# Timetable (CFMW01)

## Dynamics of active suspensions, gels, cells and tissues

Monday 24th June 2013 to Friday 28th June 2013

 09:00 to 09:45 D Crowdy (Imperial College London)Models of low-Reynolds-number swimmers and colloidal particles in confined domains The talk will survey some simple mathematical models to gain insights into the dynamics of particles or swimmers of various kinds moving at zero Reynolds numbers in geometrically complex domains bounded by no-slip walls and/or free surfaces. INI 1 09:45 to 10:30 S Spagnolie (University of Wisconsin-Madison)Locomotion of helical bodies in viscoelastic fluids Many microorganisms swim by rotating one or many helical flagella, often propelling themselves through fluids that exhibit both viscous and elastic qualities in response to deformations. In an effort to better understand the complex interaction between the fluid and body in such systems, we have studied numerically the force-free swimming of a rotating helix in a viscoelastic (Oldroyd-B) fluid. The introduction of viscoelasticity can either enhance or retard the swimming speed depending on the body geometry and the properties of the fluid (through a dimensionless Deborah number). The numerical results show how small-amplitude theoretical calculations connect smoothly to large-amplitude experimental measurements. Co-authors: Bin Liu (Brown University), Thomas R. Powers (Brown University) INI 1 10:30 to 11:00 Morning Coffee at INI 11:00 to 11:45 G Subramanian ([Engineering Mechanics Unit, JNCASR, Bangalore])Concentration fluctuations in a bacterial suspension Recent analyses and simulations have identified an instability of a quiescent bacterial suspension above a threshold concentration, (nL3)crit = (5/C)(L/U\tau), where n is the bacterium number density, L and U the bacterium length and swimming speed, t the mean interval between tumbles, and C a measure of the intrinsic force-dipole. This instability is thought to underlie the large-scale coherent motions observed in experiments. There, however, remains a discrepancy between theory and simulations. While the former predicts a spatially homogeneous instability with coupled orientation and velocity fluctuations, simulations have observed large-scale concentration fluctuations. Even in the stable regime, solutions of the linearized equations reveal significant concentration fluctuations. We will formulate an analytical solution that illustrates the linearized evolution of the velocity, orientation and concentration fields in a bacterial suspension starting from an arbitrary initial condition. The analysis relies on a remarkable correspondence between orientation fluctuations in a bacterial suspension and vorticity fluctuations in an inviscid fluid. The governing operators in both cases possess singular continuous spectra in addition to discrete modes. The dynamics of the singular orientation modes leads to transient growth of concentration fluctuations in the manner that the singular vorticity modes lead to kinetic energy growth in high-Reynolds-number shearing flows. We will discuss the velocity, orientation and stress correlations, emerging from an uncorrelated Poisson field, both below and above the critical concentration. We also analyze the role of tumbling as a source of fluctuations. Regarding a tumble as a ‘linear collision’ governed by Poisson statistics allows one to write down the orientation-space noise, and this in turn leads to the analog of the fluctuating hydrodynamic equations for a bacterial suspension. Co-author: Donald Koch (Chemical and bio-molecular engineering, Cornell University, NY, USA.) INI 1 11:45 to 12:30 M Graham (University of Wisconsin-Madison)Hydrodynamic coordination of bacterial motions: from bundles to biomixing Many bacteria propel themselves though their fluid environment by means of multiple rotating flagella that self-assemble to form bundles. At a larger scale, the fluid motion generated by an individual microbe as it swims affects the motions of its neighbors. Experimental observations indicate the presence of long-range order and enhanced transport in suspensions of bacteria -- these phenomena may be important in many aspects of bacterial dynamics including chemotaxis and development of biofilms. This talk focuses on the role of fluid dynamics in the bundling of flagella and the interactions between swimming organisms. We first describe theory and simulations of hydrodynamically interacting microorganisms, using very simple models of the individual organisms. In the dilute limit, simple arguments reveal the dependence of swimmer and tracer velocities and diffusivities