical scientific importance.
GFSW01 21st September 2017
11:30 to 12:10
Derek Moulton A story in shells
In every seashell there is a story. It is the story of the creature – a mollusc – that lived in and built the shell. Through an incremental growth process, the mollusc builds its own house, one layer at a time. It is a process that generates a shell surface with geometrical precision, regularity, and self-similarity, properties that have been observed and appreciated by palaeontologists and geometers alike for centuries, and formed a focus point in D'Arcy Thompson's famous book. In that process, there is a mechanical story as well: the form of the shell is driven by the mechanical interaction of a soft body and the rigid shell which it is itself secreting. We hypothesise that this interaction underlies a wide array of secondary patterns termed ornamentations, including ribs, needle sharp spines, travelling waves, and fractal-like structures. With such an abundance of shapes generated through a relatively simple growth process, the mollusc shell thus provides an excellent case study for morphomechanical pattern formation. And with a fossil record over 500 million years old and 100,000 extant species of shell building mollusc, mollusc shells all together tell a story of change and increasing complexity, making an excellent case study for evolution and the physical processes that govern it. In this talk I will present several chapters of the mollusc’s story and progress we have made in trying to understand the role of solid mechanics in their unique form.
GFSW01 21st September 2017
12:10 to 12:30
Davide Ambrosi Mechanics and polarity in cell motility
The motility of a fish keratocyte on a flat substrate exhibits two distinct regimes: the non-migrating and the migrating one. In both configurations the shape is fixed in time and, when the cell is moving, the velocity is constant in magnitude and direction. Transition from a stable configuration to the other one can be produced by a mechanical or chemotactic perturbation.
In order to point out the mechanical nature of such a bistable behaviour, I will focus on the actin dynamics inside the cell using a minimal mathematical model. While the protein diffusion, recruitment and segregation govern the polarization process, I will show that the free actin mass balance, driven by diffusion, and the polymerized actin
retrograde flow, regulated by the active stress, are sufficient ingredients to account for the motile bistability.
The length and velocity of the cell are predicted on the basis of the parameters of the substrate and of the cell itself. The key physical ingredient of the theory is the exchange among actin phases at the edges of the cell, that plays a central role both in kinematics and in dynamics.
GFSW01 21st September 2017
13:30 to 14:10
Sunghwan (Sunny) Jung Drinking and Diving
I will discuss two fluid-mechanics problems exploited by biological systems.

First, animals that drink must transport water into the mouth using either a pressure-driven (suction) or inertia-driven (lapping) mechanism. Previous work on cats shows that these mammals lap using a fast motion of the tongue with relatively small acceleration (~1g), in which gravity is balanced with steady inertia in the liquid. Do dogs employ the same physical mechanism to lap? To answer this question, we recorded 19 dogs while lapping and conducted physical modeling of the tongue's ejection mechanism. In contrast to cats, dogs accelerate the tongue upward quickly (~1-4g) to pinch off the liquid column. The amount of liquid extracted from the column depends on whether the dog closes the jaw before or after the pinch-off. Our recordings show that dogs close the jaw at the moment of pinch-off time, enabling them to maximize volume per lap.

Second, several seabirds (e.g. Gannets and Boobies) dive into water at up to 24 m/s as a hunting mechanism. We studied how diving birds survive water impacts because of their beak shape, neck muscles even with a long slender neck. The birds’ slender necks appear fragile but do not crumble under the compression due to high-speed impact. First of all, we use a salvaged bird to resolve plunge-diving phases and the skull and neck anatomical features to generate a 3D-printed skull and to quantify the effect of the neck’s musculature to provide the necessary stability. Then, physical experiments of an elastic beam as a model for the neck attached to a skull-like cone revealed the limits for the stability of the neck during the bird’s dive as a function of impact velocity and geometric factors. We find that the small angle of the bird's beak and the muscles in the neck predominantly reduce the likelihood of injury during a high-speed plunge-dive. Finally, we di scuss maximum diving speeds for humans using our results to elucidate injury avoidance.
GFSW01 21st September 2017
14:10 to 14:30
Marino Arroyo Dynamical remodelling of biological interfaces
Biological interfaces organise animal life at various scales. Cell organelles or in the cell envelop, lipid membranes and cortical layers determine the mechanical properties and provide structural integrity, but at the same time are required to be malleable to drive or accommodate dramatic remodelling events. Mechanically, these interfaces exhibit features of solids and of fluids, are chemically responsive, and can generate active forces. Mathematically, they can be modelled using partial differential equations on time-evolving surfaces. In this talk I will present our efforts to develop a transparent modelling framework and numerical methods for the chemo-elasto-hydrodynamics of such systems, with applications to dynamical shape transformations of lipid bilayers and thin active fluids.
GFSW01 21st September 2017
14:30 to 14:50
Buddhapriya Chakrabarti Elasticity and fluid mechanics of lipid tethers
In this talk I will describe our research involving laser-matter interaction in surfactant modified fluid droplets using theory, experiment and simulations.
GFSW01 21st September 2017
14:50 to 15:10
Andreas Muench Thin film models for active liquid crystals
Active liquid crystals - or active polar gels - have been discussed as a model for cell-motion induced by the cytoskeleton. We discuss the derivation of a thin film model based on the Beris-Edwards theory for liquid crystals.
GFSW01 21st September 2017
15:10 to 15:30
Axel Voigt Defects in positional and orientational order on surfaces and their potential influence on shape
Co-authors: Sebastian Reuther (TU Dresden), Sebastian Aland (HTW Dresden), Ingo Nitschke (TU Dresden), Simon Praetorius (TU Dresden), Michael Nestler (TU Dresden)

We consider continuum models for positional and orientational order on curved surfaces. They include surface phase field crystal models in the first case [4,6] and surface Navier-Stokes [2,3,5], surface Frank-Oseen [1] and surface Landau-deGenne models for the second case. We demonstrate the emergence of topological defects in these models and show the strong interplay between topology, geometry, dynamics and defect type and position. We comment on the derivation of these models and their numerical solution. To couple these surface models with an evolution equation for the shape of the surface is work in progress and leads to defect mediated morphologies [6].

[1] M. Nestler, I. Nitschke, S. Praetorius, A. Voigt: Orientational order on surfaces - the coupling of topology, geometry and dynamics. Journal of Nonlinear Science DOI:10.1007/s00332-017-9405-2 [2] I. Nitschke, S. Reuther, A. Voigt: Discrete exterior calculus (DEC) for the surface Navier-Stokes equation. In Transport Processes at Fluidic Interfaces. Birkhäuser, Eds. D. Bothe, A.Reusken, (2017), 177 - 197 [3] S. Reuther, A. Voigt: The interplay of curvature and vortices in flow on curved surfaces. Multiscale Model. Simul., 13 (2), (2015), 632-643 [4] V. Schmid, A. Voigt: Crystalline order and topological charges on capillary bridges. Soft Matter, 10 (26), (2014), 4694-4699 [5] I. Nitschke, A. Voigt, J. Wensch: A finite element approach to incomressible two-phase flow on manifolds. J. Fluid Mech., 708 (2012), 418-438 [6] S. Aland, A. Rätz, M. Röger, A. Voigt: Buckling instability of viral capsides - a continuum approach. Multiscale Model. Simul., 10 (2012), 82-110
GFSW01 22nd September 2017
09:00 to 09:40
Martine Ben Amar Patterns of bacterial colonies
In this talk I will present  the genesis of patterns occurring in bacterial colonies:  in biofilms and  in fluid suspensions. The first case concerns the growth of a simple drop containing bacteria with moderate adhesion to a rigid substrate. The initial circular geometry is lost during the growth expansion, contour undulations and buckling appear, ultimately a rather regular periodic focusing of folds repartition emerges. Predictions of these morphological instabilities, according simple rules,  will be presented as bifurcations of solutions in nonlinear elasticity, characterized by typical driving parameters. The substrate plays a critical role limiting the geometry of the possible modes of instabilities and anisotropic growth, adhesion and toughness compete to eventually give rise to wrinkling, buckling or both.  In the second part, I will present a continuous model for the self-organization of expanding bacterial colonies under chemotaxis, proliferation and eventually active-reaction which either give cohesion or on the contrary dispersion to the colony. Taking into account the diffusion and capture of morphogens complicates the model since it induces a bacterial density gradient coupled to bacterial density fluctuations and dynamics. Nevertheless under some specific conditions, it is possible to investigate the pattern formation as a usual viscous fingering instability. This explains the similarity and differences of patterns according to the physical bacterial suspension properties and explain the factors which favor compactness or branching.

