2,025 research outputs found
Effective equilibrium picture in model with exponentially correlated noise
We study the effect of exponentially correlated noise on model in the
limit of small correlation time discussing the order-disorder transition in
mean-field and the topological transition in two dimensions. We map the steady
states of the non-equilibrium dynamics into an effective equilibrium theory. In
mean-field, the critical temperature increases with the noise correlation time
indicating that memory effects promote ordering. This finding is
confirmed by numerical simulations. The topological transition temperature in
two dimensions remains untouched. However, finite size effects induce a
crossover in the vortices proliferation that is confirmed by numerical
simulations
Pressure and surface tension of an active simple liquid: a comparison between kinetic, mechanical and free-energy based approaches
We discuss different definitions of pressure for a system of active spherical
particles driven by a non-thermal coloured noise. We show that mechanical,
kinetic and free-energy based approaches lead to the same result up to first
order in the non-equilibrium expansion parameter. The first prescription is
based on a generalisation of the kinetic mesoscopic virial equation and
expresses the pressure exerted on the walls in terms of the average of the
virial of the inter-particle forces. In the second approach, the pressure and
the surface tension are identified with the volume and area derivatives,
respectively, of the partition function associated with the known stationary
non-equilibrium distribution of the model. The third method is a mechanical
approach and is related to the work necessary to deform the system. The
pressure is obtained by comparing the expression of the work in terms of local
stress and strain with the corresponding expression in terms of microscopic
distribution. This is determined from the force balance encoded in the
Born-Green-Yvon equation. Such a method has the advantage of giving a formula
for the local pressure tensor and the surface tension even in inhomogeneous
situations. By direct inspection, we show that the three procedures lead to the
same values of the pressure, and give support to the idea that the partition
function, obtained via the unified coloured noise approximation, is more than a
formal property of the system, but determines the stationary non-equilibrium
thermodynamics of the model
Effective potential method for active particles
We investigate the steady state properties of an active fluid modeled as an
assembly of soft repulsive spheres subjected to Gaussian colored noise. Such a
noise captures one of the salient aspects of active particles, namely the
persistence of their motion and determines a variety of novel features with
respect to familiar passive fluids. We show that within the so-called
multidimensional unified colored noise approximation, recently introduced in
the field of active matter, the model can be treated by methods similar to
those employed in the study of standard molecular fluids. The system shows a
tendency of the particles to aggregate even in the presence of purely repulsive
forces because the combined action of colored noise and interactions enhances
the the effective friction between nearby particles. We also discuss whether an
effective two-body potential approach, which would allow to employ methods
similar to those of density functional theory, is appropriate. The limits of
such an approximation are discussed.Comment: 14 pages, 6 figures in Molecular Physics, 11 march 2016. arXiv admin
note: text overlap with arXiv:cond-mat/0605094 by other author
Heat, temperature and Clausius inequality in a model for active brownian particles
Methods of stochastic thermodynamics and hydrodynamics are applied to the a
recently introduced model of active particles. The model consists of an
overdamped particle subject to Gaussian coloured noise. Inspired by stochastic
thermodynamics, we derive from the system's Fokker-Planck equation the average
exchanges of heat and work with the active bath and the associated entropy
production. We show that a Clausius inequality holds, with the local
(non-uniform) temperature of the active bath replacing the uniform temperature
usually encountered in equilibrium systems. Furthermore, by restricting the
dynamical space to the first velocity moments of the local distribution
function we derive a hydrodynamic description where local pressure, kinetic
temperature and internal heat fluxes appear and are consistent with the
previous thermodynamic analysis. The procedure also shows under which
conditions one obtains the unified coloured noise approximation (UCNA): such an
approximation neglects the fast relaxation to the active bath and therefore
yields detailed balance and zero entropy production. In the last part, by using
multiple time-scale analysis, we provide a constructive method (alternative to
UCNA) to determine the solution of the Kramers equation and go beyond the
detailed balance condition determining negative entropy production.Comment: 19 pages, 1 figure. Major changes in the text. 1 figure has been
replace
Multidimensional Stationary Probability Distribution for Interacting Active Particles
We derive the stationary probability distribution for a non-equilibrium
system composed by an arbitrary number of degrees of freedom that are subject
to Gaussian colored noise and a conservative potential. This is based on a
multidimensional version of the Unified Colored Noise Approximation. By
comparing theory with numerical simulations we demonstrate that the theoretical
probability density quantitatively describes the accumulation of active
particles around repulsive obstacles. In particular, for two particles with
repulsive interactions, the probability of close contact decreases when one of
the two particle is pinned. Moreover, in the case of isotropic confining
potentials, the radial density profile shows a non trivial scaling with radius.
