We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing an “index-ordered” update rule, mimicking a scenario in which agents have a distribution of times with which they react to information. This model retains the usual disorder-to-order transition common in flocking models, but we show that it also possesses a second transition, deep in the polar flocking phase, to a state with spatially patterned transverse velocities. We characterize this transition and its sensitivity to finite-size effects using the Binder cumulant, and demonstrate – via direct measurements and by measuring a susceptibility of the phase to particle index permutations – that the stability of this phase is directly tied to a subtle spatial organization of a slow-relaxing index-order field. These results highlight the potential for even seemingly insignificant temporal asymmetries to fundamentally alter the collective behavior of active matter.

A large number of powerful, high-quality, and open-source simulation packages exist to efficiently perform molecular dynamics simulations, and their prevalence has greatly accelerated discoveries across a wide range of scientific domains. These packages typically simulate particles in free (Euclidean) space, with options to specify a variety of boundary conditions. While more exotic, many physical systems are constrained to and interact across curved surfaces, such as organisms moving across the landscape, colloids pinned at curved fluid-fluid interfaces, and layers of epithelial cells forming highly curved tissues. The calculation of distances and the updating of equations of motion in idealized geometries (namely, on surfaces of constant curvature) can be done analytically, but it is much more challenging to efficiently perform molecular-dynamics-like simulations on arbitrarily curved surfaces. This article discusses a simulation framework which combines tools from particle-based simulations with recent work in discrete differential geometry to model particles that interact via geodesic distances and move on an arbitrarily curved surface. We present computational cost estimates for a variety of surface complexities with and without various algorithmic specializations (e.g., restrictions to short-range interaction potentials, or multi-threaded parallelization). Our flexible and extensible framework is set up to easily handle both equilibrium and non-equilibrium dynamics, and will enable researchers to access time- and particle-number-scales previously inaccessible.

Understanding the structural dynamics of many-particle glassy systems remains a key challenge in statistical physics. Over the last decade, glassy dynamics has also been reported in biological tissues, but is far from being understood. It was recently shown that vertex models of dense biological tissue exhibit very atypical, sub-Arrhenius dynamics, and here we ask whether such atypical structural dynamics of vertex models are related to unusual elastic properties. It is known that at zero temperature these models have an elasticity controlled by their underconstrained or isostatic nature, but little is known about how their elasticity varies with temperature. To address this question we investigate the 2D Voronoi model and measure the temperature dependence of the intermediate-time plateau shear modulus and the bulk modulus. We find that unlike in conventional glass formers, these moduli increase monotonically with temperature until the system fluidizes. We further show that the structural relaxation time can be quantitatively linked to the plateau shear modulus G_{p}, i.e. G_{p} modulates the typical energy barrier scale for cell rearrangements. This suggests that the anomalous, structural dynamics of the 2D Voronoi model originates in its unusual elastic properties. Based on our results, we hypothesize that underconstrained systems might more generally give rise to a new class of "ultrastrong" glass formers.

Flocking phase transitions arise in many aligning active soft matter systems, and an interesting question concerns the role of "topological" vs. "metric" interactions on these transitions. While recent theoretical work suggests that the order-disorder transition in these polar aligning models is universally first order, numerical studies have suggested that topological models may instead have a continuous transition. Some recent simulations have found that some variations of topologically interacting flocking agents have a discontinuous transition, but unambiguous observations of phase coexistence using common Voronoi-based alignment remains elusive. In this work, we use a custom GPU-accelerated simulation package to perform million-particle-scale simulations of a Voronoi-Vicsek model in which alignment interactions stem from an XY-like Hamiltonian. By accessing such large systems on appropriately long time scales and in the time-continuous limit, we are able to show a regime of stable phase coexistence between the ordered and disordered phases, confirming the discontinuous nature of this transition in the thermodynamic limit.

Observations of glassy dynamics in dense cellular tissues have inspired a wealth of research modeling their collective behavior. Initial studies of the physical properties of several geometric cell models have highlighted anomalous sub-Arrhenius, or "ultrastrong," scaling of the dynamics with temperature. Here we show that the dynamics in this sub-Arrhenius regime deviate even further from the standard glassforming paradigm, displaying unusual scaling of the viscosity with temperature, a lack of breakdown of the Stokes-Einstein-Sutherland relation, and strongly suppressed dynamical heterogeneities. The dynamics in this regime, despite not possessing these hallmarks of glassy behavior, are also distinct from those of simple liquids at low temperatures. These unusual dynamical behaviors can be tuned by controlling the characteristic cell shape index of the model: decreasing this parameter tunes the model between an anomalous and a standard set of glassforming dynamics. Our results add to the growing evidence that these geometric cell models display universal features distinct from those observed in standard glassformers.

