arXiv subjects

Michael E. Cates

Publications and source records attributed to Michael E. Cates.

At least 55 records · Page 3Linked to original sources

arXiv2022

Orientation-dependent propulsion of active Brownian spheres: from self-advection to programmable cluster shapes

Applications of active particles require a method for controlling their dynamics. While this is typically achieved via direct interventions, indirect interventions based, e.g., on an orientation-dependent self-propulsion speed of the particles, become increasingly popular. In this work, we investigate systems of interacting active Brownian spheres in two spatial dimensions with orientation-dependent propulsion using analytical modeling and Brownian dynamics simulations. It is found that the orientation-dependence leads to self-advection, circulating currents, and programmable cluster shapes.

cond-mat.soft↗

arXiv2022

Entropy production and its large deviations in an active lattice gas

Active systems are characterized by a continuous production of entropy at steady state. We study the statistics of entropy production within a lattice-based model of interacting active particles that is capable of motility-induced phase separation. Exploiting a recent formulation of the exact fluctuating hydrodynamics for this model, we provide analytical results for its entropy production statistics in both typical and atypical (biased) regimes. This complements previous studies of the large deviation statistics of entropy production in off-lattice active particle models that could only be addressed numerically. Our analysis uncovers an unexpectedly intricate phase diagram, with five different phases arising (under bias) within the parameter regime where the unbiased system is in its homogeneous state. Notably, we find the concurrence of first order and second order nonequilibrium phase transition curves at a bias-induced tricritical point, a feature not yet reported in previous studies of active systems.

cond-mat.stat-mech↗

arXiv2022

Rectification in a mixture of active and passive particles subject to a ratchet potential

We study by simulation a mixture of active (run-and-tumble) and passive (Brownian) particles with repulsive exclusion interactions in one dimension, subject to a ratchet (smoothed sawtooth) potential. Such a potential is known to rectify active particles at one-body level, creating a net current in the `easy direction'. This is the direction in which one encounters the lower maximum force en route to the top of a potential barrier. The exclusion constraint results in single-file motion, so the mean velocities of active and passive particles are identical; we study the effects of activity level, Brownian diffusivity, particle size, initial sequence of active and passive particles, and active/passive concentration ratio on this mean velocity (i.e., the current per particle). We show that in some parameter regimes the sign of the current is reversed. This happens when the passive particles are at high temperature and so would cross barriers relatively easily, and without rectification, except that they collide with `cold' active ones, which would otherwise be localized near the potential minima. In this case, the reversed current arises because hot passive particles push cold active ones preferentially in the direction with the lower spatial separation between the bottom and top of the barrier. A qualitatively similar mechanism operates in a mixture containing passive particles of two very different temperatures, although there is no quantitative mapping between that case and the systems studied here.

cond-mat.stat-mech↗

arXiv2022

Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics

Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained individual motion. It can lead to collective effects without any equilibrium equivalent, such as a phase separation for purely repulsive particles, or a collective motion (flocking) for aligning particles. Some of these effects can be rationalized by using equilibrium tools to recapitulate nonequilibrium transitions. An important challenge is then to delineate systematically to which extent the character of these active transitions is genuinely distinct from equilibrium analogs. We review recent works that use stochastic thermodynamics tools to identify, for active systems, a measure of irreversibility comprising a coarse-grained or informatic entropy production. We describe how this relates to the underlying energy dissipation or thermodynamic entropy production, and how it is influenced by collective behavior. Then, we review the possibility to construct thermodynamic ensembles out-of-equilibrium, where trajectories are biased towards atypical values of nonequilibrium observables. We show that this is a generic route to discovering unexpected phase transitions in active matter systems, which can also inform their design.

cond-mat.soft↗

arXiv2022

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff -- which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing for simplicity on models with a purely diffusive scalar field, such as `Model B' which describes phase separation in binary fluid mixtures. We address the requirement that the steady state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for `active field theories' in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR) we must make a careful treatment of so-called `spurious drift' and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative, via off-diagonal couplings to additional fields that encode thermodynamically the underlying chemical processes responsible for activity. In this case the spurious drift terms need careful accounting, not just to evaluate correctly the EPR, but also to numerically implement the Langevin dynamics itself.

cond-mat.soft↗

arXiv2022

Tracer dynamics in one dimensional gases of active or passive particles

We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer particle embedded in such a system - this tracer may be either active or passive, with hardcore exclusion from environmental particles. In an active hardcore environment, both active and passive tracers show long-time subdiffusion: displacements scale as $t^{1/4}$ with a density-dependent prefactor that is independent of tracer type, and differs from the corresponding result for passive-in-passive subdiffusion. In an environment of noninteracting active particles, the passive-in-passive results are recovered at low densities for both active and passive tracers, but transient caging effects slow the tracer motion at higher densities, delaying the onset of any $t^{1/4}$ regime. For an active tracer in a passive environment, we find more complex outcomes, which depend on details of the dynamical discretization scheme. We interpret these results by studying the density distribution of environmental particles around the tracer. In particular, sticking of environment particles to the tracer cause it to move more slowly in noninteracting than in interacting active environments, while the anomalous behaviour of the active-in-passive cases stems from a `snowplough' effect whereby a large pile of diffusive environmental particles accumulates in front of a RTP tracer during a ballistic run.