on concentration. As concentration increases, we show that cases exist in which the swimming motion generates large-scale flows and dramatically enhanced transport in the fluid. A physical argument supported by a mean field theory sheds light on the origin of these effects. The second part of the talk focuses on the dynamics of the flagellar bundling process, using a mathematical model that incorporates the fluid motion generated by each flagellum as well as the finite flexibility of the flagella. The initial stage of bundling is driven purely by hydrodynamics, while the final state of the bundle is determined by a nontrivial and delicate balance between hydrodynamics and elasticity. As the flexibility of the flagella increases a regime is found where, depending on initial conditions, one finds bundles that are either tight, with the flagella in mechanical contact, or loose, with the flagella intertwined but not touching. That is, multiple coexisting states of bundling are found. The parameter regime at which this multiplicity occurs is comparable to the parameters for a number of bacteria. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 14:45 J Yeomans (University of Oxford)Active Nematics Active systems, such as the cytoskeleton and bacterial suspensions, provide their own energy and hence operate out of thermodynamic equilibrium. Continuum models describing active systems are closely related to those describing liquid crystal hydrodynamics, together with an additional ‘active’ stress term. We discuss how the behaviour of the active continuum models depends on model parameters, such as the strength of the activity and the liquid crystal tumbling parameter, and we compare our results to recent experiments on cytoskeletal gels. 14:45 to 15:30 Z Dogic (Brandeis University)Hierarchical active matter: from extensible bundles to active gels, streaming liquid crystals and motile emulsions The emerging field of active matter promises an entirely new category of materials, with highly sought after properties such as autonomous motility and internally generated flows. In this vein, I will describe recent experiments that have focused on reconstituting dynamical structures from purified biochemical components. In particular I will describe recent advances that include: (1) assembly of a minimal model of synthetic cilia capable of generating periodic beating patterns, and conditions under which they exhibit metachronal traveling waves, (2) study of 2D active nematic liquid crystals whose streaming flows are determined by internal fractures and self-healing as well as spontaneous unbinding and recombination of oppositely charged disclination defects, (3) reconstitution of active gels characterized by highly tunable and controllable spontaneous internal flows, and (4) assembly of active emulsions in which aqueous droplets spontaneously crawl when in contact with a ha rd wall. 15:30 to 16:00 Afternoon Tea at INI 16:00 to 16:45 J Toner (University of Oregon)Rice, Locusts and Chemical Waves: A Hydrodynamic Theory of Polar Active Smectics We present a hydrodynamic theory of polar active smectics, by which we mean active striped systemsactive systems, both with and without number conservation. For the latter, we find quasi long-ranged smectic order in $d=2$ and long-ranged smectic order in $d=3$. In $d=2$ there is a Kosterlitz-Thouless type phase transition from the smectic phase to the ordered fluid phase driven by increasing the noise strength. For the number conserving case, we find that giant number fluctuations are greatly suppressed by the smectic order; that smectic order is long-ranged in $d=3$; and that nonlinear effects become important in $d=2$. Co-author: Leiming Chen (The China University of Mining and Technology) , 17:00 to 21:00 Walk to Grantchester, pub dinner* (either on Tues or Thu)
 09:00 to 09:45 J Brady (CALTECH (California Institute of Technology))The Five S's: Chemical Swimming, Sailing, Surfing, Squirming and Swarming The design of nanoengines that can convert stored chemical energy into motion is an important challenge of nanotechnology, especially for engines that can operate autonomously. Recent experiments have demonstrated that it is possible to power the motion of nanoscale and microscale objects by using surface catalytic reactions -- so-called catalytic nanomotors. The precise mechanism(s) responsible for this motion is(are) still debated, although a number of ideas have been put forth. Here, a very simple mechanism is discussed: A surface chemical reaction creates local concentration gradients of the reactant (the fuel) and product species. As these