Joined work with Min Wu
GFSW01 22nd September 2017
09:40 to 10:20
De Witt Sumners Helicity, Reconnection and Seifert Surfaces
Co-author: Renzo Ricca (University of Milano-Bicocca)

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the total helicity of a linked configuration of flux tubes can be calculated in terms of linking, writhe and twist contributions. We prove that writhe helicity is conserved under anti-parallel reconnection [1]. We discuss the Seifert framing (isophase surfaces in GPE models) for a link. We give necessary and sufficient conditions for the existence of a Seifert surface for a framed link. We give a rigorous topological proof of the result that total helicity is zero for linked vortices with Seifert framing. We will discuss parallels between the links in the Belusov-Zhabotinsky reaction and links in fluid dynamics. This is joint work with Renzo Ricca.

[1] Laing, C.E., Ricca, R.L. & Sumners, De W. L. (2015) Conservation of writhe helicity under anti-parallel reconnection. Nature Sci. Rep. 5, 9224.
GFSW01 22nd September 2017
10:20 to 11:00
Darryl Holm Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics
Co-authors: Colin J Cotter (Imperial College London), Georg A Gottwald (University of Sydney)

In [Holm, Proc. Roy. Soc. A 471 (2015)] stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby justifying stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centering condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Joint work with Colin J Cotter (Imperial College London) Georg A Gottwald (University of Sydney).
GFSW01 22nd September 2017
11:30 to 12:10
Renzo Ricca Quantum vortex dynamics by Seifert surface information
Co-author: Simone Zuccher (U. Verona)

Time evolution and interaction of filamentary structures is often studied by analysing dynamics in terms of local forces. An alternative route is to investigate physical or biological properties by focussing on geometric and topological properties of the surface swept out by filament motion. In this work we present new results on the evolution, interaction and decay of a Hopf link of quantum vortices governed by the Gross-Pitaevskii equation by analysing physical information in terms of the iso-phase Seifert surface swept out during the process [1]. We interpret the surface local twist as an axial flow acting along the vortex filament [2] and the Seifert surface of minimal area in terms of linear momentum of the system. We show that GP evolution is associated with a continuous minimisation of this surface in agreement with the physical cascade process observed. This approach sheds new light on filament dynamics and bears similarities to the study of fluid membranes in biological and chemical systems.

[1] Zuccher, S. & Ricca, R.L. (2017) Relaxation of twist helicity in the cascade process of linked quantum vortices. Phys. Rev. E 95, 053109.
[2] Zuccher, S. & Ricca, R.L. (2017) Twist effects in quantum vortices and phase defects. Fluid Dyn. Res., doi.org/10.1088/1873-7005/aa8164.
GFSW01 22nd September 2017
13:30 to 14:10
Alain Goriely Modelling brain and skull morphogenesis
In this talk, I will describe models for brain and skull morphogenesis (Joint work with many people but mostly Ellen Kuhl).
GFSW01 22nd September 2017
14:10 to 14:50
Lisa Fauci Swimming of a simple vertebrate: Insights from computational and robotic models.
The swimming of a simple vertebrate, the lamprey, can shed light on the coupling of neural signals to muscle mechanics and passive body dynamics in animal locomotion. We will present recent progress in the development of a computational model of a lamprey with sensory feedback and examine the emergent swimming behavior of the coupled fluid-neural-muscle-body system. A long-term goal of this research is to investigate the relation of spinal chord injuries to movement in a very simple system. In addition, even though the fish's material properties most likely have a strong effect on swimming performance, it is extremely difficult to use animal experiments to identify its role. While one species of fish may be stiffer than another, they also typically differ in numerous other ways, such as the anatomy of the muscle and skeleton and the way they activate their muscles during swimming. We will discuss how computational and robotic models offer a more controlled way to probe the effects of body stiffness.
GFSW01 22nd September 2017
14:50 to 15:30
Gunnar Hornig Structure formation in magnetised plasmas
Magnetic fields in high temperature plasmas have a tendency to take on the structure of Beltrami fields, also known as force-free fields. These fields play also an important role in vortex dynamics as they form stationary solutions of the Euler equation. While it is comparatively easy to show that the class of Beltrami fields are minimum energy states under certain constraints, it is much harder to predict to which particular force-free state a given magnetic field will relax to. We review what is known about the various routes of relaxation and present some newer results of simulations which show that the dynamics depends strongly on the existence of turbulence during the relaxation process and the environment in which this turbulent plasma is embedded.
GFS 26th September 2017
11:00 to 12:00
Neil Ribe Forms and Patterns of Viscous and Elastic Threads
Some of the most beautiful and easy-to-produce instabilities in fluid mechanics
are those that occur when a thin stream of viscous fluid like honey falls steadily
from a certain height onto a solid surface. In addition to the familiar 'liquid rope
coiling' effect, one can observe periodic folding with or without rotation of the
folding plane; periodic collapse and rebuilding of the hollow cylinder formed by a
primary coiling instability; and 'liquid supercoiling', in which the cylinder as a
whole undergoes steady secondary folding and rotation. Using a combination of
laboratory experiments, analytical theory, and numerical simulation, I and my
colleagues have determined a phase diagram for these states in the space of
dimensionless fall height and flow rate, and have identified the dimensionless
parameter that controls which state or states are observed under given
conditions. We have also studied pattern formation in the closely related 'fluid
mechanical sewing machine’ (FMSM), wherein a viscous thread falling onto a
moving belt generates a wealth of complicated 'stitch' patterns including
meanders, alternating loops, and doubly periodic patterns. We have determined
experimentally and numerically the phase diagram for these patterns in the
space of dimensionless fall height and belt speed, and have formulated a simple
reduced (three degrees of freedom) model that successfully predicts the patterns
in the limit of negligible inertia. In closing, I shall compare the observed FMSM
patterns with those of the ‘elastic sewing machine’ in which a normal elastic
thread falls onto a moving belt.

GFS 2nd October 2017
11:00 to 12:00
Michael Brenner The Shape and Function of the Nasal Cavity
The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates.  In this talk, I will describe a recent research program aimed to understand the peculiarities of the nasal cavity shape, as it pertains both to evolution and medicine. The first part of the talk will focus on evolutionary considerations: despite the common function of the nasal cavity, the shapes of nasal cavities vary widely across animals. We aim to understand this variability by connecting the nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, but their overall shape is restricted only by the geometry of the head. This provides an explanation for  the geometric variations of natural nasal cavities quantitatively. The second part of the talk focuses on medical diagnostics; with a nasal surgeon we are trying to understand the consequences and effects of nasal surgery. The flow in the nose is at a sufficiently small scale that it has never been directly measured. Working with a computational scientist we use CT scans of the human nasal cavity to compute internal fluid flows and then study their characteristics. [Work joint with David Zwicker (SEAS, Harvard); Rodolfo Ostillo Monico (SEAS, Harvard); Daniel Lieberman (Human and Evolutionary Biology, Harvard); Simone Melichionna (Rome) and Robin Lindsay (Mass. Eye & Ear)

GFS 3rd October 2017
11:00 to 12:00
title and abstract tba
GFS 5th October 2017
15:00 to 16:30
Jay Tang Dynamic pattern evolution in growing bacterial colonies
A microliter droplet of bacteria can grow and spread into a centimeter-sized colony on an agar gel surface within several hours, forming a variety of patterns. An expanding bacterial colony is often referred to as a swarm, indicating collective motion of the constituent bacteria that are individually motile. A bacterial swarm is an active fluid with rapid increase in total particle number and collective motion, but the swarm expansion is limited by water availability and surface tension. The strong coupling between the activity of individually motile bacteria and their surrounding fluid flow leads to rich pattern dynamics involving many coupled physical parameters. We study the swarming dynamics and pattern evolution following either conventional dot inoculation, a line inoculation, or an annular inoculation of Psuedomonas aeruginosa on the gel surface. With slight changes in agar percentage, ambient humidity, temperature, or level of surfactants, the dot inoculation is known to produce a rich variety of patterns. The ring inoculation leads to observation of edge-directed accumulation, wavelike structures due to hyper-elastic buckling, droplet formation due to the Rayleigh–Plateau instability, and collective migration of droplets and their coalescence in subsequent growth. Our experiments offer strong evidence that physical effects largely account for most patterns that develop in expanding bacterial colonies.