cond-mat.stat-mech↗

arXiv2021

Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, MCMC sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

stat.ME↗

arXiv2021

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffice to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We first detail the perturbative derivation of the steady state of AOUPs in the small persistence time limit. We show the existence of an effective equilibrium regime in which detailed-balance is obeyed with respect to a non-Boltzmann distribution and detail the corresponding fluctuation-dissipation theorem. We then characterize the departure from equilibrium by computing several relevant observables (entropy production, ratchet current). At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. The latter can be accounted for by considering the steady-state of AOUPs with spatially varying propulsion speed or persistence time. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes, which we construct explicitly.

cond-mat.stat-mech↗

arXiv2021

Power fluctuations in sheared amorphous materials: A minimal model

The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-solid transition; the existence of a fluctuation relation in limiting regimes but its replacement in general by stretched-exponential power-distribution tails; and a crossover between two distinct mechanisms for negative power fluctuations in the liquid and the yielding solid phases. We connect these predictions with recent results from particle-based, numerical micro-rheological experiments.

cond-mat.soft↗

arXiv2021

Thermodynamics of active field theories: Energetic cost of coupling to reservoirs

The hallmark of active matter is the autonomous directed motion of its microscopic constituents driven by consumption of energy resources. This leads to the emergence of large scale dynamics and structures without any equilibrium equivalent. Though active field theories offer a useful hydrodynamic description, it is unclear how to properly quantify the energetic cost of the dynamics from such a coarse-grained description. We provide a thermodynamically consistent framework to identify the energy exchanges between active systems and their surrounding thermostat at the hydrodynamic level. Based on linear irreversible thermodynamics, we determine how active fields couple with the underlying reservoirs at the basis of nonequilibrium driving. This leads to evaluating the rate of heat dissipated in the thermostat, as a measure of the cost to sustain the system away from equilibrium, which is related to the irreversibility of the active field dynamics. We demonstrate the applicability of our approach in two popular active field theories: (i) the dynamics of a conserved density field reproducing active phase separation, and (ii) the coupled dynamics of density and polarization describing motile deformable droplets. Combining numerical and analytical approaches, we provide spatial maps of dissipated heat, compare them with the irreversibility measure of the active field dynamics, and explore how the overall dissipated heat varies with the emerging order.

cond-mat.stat-mech↗

arXiv2021

Hierarchical microphase separation in non-conserved active mixtures

Non-equilibrium phase separating systems with reactions can break time-reversal symmetry (TRS) in two distinct ways. Firstly, the conservative and non-conservative sectors of the dynamics can be governed by incompatible free energies; when both sectors are present, this is the leading-order TRS violation, captured in its simplest form by 'Model AB'. Second, the diffusive dynamics can break TRS in its own right. This happens only at higher order in the gradient expansion (but is the leading behaviour without reactions present) and is captured by 'Active Model B+' (AMB+). Each of the two mechanisms can lead to microphase separation, by quite different routes. Here we introduce Model AB+, for which both mechanisms are simultaneously present, and show that for slow reaction rates the system can undergo a new type of hierarchical microphase separation, whereby a continuous phase of fluid 1 contains large droplets of fluid 2 within which small droplets of fluid 1 are continuously created and then absorbed into the surrounding fluid-1 phase. In this state of 'bubbly microphase separation' the small-scale 1-in-2 droplets arise by the conservative diffusive dynamics with the larger scale 2-in-1 structure governed by the nonconservative reactions.

cond-mat.soft↗

arXiv2021

Active engines: Thermodynamics moves forward

The study of thermal heat engines was pivotal to establishing the principles of equilibrium thermodynamics, with implications far wider than only engine optimization. For nonequilibrium systems, which by definition dissipate energy even at rest, how to best convert such dissipation into useful work is still largely an outstanding question, with similar potential to illuminate general physical principles. We review recent theoretical progress in studying the performances of engines operating with active matter, where particles are driven by individual self-propulsion. We distinguish two main classes, either autonomous engines exploiting a particle current, or cyclic engines applying periodic transformation to the system, and present the strategies put forward so far for optimization. We delineate the limitations of previous studies, and propose some futures perspectives, with a view to building a consistent thermodynamic framework far from equilibrium.

cond-mat.stat-mech↗

arXiv2020

Time-reversal symmetry violations and entropy production in field theories of polar active matter

