public 01:34:49

Camille Scalliet : When is the Gardner transition relevant?

  -   Nonlinear and Complex Systems ( 289 Views )

The idea that glasses can become marginally stable at a Gardner transition has attracted significant interest among the glass community. Yet, the situation is confusing: even at the theoretical level, renormalization group approaches provide contradictory results on whether the transition can exist in three dimensions. The Gardner transition was searched in only two experimental studies and few specific numerical models. These works lead to different conclusions for the existence of the transition, resulting in a poor understanding of the conditions under which a marginally stable phase can be observed. The very relevance of the Gardner transition for experimental glasses is at stake.

We study analytically and numerically the Weeks-Chandler-Andersen model. By changing external parameters, we continuously explore the phase diagram and regimes relevant to granular, colloidal, and molecular glasses. We revisit previous numerical studies and confirm their conclusions. We reconcile previous results and rationalise under which conditions a Gardner phase can be observed. We find that systems in the vicinity of a jamming transition possess a Gardner phase. Our findings confirm the relevance of a Gardner transition for colloidal and granular glasses, and encourage future experimental work in this direction. For molecular glasses, we find that no Gardner phase is present, but our studies reveal instead the presence of localised excitations presumably relevant for mechanical and vibrational properties of glasses.

public 01:29:47

Marija Vucelja : A glass transition in population genetics: Emergence of clones in populations

  -   Nonlinear and Complex Systems ( 222 Views )

The fields of evolution and population genetics are undergoing a renaissance, due to the abundance of sequencing data. On the other hand, the existing theories are often unable to explain the experimental findings. It is not clear what sets the time scales of evolution, whether for antibiotic resistance, an emergence of new animal species, or the diversification of life. The emerging picture of genetic evolution is that of a strongly interacting stochastic system with large numbers of components far from equilibrium. In this talk, I plan to focus on the clone competition and discuss the diversity of a random population that undergoes selection and recombination (sexual reproduction). Recombination reshuffles genetic material while selection amplifies the fittest genotypes. If recombination is more rapid than selection, a population consists of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, selection can amplify individual genotypes into large clones, and the population reaches the so-called "clonal condensation". I hope to convince you that our work provides a qualitative explanation of clonal condensation. I will point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. I will conclude with a summary of our present understanding of the clonal condensation phenomena and describe future directions and connections to statistical physics.

public 01:34:44

Gaby Katul : TBA

  -   Nonlinear and Complex Systems ( 204 Views )

public 01:34:44

Luis Bonilla : Bifurcation theory of swarm formation

  -   Nonlinear and Complex Systems ( 192 Views )

In nature, insects, fish, birds and other animals flock. A simple two-dimensional model due to Vicsek et al treats them as self-propelled particles that move with constant speed and, at each time step, tend to align their velocities to an average of those of their neighbors except for an alignment noise (conformist rule). The distribution function of these active particles satisfies a kinetic equation. Flocking appears as a bifurcation from an uniform distribution of particles whose order parameter is the average of the directions of their velocities (polarization). This bifurcation is quite unusual: it is described by a system of partial differential equations that are hyperbolic on the short time scale and parabolic on a longer scale. Uniform solutions provide the usual diagram of a pitchfork bifurcation but disturbances about them obey the Klein-Gordon equation in the hyperbolic time scale. Then there are persistent oscillations with many incommensurate frequencies about the bifurcating solution, they produce a shift in the critical noise and resonate with a periodic forcing of the alignment rule. These predictions are confirmed by direct numerical simulations of the Vicsek model. In addition, if the active particles may choose with probability p at each time step to follow the conformist Vicsek rule or to align their velocity contrary or almost contrary to the average one, the bifurcations are of either period doubling or Hopf type and we find stable time dependent solutions. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, non-uniform polarized phases appear as the noise surpasses threshold.

public 01:39:58

Stephen Teitel : Shear Banding, Discontinuous Shear Thickening, and Rheological Transitions in Athermally Sheared Frictionless Disks

  -   Nonlinear and Complex Systems ( 190 Views )