GFS 10th October 2017
17:00 to 18:00
Alain Goriely Rothschild Lecture: On Growth and Form and Mathematics: Reading d'Arcy Thompson 100 Years On
In 1917, the Scottish scientist D’Arcy Wentworth Thompson published “On Growth and Form”. In this book, d’Arcy Thompson, through many beautifully illustrated examples, studies the variety of forms appearing in nature from a mechanistic and mathematical perspective. Hailed as “the finest work of literature in all the annals of science that have been recorded in the English tongue” and criticised as “a work widely praised, but seldom used”, it still stands, a hundred years later, as a masterpiece despite some obvious shortcomings. What is the real influence and impact of this book? How did it shape questions and methodologies in modern science? In this talk, I will delve into “On Growth and Form,” extract its main themes, and show how d’Arcy Thompson’s ideas are still relevant today to unravel the physical basis of morphogenesis.

GFS 12th October 2017
15:00 to 16:30
Christophe Eloy How competition for light and wind resistance shape tree forms
Trees are self-similar branching structures, hierarchically organized with longer and thicker branches near the roots. With a mechanically-based numerical model, we show how self-similarity can emerge through natural selection. In this model, trees grow into fractal structures to promote efficient photosynthesis in a competing environment. In addition, branch diameters increase in response to wind-induced loads. Remarkably, the virtual tree species emerging from this model have the same self-similar properties as those measured on conifers and angiosperms.

GFS 7th November 2017
11:00 to 12:00
Martins Bruveris Shape Analysis — An Introduction to Its Ideas, Methods and Questions
The word “shape" denotes the external form, contour or outline of something. Shape is a basic physical property of objects and plays an important role in applications, from evolutionary biology to medical image analysis. In this talk, I will give an overview of the ideas underlying shape analysis and computational analysis, the mathematical methods and the questions one tries to answer.
GFS 9th November 2017
15:00 to 16:30
Francis Woodhouse Geometric control of active matter
The ability of chemically or optically powered active matter to self-organise and spontaneously flow makes these systems increasingly attractive in smart microfluidics and materials design. Active matter has the potential to serve as the bedrock of customisable, controllable transport and processing systems, but to fully harness this potential, its intrinsic tendency toward turbulence must be tamed. Geometric confinement has recently emerged as an excellent stabilising scheme, allowing complex yet controllable behaviours to be engineered by careful design of the flow environment. First, we will take a tour through recent experimental and theoretical studies showcasing the power of geometry over active matter, including a recent realisation of a bacterial Ising model. I will then introduce a new model for active flow in complex network-like environments, where network topology is the key driver of self-organising behaviour. This will culminate in the theory of active matter logic, proposing how carefully designed flow topologies could be harnessed to construct logic gates and to store data, thus laying the foundation for autonomous microfluidic logic devices driven by bacterial fluids, active liquid crystals or chemically engineered motile colloids.

GFSW03 13th November 2017
09:45 to 10:30
Peter Michor General Sobolev metrics on the manifold of all Riemannian metrics
Based on collaborations with M.Bauer, M.Bruveris, P.Harms. For a compact manifold $M^m$ equipped with a smooth fixed background Riemannian metric $\hat g$ we consider the space $\operatorname{Met}_{H^s(\hat g)}(M)$ of all Riemannian metrics of Sobolev class $H^s$ for real $s>\frac m2$ with respect to $\hat g$. The $L^2$-metric on $\operatorname{Met}_{C^\infty}(M)$ was considered by DeWitt, Ebin, Freed and Groisser, Gil-Medrano and Michor, Clarke. Sobolev metrics of integer order on $\operatorname{Met}_{C^\infty}(M)$ were considered in [M.Bauer, P.Harms, and P.W. Michor: Sobolev metrics on the manifold of all Riemannian metrics. J. Differential Geom., 94(2):187-208, 2013.] In this talk we consider variants of these Sobolev metrics which include Sobolev metrics of any positive real (not integer) order $s$. We derive the geodesic equations and show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping.
GFSW03 13th November 2017
11:00 to 11:30
Jean Feydy An efficient kernel product for automatic differentiation libraries, with applications to measure transport
Authors : Benjamin Charlier, Jean Feydy, Joan Alexis Glaunès and Alain Trouvé This paper presents a memory-efficient implementation of the kernel matrix-vector product, which is suitable for use with automatic differentiation libraries -- in our case, PyTorch. This piece of software alleviates the major bottleneck of autodiff libraries as far as diffeomorphic image registration is concerned: symbolic python code can now scale up to large point clouds and shapes (100,000+ vertices). To showcase the value of automatic differentiation to the LDDMM community, we introduce the "normalized Hamiltonian" setting and show that it corresponds to a spatially regularized optimal transport of mass distributions: made tractable by autodiff libraries, the kernel normalization trick turns an extrinsic image deformation routine into an intrinsic measure transportation program.
GFSW03 13th November 2017
11:30 to 12:15
tba
GFSW03 13th November 2017
14:00 to 14:45
Klas Modin Riemannian Gradient Flows in Shape Analysis
In this talk I show how the framework of Riemannian gradient flows on Lie group action orbits is connected to several branches of mathematics: optimal transport, information geometry, matrix decompositions, multivariate Gaussians, entropy flows, etc. The framework guides analysis, numerics, and software implementation.
GFSW03 13th November 2017
14:45 to 15:30
Alain Goriely Morphoelasticity and the Geometry of Growth
GFSW03 13th November 2017
16:00 to 16:45
François Gay-Balmaz Towards a geometric variational discretization of compressible fluid dynamics
We present a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Our framework applies to irregular mesh discretizations in 2D and 3D. It systematically extends work previously made for incompressible fluids to the compressible case. We consider in detail the numerical scheme on 2D irregular simplicial meshes and evaluate the behavior of the scheme for the rotating shallow water equations. While our focus is fluid mechanics, our approach is potentially useful for discretizing problems involving evolution equations on diffeomorphism groups. This is a joint work with W. Bauer.
GFSW03 14th November 2017
09:00 to 09:45
Sarang Joshi Bridge Simulation and Metric Estimation on Lie Groups and Orbit Spaces
Joint work with Stefan Sommer Alexis Arnaudon and Line Kuhnel. Performing statistical inference of non-linear Manifold valued data has wide ranging applications in wide ranging fields including bioinformatics, shape analysis, medical imaging, computational anatomy, computer vision, and information geometry. Most common existing statistical inference techniques assume that the Manifold is a Riemannian Manifold with a pre defined canonical metric. In this talk I will present some of our recent work in estimating the Metric structure of the manifold.
GFSW03 14th November 2017
09:45 to 10:30
Ganesh Sundaramoorthi Accelerated optimization on manifolds
GFSW03 14th November 2017
11:00 to 11:30
Sophie Hecht Incompressible limit of a mechanical models for tissue growth
We consider mathematical models for tissue growth. These models describes the dynamics of the density of cells due to pressure forces and proliferation. It is known that some cell population models of this kind converge at the incompressible limit towards a Hele-Shaw type free boundary problem. The first model introduce a non-overlapping constraint of a population choosing a singular pressure law. The second model represents two interacting populations of cells which avoid mixing. Following earlier works, we show that the models approximate a free boundary Hele Shaw type model that we characterise using both analytical and numerical argument.
GFSW03 14th November 2017
11:30 to 12:15
Krastan Blagoev On loss of form in cancer growth
GFSW03 14th November 2017
14:00 to 14:45
Stephen Marsland Differential invariants for the actions of planar Lie groups
Co-authors: Richard Brown (Massey University), Robert McLachlan (Massey University)

