## 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.

## 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.

## 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.

## 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.

## 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.

## Farhang Radjai : Fabric and force anisotropy in cohesive granular materials

- Nonlinear and Complex Systems ( 179 Views )The cohesive strength of granular materials is a consequence of either cohesive bonding (capillary bridging, van der Waals forces) between the grains or the action of a binding solid or liquid material in the pore space. I first discuss the constitutive framework of the plastic behavior of granular materials with internal variables pertaining to the granular fabric. Then, I show how cohesive granular systems can be simulated by different methods accounting for capillary or solid bonding and in the presence of a binding solid or liquid. Finally, I focus on two issues: (1) How does local granular disorder affects the scale-up of cohesive interactions? (2) What are the respective roles of adhesion and volume fraction in the case of binding materials?

## Shane Ross : Geometric and probabilistic descriptions of chaotic phase space transport

- Nonlinear and Complex Systems ( 178 Views )Several geometric and probabilistic methods for studying chaotic phase space transport have been developed and fruitfully applied to diverse areas from orbital mechanics to fluid mechanics and beyond. Increasingly, systems of interest are determined not by analytically defined model systems, but by data from experiments or large-scale simulations. This emphasis on real-world systems sharpens our focus on those features of phase space transport in finite-time systems which seem robust, leading to the consideration of not only invariant manifolds and invariant manifold-like objects, but also their connection with concepts such as symbolic dynamics, chaos, coherent sets, and optimal control. We will highlight some recent applications to areas such as spacecraft trajectories, microfluidic mixing, ship capsize prediction, and biological invasions.

## Patrick Charbonneau : Glass transition and random close packing in 3+ dimensions

- Nonlinear and Complex Systems ( 162 Views )Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode- coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimension.

## Hugo L. D. de S. Cavalcante : Digital Chaotic Circuits: part II - Characterization and Application

- Nonlinear and Complex Systems ( 162 Views )We discuss the characterization of chaos displayed by continuous time digital circuits, both numerically and experimentally. Continuous models for physical systems with switch-like behavior are used to simulate those circuits and their coupling. The effect of perturbations in the coupling and synchronization is also studied experimentally and numerically.

## Heinrich M. Jaeger : Granular Fluids: Liquids with Vanishing Surface Tension?

- Nonlinear and Complex Systems ( 151 Views )Qualitatively new behavior often emerges when large numbers of similar entities are interacting at high densities, no matter how simple the individual components. One prototypical example is granular matter such as fine dry sand, where individual grains are solids. In this talk I will discuss several striking phenomena, including the formation of jets and their break-up into droplets, where large ensembles of grains behave very much like a liquid, except that they do so without apparent surface tension.

## Lawrence Virgin : Identifying chaos using spectral content

- Nonlinear and Complex Systems ( 117 Views )The characterization of chaos as a random-like response from a deterministic dynamical system with an extreme sensitivity to initial conditions is well-established, and has provided a stimulus to research in nonlinear dynamical systems in general. In a formal sense, the computation of the Lyapunov Exponent (LE) spectrum establishes a quantitative measure, with
at least one positive LE (and generally bounded motion) indicating a local exponential divergence of adjacent trajectories. Other measures are associated with certain geometric features of a chaotic attractor, e.g., the fractal dimension, and broadband frequency content. However, although the extraction of LE's can be accomplished with (necessarily noisy) experimental data, this is still a relatively data-intensive, sensitive (and frustrating) endeavor.

We present here an alternative, pragmatic approach to identifying chaos as a function of system parameters, based on frequency content and extending the concept of the spectrogram. This talk will describe this approach applied to systems of increasing complexity, ranging from direct numerical simulations of familiar archetypal systems like Lorenz and the pendulum to experimental data generated from mechanical systems. The accuracy and utility of the approach, including the effect of noise, is tested relative to the standard (LE) approach.

## Chuan-Hua Chen : Harnessing Surface Energy for Thermal Rectification and Resistive Sensing

- Nonlinear and Complex Systems ( 116 Views )Surface energy can be harnessed to introduce new features essential to a variety of engineering systems, such as large-area scalability for phase-change thermal diodes and non-clogging apertures for resistive Coulter counting. In the first case, surface energy drives dropwise condensate to spontaneously jump on a superhydrophobic surface, and the self-propelled motion is exploited to create a planar and orientation-independent thermal diode. In the second case, surface tension is manipulated electrohydrodynamically to produce a cone-jet liquid bridge, which serves as a tunable and deformable aperture for resistive pulse sensing. This presentation will cover both fundamental interfacial phenomena and practical engineering applications.

## Karin Dahmen : Unifying theory for tuned-critical quake statistics: from compressed nanopillars to earthquakes

- Nonlinear and Complex Systems ( 103 Views )The deformation of many solid and granular materials is not continuous, but discrete, with intermittent slips similar to earthquakes. A simple model suggests that the statistical distributions of the slips, such as the slip-size distributions, reflect tuned criticality, with approximately the same regular (power-law) functions, and the same tunable exponential cutoffs, for systems spanning 13 decades in length, from tens of nanometers to hundreds of kilometers; for compressed nano-crystals, amorphous materials, possibly sheared granular materials, lab-sized rocks, and earthquakes. The similarities are explained by a simple analytic model, which suggests that results are transferable across scales. This study provides a unified understanding of fundamental properties of shear-induced deformation in systems ranging from nanocrystals to earthquakes. It also provides many new predictions for future experiments and simulations. The studies draw on methods from the theory of phase transitions, the renormalization group, and numerical simulations. Connections to other systems with avalanches, such as magnets and neuron firing avalanches in the brain are also discussed.