## 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.

## 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.

## 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.

## 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.

## 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.

## Roberto Camassa : Spinning rods, microfluidics, and mucus propulsion by cilia in the lung

- Nonlinear and Complex Systems ( 178 Views )Understanding and modeling how human lungs function is in large part based on the hydrodynamics of the mucus fluid layers that coat lung airways. In healthy subjects, the beating of cilia is the primary method of moving mucus. With the aim of establishing a quantitative benchmark of how cilia motion propels the surrounding fluid, we study the idealized situation of one rod spinning in a fluid obeying the Stokes approximation, the appropriate limit for a Newtonian fluid with typical dimensions and time scales of cilia dynamics. New approximate -- for cylindrical rods pinned to a flat plane boundary, and exact -- for ellipsoidal rods freely spinning around their center -- solutions for the fluid motion will be presented and compared with the experimental data collected with spinning magnetic nano-rods in water. In order to assess the influence of Brownian perturbations in this micro-scale experiment, data from an experimental set-up scaled by dynamical similarity to macroscopic (table-top) dimensions will also be presented and compared to the theoretical predictions.

## Patrick Charbonneau : From glass to jamming via a Gardner transition

- Nonlinear and Complex Systems ( 174 Views )The glass problem is notoriously hard, but the recent exact solution of a microscopic model offers a novel perspective on the problem. In this seminar, I will discuss how contrasting entropic caging and isostaticity at the glass and the jamming transitions, respectively, reveals the presence of a Gardner transition. This onset of mechanical marginality then explains the presence of non-trivial critical exponents. I will also discuss how a family of finite-dimensional models reveals the clear role for caging geometry and hopping in the dynamical slowdown of colloid-like glass formers. Both advances greatly enrich the traditional mean-field description of glasses.

## Itai Cohen : Q: How many folded angels can dance on the head of pin? A: 22+/-5

- Nonlinear and Complex Systems ( 169 Views )For centuries, origami, the Japanese art of paper folding, has been a powerful technique for transforming two dimensional sheets into beautiful three dimensional sculptures. Recently, origami has made its foray into a new realm, that of physics and engineering, where it has been revolutionizing our concept of materials design. In this talk I will describe the new design principles we are uncovering for determining the shape, mechanics, and transformations of origami structures along with their usefulness in areas as diverse as solar sail design, architecture, and even fashion. Arguably however, the greatest strength of this new paradigm is the fact that origami is intrinsically scalable. Thus sculptures built at one size can be shrunk down smaller and smaller. This begs the question: what is the smallest fold one can make? Or in other words, how many folded angels can dance on the head of a pin? The rest of this talk will take a deep dive into how origami has been marching smaller and smaller in size. From folding by hand, to self-folding through shape memory alloys and even folding via polymer layers, I will argue that the ultimate limit for scaling down origami is set by folding a sheet of atomic dimensions. I will conclude by showing this vision: realized in the folds of a single sheet of graphene.

## Holger Stark : Active motion: Understanding the nonequilibrium

- Nonlinear and Complex Systems ( 168 Views )Active motion of microorganisms or artificial microswimmers in a fluid at low Reynolds number is an appealing subject which has attracted much attention recently. Since these swimmers move constantly in nonequilibrium, they give rise to novel phenomena which, in particular, occur when external fields are applied or when they move collectively.

The talk reviews three situations where active motion manifests itself. First, a swimmer under Poiseuille flow shows nonlinear dynamics reminiscent of the nonlinear pendulum. Bounding walls introduce "dissipation" [1] and an elliptical crosssection of the microchannel leads to chaotic motion. Secondly, I discuss the collective motion of model swimmers, so-called squirmers, in a quasi 2D geometry by means of multi-particle collision dynamics. This is a particle based method to solve the Navier-Stokes equations and helps to elucidate the role of hydrodynamics in collective phenomena. Indeed, we find gas-like and cluster phases as well as phase separation which is strongly influenced by hydrodynamic near-field interactions and the swimmer type. Thirdly, I discuss dynamic clustering of active or self-propelling colloids that interact by diffusiophoresis reminiscent of chemotaxis in bacterial systems.

[1] A. Zoettl and H. Stark, Phys. Rev. Lett. 108, 218104 (2012).

## 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.

## Sreekanth Pannala : Multiscale/Multiphysics simulation strategy for gas-solids flow reactors

- Nonlinear and Complex Systems ( 154 Views )Gas-solids chemically reacting flows are omnipresent in many multiphase flow reactors in various industries like Chemical, Fossil and Nuclear. The challenging aspect of modeling these reacting flows are the wide range of both temporal and spatial scales encountered in these systems. The challenge is to accurately account and bridge (as seamlessly as possible) the length and time scales involved in the problem. First, the problem is introduced using biomass gasifier/pyrolyser and nuclear fuel coater with sample results as examples and provide an overview of the various models currently used at the different scales. In particular, the critical role of the granular dynamics in the overall performance of the reactors will be highlighted. The ongoing development of a multiphysics and multiscale mathematics framework for coupling various modeling methods over a range of scales will be presented. The development of a general wavelet-based multiscale methodology called compound wavelet matrix (CWM) for bridging spatial and temporal scales will be reported. Finally, the steps needed to generalize the current methodology for arbitrary heterogeneous chemically reacting flows or other applications involving multiscale/multiphysics coupling will be elucidated. The challenges and opportunities of employing these models for rapid deployment of clean energy solutions based on multiphase flow reactors to the market place will be discussed.

## Brian Utter : Jamming in Vibrated Granular Systems

- Nonlinear and Complex Systems ( 129 Views )Granular materials exist all around us, from avalanches in nature to the mixing of pharmaceuticals, yet the behavior of these ``fluids'' is poorly understood. Their flow can be characterized by the continuous forming and breaking of a strong force network resisting flow. This jamming/unjamming behavior is typical of a variety of systems, including granular flows, and is influenced by factors such as grain packing fraction, applied shear stress, and the random kinetic energy of the particles. I'll present experiments on quasi-static shear and free-surface granular flows under the influence of external vibrations. By using photoelastic grains, we are able to measure both particle trajectories and the local force network in these 2D flows. We find through particle tracking that dense granular flow is composed of comparable contributions from the mean flow, affine, and non-affine deformations. During shear, sufficient external vibration weakens the strong force network and reduces the amount of flow driven by sidewalls. In a rotating drum geometry, large vibrations induce failure as might be expected, while small vibration leads to strengthening of the pile. The avalanching behavior is also strongly history dependent, as evident when the rotating drum is driven in an oscillatory motion, and we find that sufficient vibration erases the memory of the pile. These results point to the central role of the mobilization of friction in quasi-static granular flow.

## Joshua Socolar : Hierarchical freezing in a lattice model

- Nonlinear and Complex Systems ( 103 Views )A certain 2D lattice model with nearest and next-nearest neighbor interactions is known to have a nonperiodic ground state. We show that during a slow quench from the high temperature, disordered phase, the ground state emerges through an infinite sequence of phase transitions. We define appropriate order parameters and show that the transitions are related by renormalizations of the temperature scale. As the temperature is decreased, sublattices with increasingly large lattice constants become ordered. A rapid quench results in glass-like state due to kinetic barriers created by simultaneous freezing on sublattices with different lattice constants.