## 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.

## Ana Barros : Down the Predictability Hole - Searching for Metrics to Understand and Replace Physical Parameterizations of Nonlinear Processes in Atmospheric Models

- Nonlinear and Complex Systems ( 274 Views )Short-term forecast skill in weather forecasting over the last 15 years has
been achieved mostly through data assimilation. Predictive ability however
has hit barriers that have not been overcome by increasing computer power
and model resolution. Model tuning has come out from hiding, and it is
arguably ``trending'' in peer-review over the last 2-3 years. The open
question is what (and how) to do next. I will address this question relying
on two-decades of research on the representation of moist processes in the
atmosphere, specifically targeting the following issues:

1) Evaluating Models to Elucidate the Physics that Matter

2) Detecting and Isolating Sources, Sinks and Barriers of Predictability

3) Meeting the Utility Challenge - Projections vs Predictability

## Pedro Saenz : Spin lattices of walking droplets

- Nonlinear and Complex Systems ( 240 Views )Understanding the self-organization principles and collective dynamics of non-equilibrium matter remains a major challenge despite considerable progress over the last decade. In this talk, I will introduce a hydrodynamic analog system that allows us to investigate simultaneously the wave-mediated self-propulsion and interactions of effective spin degrees of freedom in inertial and rotating frames. Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding wave fields. A walking droplet, or `walker, may be trapped by a submerged circular well at the bottom of the fluid bath, leading to a clockwise or counter-clockwise angular motion centered at the well. When a collection of such wells is arranged in a 1D or 2D lattice geometry, a thin fluid layer between wells enables wave-mediated interactions between neighboring walkers. Through experiments and mathematical modeling, we demonstrate the spontaneous emergence of coherent droplet rotation dynamics for different types of lattices. For sufficiently strong pair-coupling, wave interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or antiferromagnetic order. Transitions between these two forms of order can be controlled by tuning the lattice parameters or by imposing a Coriolis force mimicking an external magnetic field. More generally, our results reveal a number of surprising parallels between the collective spin dynamics of wave-driven droplets and known phases of classical condensed matter systems. This suggests that our hydrodynamic analog system can be used to explore universal aspects of active matter and wave-mediated particle interactions, including spin-wave propagation and topologically protected dynamics far from equilibrium.

## Maciej Balajewicz : Nonlinear dimensionality reduction: from turbulent fluid flows to computational finance

- Nonlinear and Complex Systems ( 230 Views )The past several decades have seen an exponential growth of computer processing speed and memory capacity. The massive, complex simulations that run on supercomputers allow exploration of fields for which physical experiments are too impractical, hazardous, and/or costly. Accurate and efficient high-fidelity simulations are critical to many energy, defense, and health applications, e.g., global climate simulations, optimal design of wind systems for power generation, combustion simulations aimed at increasing fuel efficiency and reducing carbon emissions, simulations of heart fibrillation, and many others. Unfortunately, even with the aid of massively parallel next-generation computers, high-fidelity simulations are still too expensive for real-time and multi-query applications such as uncertainty quantification, design, optimization, and control. For this reason, interest in model order reduction continues to grow. In this talk I will summarize recent advances in nonlinear model reduction for high-Reynolds-number fluid flows, structural dynamics, and computational finance.

## 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.

## Abram Clark : Yielding in granular materials, from riverbeds to renormalization group

- Nonlinear and Complex Systems ( 217 Views )Granular materials are a part of a broad class of amorphous materials that display yield stress behavior. When the applied shear stress is below the yield stress, grains move temporarily, but only until finding a mechanically stable (MS) configuration that is able to resist the applied shear stress. Above the yield stress, the material is no longer able to find MS configurations. However, the geometrical reasons why MS states vanish at the yield stress is not well understood. In this talk, I will show evidence from molecular dynamics simulations that yielding in granular materials is akin to a second-order critical point, where the mechanical behavior is dominated by a correlation length that diverges at the yield stress. MS states exist above the yield stress for finite systems, but they vanish as the system size becomes large according to a critical scaling function. The packing fraction and coordination number for MS states are independent of the applied shear stress, implying that the critical behavior we observe is distinct from the well known jamming scenario. However, MS states at nonzero shear stress possess anisotropic force and contact networks, suggesting that the yield stress is set by the maximum anisotropy that can be realized in the large-system limit.

