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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., Comment: 5 pages, 5 figures

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., Comment: 7 pages, 7 figures, many simulations

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., Comment: 10 pages, 4 figures

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., Comment: 9 pages, 7 figures

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., Comment: 12 pages, 7 figures, the whole megillah

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., Comment: Version 2: 11 pages, 9 figures, even more data than before

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., Comment: 9 pages, 9 figures

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.

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., Comment: We have found an important bug in the code used to implement the simulations described in this work. We have fixed the bug but cannot yet verify that the numerical claims made are correct

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.

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., Comment: These are lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter." (http://active-matter.eu)

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., Comment: 13 pages, 7 figures, questions both answered and unanswered

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., Comment: 16 pages, 14 figures

Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity in two-dimensional vertex models confined to the surface of a sphere. By considering shapes of cells defined by perimeters whose magnitude depends on geodesic distances and areas determined by spherical polygons, the critical shape index in such models is affected by the size of the cell relative to the radius of the sphere on which it is embedded. This implies that cells can collectively rigidify by growing the size of the sphere, i.e. by tuning the curvature of their domain. Finite-temperature studies indicate that cell motility is affected well away from the zero-temperature transition point., Comment: 8 pages, 4 figures, fun numerical results

Numerical modeling of nematic liquid crystals using the tensorial Landau-de Gennes (LdG) theory provides detailed insights into the structure and energetics of the enormous variety of possible topological defect configurations that may arise when the liquid crystal is in contact with colloidal inclusions or structured boundaries. However, these methods can be computationally expensive, making it challenging to predict (meta)stable configurations involving several colloidal particles, and they are often restricted to system sizes well below the experimental scale. Here we present an open-source software package that exploits the embarrassingly parallel structure of the lattice discretization of the LdG approach. Our implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate simulations using both CPU and GPU resources in either single- or multiple-core configurations. We make use of an efficient minimization algorithm, the Fast Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale parallelization, requiring little additional memory or computational cost while offering performance competitive with other commonly used methods. In multi-core operation we are able to scale simulations up to supra-micron length scales of experimental relevance, and in single-core operation the simulation package includes a user-friendly GUI environment for rapid prototyping of interfacial features and the multifarious defect states they can promote. To demonstrate this software package, we examine in detail the competition between curvilinear disclinations and point-like hedgehog defects as size scale, material properties, and geometric features are varied. We also study the effects of an interface patterned with an array of topological point-defects., Comment: 16 pages, 6 figures, 1 youtube link. The full catastrophe

Recent work on particle-based models of tissues has suggested that any finite rate of cell division and cell death is sufficient to fluidize an epithelial tissue. At the same time, experimental evidence has indicated the existence of glassy dynamics in some epithelial layers despite continued cell cycling. To address this discrepancy, we quantify the role of cell birth and death on glassy states in confluent tissues using simulations of an active vertex model that includes cell motility, cell division, and cell death. Our simulation data is consistent with a simple ansatz in which the rate of cell-life cycling and the rate of relaxation of the tissue in the absence of cell cycling contribute independently and additively to the overall rate of cell motion. Specifically, we find that a glass-like regime with caging behavior indicated by subdiffusive cell displacements can be achieved in systems with sufficiently low rates of cell cycling., Comment: Main text (10 pages, 5 figures) and Appendices (7 pages, 7 figures)

Surface tension governed by differential adhesion can drive fluid particle mixtures to sort into separate regions, i.e., demix. Does the same phenomenon occur in confluent biological tissues? We begin to answer this question for epithelial monolayers with a combination of theory via a vertex model and experiments on keratinocyte monolayers. Vertex models are distinct from particle models in that the interactions between the cells are shape-based, as opposed to distance-dependent. We investigate whether a disparity in cell shape or size alone is sufficient to drive demixing in bidisperse vertex model fluid mixtures. Surprisingly, we observe that both types of bidisperse systems robustly mix on large lengthscales. On the other hand, shape disparity generates slight demixing over a few cell diameters, a phenomenon we term micro-demixing. This result can be understood by examining the differential energy barriers for neighbor exchanges (T1 transitions). Experiments with mixtures of wild-type and E-cadherin-deficient keratinocytes on a substrate are consistent with the predicted phenomenon of micro-demixing, which biology may exploit to create subtle patterning. The robustness of mixing at large scales, however, suggests that despite some differences in cell shape and size, progenitor cells can readily mix throughout a developing tissue until acquiring means of recognizing cells of different types., Comment: 32 pages, 17 figures

Purely repulsive active particles spontaneously undergo motility-induced phase separation (MIPS) into condensed and dilute phases. Remarkably, the mechanical tension measured along the interface between these phases is negative. In equilibrium this would imply an unstable interface that wants to expand, but these out-of-equilibrium systems display long-time stability and have intrinsically stiff boundaries. Here, we study this phenomenon in detail using active Brownian particle simulations and a novel frame of reference. By shifting from the global (or laboratory) frame to a local frame that follows the dynamics of the phase boundary, we observe correlations between the local curvature of the interface and the measured value of the tension. Importantly, our analysis reveals the presence of sustained local tangential motion of particles within a surface layer in both the gas and the dense regions. The combined tangential current in the gas and self-shearing of the surface of the dense phase suggest a stiffening interface that redirects particles along itself to heal local fluctuations. These currents restore the otherwise wildly fluctuating interface through an out-of-equilibrium Marangoni effect. We discuss the implications of our observations on phenomenological models of interfacial dynamics., Comment: 10 pages, 9 figures

