Bringing Together Two Paradigms of Nonequilibrium: Fragile versus Robust Aging in Driven Glassy Systems.

There are two key paradigms for nonequilibrium dynamics: on the one hand, aging toward an equilibrium state that cannot be reached on reasonable timescales; on the other, external driving that can lead to nonequilibrium steady states. We explore how these two mechanisms interact by studying the behavior of trap models, which are paradigmatic descriptions of slow glassy dynamics, when driven by trajectory bias toward high or low activity. To diagnose whether the driven systems continue to age, we establish a framework for mapping the biased dynamics to a Markovian time evolution with time-dependent transition rates.

Ductile and brittle yielding of athermal amorphous solids: A mean-field paradigm beyond the random-field Ising model.

Amorphous solids can yield in either a ductile or brittle manner under strain: plastic deformation can set in gradually, or abruptly through a macroscopic stress drop. Developing a unified theory describing both ductile and brittle yielding constitutes a fundamental challenge of nonequilibrium statistical physics. Recently, it has been proposed that, in the absence of thermal effects, the nature of the yielding transition is controlled by physics akin to that of the quasistatically driven random field Ising model (RFIM), which has served as the paradigm for understanding the effect of quenched disorder in slowly driven systems with short-ranged interactions.

Robustness of traveling states in generic nonreciprocal mixtures.

Emergent nonreciprocal interactions violating Newton's third law are widespread in out-of-equilibrium systems. Phase separating mixtures with such interactions exhibit traveling states with no equilibrium counterpart. Using extensive Brownian dynamics simulations, we investigate the existence and stability of such traveling states in a generic nonreciprocal particle system.

Thawed matrix method for computing local mechanical properties of amorphous solids.

We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly penalizes large nonaffine displacements. With increasing strength of the field, plastic deformation can be localized.

Non-reciprocity across scales in active mixtures.

In active matter, particles typically experience mediated interactions, which are not constrained by Newton's third law and are therefore generically non-reciprocal. Non-reciprocity leads to a rich set of emerging behaviors that are hard to account for starting from the microscopic scale, due to the absence of a generic theoretical framework out of equilibrium. Here we consider bacterial mixtures that interact via mediated, non-reciprocal interactions (NRI) like quorum-sensing and chemotaxis.

Composition Dependent Instabilities in Mixtures with Many Components.

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study phase ordering instabilities in a paradigmatic model that represents the complexity of-e.g.

Nonequilibrium mixture dynamics: A model for mobilities and its consequences.

Extending the famous model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples different mixture components. This approach is based on a single component fluid with particles that are artificially grouped into separate species labeled by "colors." The resulting mobility matrix depends on a single dimensionless parameter, which can be determined efficiently from experimental data or numerical simulations, and includes existing standard forms as special cases.

Intermittent relaxation and avalanches in extremely persistent active matter.

We use numerical simulations to study the dynamics of dense assemblies of self-propelled particles in the limit of extremely large, but finite, persistence times. In this limit, the system evolves intermittently between mechanical equilibria where active forces balance interparticle interactions. We develop an efficient numerical strategy allowing us to resolve the statistical properties of elastic and plastic relaxation events caused by activity-driven fluctuations.

Exponential increase of transition rates in metastable systems driven by non-Gaussian noise.

Noise-induced escape from metastable states governs a plethora of transition phenomena in physics, chemistry, and biology. While the escape problem in the presence of thermal Gaussian noise has been well understood since the seminal works of Arrhenius and Kramers, many systems, in particular living ones, are effectively driven by non-Gaussian noise for which the conventional theory does not apply. Here we present a theoretical framework based on path integrals that allows the calculation of both escape rates and optimal escape paths for a generic class of non-Gaussian noises.

Robust prediction of force chains in jammed solids using graph neural networks.

Force chains are quasi-linear self-organised structures carrying large stresses and are ubiquitous in jammed amorphous materials like granular materials, foams or even cell assemblies. Predicting where they will form upon deformation is crucial to describe the properties of such materials, but remains an open question. Here we demonstrate that graph neural networks (GNN) can accurately predict the location of force chains in both frictionless and frictional materials from the undeformed structure, without any additional information.

Localization properties of the sparse Barrat-Mézard trap model.

Inspired by works on the Anderson model on sparse graphs, we devise a method to analyze the localization properties of sparse systems that may be solved using cavity theory. We apply this method to study the properties of the eigenvectors of the master operator of the sparse Barrat-Mézard trap model, with an emphasis on the extended phase. As probes for localization, we consider the inverse participation ratio and the correlation volume, both dependent on the distribution of the diagonal elements of the resolvent.

Mean-Field Theory of Yielding under Oscillatory Shear.

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behavior of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a nontrivial, nonmonotonic approach to the yielded state.

Delayed elastic contributions to the viscoelastic response of foams.