## Sidney Nagel : Exploiting disorder for global response: independence of bond-level contributions

- Nonlinear and Complex Systems ( 213 Views )We are customarily taught to understand ordinary solids by considering perturbations about a perfect crystal. This approach becomes increasingly untenable as the amount of disorder in the solid increases; for a glass with no well-defined long-range order, a crystal is a terrible starting point for understanding the glasss rigidity or its excitations. Is there an alternative the opposite of a crystal where order, rather than disorder is the perturbation? Jamming is an alternate way of creating rigid solids that are qualitatively different from crystals. In a crystal with only one atom per unit cell, all atoms play the same role in producing the solid's global response to external perturbations. Jammed disordered materials are not similarly constrained and a new principle emerges: independence of bond-level response. Using networks where individual bonds can be successively removed, one can drive the overall system to different regimes of behavior. Consequently one can exploit disorder to achieve unique, varied, textured and tunable global response.

## Kyoung Jin Lee : A scary, yet interesting, scenario to the fibrillating heart

- Nonlinear and Complex Systems ( 213 Views )Alternans, a beat-to-beat temporal alternation in the sequence of heart beats, is a known precursor of the development of cardiac fibrillation, leading to sudden cardiac death. The equally important precursor of cardiac arrhythmias is the rotating spiral wave of electro-mechanical activity, or reentry, on the heart tissue. In this talk, I will show that these two seemingly different phenomena can have a remarkable relationship: In well controlled in-vitro tissue cultures, isotropic populations of rat ventricular myocytes sustaining a temporal rhythm of alternans can support period-2 oscillatory re-entries, and vice versa. These re-entries bear `line defects' across which the phase of local excitation slips rather abruptly by $2\pi$, when a full period-2 cycle of alternans completes in $4\pi$. In other words, the cells belonging to the line defects are period-1 oscillatory whereas all the others in the bulk medium are period-2 oscillatory. We also find that a slowly rotating line defect results in a quasi-periodic like oscillation in the bulk medium. Some key features of these phenomena can be well reproduced in computer simulations of a nonlinear reaction-diffusion model.

## Beatriz Seoane : The Gardner threshold: a border between two glasses

- Nonlinear and Complex Systems ( 211 Views )Glasses (aka amorphous solids) exhibit various anomalies when compared with crystals (aka ordered solids), for instance, they display enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (the so-called Boson Peak) or respond drastically to very small mechanical deformations. In this work, we identify the common, universal origin to these anomalies in a realistic, three-dimensional model of glasses. We show that in highly packed hard spheres, vibrations become highly correlated in space and time at a sharply defined threshold, which we call the "Gardner threshold". This work is deeply related with the last developments in the analytical theory of glasses, where the glass problem has been finally solved exactly in the artificial limit of infinite spatial dimensions. The analytical solution predicts the existence of a genuine phase transition (a Gardner phase transition) within the glass, separating the glass and the jamming transitions. In this work we, not only establish the relevance of the (remanent of the) Gardner transition for real glasses, but also characterize it using well-defined observables, including time-dependent quantities and spatial correlations, that should be experimentally measurable. See arxiv.org/abs/1511.04201

## Peter Morse : Generic failure in granular packings: finding the relationship between shear and random forces

- Nonlinear and Complex Systems ( 208 Views )Under shear, a jammed packing of particles will break in characteristic ways and transition between mechanically stable states. One can then ask whether the signatures of failure are specific to shear, or whether they are the same in more generic perturbations. Interestingly, recent mean-field calculations suggest that in infinite dimensions, the response of a system to global shear and random forces may be equivalent. Whether or not this is true in 2D or 3D systems remains an open question. Therefore, I've developed a method for driving 2D jammed packings of disks by quasti-static persistent random forces to demonstrate that the response is similar to what is observed in athermal quasi-static shear simulations. I will also comment on how we expect the similarities to break in finite dimensions and what these results might imply for active matter systems.