Droplet coalescence is essential in a host of biological and industrial processes, involving complex systems as diverse as cellular aggregates, colloidal suspensions, and polymeric liquids. Classical solutions for the time evolution of coalescing clusters are typically based on tractable limiting physics, such as analytical solutions to the Stokes equation. By combining computational and theoretical analyses, we show that there is an unexplored family of coalescence processes: those governed by highly dissipative coupling to the environment. This leads to new scaling laws characterizing droplet coalescence, as well as new time-invariant parameterizations of the shape evolution of the coalescing system. We demonstrate these effects via particle-based simulations and both continuum and boundary-integral solutions to hydrodynamic equations, which we then understand in the context of a generalized Navier-Stokes-like equation. Our theoretical description of highly frictional coalescence mathematically maps onto Darcy flow in the presence of surface tension effects, opening up exciting avenues of research in applying well-studied fluid dynamical techniques to a broad range of novel systems.

Flocking behavior is observed in biological systems from the cellular to superorganismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase has many qualitative similarities with the spontaneous polar flocking phases predicted by Toner-Tu theory, such as anisotropic giant number fluctuations and nontrivial transverse density correlations, despite the induced nature of the phase and the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. We also find a self-organized global vortex state of the sperm cells, and map out an experimental phase diagram of states of collective motion as a function of cell density and motility statistics. We compare our experiments with a parameter-matched computational model of persistently turning active particles and find that the experimental order-disorder phase boundary as a function of cell density and persistence time can be approximately predicted from measures of single-cell properties. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm.

The properties of tissue interfaces - between separate populations of cells, or between a group of cells and its environment - has attracted intense theoretical, computational, and experimental study. Recent work on shape-based models inspired by dense epithelia have suggested a possible "topological sharpening" effect, by which four-fold vertices spatially coordinated along a cellular interface lead to a cusp-like restoring force acting on cells at the interface, which in turn greatly suppresses interfacial fluctuations. We revisit these interfacial fluctuations, focusing on the distinction between short length scale reduction of interfacial fluctuations and long length scale renormalized surface tension. To do this, we implement a spectrally resolved analysis of fluctuations over extremely long simulation times. This leads to more quantitative information on the topological sharpening effect, in which the degree of sharpening depends on the length scale over which it is measured. We compare our findings with a Brownian bridge model of the interface, and close by analyzing existing experimental data in support of the role of short-length-scale topological sharpening effects in real biological systems.

Flocking phase transitions found in models of polar active matter are paradigmatic examples of active phase transitions in soft matter. An interesting specialization of flocking models concerns a ``topological'' vs ``metric'' choice by which agents are considered to be interacting neighbors. While recent theoretical work suggests that the order-disorder transition in these polar aligning models is universally first order, numerical studies have suggested that topological models may instead have a continuous transition. Some recent simulations have found that some variations of topologically interacting flocking agents have a discontinuous transition, but unambiguous observations of phase coexistence using common Voronoi-based alignment remains elusive. In this work, we use a custom GPU-accelerated simulation package to perform million-particle-scale simulations of these Voronoi-Vicsek flocking models. By accessing such large systems on appropriately long time scales, we are able to show that a regime of stable phase coexistence between the ordered and disordered phases, confirming the discontinuous nature of this transition in the thermodynamic limit.

We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.

In development and homeostasis, multi-cellular systems exhibit spatial and temporal heterogeneity in their biochemical and mechanical properties. Nevertheless, it remains unclear how spatiotemporally heterogeneous forces affect the dynamical and mechanical properties of confluent tissue. To address this question, we study the dynamical behavior of the two-dimensional cellular vertex model for epithelial monolayers in the presence of fluctuating cell-cell interfacial tensions, which is a biologically relevant source of mechanical spatiotemporal heterogeneity. In particular, we investigate the effects of the amplitude and persistence time of fluctuating tension on the tissue dynamics. We unexpectedly find that the long-time diffusion constant describing cell rearrangements depends non-monotonically on the persistence time, while it increases monotonically as the amplitude increases. Our analysis indicates that at low and intermediate persistence times tension fluctuations drive motion of vertices and promote cell rearrangements, while at the highest persistence times the tension in the network evolves so slowly that rearrangements become rare.