We investigate the steady-state entropy production rate (EPR) in the Hydrodynamic Vicsek Model (HVM) and Diffusive Flocking Model (DFM). Both models display a transition from an isotropic gas to a polar liquid (flocking) phase, in addition to traveling polar clusters and microphase-separation in the miscibility gap. The phase diagram of the DFM, which may be considered an extension of the HVM, contains additional structure at low densities where we find a novel crystal phase in which a stationary hexagonal lattice of high-density ridges surround low density valleys. From an assessment of the scaling of the EPR at low noise, we uncover that the dynamics in this limit may be organised into three main classes based on the dominant contribution. Truly nonequilibrium dynamics is characterised by a divergent EPR in this limit, and sustains global time-reversal symmetry (TRS) violating currents at zero noise. On the other hand, marginally nonequilibrium and effectively equilibrium dynamics have a finite EPR in this limit, and TRS is broken only at the level of fluctuations. For the latter of these two cases, detailed balance is restored in the small noise limit and we recover effective Boltzmann statistics to lowest nontrivial order. We further demonstrate that the scaling of the EPR may change depending on the dynamical variables that are tracked when it is computed, and the protocol chosen for time-reversal. Results acquired from numerical simulations of the dynamics confirm both the asymptotic scaling relations we derive and our quantitative predictions.

cond-mat.stat-mech↗

arXiv2020

Steady state entropy production rate for scalar Langevin field theories

The entropy production rate (EPR) offers a quantitative measure of time reversal symmetry breaking in non-equilibrium systems. It can be defined either at particle level or at the level of coarse-grained fields such as density; the EPR for the latter quantifies the extent to which these coarse-grained fields behave irreversibly. In this work, we first develop a general method to compute the EPR of scalar Langevin field theories with additive noise. This large class of theories includes active versions of Model A (non-conserved density dynamics) and Model B (conserved) and also models where both types of dynamics are simultaneously present (such as Model AB). Treating the scalar field $ϕ$ (and its time derivative $\dotϕ$) as the sole observable(s), we arrive at an expression for the EPR that is non-negative for every field configuration and is quadratic in the time-antisymmetric component of the dynamics. Our general expression is a function of the quasipotential, which determines the full probability distribution for configurations, and is not generally calculable. To alleviate this difficulty, we present a small-noise expansion of the EPR, which only requires knowledge of the deterministic (mean-field) solution for the scalar field in steady state, which generally is calculable, at least numerically. We demonstrate this calculation for the case of Model AB. We then present a similar EPR calculation for Model AB with the conservative and non-conservative contributions to $\dotϕ= \dotϕ_{\rm A} + \dotϕ_{\rm B}$ viewed as separately observable quantities. The results are qualitatively different, confirming that the field-level EPR depends on the choice of coarse-grained information retained within the dynamical description.

cond-mat.stat-mech↗

arXiv2020

Non-equilibrium phase separation with reactions: A canonical model and its behaviour

Materials undergoing both phase separation and chemical reactions (defined here as all processes that change particle type or number) form an important class of non-equilibrium systems. Examples range from suspensions of self-propelled bacteria with birth-death dynamics, to bio-molecular condensates, or 'membraneless organelles', within cells. In contrast to their passive counterparts, such systems have conserved and non-conserved dynamics that do not, in general, derive from a shared free energy. This mismatch breaks time-reversal symmetry and leads to new types of dynamical competition that are absent in or near equilibrium. We construct a canonical scalar field theory to describe such systems, with conserved and non-conserved dynamics obeying Model B and Model A respectively (in the Hohenberg-Halperin classification), chosen such that the two free energies involved are incompatible. The resulting minimal model is shown to capture the various phenomenologies reported previously for more complicated models with the same physical ingredients, including microphase separation, limit cycles and droplet splitting. We find a low-dimensional subspace of parameters for which time-reversal symmetry is accidentally recovered, and show that here the dynamics of the order parameter field (but not its conserved current) is exactly the same as an equilibrium system in which microphase separation is caused by long-range attractive interactions.

cond-mat.soft↗

arXiv2020

Collective motion in large deviations of active particles

We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyse the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.

cond-mat.stat-mech↗

arXiv2020

Self-propulsion of active droplets without liquid-crystalline order

The swimming of cells, far from any boundary, can arise in the absence of long-range liquid-crystalline order within the cytoplasm, but simple models of this effect are lacking. Here we present a two-dimensional model of droplet self-propulsion involving two scalar fields, representing the cytoplasm and a contractile cortex. An active stress results from coupling between these fields; self-propulsion results when rotational symmetry is spontaneously broken. The swimming speed is predicted, and shown numerically, to vary linearly with the activity parameter and with the droplet area fraction. The model exhibits a Crowley-like instability for an array of active droplets.

cond-mat.soft↗

arXiv2020

Constitutive model for time-dependent flows of shear-thickening suspensions

We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent materials with ideas developed previously to explain the steady flow of shear-thickening ones, whereby friction proliferates among compressive contacts at large particle stresses. We apply our model to shear reversal, and find good qualitative agreement with particle-level, discrete-element simulations whose results we also present.

physics.flu-dyn↗