## Eckehard Schoell : Time-delayed feedback control - from nano to neuro

- Nonlinear and Complex Systems ( 203 Views )We review recent developments in the control of deterministic and stochastic nonlinear dynamics by time-delayed feedback methods [1]. We point out how to overcome the alleged odd number limitation for unstable periodic orbits, and discuss the control of complex chaotic or noise-induced space-time patterns. Our findings are applied to a selection of models ranging from semiconductor nanostructures, like resonant-tunneling diodes [2], to neural systems. [1] E. Sch{\"o}ll and H.G. Schuster (Eds.): Handbook of Chaos Control (Wiley-VCH, Weinheim, 2008), second completely revised and enlarged edition. [2] E. Sch{\"o}ll, Nonlinear spatio-temporal dynamics and chaos in semiconductors (Cambridge University Press, Cambridge, 2001).

## Eric Vanden-Eijnden : Transition Pathways of Rare Events

- Nonlinear and Complex Systems ( 201 Views )Many processes in nature occur in the form of rare but important events. Well known examples of such events include conformation changes of biomolecules, chemical reactions, and nucleation events during phase transformation. Rare events do not happen very often on the internal clock of the system (which makes their simulation very challenging), but this clock can be very fast and this leaves plenty of room for the appearance of rare events in our daily life. I will review classical theories for the description of rare events, recent theoretical developments such as Transition Path Theory, concept such as reaction coordinate or free energy of a reaction and I will discuss how to compute the pathway and rate of rare events efficiently using the String Method. As illustrations, I will discuss the hydrophobic collapse of a polymeric chain, phase transitions in the Ising model, and a genetic toggle switch.

## Yuhai Tu : Physics of information processing in living systems

- Nonlinear and Complex Systems ( 201 Views )Living organisms need to obtain and process information crucial for their survival. Information processing in living systems, ranging from signal transduction in a single cell to image processing in the human brain, are performed by biological circuits (networks), which are driven out of equilibrium. These biochemical and neural circuits are inherently noisy. However, certain accuracy is required to carry out proper biological functions. How do biological networks process information with noisy components? What is the free energy cost of accurate biological computing? Is there a fundamental limit for its performance of the biological functions? In this talk, we will describe our recent work in trying to address these general questions in the context of two basic cellular computing tasks: sensory adaptation for memory encoding [1,2]; biochemical oscillation for accurate timekeeping [3].

[1] The energy-speed-accuracy trade-off in sensory adaptation, G. Lan, P.
Sartori, S. Neumann, V. Sourjik, and Yuhai Tu, Nature Physics 8, 422-428,
2012.

[2] Free energy cost of reducing noise while maintaining a high
sensitivity, Pablo Sartori and Yuhai Tu, Phys. Rev. Lett. 2015. 115:
118102.

[3] The free-energy cost of accurate biochemical oscillations, Y. Cao, H.
Wang, Q. Ouyang, and Yuhai Tu, Nature Physics 11, 772, 2015.

## Lenka Zdeborova : Network Dismantling

- Nonlinear and Complex Systems ( 200 Views )Many systems of interest can be represented by a network of nodes connected by edges. In many circumstances the existence of a giant component is necessary for the network to fulfill its function. Motivated by the need to understand optimal attack strategies, optimal spread of information or immunization policies, we study the network dismantling problem, i.e. the search of a minimal set of nodes whose removal leaves the network broken into components of sub-extensive size. Building on the statistical mechanics perspective we compute the size of the optimal dismantling set for random networks, propose an efficient dismantling algorithm for general networks that outperforms by a large margin existing strategies, and we provide various insights about the problem.

## Tom Solomon : Front propagation and pattern formation in the Belousov-Zhabotinsky reaction

- Nonlinear and Complex Systems ( 196 Views )We present experiments on pattern formation and front propagation in the Belousov-Zhabotinsky (BZ) chemical reaction in flowing systems with chaotic advection. The flow is a chain of alternating vortices that oscillate and/or drift in the lateral direction. Mixing between the vortices is chaotic in this flow with either (enhanced) diffusive or superdiffusive transport. Experiments with the excitable BZ reaction are used to study the motion of reaction fronts in this system. If the vortices oscillates laterally, reaction fronts typically mode-lock to the external forcing. If the vortices drift with constant velocity, fronts typically pin to the leading vortex, remaining motionless in a reference frame that drifts with the vortices. Experiments with the oscillatory BZ reaction are used to study synchronization of a network of oscillators by chaotic mixing. We find that the system is globally-synchronized only if the long-range transport is superdiffusive, characterized by Levy flight trajectories. Time-permitting, we will also present results of experiments on chemical fronts and patterns in a two-dimensional array of vortices.