A classic problem in image processing is to recognise the similarity or planar objects (point sets, curves, or images) up to transformations from a local planar group such as the Euclidean, similarity, and projective groups. Building on Cartan’s solution to the equivalence problem, an influential new paradigm for this problem was introduced by Calabi et al., the differential invariant signature. The general theory has been developed extensively and many examples computed for planar curves, including the Euclidean, equi-affine, and projective groups. In this talk we demonstrate how to develop and apply differential invariant signatures for planar images.
GFSW03 14th November 2017
14:45 to 15:30
Barbara Gris Shape analysis through a deformation prior
A general approach for matching two shapes is based on the estimation of a deformation (a diffeomorphism) transforming the first one into the second one. We developed a new framework in order to build diffeomorphisms so that a prior on deformation patterns can be easily incorporated. This prior can for instance correspond to an additional knowledge one has on the data under study. Our framework is based on the notion of deformation modules which are structures capable of generating vector fields of a particular chosen type and parametrized in small dimension. Several deformation modules can combine and interact in order to general a multi-modular diffeomorphisms. I will present how this framework allows to incorporate a prior in a deformation model thanks to an adapted deformation module. I will also present how an adapted deformation module can be automatically built given a sequence of data.
GFSW03 14th November 2017
16:00 to 16:45
Irene Kaltenmark Geometrical Growth Models for Computational Anatomy
In the field of computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has proved to be highly efficient for addressing the problem of modeling and analysis of the variability of populations of shapes, allowing for the direct comparison and quantization of diffeomorphic morphometric changes. However, the analysis of medical imaging data also requires the processing of more complex changes, which especially appear during growth or aging phenomena. The observed organisms are subject to transformations over time that are no longer diffeomorphic, at least in a biological sense. One reason might be a gradual creation of new material uncorrelated to the preexisting one. The evolution of the shape can then be described by the joint action of a deformation process and a creation process.
For this purpose, we offer to extend the LDDMM framework to address the problem of non diffeomorphic structural variations in longitudinal data. We keep the geometric central concept of a group of deformations acting on embedded shapes. The necessity for partial mappings leads to a time-varying dynamic that modifies the action of the group of deformations. Ultimately, growth priors are integrated into a new optimal control problem for assimilation of time-varying surface data, leading to an interesting problem in the field of the calculus of variations where the choice of the attachment term on the data, current or varifold, plays an unexpected role.

The underlying minimization problem requires an adapted framework to consider a new set of cost functions (penalization term on the deformation). This new model is inspired by the deployment of animal horns and will be applied to it.

Keywords: computational anatomy, growth model, shape spaces, Riemannian metrics, group of diffeomorphisms, large deformations, variational methods, optimal control.
GFSW03 15th November 2017
09:00 to 09:45
Chris Klingenberg How organisms shape themselves: using geometric morphometrics for understanding evolution and development
Over the last three decades, geometric morphometrics has seen tremendous progress in terms of new techniques for analyzing shape variation. Statistical shape analysis provides a solid mathematical foundation, and a broad range of sophisticated tools is available for characterizing shapes and for extracting specific information that can answer a variety of biological questions. Biological datasets usually have an inherent structure that can potentially reveal important insights about the processes and mechanisms responsible for the observed variation. For instance, many organisms or their organs are symmetric, and the usually slight deviations from perfect symmetry can be characterized with morphometric methods and provide useful biological insight. Such analyses of fluctuating asymmetry can provide information on the developmental basis of integration among traits. Likewise, organisms with modular body plans consisting of repeated parts, such as most plants, provide opportuni ties to examine additional levels of variation within individuals. Many morphometric studies use samples of specimens from multiple taxa, and considering both the variation within taxa and the evolved differences among taxa permits to make inferences about evolutionary mechanisms. Adopting a multi-level approach that considers all the morphological information that can be obtained in a given study design promises rich biological insights, often for little extra effort by the investigator. My lecture will illustrate this approach with examples from animals and plants.
GFSW03 15th November 2017
09:45 to 10:30
Ian Dryden Bayesian analysis of object data using Top Space and Quotient Space models
The analysis of object data is becoming common, where example objects under study include functions, curves, shapes, images or trees. Although the applications can be very broad, the common ingredient in all the studies is the need to deal with geometrical invariances. For the simple example of landmark shapes, one can specify a model for the landmark co-ordinates (in the Top Space) and then consider the marginal distribution of shape after integrating out the invariance transformations of translation, rotation and scale. An alternative approach is to optimize over translation, rotation and scale, and carry out modelling and analysis in the resulting Quotient Space. We shall discuss several examples, including functional alignment of growth curves via diffeomorphisms, molecule matching, and 3D face regression where translation and rotation are removed. Bayesian inference is developed and the Top space versus Quotient space approaches are compared.
GFSW03 15th November 2017
11:00 to 11:30
Arezki Boudaoud Reconstructing leaf morphogenesis using two-dimensional shape analysis
Ref. Biot et al. Multiscale quantification of morphodynamics: MorphoLeaf software for 2D shape analysis. Development 2016
GFSW03 15th November 2017
11:30 to 12:15
Ian Jermyn The elastic metric for surfaces and its use
Shape analysis requires methods for measuring distances between shapes, to define summary statistics, for example, or Gaussian-like distributions. One way to construct such distances is to specify a Riemannian metric on an appropriate space of maps, and then define shape distance as geodesic distance in a quotient space. For shapes in two dimensions, the 'elastic metric' combines tractability with intuitive appeal, with special cases that dramatically simplify computations while still producing state of the art results. For shapes in three dimensions, the situation is less clear. It is unknown whether the full elastic metric admits simplifying representations, and while a reduced version of the metric does, the resulting transform is difficult to invert, and its usefulness has therefore been questionable. In this talk, I will motivate the elastic metric for shapes in three dimensions, elucidate its interesting structure and its relation to the two-dimensional case, and describe what is known about the representation used to construct it. I will then focus on the reduced metric. This admits a representation that greatly simplifies computations, but which is probably not invertible. I will describe recent work that constructs an approximate right inverse for this representation, and show how, despite the theoretical uncertainty, this leads in practice to excellent results in shape analysis problems. This is joint work with Anuj Srivastava, Sebastian Kurtek, Hamid Laga, and Qian Xie.
GFSW03 16th November 2017
09:00 to 09:45
Laurent Younes What can we learn from large deformation diffeomorphic metric mapping on spaces of rigid bodies?
The Large Deformation Diffeomorphic Metric Mapping (LDDMM) algorithms rely on a sub-Riemannian metric on the diffeomorphism group with strong smoothness requirements. This talk will describe a series of simple simulations illustrating the effect of such metrics when considering, in particular, the motion of rigid objects subject to the associated least action principle. It will also show why modifications of this metric can be useful in some cases, with some examples provided.
GFSW03 16th November 2017
09:45 to 10:30
Nina Miolane Template shape estimation: correcting an asymptotic bias
Computational Anatomy studies the normal and pathological variations of organs' shapes, often with respect to a mean organ shape called the template shape. Estimating the template shape is then the first step of the analysis. We use tools from geometric statistics to demonstrate the asymptotic biasedness of the “Frechet mean algorithm”, also called "Max-max algorithm", used for template shape estimation. The geometric intuition provided by this study leads us to suggest two debiasing procedures that we compare. Our results are illustrated on synthetic and real data sets. This is joint work with Dr. Xavier Pennec and Pr. Susan Holmes.
GFSW03 16th November 2017
11:00 to 11:30
Alexandre Bône Learning distributions of shape trajectories: a hierarchical model on a manifold of diffeomorphisms
Co-authors: Olivier Colliot (CNRS), Stanley Durrleman (INRIA)

We propose a mixed effects statistical model to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. Shape trajectories and their variations are defined via the action of a group of deformations. The model is built on a generic statistical model for manifold-valued longitudinal data, for which we propose to use a finite-dimensional set of diffeomorphisms with a manifold structure, an efficient numerical scheme to compute parallel transport on this manifold and a specific sampling strategy for estimating shapes within a Markov Chain Monte Carlo (MCMC) method. The method allows the estimation of an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory in terms of shape and pace of shape changes. This estimation is obtained by a Stochastic Approximation of the Expectation-Maximization (MCMC-SAEM). We show that the algorithm recovers the optimal model parameters with simulated 2D shapes. We apply the method to estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease.
GFSW03 16th November 2017
11:30 to 12:15
Alexis Arnaudon How to deform and shake images?
In recent years, several methods and frameworks have been developed to deform images in the aim of solving problems such as shape analysis or image registration. The application and usefulness of these methods is now well established as well as their mathematical foundation. Nevertheless, because various uncertainties remain at all stages of the image analysis procedure (from data capture to intrinsic variability within a dataset), practical extensions of these deterministic methods should be available. In this talk, I will walk you through one of them, by starting from the geometrical formulation of the theory of large deformation matching, then implementing a particular type of stochastic deformation to preserve the original geometrical structure to end with the description of practical methods for the estimation of the unknown noise parameters of the model. I will illustrate this theory with numerical solutions for a discrete representation of images, where the method of moments can easily be implemented to solve this inverse problem of estimating the noise parameters. This is joint work with Stefan Sommer and Darryl Holm.
GFSW03 16th November 2017
14:00 to 14:45
Stefan Sommer Statistical Inference in Nonlinear Spaces via Maximum Likelihood and Diffusion Bridge Simulation
Co-authors: Darryl D. Holm (Imperial College London), Alexis Arnaudon (Imperial College London) , Sarang Joshi (University of Utah)