Simple models of classical particles, interacting via soft- or hard-core repulsive contact interactions, have been used to model a wide variety of granular and soft-matter materials, such as dry granular particles, foams, emulsions, non-Brownian suspensions, and colloids. Such materials display a variety of complex behaviors when in a state of steady shear driven flow. These include (i) Jamming: where the system transitions from a flowing liquid to a rigid but disordered solid as the particle packing increases; (ii) Shear Banding: where the system becomes spatially inhomogeneous, separating into distinct bands flowing at different sh ear strain rates; (iii) Discontinuous Shear Thickening: where the shear stress jumps discontinuously as the shear strain rate is increased. In this talk we will consider a simple numerical model of athermal soft-core interacting frictionless disks in steady state shear flow. We will show that the mechanism by which energy is dissipated plays a key role in determining the rheology of the system. For a model with a tangential viscous collisional dissipation, but no elastic friction, we will show that as the particle packing increases there is a sharp first order phase transition from a region of Bagnoldian rheology (stress ~ strain-rate^2) to a region of Newtonian rheology (stress ~ strain-rate), that takes place below the jamming transition. In a phase diagram of varying strain-rate and packing fraction (or strain-rate and pressure) this first order rheological phase transition manifests itself as a coexistence region, consisting of coexisting bands of Bagnoldian and Newtonian rheology in mechanical equilibrium with each other. Crossing this coexistence region by increasing the strain-rate at fixed packing, we find that discontinuous shear thickening can result if the strain-rate is varied too rapidly for the system to relax to the true shear-banded steady state. We thus demonstrate that the rheology of simply interacting sheared disks can be considerably more complex than previously realized, and our model suggests a simple mechanism for both the phenomena of shear banding and discontinuous shear thickening in spatially homogeneous systems, without the need to introduce elastic friction.

public 01:39:40

Frederic Lechenault : Experimental investigation of equilibration properties in model granular subsystems

  -   Nonlinear and Complex Systems ( 181 Views )

We experimentally investigate the statistical features of the stationary states reached by two idealized granular liquids able to exchange volume. The system consists in two binary mixtures of the same number of soft disks, hence covering the same area, but with different surface properties. The disks sit on a horizontal air table, which provides ultra low friction at the cell bottom, and are separated by a mobile wall. Energy is injected in the system by means of an array of randomly activated coil bumpers standing as the edges of the cell. Due to the energy injection, the system acts like a slow liquid and eventually jams at higher packing fraction. We characterize the macroscopic states by studying the motion of the piston. We find that its average position is different from one half, and a non monotonic function of the overall packing fraction, which reveals the crucial role played by the surface properties in the corresponding density of states. We then study the bulk statistics of the packing fraction and the dynamics in each subsystem. We find that the measured quantities do not equilibrate, and become dramatically different as the overall packing fraction is increased beyond the onset of supercooling. However, the local fluctuations of the packing fraction are uniquely determined by its average, and hence independent of the interaction between disks. We then focus on the mixing properties of such an assembly. We characterize mixing by computing the topological entropy of the braids formed by the stationary trajectories of the grains at each pressure. This quantity is shown to be well defined, very sensitive to onset of supercooling, reflecting the dynamical arrest of the assembly, and to equilibrate in the two subsystems. Joint work with Karen Daniels.

public 01:29:47

John Dolbow : On the Surfactant-Driven Fracture of Particulate Rafts

  -   Nonlinear and Complex Systems ( 180 Views )

Over the past decade, much attention has focused on the behavior of hydrophobic particles at interfaces. These systems are of interest to scientists and engineers, for example, due to their potential for stabilizing drops and emulsions via jamming. This seminar will focus on the behavior of particulate 'rafts' that form when a monolayer of particles are placed at an air- liquid interface. The particles interact with the underlying fluid to form a quasi two-dimensional solid. Such particulate rafts can support both tension and compression, and they buckle under sufficiently large compressive loads. When a drop of surfactant is introduced into the system, fracture networks develop in the rafts. The fracture process exhibits features observed in other elastic systems, such as crack kinking, crack branching, and crack arrest. Moreover, there is a clear coupling between the praft fracture and the diffusion of the surfactant on the surface and through the 'porous' liquid-particle monolayer. As such, one can draw analogies between this system and others where crack growth interacts with fluid flow or mass transport. The seminar will present recent work in modeling the diffusion of surfactant into particle raft systems and the resulting formation of fracture networks. We will present both discrete models that track the motion of individual particles, as well as a new continuum model for poro-chemo-elasticity. Results that reproduce some of the quantitative and qualitative aspects of recent experimental studies of these systems will also be shown.