Finally we show that the theory well approximates the "pressure" generated by
the active particles allowing to derive an equation of state for a system of
non-interacting colored noise-driven particles.Comment: 5 pages, 2 figure
Pressure in an exactly solvable model of active fluid
We consider the pressure in the steady-state regime of three stochastic
models characterized by self-propulsion and persistent motion and widely
employed to describe the behavior of active particles, namely the Active
Brownian particle (ABP) model, the Gaussian colored noise (GCN) model and the
unified colored noise model (UCNA). Whereas in the limit of short but finite
persistence time the pressure in the UCNA model can be obtained by different
methods which have an analog in equilibrium systems, in the remaining two
models only the virial route is, in general, possible.
According to this method, notwithstanding each model obeys its own specific
microscopic law of evolution, the pressure displays a certain universal
behavior. For generic interparticle and confining potentials, we derive a
formula which establishes a correspondence between the GCN and the UCNA
pressures. In order to provide explicit formulas and examples, we specialize
the discussion to the case of an assembly of elastic dumbbells confined to a
parabolic well. By employing the UCNA we find that, for this model, the
pressure determined by the thermodynamic method coincides with the pressures
obtained by the virial and mechanical methods. The three methods when applied
to the GCN give a pressure identical to that obtained via the UCNA. Finally, we
find that the ABP virial pressure exactly agrees with the UCNA and GCN result.Comment: 12 pages, 1 figure Submitted for publication 23rd of January 2017 The
introduction has been modifie
Collective effects in confined Active Brownian Particles
We investigate a two-dimensional system of active particles confined to a
narrow annular domain. Despite the absence of explicit interactions among the
velocities or the active forces of different particles, the system displays a
transition from a disordered and stuck state to an ordered state of global
collective motion where the particles rotate persistently clockwise or
anticlockwise. We describe this behavior by introducing a suitable order
parameter, the velocity polarization, measuring the global alignment of the
particles' velocities along the tangential direction of the ring. We also
measure the spatial velocity correlation function and its correlation length to
characterize the two states. In the rotating phase, the velocity correlation
displays an algebraic decay that is analytically predicted together with its
correlation length while in the stuck regime the velocity correlation decays
exponentially with a correlation length that increases with the persistence
time. In the first case, the correlation (and, in particular, its correlation
length) does not depend on the active force but the system size only. The
global collective motion, an effect caused by the interplay between
finite-size, periodicity, and persistent active forces, disappears as the size
of the ring becomes infinite, suggesting that this phenomenon does not
correspond to a phase transition in the usual thermodynamic sense
Activity-controlled clogging and unclogging of micro-channels
We propose a mechanism to control the formation of stable obstructions in
two-dimensional micro-channels of variable sections taking advantage of the
peculiar clustering property of active systems. Under the activation of the
self-propulsion by external stimuli, the system behaves as a switch according
to the following principle: by turning-on the self-propulsion the particles
become active and even at very low densities stick to the walls and form
growing layers eventually blocking the channel bottleneck, while the
obstruction dissolves when the self-propulsion is turned off. We construct the
phase diagram distinguishing clogged and open states in terms of density and
bottleneck width. The study of the average clogging time, as a function of
density and bottleneck width, reveals the marked efficiency of the active
clogging that swiftly responds to the self-propulsion turning on. The resulting
picture shows a profound difference with respect to the clogging obtained
through the slow diffusive dynamics of attractive passive Brownian disks. This
numerical work suggests a novel method to use particles with externally tunable
self-propulsion to create or destroy plugs in micro-channels
Effective equilibrium states in the colored-noise model for active matter II. A unified framework for phase equilibria, structure and mechanical properties
Active particles driven by colored noise can be approximately mapped onto a system that obeys detailed balance. The effective interactions which can be derived for such a system allow the description of the structure and phase behavior of the active fluid by means of an effective free energy. In this paper we explain why the related thermodynamic results for pressure and interfacial tension do not represent the results one would measure mechanically. We derive a dynamical density functional theory, which in the steady state simultaneously validates the use of effective interactions and provides access to mechanical quantities. Our calculations suggest that in the colored-noise model the mechanical pressure in the coexisting phases might be unequal and the interfacial tension can become negative
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