Many models of flocking involve alignment rules based on the mean orientation of neighboring particles, which we show introduces microscopic non-reciprocal interactions. In the absence of this microscopic non-reciprocity an exceptional phase transition is predicted at low noise strength within the Toner-Tu framework of polar aligning matter; we demonstrate this transition via large-scale numerical simulations. By coarse-graining the microscopic non-reciprocal forces found in more common models of flocking, we identify additional terms in a hydrodynamic description which lead to a highly ordered clustered phase in metric models and restore the homogeneous flocking phase in topological models.

Data-driven approaches to inferring the local structures responsible for plasticity in amorphous materials have made substantial contributions to our understanding of the failure, flow, and rearrangement dynamics of supercooled fluids. Some of these methods, such as the “softness” approach based on linear support vector machines, have identified combinations of local structural features of a supercooled particle's environment that predict energy barriers associated with particle rearrangements. This approach also predicts the onset temperature, often characterized as the temperature below which the system's dynamics becomes non-Arrhenius and above which local structures are no longer predictive of dynamical activity. We implement a transfer-learning approach in which we first show that classifiers can be trained to predict dynamical activity even far above the onset temperature. We then show that applying these classifiers to data from the supercooled phase recovers essentially the same physical information about the relationship between local structures and energy barriers that softness does.

The Voronoi model is a popular tool for studying confluent living tissues. It exhibits an anomalous glassy behavior even at very low temperatures or weak active self-propulsion, and at zero temperature the model exhibits a disordered solid structure with no evidence of a rigidity transition. Here we investigate the properties of the energy landscape in this limit. We find two disordered solid phases that have similar structural features but that differ in the ultrametricity of their energy landscapes; the crossover between these two states shares phenomenological properties with a Gardner transition. We further highlight how the metric used to calculate distances between configurations influences the ability to detect hierarchical arrangements of basins in the energy landscape.

It is common in the study of a dizzying array of soft matter systems to perform agent-based simulations of particles interacting via conservative and often short-ranged forces. In this context, well-established algorithms for efficiently computing the set of pairs of interacting particles have established excellent open-source packages to efficiently simulate large systems over long time scales – a crucial consideration given the separation in time- and length-scales often observed in soft matter. What happens, though, when we think more broadly about what it means to construct a neighbor list? What if interactions are non-reciprocal, or if the "range" of an interaction is determined not by a distance scale but according to some other consideration? As the field of soft and active matter increasingly considers the properties of living matter – from the cellular to the super-organismal scale – these questions become increasingly relevant, and encourage us to think about new physical and computational paradigms in the modeling of active matter. In this chapter we examine case studies in the use of non-metric interactions.

Tissue, cell, and nucleus morphology change during tumor progression. In 2D confluent cell cultures, different tissue states, such as fluid (unjammed) and solid (jammed), are correlated with cell shapes. These results do not have to apply a priori to three dimensions. Cancer cell motility requires and corresponds to a fluidization of the tumor tissue on the bulk level. Here, we investigate bulk tissue fluidity in 3D and determine how it correlates with cell and nucleus shape. In patient samples of mamma and cervix carcinoma, we find areas where cells can move or are immobile. We compare 3D cell spheroids composed of cells from a cancerous and a noncancerous cell line. Through bulk mechanical spheroid-fusion experiments and single live-cell tracking, we show that the cancerous sample is fluidized by active cells moving through the tissue. The healthy, epithelial sample with immobile cells behaves more solidlike. 3D segmentations of the samples show that the degree of tissue fluidity correlates with elongated cell and nucleus shapes. This correlation links cell shapes to cell motility and bulk mechanical behavior. We find two active states of matter in solid tumors: an amorphous glasslike state with characteristics of 3D cell jamming and a disordered fluid state. Individual cell and nucleus shape may serve as a marker for metastatic potential to foster personalized cancer treatment.

Machine learning techniques have been used to quantify the relationship between local structural features and variations in local dynamical activity in disordered glass-forming materials. To date these methods have been applied to an array of standard (Arrhenius and super-Arrhenius) glass formers, where work on "soft spots" indicates a connection between the linear vibrational response of a configuration and the energy barriers to non-linear deformations. Here we study the Voronoi model, which takes its inspiration from dense epithelial monolayers and which displays anomalous, sub-Arrhenius scaling of its dynamical relaxation time with decreasing temperature. Despite these differences, we find that the likelihood of rearrangements can nevertheless vary by several orders of magnitude within the model tissue and extract a local structural quantity, "softness," that accurately predicts the temperature dependence of the relaxation time. We use an information-theoretic measure to quantify the extent to which softness determines impending topological rearrangements; we find that softness captures nearly all of the information about rearrangements that is obtainable from structure, and that this information is large in the solid phase of the model and decreases rapidly as state variables are varied into the fluid phase.