arXiv subjects

Daniel M. Sussman

Publications and source records attributed to Daniel M. Sussman.

At least 19 recordsLinked to original sources

arXiv2026

Conservative yet constitutively odd elasticity in prestressed metamaterials

We introduce a design principle for mechanical metamaterials based on "odd elasticity, once removed." By revisiting classic results relating the variation of Cauchy stress and Lagrangian strain around a prestressed reference state, we show how anisotropic, equilibrium prestress can generate a major anti-symmetry in the material's constitutive response. Tuning the system to such a state drives it to a critical instability, radically transforming its acoustic properties. We demonstrate this by inverse-designing uniform 2D solids that act as unique waveguides supporting decoupled modes along special lattice directions: a string-like mode and an exotic soft mode that is in-plane but has flexural character ($ω\sim q^2$) and exhibits a remarkable "DC" energy current. The magnitude of the anisotropic prestress acts as a control parameter for small-$q$ stability, and, when taken to zero, transforms the string-like mode into another soft mode, giving support for circularly polarized "spin" waves with arbitrary $q$. This principle of harnessing conservative "oddness" to unlock instability-driven wave phenomena provides a powerful new route to creating tunable materials for guiding and controlling mechanical waves.

cond-mat.soft↗

arXiv2026

Universal scaling in the rheology of dense cellular systems

Biological tissues must dynamically transition between rigid and fluid-like states during processes like morphogenesis and collective migration, often while simultaneously resisting physiological shear stresses. It remains unclear whether these tissue dynamics are governed by the same non-equilibrium critical phenomena that control conventional disordered matter. Here we show that model cell monolayers under constant stress display a rich phase diagram of nonlinear rheology. In rigid regimes, small internal fluctuations maintain a solid-like state up to a finite yield stress, above which the tissue shear-thins; conversely, fluid-like regimes exhibit robust continuous and discontinuous shear thickening, culminating in structural arrest via shear jamming. This space-filling shear-jamming transition is accompanied by structural changes including the formation of system-spanning force chains and the emergence of orientational ordering. We demonstrate that the macroscopic viscosity across these disparate regimes is described by universal scaling behavior controlled by the same underlying physical parameters. These results establish confluent tissues as a distinct class of disordered matter, demonstrating that universal jamming phenomena can emerge entirely through shape-driven topological constraints to regulate biological mechanics.

cond-mat.soft↗

arXiv2026

Models of 3D confluent tissue as under-constrained glasses

The dynamics of glassy materials slows down upon cooling, typically showing either Arrhenius or super-Arrhenius behavior. However, it was recently shown that 2D cell-based models for biological tissues can be continuously tuned between Arrhenius and sub-Arrhenius dynamics. In previous work, using the 2D Voronoi model, we proposed that such atypical dynamical behavior could be a generic feature of the broad class of mechanically under-constrained materials. Our earlier study had left two important points open: (1) many 2D systems are affected by long-wavelength fluctuations and the 2D melting scenario, and (2) the 2D Voronoi model sits exactly at the isostatic point, making it a marginal case rather than a strictly under-constrained one. Both points complicate the interpretation of our 2D Voronoi model results and their generalization to other systems; to remedy this, here we use large-scale simulations to study the glassy behavior of the 3D extension of the Voronoi model. We first show that the structural relaxation time $τ_α$ of the 3D Voronoi model can be tuned between sub-Arrhenius and Arrhenius behavior, like the 2D Voronoi model. We then establish that the four-point susceptibility, the structure factor, and the model's mechanical properties all display trends consistent with the 2D Voronoi model. These results provide strong evidence that sub-Arrhenius glassy dynamics are a generic feature of under-constrained materials across dimensions. Our work thus broadens the class of disordered materials known to have highly unusual glassy phenomenology.

