Mode-coupling theory for mixtures of athermal self-propelled particles

Dense or glassy active matter, as a result of its remarkable resemblance to passive glass-forming materials, is enjoying increasing scientific interest. To better grasp the subtle effect of active motion on the process of vitrification, a number of active mode-coupling theories (MCTs) have recently been developed. These have proven capable of qualitatively predicting important parts of the active glassy phenomenology. However, most efforts so far have only considered single-component materials, and their derivations are arguably more complex than the standard MCT case, which might hinder broader usage. Here we present a detailed derivation of a distinct active MCT for mixtures of athermal self-propelled particles that is more transparent than previously introduced versions. The key insight is that we can follow a similar strategy for our overdamped active system as is typically used for passive underdamped MCT. Interestingly, when only considering one particle species, our theory gives the exact same result as the one obtained in previous work which employed a highly different mode-coupling strategy. Moreover, we assess the quality of the theory and its novel extension to multi-component materials by using it to predict the dynamics of a Kob-Andersen mixture of athermal active Brownian quasi-hard spheres. We demonstrate that our theory is able to capture all qualitative features, most notably the location of the optimum of the dynamics when the persistence length and cage length coincide, for each combination of particle types

Active Glassy Dynamics is Unaffected by the Microscopic Details of Self-Propulsion

Recent years have seen a rapid increase of interest in dense active materials, which, in the disordered state, share striking similarities with conventional passive glass-forming matter. For such passive glassy materials, it is well established (at least in three dimensions) that the details of the microscopic dynamics, e.g., Newtonian or Brownian, do not influence the long-time glassy behavior. Here we investigate whether this still holds true in the non-equilibrium active case by considering two simple and widely used active particle models, i.e., active Ornstein-Uhlenbeck particles (AOUPs) and active Brownian particles (ABPs). In particular, we seek to gain more insight into the role of the self-propulsion mechanism on the glassy dynamics by deriving a mode-coupling theory (MCT) for thermal AOUPs, which can be directly compared to a recently developed MCT for ABPs. Both theories explicitly take into account the active degrees of freedom. We solve the AOUP- and ABP-MCT equations in two dimensions and demonstrate that both models give almost identical results for the intermediate scattering function over a large variety of control parameters (packing fractions, active speeds, and persistence times). We also confirm this theoretical equivalence between the different self-propulsion mechanisms numerically via simulations of a polydisperse mixture of active quasi-hard spheres, thereby establishing that, at least for these model systems, the microscopic details of self-propulsion do not alter the active glassy behavior

Enhanced persistence and collective migration in cooperatively aligning cell clusters

Most cells possess the capacity to locomote. Alone or collectively, this allows them to adapt, to rearrange, and to explore their surroundings. The biophysical characterization of such motile processes, in health and disease, has so far focused mostly on two limiting cases: single-cell motility on the one hand, and the dynamics of confluent tissues such as the epithelium on the other. The in-between regime of clusters, composed of relatively few cells, moving as a coherent unit has received less attention. Such small clusters are, however, deeply relevant in development but also in cancer metastasis. In this work, we use cellular Potts models and analytical active matter theory to understand how the motility of small cell clusters changes with N, the number of cells in the cluster. Modeling and theory reveal our two main findings: Cluster persistence time increases with N while the intrinsic diffusivity decreases with N. We discuss a number of settings in which the motile properties of more complex clusters can be analytically understood, revealing that the focusing effects of small-scale cooperation and cell-cell alignment can overcome the increased bulkiness and internal disorder of multicellular clusters to enhance overall migrational efficacy. We demonstrate this enhancement for small-cluster collective durotaxis, which is shown to proceed more effectively than for single cells. Our results may provide some novel insights into the connection between single-cell and large-scale collective motion and may point the way to the biophysical origins of the enhanced metastatic potential of small tumor cell clusters

Glassy Dynamics in Chiral Fluids

Chiral active matter is enjoying a rapid increase of interest, spurred by the rich variety of asymmetries that can be attained in e.g. the shape or self-propulsion mechanism of active particles. Though this has already led to the observance of so-called chiral crystals, active chiral glasses remain largely unexplored. A possible reason for this could be the naive expectation that interactions dominate the glassy dynamics and the details of the active motion become increasingly less relevant. Here we show that quite the opposite is true by studying the glassy dynamics of interacting chiral active Brownian particles (cABPs). We demonstrate that when our chiral fluid is pushed to glassy conditions, it exhibits highly nontrivial dynamics, especially compared to a standard linear active fluid such as common ABPs. Despite the added complexity, we are still able to present a full rationalization for all identified dynamical regimes. Most notably, we introduce a new 'hammering' mechanism, unique to rapidly spinning particles in high-density conditions, that can fluidize a chiral active solid

Multi-component generalized mode-coupling theory: Predicting dynamics from structure in glassy mixtures

The emergence of glassy dynamics and the glass transition in dense disordered systems is still not fully understood theoretically. Mode-coupling theory (MCT) has shown to be effective in describing some of the non-trivial features of glass formation, but it cannot explain the full glassy phenomenology due to the strong approximations on which it is based. Generalized mode-coupling theory (GMCT) is a hierarchical extension of the theory, which is able to outclass MCT by carefully describing the dynamics of higher order correlations in its generalized framework. Unfortunately, the theory has so far only been developed for single component systems and as a result works poorly for highly polydisperse materials. In this paper, we solve this problem by developing GMCT for multi-component systems. We use it to predict the glassy dynamics of the binary Kob-Andersen Lennard-Jones mixture, as well as its purely repulsive Weeks-Chandler-Andersen analogue. Our results show that each additional level of the GMCT hierarchy gradually improves the predictive power of GMCT beyond its previous limit. This implies that our theory is able to harvest more information from the static correlations, thus being able to better understand the role of attraction in supercooled liquids from a first-principles perspective

Microscopic theory for nonequilibrium correlation functions in dense active fluids

One of the key hallmarks of dense active matter in the liquid, supercooled, and solid phases is so-called equal-time velocity correlations. Crucially, these correlations can emerge spontaneously, i.e., they require no explicit alignment interactions, and therefore represent a generic feature of dense active matter. This indicates that for a meaningful comparison or possible mapping between active and passive liquids one not only needs to understand their structural properties, but also the impact of these velocity correlations. This has already prompted several simulation and theoretical studies, though they are mostly focused on athermal systems and thus overlook the effect of translational diffusion. Here we present a fully microscopic method to calculate nonequilibrium correlations in systems of thermal active Brownian particles (ABPs). We use the integration through transients (ITT) formalism together with (active) mode-coupling theory (MCT) and analytically calculate qualitatively consistent static structure factors and active velocity correlations. We complement our theoretical results with simulations of both thermal and athermal ABPs which exemplify the disruptive role that thermal noise has on velocity correlations

A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics

Memory effects are ubiquitous in a wide variety of complex physical phenomena, ranging from glassy dynamics and metamaterials to climate models. The Generalised Langevin Equation (GLE) provides a rigorous way to describe memory effects via the so-called memory kernel in an integro-differential equation. However, the memory kernel is often unknown, and accurately predicting or measuring it via e.g. a numerical inverse Laplace transform remains a herculean task. Here we describe a novel method using deep neural networks (DNNs) to measure memory kernels from dynamical data. As proof-of-principle, we focus on the notoriously long-lived memory effects of glassy systems, which have proved a major challenge to existing methods. Specifically, we learn a training set generated with the Mode-Coupling Theory (MCT) of hard spheres. Our DNNs are remarkably robust against noise, in contrast to conventional techniques which require ensemble averaging over many independent trajectories. Finally, we demonstrate that a network trained on data generated from analytic theory (hard-sphere MCT) generalises well to data from simulations of a different system (Brownian Weeks-Chandler-Andersen particles). We provide a general pipeline, KernelLearner, for training networks to extract memory kernels from any non-Markovian system described by a GLE. The success of our DNN method applied to glassy systems suggests deep learning can play an important role in the study of dynamical systems that exhibit memory effects

Many-body correlations are non-negligible in both fragile and strong glassformers

It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static two-point correlations as input, yet it cannot capture all of the observed dynamical behavior. Here we go beyond two-point spatial correlation functions by extending MCT systematically to include higher-order static and dynamic correlations. We demonstrate that only adding the static triplet direct correlations already qualitatively changes the predicted glass-transition diagram of binary hard spheres and silica. Moreover, we find a non-trivial competition between static triplet correlations that work to stabilize the glass state, and dynamic higher-order correlations which destabilize it for both materials. We conclude that the conventionally neglected static triplet direct correlations as well as higher-order dynamic correlations are in fact non-negligible in both fragile and strong glassformers.Comment: 2 figures, accepted for publication in Physical Review Letter

Dead or alive: Distinguishing active from passive particles using supervised learning

A longstanding open question in the field of dense disordered matter is how precisely structure and the dynamics are related to each other. With the advent of machine learning, it has become possible to agnostically predict the dynamic propensity of a particle in a dense liquid based on its local structural environment. Thus far, however, these machine learning studies have focused almost exclusively on simple liquids composed of passive particles. Here we consider a mixture of both passive and active (i.e. self-propelled) Brownian particles, with the aim to identify the active particles from minimal local structural information. We find that the established machine learning approaches for passive systems are ineffective for our goal, implying that dynamic propensity and non-equilibrium activity carry a fundamentally different structural signature. To distinguish passive from active particles, we instead develop a pseudo-static machine learning method that uses both local structural order parameters and their averaged fluctuations as input. Our final neural network is able to detect with almost 100% accuracy which particles are active and which ones are not. Hence, our machine learning model can identify distinct dynamical single-particle properties with minimal dynamical information. Ultimately, these efforts might also find relevance in the context of biological active glasses such as confluent cell layers, where subtle changes in the microstructure can hint at pathological changes in cell dynamics