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.

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.

The tracking of small, colloidal particles is a common technique for measuring fluid velocities, highly successful at the micro-scale and recently extended to measurements at nano-scales. The Brownian fluctuations of the colloidal tracers are typically isotropic in the bulk; but in the near-wall region, these fluctuations are strongly affected by the hydrodynamic interaction with the wall and by the no-flux condition imposed there. Such wall effects can, under appropriate conditions, bias particle image velocimetry (PIV) measurements based on colloidal tracers, potentially leading to significant overestimation of near-wall velocities. The quantification of the resulting bias is presented in terms of the size of the imaged region and the measurement interval between PIV images. The effect of the steady state particle distribution is additionally explored, and implications for near-wall velocimetry measurements are briefly discussed.

This talk represents collaborative work with Christel Hohenegger, Minami Yoda, Reza Sadr, and Haifeng Li.

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?

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.

Brains have an impressive ability to store information about the external world on time scales that range from seconds to years. The rules of information storage in neuronal circuits are the subject of ongoing debate. Two scenarios have been proposed by theorists: In the first scenario, specific patterns of activity representing external stimuli become fixed point attractors of the dynamics of the network. In the second, the network stores sequences of patterns of network activity so that when the first pattern is presented the network retrieves the whole sequence. In both scenarios, the correct dynamics are achieved thanks to appropriate changes in network connectivity. I will describe how methods from statistical physics can be used to investigate the storage capacity of such networks, and the statistical properties of network connectivity that optimizes information storage (distribution of synaptic weights, probabilities of specific network motifs, degree distributions, etc) in both scenarios. Finally, I will compare the theoretical results with available data on cortical connectivity.

Diffusion over a network depends crucially on the pattern and timing of relations. This is particularly important for diseases carried over networks with relatively low volume and turnover. Here we explore both aspects using simulation tools. First, we ask how the shape of the distribution of number of partners affects multiple connectivity, and second we measure the exposure potential in dynamic networks across a wide array of structural patterns to identify the influence of "concurrency," the overlap in time of interactions among network nodes. We find that concurrency in low-volume settings has the same effect on epidemic spreading as a structural increase in the average degree. 

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.

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.

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.

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.

A drop translating in the presence of an electric field is studied using a combination of experiments and numerical analysis to determine the underly- ing mechanism that leads to chaotic advection. The flow is a combination of a Hadamard-Rybczynski, and a Taylor circulation due to the translation and electric field, respectively. Two cases for generating chaotic advection by, (i) tilting the electric field relative to the drops translation motion and (ii) time-dependent modulation of the electric field, will be considered. The numerical analysis includes qualitative analysis of the degree of mixing by Poincare mapping and quantitative estimates of the largest percentage of drop volume mixed by a single streamline as well as the rate of mixing by calculating the largest Lyapunov exponent. Experiments are performed using a castor oil/silicone oil system for the continuous and dispersed phases respectively.

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.

Motivated by the dewetting of viscous thin films on hydrophobic substrates, we study models for the coarsening dynamics of interacting localized structures in one dimension. For the thin films problem, lubrication theory yields a Cahn-Hilliard-type governing PDE which describes spinodal dewetting and the subsequent formation of arrays of metastable fluid droplets. The evolution for the masses and positions of the droplets can be reduced to a coarsening dynamical system (CDS) consisting of a set of coupled ODEs and deletion rules. Previous studies have established that the number of drops will follow a statistical scaling law, N(t)=O(t^{-2/5}). We derive a Lifshitz-Slyozov-Wagner-type (LSW) continuous model for the drop size distribution and compare it with discrete models derived from the CDS. Large deviations from self-similar LSW dynamics are examined on short- to moderate-times and are shown to conform to bounds given by Kohn and Otto. Insight can be applied to similar models in image processing and other problems in materials science. Joint work with M.B. Gratton (Northwestern Applied Math).

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.

