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Timetable (GFSW01)

Form and deformation in solid and fluid mechanics

Monday 18th September 2017 to Friday 22nd September 2017

Monday 18th September 2017
09:00 to 09:30 Registration
09:30 to 09:40 Welcome from Christie Marr (INI Deputy Director)
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.
10:20 to 11:00 Jose Bico (ESPCI ParisTech)
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. 
11:00 to 11:30 Morning Coffee
11:30 to 12:10 Daniel Goldman (Georgia Institute of Technology)
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.
12:10 to 12:30 Sungyon Lee (University of Minnesota)
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. 
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:10 Shreyas Mandre (Brown University)
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.

14:10 to 14:30 Cathal Cummins (University of Edinburgh)
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)

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

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

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

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

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

a) Electronic mail: Cathal.Cummins[at][dot]uk
b) Electronic mail: I.M.Viola[at][dot]uk
c)Electronic mail: Naomi.Nakayama[at][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. 
14:30 to 14:50 Marina Ferreira (Imperial College London)
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.
14:50 to 15:10 Sharon Lubkin (North Carolina State University)
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. 
15:10 to 15:30 Simon Pearce (University of Manchester)
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.
15:30 to 16:00 Afternoon Tea
16:00 to 17:00 Free Discussions INI 1
17:00 to 18:00 Welcome Wine Reception at INI
Tuesday 19th September 2017
09:00 to 09:40 Neil Balmforth (University of British Columbia)
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
09:40 to 10:20 Pasquale Ciarletta (Politecnico di Milano); (CNRS (Centre national de la recherche scientifique))
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.
[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
10:20 to 11:00 Eva Kanso (University of Southern California); (New York University)
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. 
11:00 to 11:30 Morning Coffee
11:30 to 12:10 David Hu (Georgia Institute of Technology)
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.
12:10 to 12:30 Ido Regev (Ben-Gurion University)
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.
12:30 to 13:30 Lunch @ Wolfson Court
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. 
14:10 to 14:30 Amir Gat (Technion - Israel Institute of Technology)
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.
14:30 to 14:50 James Hanna (Virginia Polytechnic Institute and State University)
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.
14:50 to 15:10 Douglas Holmes (Boston University)
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.
15:10 to 15:30 Scott Waitukaitis (Universiteit Leiden); (FOM Institute AMOLF)
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.
15:30 to 16:00 Afternoon Tea
16:00 to 17:00 Free Discussions INI 1
Wednesday 20th September 2017
09:00 to 09:40 François Gay-Balmaz (CNRS - Ecole Normale Superieure Paris)
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.
09:40 to 10:20 Denis Weaire (Trinity College Dublin); Adil Mughal (Aberystwyth University)
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].
10:20 to 11:00 Jean-Luc Thiffeault (University of Wisconsin-Madison)
Unraveling hagfish slime
11:00 to 11:30 Morning Coffee
11:30 to 12:10 Michael Shelley (New York University); (Simons Foundation)
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.
12:10 to 12:50 Saverio Spagnolie (University of Wisconsin-Madison)
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.
12:50 to 13:30 Lunch @ Wolfson Court
13:30 to 17:00 Free Afternoon
19:30 to 22:00 Formal Dinner at Emmanuel College
Thursday 21st September 2017
09:00 to 09:40 Laura Miller (University of North Carolina); (University of North Carolina)
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.
09:40 to 10:20 Yves Couder (Laboratoire Matière et Systèmes Complexes)
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. 
10:20 to 11:00 Pierre Degond (Imperial College London)
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.
11:00 to 11:30 Morning Coffee
11:30 to 12:10 Derek Moulton (University of Oxford)
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.
12:10 to 12:30 Davide Ambrosi (Politecnico di Milano); (Politecnico di Milano)
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.
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:10 Sunghwan (Sunny) Jung (Virginia Polytechnic Institute and State University)
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. 
14:10 to 14:30 Marino Arroyo (Universitat Politècnica de Catalunya)
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. 
14:30 to 14:50 Buddhapriya Chakrabarti (University of Sheffield); (University of Sheffield)
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. 
14:50 to 15:10 Andreas Muench (University of Oxford); (University of Oxford)
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.
15:10 to 15:30 Axel Voigt (Technische Universität Dresden)
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
15:30 to 16:00 Afternoon Tea
16:00 to 17:00 Free Discussions INI 1
Friday 22nd September 2017
09:00 to 09:40 Martine Ben Amar (CNRS - Ecole Normale Superieure Paris)
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
09:40 to 10:20 De Witt Sumners (Florida State University)
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.
10:20 to 11:00 Darryl Holm (Imperial College London)
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).
11:00 to 11:30 Morning Coffee
11:30 to 12:10 Renzo Ricca (University of Milan - Bicocca)
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.,
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:10 Alain Goriely (University of Oxford); (University of Oxford)
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).
14:10 to 14:50 Lisa Fauci (Tulane University); (Tulane University)
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.
14:50 to 15:30 Gunnar Hornig (University of Dundee)
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.
15:30 to 16:00 Afternoon Tea
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons