arXiv subjects

Michael E. Cates

Publications and source records attributed to Michael E. Cates.

At least 73 records · Page 4Linked to original sources

arXiv2020

Thermodynamic cycles with active matter

Active matter constantly dissipates energy to power the self-propulsion of its microscopic constituents. This opens the door to designing innovative cyclic engines without any equilibrium equivalent. We offer a consistent thermodynamic framework to characterize and optimize the performances of such cycles. Based on a minimal model, we put forward a protocol which extracts work by controlling only the properties of the confining walls at boundaries, and we rationalize the transitions between optimal cycles. We show that the corresponding power and efficiency are generally proportional, so that they reach their maximum values at same cycle time in contrast with thermal cycles, and we provide a generic relation constraining the fluctuations of the power.

cond-mat.soft↗

arXiv2020

Stealth entropy production in active field theories near Ising critical points

We address the steady-state entropy production rate (EPR) of active scalar $ϕ^4$ theories, which lack time-reversal symmetry, close to a phase-separation critical point. We consider both nonconserved (Model A) and conserved (Model B) dynamics at Gaussian level, and also address the former at leading order in $ε= 4-d$. In each case, activity is irrelevant in the RG sense: the active model lies in the same (dynamic Ising) universality class as its time-reversible counterpart. Hence one might expect that activity brings no new critical behavior. Here we show instead that the EPR per spacetime correlation volume either remains finite or diverges on approach to criticality. A nontrivial critical scaling for entropy production thus ranks among universal dynamic Ising-class properties.

cond-mat.stat-mech↗

arXiv2020

Inference, prediction and optimization of non-pharmaceutical interventions using compartment models: the PyRoss library

PyRoss is an open-source Python library that offers an integrated platform for inference, prediction and optimisation of NPIs in age- and contact-structured epidemiological compartment models. This report outlines the rationale and functionality of the PyRoss library, with various illustrations and examples focusing on well-mixed, age-structured populations. The PyRoss library supports arbitrary structured models formulated stochastically (as master equations) or deterministically (as ODEs) and allows mid-run transitioning from one to the other. By supporting additional compartmental subdivision ad libitum, PyRoss can emulate time-since-infection models and allows medical stages such as hospitalization or quarantine to be modelled and forecast. The PyRoss library enables fitting to epidemiological data, as available, using Bayesian parameter inference, so that competing models can be weighed by their evidence. PyRoss allows fully Bayesian forecasts of the impact of idealized NPIs by convolving uncertainties arising from epidemiological data, model choice, parameters, and intrinsic stochasticity. Algorithms to optimize time-dependent NPI scenarios against user-defined cost functions are included. PyRoss's current age-structured compartment framework for well-mixed populations will in future reports be extended to include compartments structured by location, occupation, use of travel networks and other attributes relevant to assessing disease spread and the impact of NPIs. We argue that such compartment models, by allowing social data of arbitrary granularity to be combined with Bayesian parameter estimation for poorly-known disease variables, could enable more powerful and robust prediction than other approaches to detailed epidemic modelling. We invite others to use the PyRoss library for research to address today's COVID-19 crisis, and to plan for future pandemics.

q-bio.PE↗

arXiv2020

Absorbing-state transitions in granular materials close to jamming

We consider a model for driven particulate matter in which absorbing states can be reached both by particle isolation and by particle caging. The model predicts a non-equilibrium phase diagram in which analogues of hydrodynamic and elastic reversibility emerge at low and high volume fractions respectively, partially separated by a diffusive, non-absorbing region. We thus find a single phase boundary that spans the onset of chaos in sheared suspensions to the onset of yielding in jammed packings. This boundary has the properties of a non-equilibrium second order phase transition, leading us to write a Manna-like mean-field description that captures the model predictions. Dependent on contact details, jamming marks either a direct transition between the two absorbing states, or occurs within the diffusive region.

cond-mat.soft↗

arXiv2019

Autonomous engines driven by active matter: Energetics and design principles

Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealised work-extraction mechanism. For a setting with many noninteracting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise noninteracting active particles, which enhances the extracted power per active particle significantly.

cond-mat.stat-mech↗

arXiv2019

Chiral active matter: microscopic `torque dipoles' have more than one hydrodynamic description

Many biological systems, such as bacterial suspensions and actomyosin networks, form polar liquid crystals. These systems are `active' or far-from-equilibrium, due to local forcing of the solvent by the constituent particles. In many cases the source of activity is chiral; since forcing is internally generated, some sort of `torque dipole' is then present locally. But it is not obvious how `torque dipoles' should be encoded in the hydrodynamic equations that describe the system at continuum level: different authors have arrived at contradictory conclusions on this issue. In this work, we resolve the paradox by presenting a careful derivation, from linear irreversible thermodynamics, of the general equations of motion of a single-component chiral active fluid with spin degrees of freedom. We find that there is no unique hydrodynamic description for such a fluid in the presence of torque dipoles of a given strength. Instead, at least three different hydrodynamic descriptions emerge, depending on whether we decompose each torque dipole as two point torques, two force pairs, or one point torque and one force pair -- where point torques create internal angular momenta of the chiral bodies (spin), whereas force pairs impart centre of mass motion that contributes to fluid velocity. By considering a general expansion of the Onsager coefficients, we also derive a new shear-elongation parameter and cross-coupling viscosity, which can lead to unpredicted phenomena even in passive polar liquid crystals. Finally, elimination of the angular variables gives an effective polar hydrodynamics with renormalized active stresses, viscosities and kinetic coefficients. Remarkably, this can include a direct contribution of chiral activity to the equation of motion for the polar order parameter, which survives even in `dry' active systems where the fluid velocity is set to zero.

cond-mat.soft↗

arXiv2019

Conching chocolate: A prototypical transition from frictionally jammed solid to flowable suspension with maximal solid content

The mixing of a powder of 10-50μm primary particles into a liquid to form a dispersion with the highest possible solid content is a common industrial operation. Building on recent advances in the rheology of such 'granular dispersions', we study a paradigmatic example of such powder incorporation: the conching of chocolate, in which a homogeneous, flowing suspension is prepared from an inhomogeneous mixture of particulates, triglyceride oil and dispersants. Studying the rheology of a simplified formulation, we find that the input of mechanical energy and staged addition of surfactants combine to effect a considerable shift in the jamming volume fraction of the system, thus increasing the maximum flowable solid content. We discuss the possible microscopic origins of this shift, and suggest that chocolate conching exemplifies a ubiquitous class of powder-liquid mixing.

cond-mat.soft↗

arXiv2019

Active Field Theories

Lecture Notes for Les Houches 2018 Summer School on Active Matter and Nonequilibrium Statistical Physics. These notes give an introduction to statistical field theories of active matter. After showing an example of how such theories can be created bottom-up by explicit coarse graining of active particle models, the main approach taken here is top-down: minimal terms are added to well-studied stochastic field theories of passive systems that break time-reversibility and thereby cause nonzero steady-state entropy production. These theories are, so far, rather poorly understood compared to their passive counterparts.

cond-mat.stat-mech↗

arXiv2019

Optimizing active work: Dynamical phase transitions, collective motion, and jamming

Active work measures how far the local self-forcing of active particles translates into real motion. Using Population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.

cond-mat.stat-mech↗

arXiv2018

From bulk to microphase separation in scalar active matter: A perturbative renormalization group analysis

We consider a dynamical field theory (Active Model B+) that minimally extends the equilibrium Model B for diffusive phase separation of a scalar field, by adding leading-order terms that break time-reversal symmetry. It was recently shown that such active terms can cause the bulk phase separation of Model B to be replaced by a steady state of microphase separation at a finite length scale. This phenomenon was understood at mean-field level as due to the activity-induced reversal of the Ostwald ripening mechanism, which provides the kinetic pathway to bulk phase separation in passive fluids. This reversal occurs only in certain ranges for the activity parameters. In this paper we go beyond such a mean-field analysis and develop a $1$-loop Renormalisation Group (RG) approach. We first show that, in the parameter range where bulk phase separation is still present, the critical point belongs formally to the same (Wilson-Fisher) universality class as the passive Model B. In contrast, in a parameter range associated with microphase separation, we find that an unstable non-equilibrium fixed point of the RG flow arises for $d\geq 2$, colliding with the Wilson-Fisher point in $d\to 2^+$ and making it unstable in $d=2$. At large activity, the flow in this region is towards strong coupling. We argue that the phase transition to microphase separation in active systems, in the physically relevant dimensions $d=2$ and $3$, very probably belongs to a new non-equilibrium universality class. Because it is governed by the strong-coupling regime of the RG flow, our perturbative analysis leaves open the quantitative characterization of this new class.

cond-mat.stat-mech↗

arXiv2018

Dynamic vorticity banding in discontinuously shear thickening suspensions

It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions, because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show however that the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. We furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.

cond-mat.soft↗

arXiv2018

Shear-induced first-order transition in polar liquid crystals

The hydrodynamic theory of polar liquid crystals is widely used to describe biological active fluids as well as passive molecular materials. Depending on the `shear-alignment parameter', in passive or weakly active polar fluids under external shear the polar order parameter ${\mathbf{p}}$ is either inclined to the flow at a fixed (Leslie) angle, or rotates continuously. Here we study the role of an additional `shear-elongation parameter' that has been neglected in the recent literature and causes $|{\mathbf{p}}|$ to change under flow. We show that this effect can give rise to a shear-induced first order phase transition %(instead of the usual second order transition) from isotropic to polar, and significantly change the rheological properties of both active and passive polar fluids.