## Brenton D. Hoffman : Assessing the Effects of Protein Load on Protein Function in Living Cells

- Nonlinear and Complex Systems ( 194 Views )Cells exist in a complex mechanical environment that is both a source of applied forces and a means of mechanical support. An incomplete understanding of the mechanisms cells use to detect mechanical stimuli, a process termed mechanotransduction, is currently preventing advances in tissue engineering and hindering the understanding of several mechanosensitive disease states. Mechanical stimuli are sensed at focal adhesions (FAs), complex dynamic structures comprised of several hundred types of proteins that mediate physical connections between the extracellular matrix and the cytoskeleton. Detection of mechanical cues is thought to be mediated by mechanically-induced changes in protein structure, which, in elegant in vitro single molecule experiments, have been shown to induce new biochemical functions, such as changes in binding affinity as well as the formation of distinct protein-protein interactions. However, the existence and role of these mechanically-induced changes in protein function in living cells are not well understood. To enable the visualization of protein loading, we create Forster Resonance Energy Transfer (FRET)-based tension sensors that emit different colors of light in response to applied forces. The next step in the development of this technology is the use of these sensors to study the effects of mechanical loading on protein functions in living cells. To begin this process, we have refined two commonly used and powerful approaches, Fluorescence Recovery After Photobleaching (FRAP) and fluorescence co-localization to be compatible with FRET-based tension sensors. Initial efforts have focused on the mechanical linker protein vinculin due to its established role in regulating the response of FAs to mechanical loading. These novel techniques reveal that force affects both vinculin turnover as well as its ability to form distinct protein-protein interactions. Further use of these techniques should enable a wide variety of studies in mechanobiology involving different load-bearing proteins, subcellular structures, extracellular contexts, and cellular functions.

## 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.

## Mary Cummings : Modeling humans in complex sociotechnical systems

- Nonlinear and Complex Systems ( 190 Views )Developing descriptive and predictive models of human behavior and decision making in complex sociotechnical systems is critical for system design and evaluation. However, developing such models is difficult due to individual variability, brittle assumptions, and the need to often integrate qualitative and quantitative data. This talk will discuss various human-systems modeling techniques developed in the Humans and Autonomy Laboratory.

## 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.

## Emanuela Del Gado : Gelation and densification of cement hydrates: a soft matter in construction

- Nonlinear and Complex Systems ( 187 Views )5-8 % of the global human CO2 production comes from the production of
cement, concrete main binder. The material strength emerges through the
development, once in contact with water, of calcium-silicate-hydrate (C-S-H)
gels that literally glue together the final compound. Current industrial
research aims at exploring alternative and more environmentally friendly
chemical compositions while enhancing rheology and mechanics, to overcome
the many technological challenges and guarantee concrete standards.
Identifying the fundamental mechanisms that control the gel properties at
the early stages of hydration and setting is crucial, although challenging,
because of far-from-equilibrium conditions, closely intertwined to the
evolution of the chemical environment, that are a hallmark of cement
hydration.

I will discuss a recently developed statistical physics approach, which
allows us to investigate the gel formation under the out-of-equilibrium
conditions typical of cement hydration and the role of the nano-scale
structure in C-S-H mechanics upon hardening. Our approach, combining Monte
Carlo and Molecular Dynamics simulations, unveils for the first time how
some distinctive features of the kinetics of cement hydration can be related
to the nano-scale effective interactions and to the changes in the
morphology of the gels. The novel emerging picture is that the changes of
the physico-chemical environment, which dictate the evolution of the
effective interactions, specifically favor the gel formation and its
continuous densification. Our findings provide new handles to design
properties of this complex material and an extensive comparison of numerical
findings for the hardened paste with experiments ranging from SANS, SEM,
adsorption/desorption of N2 and water to nano-indentation provide new,
fundamental insights into the microscopic origin of the properties measured.