An alternative to performing statistical inference in manifolds by optimizating least squares criterions such as those defining the Frechet mean is to optimize the likelihood of data. This approach emphasizes maximum likelihood means over Frechet means, and it in general allows generalization of Euclidean statistical procedures defined via the data likelihood. While parametric families of probability distributions are generally hard to construct in nonlinear spaces, transition densities of stochastic processes provide a geometrically natural way of defining data likelihoods. Examples of this includes the stochastic EPDiff framework, Riemannian Brownian motions and anisotropic generalizations of the Euclidean normal distribution. In the talk, we discuss likeliood based inference on manifolds and procedures for approximating data likelihood by simulation of manifold and Lie group valued diffusion bridges.

Related Links
GFSW03 16th November 2017
14:45 to 15:30
Alain Trouve Distortion minimizing geodesic subspaces on shape ensembles
We have seen great progress during the last ten years in the understanding of the riemaniann framework on shape spaces, also supported by the steady exponential growth of the computational resources. The outcome is that the modeling possibilities for shapes ensembles are now fairly large. However, it is not that clear how to address concretely the selection of different metric structures for the analysis of a shape ensembles. In this talk, we will discuss some simple geometrical point of view going in that direction and with interesting links with matrix completion. Joint work with David Jacobs, Benjamin Charlier and J. Feydy.
GFSW03 16th November 2017
16:00 to 16:45
Marc Niethammer Machine Learning Approaches for Deformable Image Registration
Image registration is a key tool for medical image analysis. This talk will cover some recent machine learning approaches for deformable image registration.
GFSW03 17th November 2017
09:00 to 09:45
Mads Nielsen Measuring shape change by registration
Longitudinal or cross-sectional differences in shape and volume has traditionally been measured as difference in shape, but recent methodologies use a dense deformation field as a large deformation diffeomorphic metric mapping or a stationary velocity field. For shapes properties of they changes along the finite flow can be obtained using surface integrals with numerical advantages. Vi show examples from longitudinal changes of brain MRIs.
GFSW03 17th November 2017
09:45 to 10:30
Kirsty Wan The Morphology of Cellular Motility
Authors: K.Y. Wan & R.E. Goldstein. Many species of microorganisms such as bacteria, algae, and ciliates self-propel using slender, deformable structures known as cilia and flagella. Great variability exists in the number of flagella, their beating modes, and the basal architecture whence the flagella emanate. For instance, the model alga Chlamydomonas reinhardtii uses two near-identical flagella to pull itself through the fluid, executing a breaststroke. Meanwhile the little-known octoflagellate Pyramimonas octopus exhibits spontaneous switching between a small number of highly reproducible gaits. Here, we show how high resolution spatiotemporal visualisation and analysis of live cell locomotion may be used for behavioural stereotyping at the microscale, and furthermore to reveal the stochastic nature of flagellar beating. Quantitative distance and shape measures are deployed to delineate even subtle changes in behaviour, providing a means by which perturbations to cellular physiology are readily detected based on optical imaging alone.
GFSW03 17th November 2017
11:00 to 11:30
Jenny Larsson Shell Shape of Snails
The beautiful, intricate, and widely diverse shapes of snail shells have fascinated people for centuries. In particular, shells have been analysed by mathematicians wanting to understand their geometric properties. One of the greatest contributors to the field is D'Arcy Thompson with his book On Growth and Form. This book celebrates one hundred years this year, and has played a major role in the field of morphometric analysis.
One well established and simple way of visualising snail shells is built on Raup's growth model, using logarithmic equations with three growth parameters. However, analysing a shell to find the correct values for the growth parameters is not always a straightforward task.

The goal of my research is to develop a method for obtaining the growth parameters from 2D images of shells. I will test my methods with a set of images of the species Littorina saxatilis. This species is biologically interesting because strong natural selection maintains different shell shapes in distinct environments. It would therefore be an advantage to have a way of describing this natural shape variation, and the shapes of laboratory hybrids, in terms of meaningful growth parameters. This is expected to give a better understanding of the operation of selection and of the underlying genetic basis of shape variation, compared to more classical PCA analysis of landmarks.
GFSW03 17th November 2017
11:30 to 12:15
Tilak Ratnanather 3D normal coordinate systems for the cortex: applications in the deafened cortices in babies, adults and cats
We describe a surface-based diffeomorphic algorithm to generate 3D coordinate grids in the cortical ribbon. In the grid, normal coordinate lines from the grey/white (inner) surface to the grey/csf (outer) surface are constrained to be normal at the surfaces. Specifically, the cortical ribbon is described by two triangulated surfaces with open boundaries. Conceptually, the inner surface sits on top of the white matter structure and the outer on top of the gray matter. It is assumed that the cortical ribbon consists of cortical columns which are orthogonal to the white matter surface. This might be viewed as a consequence of the development of the columns in the embryo. It is also assumed that the columns are orthogonal to the outer surface. So if we construct a vector field such that the inner surface evolves diffeomorphically towards the outer one, the distance of the resultant trajectories will be a measure of thickness. Applications will be described for the deafened auditory cortices in babies, adults and cats. The approach offers potential for quantitative functional and histological analysis of cortical activity and anatomy.

(Joint work with Laurent Younes, Sylvain Arguillère, Kwame Kutten, Andrej Kral, Peter Hubka and Michael Miller).
GFSW03 17th November 2017
14:00 to 14:45
François-Xavier Vialard Around unbalanced optimal transport: fluid dynamic, growth model, applications.
In this talk, we present the so-called Wasserstein-Fisher-Rao metric (also called Hellinger-Kantorovich) by its dynamical and static formulation. The link between these two formulations is made clear by generalizing the Riemannian submersion of Otto to this new setting. Then the link with the Camassa-Holm equation can be made with this metric, in the same way Brenier made it between optimal transport and incompressible Euler. Passing by, we prove that the Camassa-Holm equation is actually an incompressible Euler equation on a bigger space. We also show the use of this metric to interpret a particular Hele-Shaw model as a gradient flow. We then finish with some examples of use of this new metric as a similarity measure on diffeomorphic registration of shapes.
GFS 23rd November 2017
15:00 to 16:30
Pierre Haas Mechanics of a Volvox Embryo Turning Itself Inside Out
The spherical embryos of the green alga Volvox turn themselves inside out through a programme of cell shape changes at the close of their development. This inversion shares features such as invagination with events of cell sheet folding in animals, and has therefore become a simple model system for morphogenesis. Through the combination of three-dimensional time-lapse visualisations of inversion and a theoretical model in which cell shape changes appear as variations of the intrinsic stretches and curvatures of an elastic shell, we identify the mechanical ingredients necessary for inversion. We go on to quantify the variability of inversion, and use it to analyse the interplay of mechanics, geometry, and regulation during inversion. These analyses begin to reveal evolutionary aspects of developmental complexity in the Volvocalean algae.
Joint work with: Stephanie Höhn, Aurelia R. Honerkamp-Smith, Julius B. Kirkegaard, and Raymond E. Goldstein

GFSW04 28th November 2017
09:30 to 10:10
Michael Berry Magic mirrors and magic windows
Ancient oriental mirrors possess a property that seemed magical and was probably unintended by those who made them: the pattern embossed on the back of such a mirror appears in light reflected onto a screen from its apparently featureless front surface. In reality, the embossed pattern is reproduced on the front, in low relief invisible to direct observation, and analysis shows that the projected image results from pre-focal ray deviation. In this interesting regime of geometrical optics, the image intensity is given simply by the Laplacian of the height function of the relief. Observation confirms this ‘Laplacian image’ interpretation, and indicates that steps on the reflecting surface are about 400 nm high, explaining their invisibility. Current research aims to create the transparent analogue of the magic mirror: ‘magic windows’, in which glass sheets, flat to unaided vision but with gentle surface relief, concentrate light onto a screen with intens ity reproducing any desired image. Laplacian image theory implies that the desired surface relief is obtained by solving Poisson’s equation.