cond-mat.soft↗

arXiv2018

Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles

Motility-induced phase separation (MIPS) leads to cohesive active matter in the absence of cohesive forces. We present, extend and illustrate a recent generalized thermodynamic formalism which accounts for its binodal curve. Using this formalism, we identify both a generalized surface tension, that controls finite-size corrections to coexisting densities, and generalized forces, that can be used to construct new thermodynamic ensembles. Our framework is based on a nonequilibrium generalization of the Cahn-Hilliard equation and we discuss its application to active particles interacting either via quorum-sensing interactions or directly through pairwise forces.

cond-mat.stat-mech↗

arXiv2018

Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process

It is known that purely repulsive self-propelled colloids can undergo bulk liquid-vapor phase separation. In experiments and large scale simulations, however, more complex steady states are also seen, comprising a dynamic population of dense clusters in a sea of vapor, or dilute bubbles in a liquid. Here we show that these microphase-separated states should emerge generically in active matter, without any need to invoke system-specific details. We give a coarse-grained description of them, and predict transitions between regimes of bulk phase separation and microphase separation. We achieve these results by extending the $ϕ^4$ field theory of passive phase separation to allow for all local currents that break detailed balance at leading order in the gradient expansion. These local active currents, whose form we show to emerge from coarse-graining of microscopic models, include a mixture of irrotational and rotational contributions, and can be viewed as arising from an effective nonlocal chemical potential. Such contributions influence, and in some parameter ranges reverse, the classical Ostwald process that would normally drive bulk phase separation to completion.

cond-mat.soft↗

arXiv2018

Theories of Binary Fluid Mixtures: From Phase-Separation Kinetics to Active Emulsions

Binary fluid mixtures are examples of complex fluids whose microstructure and flow are strongly coupled. For pairs of simple fluids, the microstructure consists of droplets or bicontinuous demixed domains and the physics is controlled by the interfaces between these domains. At continuum level, the structure is defined by a composition field whose gradients which are steep near interfaces drive its diffusive current. These gradients also cause thermodynamic stresses which can drive fluid flow. Fluid flow in turn advects the composition field, while thermal noise creates additional random fluxes that allow the system to explore its configuration space and move towards the Boltzmann distribution. This article introduces continuum models of binary fluids, first covering some well-studied areas such as the thermodynamics and kinetics of phase separation, and emulsion stability. We then address cases where one of the fluid components has anisotropic structure at mesoscopic scales creating nematic (or polar) liquid-crystalline order; this can be described through an additional tensor (or vector) order parameter field. We conclude by outlining a thriving area of current research, namely active emulsions, in which one of the binary components consists of living or synthetic material that is continuously converting chemical energy into mechanical work.

cond-mat.soft↗

arXiv2018

Strong coupling in conserved surface roughening: A new universality class?

The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (cKPZ) is thought to set the universality class instead. This has non-mean-field behavior only in spatial dimension $d<2$. We point out here that cKPZ is incomplete: it omits a symmetry-allowed nonlinear gradient term of the same order as the one retained. Adding this term, we find a parameter regime where the $1$-loop renormalization group flow diverges. This suggests a phase transition to a new growth phase, possibly ruled by a strong coupling fixed point and thus described by a new universality class, for any $d>1$. In this phase, numerical integration of the model in $d=2$ gives clear evidence of non mean-field behavior.

cond-mat.stat-mech↗

arXiv2018

Generalized Thermodynamics of Phase Equilibria in Scalar Active Matter

Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter, akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy. We illustrate our approach on two well-known models: self-propelled particles interacting either through a density-dependent propulsion speed or via direct pairwise forces. Our theory accounts quantitatively for their phase diagrams, providing a unified description of MIPS.

cond-mat.stat-mech↗

arXiv2017

Spatiotemporal Self-Organization of Fluctuating Bacterial Colonies

We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population causes a dense bacterial colony to form, which then declines by local cell death, before dispersing to re-initiate the cycle. Adding fluctuations, we find that static colonies are now metastable, moving between spatial locations via rare and strongly nonequilibrium pathways, whereas the limit cycle becomes almost periodic such that after each redispersion event the next colony forms in a random location. These results, which hint at some aspects of the biofilm-planktonic life cycle, can be explained by combining tools from large deviation theory with a bifurcation analysis in which the global population density plays the role of control parameter.

cond-mat.stat-mech↗