The problem of reforestation is studied by solving a vegetation model in drylands. The "shikim" water harvesting method is seen as a parametric periodic forcing of a pattern forming system, where the resulting stripes and spots patterns are 1:1 and 2:1 resonant solutions. A modified Swift-Hohenberg equation helps us understand the dynamics of collapse and expansion of patterned states. I conclude by addressing preventive measures that make the vegetation system more resilient to climatic changes, and help avoid catastrophic regime shifts.

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.

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.

The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present new methodologies that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape at multiple resolutions. Recent results and possible applications will be discussed.

Buoyancy-driven flows, which are fluid flows driven by spatial variations of fluid density, play many key roles in the environment. Examples include winds in valleys and over glaciers, mineral transport in rock fissures, and ocean boundary mixing. To date, however, all investigations of buoyancy-driven flow have considered flow induced by a fixed boundary that influences fluid density (e.g. by heating or cooling). We have discovered that buoyancy-driven flows provide a previously unrecognized means of propulsion for freely-floating objects, and we demonstrate this new concept to surprising effect in a series of laboratory experiments.

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.

I will describe two simple models that incorporate only hard-sphere and geometrical constraints, yet provide quantitatively accurate predictions for the structural and mechanical properties of frictional packings of granular media and proteins. We first model static friction between grains by considering nominally spherical particles with periodically spaced asperities on the surface of the grains. This model captures the dependence of the average packing fraction and number of interparticle contacts on the static friction coefficient obtained from experiments, and has significant advantages over other models. Second, in the spirit of the Ramachandran map for the backbone dihedral angles of proteins, we develop a model for nonpolar amino acids that allows us to predict the allowed conformations of sidechain dihedral angles. Our predictions are quantitatively similar to the sidechain dihedral angle distributions obtained from known crystal structures. These two examples emphasize the power of simple physical models, which are able to predict important properties of soft and biological materials.

The immune system normally protects the human host against death by infection. I will introduce a hierarchical spin glass model of the evolutionary dynamics that occurs in the antibody-mediated and T cell-mediated immune responses. The theory will be used to provide a mechanism for original antigenic sin, wherein an initial exposure to antigen degrades the response of the immune system upon subsequent exposure to related, but different, antigens. A new order parameter to characterize antigenic distance will be introduced from the theory. This order parameter predicts effectiveness of the influenza vaccine more reliably than do results from animal model studies currently used by world health authorities. This order parameter would seem to be a valuable new tool for making vaccine-related public health policy decisions. Next, I will note that while the immune system normally protects the human host against death by infection, the method used by the immune system to search sequence space is rather slow --- interestingly there exist biological mechanisms that can find antibodies with higher affinity and also find them more quickly. Thus, one would think that these more powerful evolutionary mechanisms would give an immune system that responds faster and more effectively against disease. So, why didn't we evolve that kind of adaptive response? I will show that the slow glassy dynamics of the immune system serves a functional role of inhibiting the autoimmune diseases that these more powerful searching mechanisms would induce. I will suggest that the controversy related to the correlation between chronic infection and autoimmune disease might be addressed by searching for the broad distribution of onset times for autoimmune disease predicted from the theory.

Despite an enormous range of applications and centuries of scientific study, understanding and predicting the flow of fluids remains a tremendous challenge, particularly when the flow is chaotic or turbulent. Turbulent flows tend to be characterized by violent fluctuations, enormous numbers of strongly coupled degrees of freedom, and significant variability in space and time. But despite all this complexity, turbulence is not random. Rather, it tends to self-organize into striking but transient patterns and features that arise from nonlinear interactions. Some of these "coherent structures," such as strong vortices, are readily apparent; others are more subtle. But how much can we learn or predict about the flow from studying coherent structures? The answer may lie in the energetics of the flow, since these same nonlinearities couple dynamics on different scales and, in turbulence, drive a net transfer of energy from the scales at which it is injected into the flow to the scales at which it is dissipated. To begin to make quantitative links between the nonlinear dynamics of the flow and the spontaneous generation of spatiotemporal order, I will discuss experimental results from a quasi-two-dimensional turbulent flow. Using a filtering technique, we extract the spatially localized scale-to-scale flux of energy, and show that it is linked to suitably defined coherent structures. I will also discuss the self-organization of the turbulent stress that drives this energy transfer.