cond-mat.soft↗

arXiv2026

Geometric control of motility-induced phase separation

Curvature fundamentally alters the collective properties of soft, active, and biological materials. Here we study motility-induced phase separation (MIPS), a canonical non-equilibrium transition, and demonstrate that even weak and slowly varying curvature provides robust geometric control over the dense MIPS phase. This includes dictating both the location and morphology of the MIPS cluster, even in regimes where the effect on the overall phase boundaries is minimal. Focusing on active Brownian particles confined to the surface of a torus, we show that varying the aspect ratio drives a structural transition of the dense cluster from a disk localized at the outer equator to a band wrapping the minor circumference. We then discuss how the curved geometry provides a platform for comparing different theoretical frameworks for the MIPS phase: by analyzing the geometries of the cluster boundaries, we compare the structures predicted by thermodynamic and kinetic pictures. Our results establish curved space not only as a tool to shape and guide non-equilibrium dynamics, but as a uniquely sensitive arena for probing the fundamental mechanisms of active matter.

cond-mat.soft↗

arXiv2025

Spatially patterned phases in a reaction-time-symmetry-broken model of flocking

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.

cond-mat.soft↗

arXiv2024

Connecting anomalous elasticity and sub-Arrhenius structural dynamics in a cell-based model

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 under-constrained 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 glassformers, 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 under-constrained systems might more generally give rise to a new class of "ultra-strong" glassformers.

cond-mat.soft↗

arXiv2024

Banded phases in topological flocks

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.

cond-mat.soft↗

arXiv2024

Tunable glassy dynamics in models of dense cellular tissue

Observations of glassy dynamics in experiments on confluent cellular tissue have inspired a wealth of computational and theoretical research to model their emergent collective behavior. Initial studies of the physical properties of several geometric cell models, including vertex-type models, have highlighted anomalous sub-Arrhenius, or "ultra-strong," scaling of the dynamics with temperature. Here we show that the dynamics and material properties of the 2d Voronoi model deviate even further from the standard glassforming paradigm. By varying the characteristic shape index $p_0$, we demonstrate that the system properties can be tuned between displaying expected glassforming behavior, including the breakdown of the Stokes-Einstein-Sutherland relation and the formation of dynamical heterogeneities, and an unusual regime in which the viscosity does not diverge as the characteristic relaxation time increase and dynamical heterogeneities are strongly suppressed. Our results provide further insight into the fundamental properties of this class of anomalous glassy materials, and provide a step towards designing materials with predetermined glassy dynamics.

cond-mat.soft↗

arXiv2024

Scale-dependent sharpening of interfacial fluctuations in shape-based models of dense cellular sheets

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.

cond-mat.soft↗

arXiv2024

Self-organized vortex phases and hydrodynamic interactions in Bos taurus sperm cells

Flocking behavior is observed in biological systems from the cellular to super-organismal 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 non-trivial 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 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.

cond-mat.soft↗

arXiv2024

curvedSpaceSim: A framework for simulating particles interacting along geodesics

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.

cond-mat.soft↗

arXiv2024

Coalescing Clusters Unveil New Regimes of Frictional Fluid Mechanics

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.

cond-mat.soft↗

arXiv2023

Non-reciprocal forces and exceptional phase transitions in metric and topological flocks

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.

cond-mat.soft↗

arXiv2023

Does fluid structure encode predictions of glassy dynamics?

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.

cond-mat.soft↗

arXiv2022

Effects of Polydispersity on the Plastic Behaviors of Dense 2D Granular Systems Under Shear

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, 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 the crossover in nonaffine motion from the low- to high-polydispersity regime, and demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes.

cond-mat.soft↗

arXiv2022

Non-monotonic fluidization generated by fluctuating edge tensions in confluent tissues

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.

cond-mat.soft↗

arXiv2021

Non-metric interaction rules in models of active matter

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.

cond-mat.soft↗

arXiv2021

Quantifying the link between local structure and cellular rearrangements using information in models of biological tissues

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 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.

cond-mat.soft↗