We show that the slow viscoelastic response of a foam is that of a power-law fluid with a terminal relaxation. Investigations of the foam mechanics in creep and recovery tests reveal that the power-law contribution is fully reversible, indicative of a delayed elastic response. We demonstrate how this contribution fully accounts for the non-Maxwellian features observed in all tests, probing the linear mechanical response function.

Diversity of self-propulsion speeds reduces motility-induced clustering in confined active matter.

Self-propelled swimmers such as bacteria agglomerate into clusters as a result of their persistent motion. In 1D, those clusters do not coalesce macroscopically and the stationary cluster size distribution (CSD) takes an exponential form. We develop a minimal lattice model for active particles in narrow channels to study how clustering is affected by the interplay between self-propulsion speed diversity and confinement.

Shear-induced orientational ordering in an active glass former.

Dense assemblies of self-propelled particles that can form solid-like states also known as active or living glasses are abundant around us, covering a broad range of length scales and timescales: from the cytoplasm to tissues, from bacterial biofilms to vehicular traffic jams, and from Janus colloids to animal herds. Being structurally disordered as well as strongly out of equilibrium, these systems show fascinating dynamical and mechanical properties. Using extensive molecular dynamics simulation and a number of distinct dynamical and mechanical order parameters, we differentiate three dynamical steady states in a sheared model active glassy system: 1) a disordered state, 2) a propulsion-induced ordered state, and 3) a shear-induced ordered state.

Fragmentation in trader preferences among multiple markets: market coexistence versus single market dominance.

Technological advancement has led to an increase in the number and type of trading venues and a diversification of goods traded. These changes have re-emphasized the importance of understanding the effects of market competition: does proliferation of trading venues and increased competition lead to dominance of a single market or coexistence of multiple markets? In this paper, we address these questions in a stylized model of zero-intelligence traders who make repeated decisions at which of three available markets to trade. We analyse the model numerically and analytically and find that the traders' decision parameters-memory length and how strongly decisions are based on past success-make the key difference between consolidated and fragmented steady states of the population of traders.

How to study a persistent active glassy system.

We explore glassy dynamics of dense assemblies of soft particles that are self-propelled by active forces. These forces have a fixed amplitude and a propulsion direction that varies on a timescale, the persistence timescale. Numerical simulations of such active glasses are computationally challenging when the dynamics is governed by large persistence times.

Precision of tissue patterning is controlled by dynamical properties of gene regulatory networks.

During development, gene regulatory networks allocate cell fates by partitioning tissues into spatially organised domains of gene expression. How the sharp boundaries that delineate these gene expression patterns arise, despite the stochasticity associated with gene regulation, is poorly understood. We show, in the vertebrate neural tube, using perturbations of coding and regulatory regions, that the structure of the regulatory network contributes to boundary precision.

Active mixtures in a narrow channel: motility diversity changes cluster sizes.

The persistent motion of bacteria produces clusters with a stationary cluster size distribution (CSD). Here we develop a minimal model for bacteria in a narrow channel to assess the relative importance of motility diversity (i.e.

Coarse graining of biochemical systems described by discrete stochastic dynamics.

Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and all steady-state fluxes except the one between the merged states.

Multiple Types of Aging in Active Glasses.

Recent experiments and simulations have revealed glassy features in, e.g., cytoplasm, living tissues and dense assemblies of self-propelled colloids.

Tractable nonlinear memory functions as a tool to capture and explain dynamical behaviors.

Mathematical approaches from dynamical systems theory are used in a range of fields. This includes biology where they are used to describe processes such as protein-protein interaction and gene regulatory networks. As such networks increase in size and complexity, detailed dynamical models become cumbersome, making them difficult to explore and decipher.

Systematic model reduction captures the dynamics of extrinsic noise in biochemical subnetworks.

We consider the general problem of describing the dynamics of subnetworks of larger biochemical reaction networks, e.g., protein interaction networks involving complex formation and dissociation reactions.

Nucleation Theory for Yielding of Nearly Defect-Free Crystals: Understanding Rate Dependent Yield Points.

Experiments and simulations show that when an initially defect-free rigid crystal is subjected to deformation at a constant rate, irreversible plastic flow commences at the so-called yield point. The yield point is a weak function of the deformation rate, which is usually expressed as a power law with an extremely small nonuniversal exponent. We reanalyze a representative set of published data on nanometer sized, mostly defect-free Cu, Ni, and Au crystals in light of a recently proposed theory of yielding based on nucleation of stable stress-free regions inside the metastable rigid solid.

Exploring the link between crystal defects and nonaffine displacement fluctuations.

We generalize and then use a recently introduced formalism to study thermal fluctuations of atomic displacements in several two- and three-dimensional crystals. We study both close-packed and open crystals with multiatom bases. Atomic displacement fluctuations in a solid, once coarse grained over some neighborhood, may be decomposed into two mutually orthogonal components.