Related Links
GFSW04 28th November 2017
10:10 to 10:50
Denis Weaire Artful foams: in memoriam Cyril Stanley Smith
Cyril Stanley Smith was a distinguished metallurgist who eventually left that discipline to pursue a wider interest in science and technology, and their relation to art. He was critical of his contemporaries, as being too preoccupied with thepursuit of perfect idealised order. Although his ideas were tentative he was(like D’Arcy Wentworth Thompson) a prophet. As such he inspired others,including the present speaker, who will describe his adventures with foam (afavourite prototype of Smith), taking him into art and architecture as Smith would have liked - for scientists, he said, should be playful.
GFSW04 28th November 2017
11:10 to 11:50
Aubrey Jaffer Physics and mathematics of marbling
Co-authors: Shufang Lu (Zhejiang University of Technology), Xiaogang Jin (Zhejiang University), Fei Gao (Zhejiang University of Technology), Xiaoyang Mao (University of Yamanashi)

Ink marbling refers to techniques for creating intricate designs in colored inks floating on a liquid surface. If the marbling motions are executed slowly, then this layer of inks can be modeled as a two-dimensional incompressible Newtonian fluid. In this highly constrained model many common marbling techniques can be exactly represented by closed-form homeomorphisms. These homeomorphisms can be composed and compute the composite mapping at any resolution orders of magnitude faster than finite-element fluid-dynamics methods.Pictorial designs for flowers and animals use short strokes of a single stylus; presented is a closed form velocity field for Oseen fluid flow and its application to creating short stroke marbling homeomorphisms.These approaches extend to three-dimensions and allow creation of coherent marbled surfaces on any shape while avoiding the process of texture mapping entirely.

Related Links
GFSW04 28th November 2017
11:50 to 12:30
Allan McRobie Catastrophe theory and art
As described in my book The Seduction of Curves, published by Princeton University Press in August 2017, there are strong links between Catastrophe Theory and many spheres of art. This talk will explore those historical links - most notably via the works of Salvador Dali and the Constructivist artist Naum Gabo. Extending beyond the book, the talk will also look at what possible new avenues this may open up for creative exploration in art and architecture, ranging from light-based works through to a proposed large scale structure/sculpture for the forthcoming Chelsea Flower Show.
GFSW04 28th November 2017
13:30 to 14:10
Roberto Zenit Hydrodynamic instabilties and modern artistic painting
Co-author: Sandra Zetina (Universidad Nacional Autonoma de Mexico)

Painting is a fluid mechanical process. The action of covering a solid surface with a layer of a viscous fluid is one of the most common human activities; virtually all manmade surfaces are covered with a layer of fluid, which eventually cures and solidifies, to provide protection against the environment or simply for decoration. The process of applying layer of fluid of uniform thickness on a surface has been vastly studied and it is well understood. In the case of artistic painting, the objective is different. Painters learn how to manipulate the fluid, through lengthy empirical testing of the action and the physical properties of the fluids, to create textures that can be used to create patterns and compositions of aesthetic value. In other words, artists aim to create non uniform paint coatings, produced at will and in a controlled manner. It has been recently identified that, for the case of modern artistic painting, one successful way to create such patterns is by provo king hydrodynamic instabilities in a controlled manner. In this presentation we analyze several particular cases used by notable modern artists in their works: David A. Siqueiros used the Rayleigh-Taylor instability for his ‘accidental painting’ technique; Jackson Pollock learned to control the curling instability of viscous filaments in his dripping technique; Max Ernst used the Saffman-Taylor instability to paint with decalcomanias, etc. Furthermore, we analyze other modern painting techniques and their relation with modern and very active fluid mechanics areas of research. We also discuss the importance of the properties of modern materials and how their evolution could have influenced the emergence of new artistic painting techniques. The aim of this investigation is to create an explicit relation between the body of knowledge of modern fluid mechanics and those of art history and conservation.

Related Links
GFSW04 28th November 2017
14:10 to 14:50
Andrzej Herczynski Paul Klee notebooks: form and mathematics
Paul Klee was one of the most prolific and original painters of the first half of the 20th century. Although he was influenced by Picasso, Kandinsky, and other contemporary artists, and engaged with Der Blaue Ritter, he forged his own artistic path apart from the currents such as cubism or surrealism. He was a dedicated art teacher, and left extensive notes for his lectures at the Bauhaus (1921-31). The notes were published in two volumes The Thinking Eye and The Nature of Nature, and constitute, in effect, Klee’s treatise on geometrical aspects of forms, perspective, motion and its depiction, growth, and many other topics. This presentation is a selective consideration of Klee’s recurring themes and a naïve attempt to organise them according to their mathematical and physical concepts.
GFSW04 28th November 2017
14:50 to 15:15
Jane Wang Music of falling paper
A piece of paper falls in a seemingly erratic manner. Each fall is a solution to the Navier-Stokes equations, but why does it evoke such a poetic feelings in us? When our eyes trace the paper as it falls, following its flutter and tumble, punctuated by a sudden lift and turn, we can feel lines of musical phrases in air. Some motions have the sound of percussion, others of a flute, a string, or even a cry or laugh. Drop small ones en mass, and they become fireworks.

I started making ‘Music of Falling Paper’ a few years ago. It is an attempt to use falling paper both as a ‘music instrument’ and a visual means to convey the connection between the movement of simple objects and the movement of living organisms. They are improvisational pieces, often in collaboration with musicians, in public space and in response to the theme of the event. I drop pieces of paper from a height, the musicians improvise, and I in turn respond to their play when choosing the next sequence to drop. When constructing the sequences, I think about many things. I shall share some of these thoughts and clips at the talk.

Related Links
GFSW04 28th November 2017
16:00 to 16:40
Alex Bateman Paper mosaics: an exploration of tiling’s through origami
Origami tessellations are a form of paper folding that first arose in the 1960s that repeats a simple origami unit to tile the plane. In this presentation I will explain how over the last 20 years folders have explored the space of mathematical tilings, as well as describe some of the tools and techniques that are used to transform tilings into foldable origami structures.

Related Links
GFSW04 28th November 2017
16:40 to 17:20
Tomohiro Tachi Computational Origami Design
Folding is a universal principle that appears both in nature and artifacts. Folding can enable various shapes from thin sheets through self-constrained complex kinematic motion. The speaker talks about computational origami, i.e., the geometry and the algorithm of origami, and its application to design. The topics involve origamizer, a universal algorithm to fold any polyhedral shape from a sheet of paper; rigid origami, the kinematics of plate and hinges utilizing its flat and singular state; computational (and actual) hardness of folding compared to unfolding; and metamaterials exploiting the geometry of origami.
GFSW04 29th November 2017
09:00 to 09:40
Jean-Marc Chomaz Art & Science, the big trail
Is science a territory and can the current Art & Science movement transform it by transplanting artists into "residence"? Do we enter into the era of the conquest of science, good scientists in the new myth of the frontier; should the artist pace the unknown of his gesture, descending the cliffs of The Big Trail to the conquest of a valley of knowledge? The knowledge is folded and complex; the implantation of artist on the territory of science, authorizes postures of ethnologist, colon or explorer but to penetrate this world of spirits we must accept the indigenous miscegenation. My practice Arts & Sciences is deeply rooted in this crossbreeding, this hybridization. A shared journey between artists and scientists, leads to a sensitive exploration of the logical spaces of regular appearance, of future non-existents. The group can also be renamed to the slope and deny the gravity by not following only the deductive lines. One route will become art and the other will become science, but in these shared journeys, each will become the other, revealing the sensitive side of science, meeting the Giants of Light. For me a common work Art & Science leads to this double initiation transforming the very nature of the sciences, questioning the value of the model, the truth and the proof.

This posture of artist-scientist rehabilitates science as an act of the mind, imaginary made of interrogations and projections of the sensible real. The logical universes are jealous of their mysteries, dark matter, foliated and sooty energy, they are infinite measured by the mesure of the proof. They often pour into submerged areas. To survey them as an artist, without believing in the rolling of stones, opens other valleys perched in the folds of the rock. Three holes drawn on the surface of a box and the space of nine trays conceals a hidden sheep of the ephemeral Prince.