In order to understand the mechanisms for glassy dynamics in biological tissues and shed light on those in non-biological materials, we study the low-temperature disordered phase of 2D vertex-like models. Recently it has been noted that vertex models have quite unusual behavior in the zero-temperature limit, with rigidity transitions that are controlled by residual stresses and therefore exhibit very different scaling and phenomenology compared to particulate systems. Here we investigate the finite-temperature phase of two-dimensional Voronoi and Vertex models, and show that they have highly unusual, sub-Arrhenius scaling of dynamics with temperature. We connect the anomalous glassy dynamics to features of the potential energy landscape associated with zero-temperature inherent states., Comment: 8 pages, 8 figures

How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the ability of cells to independently regulate adhesivity and tension, together with neighbor-based interaction rules, lets them support strikingly unusual interfaces. In particular, we show that mechanical- and fluctuation-based measurements of the effective surface tension of a cellular aggregate yield different results, leading to mechanically soft interfaces that are nevertheless extremely sharp.

Vertex models are a popular approach to modeling the mechanical and dynamical properties of dense biological tissues, describing the tissue as a network of connected polygons representing the cells. Recently a class of two-dimensional vertex models was shown to exhibit a disordered rigidity transition controlled by the preferred cellular geometry, echoing experimental findings. An attractive variant of these models uses a Voronoi tessellation to describe the cells and endows them with a non-equilibrium model of cellular motility, leading to rich, glassy behavior. This glassy behavior was suggested to be inextricably linked to an underlying jamming transition. We test this conjecture, exploring the low-effective-temperature limit of the Voronoi model by studying cell trajectories from detailed dynamical simulations in combination with rigidity measurements of energy-minimized disordered cell configurations. We find that the zero-temperature limit of this model has no unjamming transition., Comment: 6 pages, 4 figures

Vertex models represent confluent tissue by polygonal or polyhedral tilings of space, with the individual cell interacting via force laws that depend on both the geometry of the cells and the topology of the tessellation. This dependence on the connectivity of the cellular network introduces several complications to performing molecular-dynamics-like simulations of vertex models, and in particular makes parallelizing the simulations difficult. cellGPU addresses this difficulty and lays the foundation for massively parallelized, GPU-based simulations of these models. This article discusses its implementation for a pair of two-dimensional models, and compares the typical performance that can be expected between running cellGPU entirely on the CPU versus its performance when running on a range of commercial and server-grade graphics cards. By implementing the calculation of topological changes and forces on cells in a highly parallelizable fashion, cellGPU enables researchers to simulate time- and length-scales previously inaccessible via existing single-threaded CPU implementations., Comment: 8 pages, 5 figures. Code available at https://gitlab.com/dmsussman/cellGPU

Nanometrically thin glassy films depart strikingly from the behavior of their bulk counterparts. We investigate whether the dynamical differences between bulk and thin film glasses can be understood by differences in local microscopic structure. We employ machine-learning methods that have previously identified strong correlations between local structure and particle rearrangement dynamics in bulk systems. We show that these methods completely fail to detect key aspects of thin-film glassy dynamics. Furthermore, we show that no combination of local structural features drawn from a very general set of two- and multi-point functions is able to distinguish between particles at the center of film and those in intermediate layers where the dynamics are strongly perturbed., Comment: 8 pages, 7 figures

We simulate entangled linear polymers in free-standing thin film geometries where the confining dimension is on the same scale or smaller than the bulk chain dimensions. We compare both film-averaged and layer-resolved, spatially inhomogeneous measures of the polymer structure and entanglement network with theoretical models. We find that these properties are controlled by the ratio of both chain- and entanglement-strand length scales to the film thickness. While the film-averaged entanglement properties can be accurately predicted, we identify outstanding challenges in understanding the spatially resolved character of the heterogeneities in the entanglement network, particularly when the scale of both the entanglement strand and the chain end-to-end vector is comparable to or smaller than the film thickness.

We numerically and analytically analyze the startup continuous shear rheology of heavily entangled rigid rod polymer fluids based on our self-consistent, force-level theory of anharmonic tube confinement. The approach is simplified by neglecting stress-assisted transverse barrier hopping, and irreversible relaxation proceeds solely via deformation-perturbed reptation. This process is self-consistently coupled to tube dilation and macroscopic rheological response. We predict that with increasing strain the tube strongly dilates, entanglements are lost, and reptation speeds up. As a consequence, a stress overshoot emerges not due to affine over-orientation, but rather to strong weakening of the entanglement network. Just beyond the stress overshoot the longest relaxation time is predicted to scale as the inverse shear rate, corresponding to the emergence of a generic form of convective constraint release (CCR). Its origin is a stress-induced local force that self-consistently couples the mesoscopic tube-scale physics with macroscopic mechanical response. Tube weakening at the overshoot occurs via the same qualitative mechanism that leads to microscopic absolute yielding in the nonlinear elastic scenario analyzed in the preceding paper. The stress overshoot and emergent CCR thus correspond to an elastic-viscous crossover due to deformation-induced disentanglement, which at long times and high shear rates results in a quantitatively sensible flow stress plateau and shear thinning behavior. We suggest that the predicted behavior for needles is relevant to flexible chain melts at low Rouse Weissenberg numbers if contour length equilibration is fast. Quantitative predictions for tube dilation in the steady state flow of chains melts are favorably compared to a recent simulation., Comment: 12 pages, 5 figures