species diffuse in an attempt to re-establish equilibrium, they entrain the motor causing it to move. This process can be viewed either as osmotic propulsion or as self-diffusiophoresis. The simplest way to break symmetry and achieve motion is by an asymmetric reactivity on the motor surface. The mathematical description of suc h motion is analogous to that used to describe the swimming of microorganisms, hence the name 'chemical swimming.' However, symmetry can also be broken by the motor's shape and, even for uniform reactivity, propulsion can be achieved -- 'chemical sailing.' A motor particle at an air-water interface can change the local concentration of surface-active agents and propel itself -- 'chemical surfing.' And even local variations of hydrodynamic mobility and interactive potential between the motor and the fuel can lead to net motion, a form of 'chemical squirming.' The implications of these mechanisms on the attainable propulsive speeds as a function of reaction rate and fuel concentration will be discussed and compared with Brownian dynamics simulations. It will also be shown that chemically active particles can attract or repel each other through long-range 'Coulomb-like' interactions. And suspensions of active particles can exhibit Debye-like screening leading to 'chemical swarming.' INI 1 09:45 to 10:30 R Lipowsky (Max-Planck-Institut für Kolloid- und Grenzflächenforschung)Remodelling of membrane compartments Biomembranes undergo continuous remodelling by budding and fission processes, which create new membrane compartments in the form of vesicles, as well as by adhesion and fusion, which combine two such compartments into a single one. The vesicles are transported by teams of molecular motors from donor membranes, where they are created, to acceptor membranes,into which they are incorporated by membrane fusion. In this talk, I will address the energetics and kinetics of these remodelling processes as well as their relevance for intracellular transport. INI 1 10:30 to 11:00 Morning Coffee at INI 11:00 to 11:45 H-G Döbereiner (Universität Bremen)Physarum Polycephalum Percolation as a Paradigm for Topological Phase Transitions in Transportation Networks We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. The universality of percolation may be used as a general gauge in the analysis of transportation networks. Some malignant tissues derive their blood vessels not by angiogenesis, i.e., remodeling of existing vessels, but rather by denovo vascularization like embryos. Since topologically, percolation is independent from detailed mechanisms and even space dimensions, i.e., 2D versus 3D growth, it may serve as a reference point in space and time when comparing the dynamics of network formation in tumors of varying size and shape. Since restricting blood supply via hindering vessel percolation is paramount for suppressing tumor growth, this may foster development of antiangiogenic therapy. INI 1 11:45 to 12:30 N Yoshinaga (Tohoku University)Spontaneous motion and deformation of a droplet driven by chemical reaction Spontaneous motion has been attracting lots of attention in last decades in nonlinear and nonequilibrium physics partially for its potential application to biological problems such as cell motility. Recently several model experiments showing spontaneous motion have been proposed in order to elucidate underlying mechanism of the motion. The systems in these works consist of relatively simple ingredients, for instance oil droplets in water, but nevertheless the results show rich motion and deformation of the droplet. Importantly, the system breaks symmetry and chooses one direction of motion. In this work, we theoretically derive a set of nonlinear equations exhibiting a transition between stationary and motile states starting from advection-reaction-diffusion equation driven away from an equilibrium state due to chemical reactions. A particular focus is on how hydrodynamic flow destabilizes an isotropic distribution of a concentration of chemicals. We also discuss a shape of the droplet. Due to self-propulsive motion and flow around the droplet, a spherical shape becomes unstable and it elongates perpendicular to the direction of motion. This fact would imply that the self-propulsion driven by chemical reaction is characterized as a pusher in terms of a flow field. INI 1 12:30 to 13:00 Lunch at Wolfson Court 14:00 to 14:30 IG Kevrekidis (Princeton University)Data mining in swarming models INI 1 14:30 to 16:00 Poster Session at INI 15:30 to 16:00 Afternoon Tea at INI 16:00 to 17:00 Free 19:30 to 22:00 Conference Dinner at Lucy Cavendish College