Related Links
GFSW04 29th November 2017
09:40 to 10:20
Mimi Koehl Art in aid of science
I was an art major as an undergraduate before being lured into biomechanics and biofluiddynamics by the beauty of natural forms, both living and physical.  Since I have done both art and science, I see two striking similarities between the two pursuits.   One is careful observation of the natural world  (but scientists have tools that let us "see" more than artists can see with their eyes alone).  The other is the use of abstraction to capture the essence of something (objects, processes), although the "language" used to communicate the abstraction is visual for the artist, while it is also mathematical for the scientist.  Most of this workshop focuses on how science and mathematics can inform and inspire art, but I will provide some examples from my own work of how collaboration with artists can aid scientific research.
GFSW04 29th November 2017
10:20 to 11:00
Stephen Morris Art, outreach, and pattern formation
For the past several years, I have been experimenting with the boundary between art and science. I have repurposed my scientific images of pattern formation experiments and pattern-forming natural phenomena by presenting them as art. I have exhibiting images and videos in art galleries and juried art shows. I have brought artists into my research lab for several hands-on workshops. I am the co-organizer of the "ArtSci Salon", an evening meet-up group at the Fields Institute of Mathematical Science in Toronto. I have released a trove of icicle shape data for free use under the Creative Commons. I have collaborated with sound artists and composers to use pattern formation images and videos as input to their creative processes. All these activities can be viewed equally as art-making or as scientific outreach. The scientific field of pattern formation has developed a distinct aesthetic sensibility, informed by mathematics and physics, but inherently visual and dynamic. This aesthetic is an essential motivation for this work. This talk will describe my experiences in this "application" of pattern formation to making, exhibiting and discussing art. My experience shows that unmodified scientific images can be well received as art and generate wide-ranging conversations across traditionally separate disciplines. The art world offers an interesting venue for science outreach activities, as well as being a lot of fun to explore. The ArtSci Salon: http://artscisalon.com
The Icicle Atlas: https://www.physics.utoronto.ca/Icicle_Atlas/
Flickr stream: https://www.flickr.com/photos/nonlin/albums
GFSW04 29th November 2017
11:30 to 12:10
Carola-Bibiane Schönlieb Mathematical approaches for virtual art restoration
Virtual image restoration, also called image inpainting, denotes the process whereby missing or occluded parts in images are filled in based on the information provided by the intact parts of the image. In this talk I will sketch and motivate different mathematical principles that can guide a digital restoration attempt. Digital photographs of art pieces are essentially mathematical objects, and this puts the vast toolbox of mathematics at the restorers’ fingertips. We will encounter the role of differential equations and patch-based methods for virtually restoring structure, texture and colour in images. In particular, we will show examples from the restoration of the Neidhart frescoes (Tuchlauben, Vienna), the restoration of a painting by Sebastiano Del Piombo (the Hamilton Kerr Institute, The Fitzwilliam Museum), and the unearthing of hidden structures in illuminated manuscripts revealed by infrared imaging (the MINIARE project, the Fitzwilliam Museum). After a critical discussion of restoration results I will conclude by pointing out the capabilities and limitations of digital restoration methods, and provide some hints towards applications of such mathematical approaches that go beyond the restoration of arts – such as medicine, forensics and geography.
GFSW04 29th November 2017
13:30 to 13:45
Mella Shaw Artists’ Session: In pursuit of tipping point
GFSW04 29th November 2017
13:45 to 14:00
Mark Francis Artists' Session: Mark Francis
GFSW04 29th November 2017
14:00 to 14:15
Emma Rodgers Artists' Session: Emma Rodgers
GFSW04 29th November 2017
14:15 to 14:30
Henry Jabbour Artists' Session: The Human Form - In Search of the Universal
GFSW04 29th November 2017
14:30 to 14:45
Nedyalka Panova Artists' Session: On the Border of Consciousness
GFSW04 29th November 2017
14:45 to 15:00
Manoel Veiga Artists' Session: How science inspired my work
GFSW04 29th November 2017
15:00 to 15:15
Ulyana Gumeniuk-Parker Artists' Session: Perception of form. Lessons form art history
GFSW04 29th November 2017
15:15 to 15:30
Melissa Murray Artists' Session: Material and Metaphor
GFSW04 29th November 2017
15:30 to 15:45
Paul Friedlander Artists' Session: Serendipity & the wave
GFSW04 30th November 2017
09:30 to 10:10
Keith Moffatt The beaver ball: a chaotic rolling robot
Equations describing the rolling of a spherical ball on a horizontal surface are obtained, the motion being activated by an internal rotor driven by a battery mechanism. The rotor is modelled as a point mass mounted inside a spherical shell, and caused to move in a prescribed circular orbit relative to the shell. The system is described in terms of four independent dimensionless parameters. The equations governing the angular momentum of the ball relative to the point of contact with the plane constitute a six-dimensional, non-holonomic, non-autonomous dynamical system with cubic nonlinearity. This system is decoupled from a subsidiary system that describes the trajectories of the center of the ball. Numerical integration of these equations for prescribed values of the parameters and initial conditions reveals a tendency towards chaotic behaviour as the radius of the circular orbit of the point mass increases (other parameters being held constant). It is further shown that there is a range of values of the initial angular velocity of the shell for which chaotic trajectories are realised while contact between the shell and the plane is maintained. The predicted behaviour has been observed in our experiments.