We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts that deformation-induced orientation leads to tube dilation. In contrast, for deformed polymers in which chain stretch does not relax we find tube compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome (a force imbalance) by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance is found to occur at a stress of order the equilibrium shear modulus and thus a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments., Comment: 16 pages, 6 figures

States of self stress, organizations of internal forces in many-body systems that are in equilibrium with an absence of external forces, can be thought of as the constitutive building blocks of the elastic response of a material. In overconstrained disordered packings they have a natural mathematical correspondence with the zero-energy vibrational modes in underconstrained systems. While substantial attention in the literature has been paid to diverging length scales associated with zero- and finite-energy vibrational modes in jammed systems, less is known about the spatial structure of the states of self stress. In this work we define a natural way in which a unique state of self stress can be associated with each bond in a disordered spring network derived from a jammed packing, and then investigate the spatial structure of these bond-localized states of self stress. This allows for an understanding of how the elastic properties of a system would change upon changing the strength or even existence of any bond in the system., Comment: 21 pages (single column), 10 figures

Granular matter at the jamming transition is poised on the brink of mechanical stability, and hence it is possible that these random systems have topologically protected surface phonons. Studying two model systems for jammed matter, we find states that exhibit distinct mechanical topological classes, protected surface modes, and ubiquitous Weyl points. The detailed statistics of the boundary modes enable tests of a standard understanding of the detailed features of the jamming transition, and show that parts of this argument are invalid., Comment: 10 pages; 11 figures

When a liquid freezes, a change in the local atomic structure marks the transition to the crystal. When a liquid is cooled to form a glass, however, no noticeable structural change marks the glass transition. Indeed, characteristic features of glassy dynamics that appear below an onset temperature, T_0, are qualitatively captured by mean field theory, which assumes uniform local structure at all temperatures. Even studies of more realistic systems have found only weak correlations between structure and dynamics. This raises the question: is structure important to glassy dynamics in three dimensions? Here, we answer this question affirmatively by using machine learning methods to identify a new field, that we call softness, which characterizes local structure and is strongly correlated with rearrangement dynamics. We find that the onset of glassy dynamics at T_0 is marked by the onset of correlations between softness (i.e. structure) and dynamics. Moreover, we use softness to construct a simple model of slow glassy relaxation that is in excellent agreement with our simulation results, showing that a theory of the evolution of softness in time would constitute a theory of glassy dynamics.

We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to the honeycomb lattice; by arranging these defect pairs properly with respect to each other and choosing an appropriate fold pattern a target stepped surface can be designed. We then present a more general method that specifies a fixed lattice of kirigami cuts to be performed on a flat sheet. This single "pluripotent" lattice of cuts permits a wide variety of target surfaces to be programmed into the sheet by changing the folding directions., Comment: 9 pages, whole megillah

Recently there has been a surge in interest in using video-microscopy techniques to infer the local mechanical properties of disordered solids. One common approach is to minimize the difference between particle vibrational displacements in a local coarse-graining volume and the displacements that would result from a best-fit affine deformation. Effective moduli are then be inferred under the assumption that the components of this best-fit affine deformation tensor have a Boltzmann distribution. In this paper, we combine theoretical arguments with experimental and simulation data to demonstrate that the above does not reveal information about the true elastic moduli of jammed packings and colloidal glasses., Comment: 12 pages, 8 figures

We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale $\omega^*$. This frequency is controlled by $\Delta Z = \langle Z \rangle - 2d$, the difference between the average coordination of the spheres and twice the spatial dimension, $d$, of the system, which vanishes at the jamming transition. In the presence of a free surface we find that there is a density of disordered vibrational modes associated with the surface that extends far below $\omega^*$. The total number of these low-frequency surface modes is controlled by $\Delta Z$, and the profile of their decay into the bulk has two characteristic length scales, which diverge as $\Delta Z^{-1/2}$ and $\Delta Z^{-1}$ as the jamming transition is approached., Comment: 7 pages, 5 figures

In this paper we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extinsically flat away from zero-dimensional sources of Gaussian curvature and one-dimensional sources of mean curvature, and our cutting and pasting rules maintain the intrinsic bond lengths on both the lattice and its dual lattice. We find that a small set of rules is allowed providing a framework for exploring and building kirigami -- folding, cutting, and pasting the edges of paper., Comment: 5 pages, 5 figures

We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot be, in general, translated from one phase to the other., Comment: 5 pages, the full catastrophe