K. Ioannidou, R.J.-M. Pellenq and E. Del Gado Controlling local packing and
growth in calcium-silicate-hydrate gels

E. Del Gado, K. Ioannidou, E. Masoero, A. Baronnet, R. J.-M. Pellenq, F. J.
Ulm and S. Yip, A soft matter in construction - Statistical physics approachfor formation and mechanics of C--S--H gels in cement,

K. Ioannidou, K.J. Krakowiak, M. Bauchy, C.G. Hoover, E. Masoero, S. Yip,
F.-J. Ulm, P. Levitz, R.J.-M. Pellenq and E. Del Gado, The mesoscale textureof cement hydrates

K. Ioannidou, M. Kanduc, L. Li, D. Frenkel, J. Dobnikar and E. Del Gado,
The crucial effect of early-stage gelation on the mechanical properties of
cement hydrates , under review

## David Weitz : Controlling Cell Stiffness

- Nonlinear and Complex Systems ( 184 Views )The stiffness of cells is commonly assumed to depend on the stiffness of their surrounding: bone cells are much stiffer than neurons, and each exists in surrounding tissue that matches the cell stiffness. In this talk, I will discuss new measurements of cell stiffness, and show that that cell stiffness is strongly correlated to cell volume. This affects both the mechanics and the gene expression in the cell, and even impacts on the differentiation of stem cells.

## Sho Yaida : Glassy slowdown and amorphous order

- Nonlinear and Complex Systems ( 182 Views )Upon approaching the glass transition a liquid gets extremely sluggish without obvious structural changes. Despite decades of work, the physical origin of this glassy slowdown remains controversial. A common explanation relies on the increasing roughness of the underlying free-energy landscape, but the theoretical and experimental underpinnings of this scenario are still lacking. In this talk, I will survey recent advances that let us unambiguously identify and track the growing amorphous order, a manifestation of the rarefaction of metastable states in the rugged landscape. I will further explore the crucial role this order plays in driving the glassy slowdown.

## 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.

## Andrew D Bragg : Lagrangian irreversibility and inversions in 3 and 2 dimensional turbulence

- Nonlinear and Complex Systems ( 181 Views )Studying how small inertial particles suspended in turbulent flows
move relative to each other provides fundamental insights into their
transport, mixing and collisions. These insights are crucial for
tackling diverse problems ranging from droplet growth in warm clouds,
to planetesimal formation through collisional aggregation in turbulent
protoplanetary nebula. A deeper understanding of the relative motion
of the particles can be obtained by investigating both their
forward-in-time (FIT) and backward-in-time (BIT) dispersion. When FIT
and BIT dispersion are different it signifies irreversibility, and
since FIT and BIT dispersion are related to different problems,
understanding the irreversibility is of fundamental and practical
importance.

I will present new theoretical arguments and asymptotic predictions,
along with results from Direct Numerical Simulations (DNS) of the
governing equations, to show that inertial particle dispersion can be
very strongly irreversible in turbulence, with BIT being much faster
than FIT dispersion in 3-dimensional turbulence. The results also show
that inertial particles can disperse much faster than fluid
(interialess) particles. I will also present arguments, confirmed by
DNS results, that in 2-dimensional turbulence the nature of the
irreversibility and the direction of the particle energy fluxes can
invert when the particle inertia exceeds a certain threshold. These
results significantly advance our understanding of dispersion
problems, and lead to new capabilities for predicting the effect of
inertia on the rate at which particles spread out and mix together in
turbulence, and the rate at which they collide.

## Changhui Tan : Self-organized dynamics: aggregation and flocking

- Nonlinear and Complex Systems ( 181 Views )Self-organized behaviors are commonly observed in nature and human societies, such as bird flocks, fish swarms and human crowds. In this talk, I will present some celebrated mathematical models, with simple small-scale interactions which lead to the emergence of global behaviors: aggregation and flocking. I will discuss the models in different scales: from microscopic agent-based dynamics, through kinetic mean-field descriptions, to macroscopic fluid systems. In particular, the macroscopic models can be viewed as compressible Euler equations with nonlocal interactions. I will show some recent results on the global wellposedness theory of the systems, large time behaviors, and interesting connections to some classical equations in fluid mechanics.

## 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.