Work in collaboration with V.A.Vladimirov and K. Ilin
GFSW04 30th November 2017
10:10 to 10:50
Daniel Goldman “Fun”-damental physics: robophysical models for General Relativity and Quantum Mechanics
What happens when physicists build robots? In my group, we do not view these machines as labor-saving devices or demonstrations of control principles, but as scientific instruments, with which to have fun and study fascinating new dynamical systems. We call this approach “robophysics” (see Aguilar et al, Rep. Prog. Phys., 2016), and in this talk I will highlight two of our recent studies in which we observe aspects of “fundamental” (or “modern”) physics in simple self-propelling robots. 1) When transiting a regular array of rigid posts, a ~80 cm long slithering snake-like robot passively scatters into preferred directions, the extent of which is inversely related to the post spacing; these behaviors thus mimic aspects of matter waves complete with diffraction patterns, the diffraction-pattern destroying “measurement” phenomena, Poisson spots, an uncertainty principle, and the beautiful Talbot carpet (a near-field diffraction effect). Of course, there is nothing quantum mechanical about our system: a model based upon robot head-post collisional dynamics and interference of neighboring posts captures much of the observed dynamics. 2) Inspired by the standard (but inaccurate) science-museum type demonstration of General Relativity (e.g. marbles orbiting a central depression), we create an experiment in which the orbiting mass does not lose energy and thus displays persistent dynamics. When confined to a ~2 m diameter flexible spandex sheet with an imposed central depression, a ~10 cm diameter circular two-wheeled robot car executes trajectories that have aspects of orbits in the Schwarzschild solution to Einstein’s field equations in General Relativity (GR). Our system displays closed orbits (like in Newtonian gravity) as well as beautiful patterns of precessing orbits. The latter obey a precession formula derived from the Schwarzschild solution, but with negative precession, indicating that the GR-like correction term in our system acts to repel orbits. In addition to the fun one can have with these systems, we argue that robophysical devices have educational utility: students (and faculty) of all ages gain insight into a diversity of natural phenomena via hands-on construction and play using low-cost but sophisticated  devices.
GFSW04 30th November 2017
11:10 to 11:50
Alain Goriely Playing with magnetic chains: from self-buckling to self-assembly
Spherical neodymium-iron-boron magnets are marketed as toys as they can be assembled into different shapes due to their high magnetic strength. In particular, we consider two simple structures, chains and cylinders of magnets. By manipulating these structures, it quickly appears that they exhibit an elastic response to small deformations. Indeed, chains buckle on their own weight, rings oscillate, and cylinders resist bending but recover their shape after poking. A natural question is then to understand the response of these structures based on the individual physical properties of the magnets and to understand to what extent they behave elastically. In this talk, I will show through illustrative experiments and simple model calculations that the idea of an effective magnetic bending stiffness is, in fact, an excellent macroscopic characterisation for the mechanical response of magnetic chains. I will then propose a more rigorous approach of the problem by considering discrete-to-continuum asymptotic analysis to derive a continuum model for the energy of a deformed chain of magnets based on the magnetostatic interactions between individual spheres.
GFSW04 30th November 2017
11:50 to 12:30
Pierre Degond Collective dynamics of bristlebots
Bristlebots are very simple small robots that are commercialized under different names as toys for children (and adults). They seem to have inspired many youtubers. In a joint work with E. Climent, F. Plouraboue and O. Praud from Toulouse fluid mechanics lab IMFT, G. Dimarco from Ferrara and my former student T. B. N Mac, we have studied the dynamics of swarms of bristlebots confined in a disk and an annulus. The talk will report on the experimental and modelling results and will feature some live experiments.
GFSW04 30th November 2017
13:30 to 14:10
Yuli D Chashechkin Self-propelled wedge
2D flows around neutral buoyancy wedge submerged in a tank with continuously stratified fluid were calculated using conventional time-dependent governing equations set in frame of OpenFOAM codes. Fine structure of different variables fields (density or pressure and their gradients, velocity, vorticity, rate of energy dissipation) was analyzed in wide range of the problem geometry and stratification. Numerical results are compared with data of schlieren visualization of the self-moving wedge in the laboratory tank.
GFSW04 30th November 2017
14:10 to 14:50
Patrick Weidman On the terminal motion of sliding/spinning discs
We review the classic problem concerning the terminal motion of a slidingspinning disk on a horizontal surface which shows that sliding and spinningstop at the same time with terminal value ǫ0 = 0.653, where ǫ = v(t)/Rω(t)is the ratio of linear speed to tip speed of a disk of radius R.We then generalize to problem to find the terminal motion of annular disksand two-tier disks. For the annular disk the terminal speed ratio ǫ0 rangesfrom 0.653 to 1 as the radius ratio η = Rin/Rout varies from 0 to 1. Fortwo-tier disks composed of a lower disk of radius R1 and height H1 attachedto upper disk of radius R2 and height H2, one has a two parameter problemdefined by η = R1/R2 and λ = H1/H2. In addition to simultaneous terminalstopping motions, we find, for small regions in η − λ parameter space, thatthe two-tier disk can either stop spinning first and slide to rest, or stop slidingand spin to rest. An experiment is devised to capture these unique terminalmotions.
GFSW04 30th November 2017
14:50 to 15:30
L Mahadevan Geometry and probability in perception and action
How do you design a coin that lands on its edge 1/3 of the time ? How might one throw accurately ? How does one walk along a straight line ? How can one visualize chance ? Each of these problems invokes geometric concepts in a probabilistic setting. I will discuss solutions to some of these problems that lie at the intersection of cognition, neuroscience and behavior -  and thus are of relevance to art and science.
GFSW04 30th November 2017
16:00 to 16:30
Neil Ribe An Introduction to the Mechanics of the Lasso
Co-authors: Pierre-Thomas Brun (Dept. of Chemical Engineering, Princeton University, Princeton, NJ USA), Basile Audoly (Laboratoire LMS, Ecole Polytechnique, Palaiseau, France)

Trick roping evolved from humble origins as a cattle-catching tool into a sport that delights audiences with its complex patterns or ‘tricks’. Its fundamental tool is the lasso, formed by passing one end of a rope through a small loop (the honda) at the other end. Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane. We first consider the case of a fixed (non-sliding) honda. Noting that the rope’s shape is steady in the reference frame rotating with the hand, we analyse a string model in which line tension is balanced by the centrifugal force and the rope’s weight. We use numerical continuation to classify the steadily rotating solutions in a bifurcation diagram and analyse their stability. In addition to Flat Loops, we find planar ‘coat-hanger’ solutions, and whirling modes in which the loop collapses onto itself. Ne xt, we treat the more general case of a honda that can slide due to a finite coefficient of friction of the rope on itself. Using matched asymptotic expansions, we resolve the shape of the rope in the boundary layer near the honda where the rope’s bending stiffness cannot be neglected. We use this solution to derive a macroscopic criterion for the sliding of the honda in terms of the microscopic Coulomb static friction criterion. Our predictions agree well with rapid- camera observations of a professional trick roper and with laboratory experiments using a ‘robo-cowboy’.
GFSW04 30th November 2017
16:30 to 17:10
Raymond Penner Physics of Sports
Sporting activities provide great examples of physics in action. Participants and observers are often intrigued by the design or motion of a particular piece of sporting equipment. Physicists are intrigued by these same questions. Topics that will be considered in the presentation will include the behavior of a curling rock, the design of a clubhead in the game of golf, and a look at the physics behind the variety of pitches thrown in the game of baseball.
GFSW04 30th November 2017
17:10 to 17:50
Christophe Clanet Forms in Olympic Games
Rowing has been part of the summer Olympics since its debut in 1896. The shape of the boat has slightly changed. We will discuss the origin of this shape with a special attention to the aspect ratio, which can reach values as high as 30, much larger than any other boat. In a second part, we will move to ball games and will focus on zig-zag trajectories which are (sometimes) observed in volley, soccer and golf.
OFBW36 1st December 2017
10:00 to 10:15
Christie Marr, Jane Leeks, Andrzej Herczynski Welcome and Introduction
OFBW36 1st December 2017
10:15 to 10:45
Siân Ede Light Echoes in Art and Science: How far do the Two Constituencies Reflect Each Other in Theory and Practice?
OFBW36 1st December 2017
10:45 to 11:15
Raymond Goldstein Growth and Form: From Stalactites to Ponytails
OFBW36 1st December 2017
11:35 to 12:10
Deirdre Gribbin Hearing Your Genes Evolve
OFBW36 1st December 2017
12:10 to 12:40
Michael Berry How Quantum Physics Democratised Music: A Meditation on Physics and Technology
OFBW36 1st December 2017
12:40 to 13:10
Carola-Bibiane Schönlieb, Stella Panayotova Re-Constructing Illuminated Manuscripts and Paintings
OFBW36 1st December 2017
14:00 to 14:35
Christopher Budd Mathematical Approaches to Toys
OFBW36 1st December 2017
14:35 to 15:10
Chris Sangwin On Form and Function in Board Games
OFBW36 1st December 2017
15:10 to 15:40
Graham Hazel Form and Shape for Lighting Virtual Worlds
OFBW36 1st December 2017
16:10 to 16:50
Tadashi Tokieda A World From a Sheet of Paper
OFBW36 1st December 2017
16:50 to 17:00
Questions/Discussions
GFS 12th December 2017
13:30 to 13:45
Andrzej Herczyński Konrad Bajer Commemorative Symposium
GFS 12th December 2017
13:45 to 14:15
Maciej Lisicki Konrad Bajer Commemorative Symposium
GFS 12th December 2017
14:15 to 14:45
Krzyszlof Mizerski Konrad Bajer Commemorative Symposium
GFS 12th December 2017
14:45 to 15:15
Marek Dudynski Konrad Bajer Commemorative Symposium
GFS 12th December 2017
15:15 to 15:45
Konrad Bajer Commemorative Symposium - TEA BREAK
GFS 12th December 2017
15:45 to 16:15
Tomasz Lipniacki Konrad Bajer Commemorative Symposium
GFS 12th December 2017
16:15 to 17:00
Andrew Gilbert Konrad Bajer Commemorative Symposium
GFS 12th December 2017
17:00 to 17:45
Keith Moffatt Konrad Bajer Commemorative Symposium
GFS 12th December 2017
17:45 to 17:50
Maria Ekiel-Jezewska Konrad Bajer Commemorative Symposium
GFS 14th December 2017
15:00 to 16:30
Mingming Wu Biophysical force regulation in cell migration
In native states, animal cells are surrounded by either fluid or a biopolymer network. The cell-environment interactions critically regulate cell function, as well as collective cell motion. The key to this interaction is the biophysical forces that cells generate. In this talk, I will focus on experimental studies of single cell force regulation in two biological systems. One is on tumor cell-extracellular matrix interaction, in which we find that matrix mechanics, and fluid flows together regulate single tumor cell shape, motility types and invasiveness. In the case of a group of tumor cells, physical forces determine the formation or dissociation of tumor spheroids. In a second example, we studied how sperm cells swim against fluid flows guided by a hydrodynamic force. Curiously, in both cases, biological matrices/fluids enhance force transmission range and promote cell-cell interaction.