2,287 research outputs found
Statistical Field Theory and Effective Action Method for scalar Active Matter
We employ Statistical Field Theory techniques for coarse-graining the
steady-state properties of Active Ornstein-Uhlenbeck particles. The computation
is carried on in the framework of the Unified Colored Noise approximation that
allows an effective equilibrium picture. We thus develop a mean-field theory
that allows to describe in a unified framework the phenomenology of scalar
Active Matter. In particular, we are able to describe through spontaneous
symmetry breaking mechanism two peculiar features of Active Systems that are
(i) The accumulation of active particles at the boundaries of a confining
container, and (ii) Motility-Induced Phase Separation (MIPS).
\textcolor{black}{We develop a mean-field theory for steric interacting active
particles undergoing to MIPS and for Active Lennard-Jones (ALJ) fluids.}
\textcolor{black}{Within this framework}, we discuss the universality class of
MIPS and ALJ \textcolor{black}{showing that it falls into Ising universality
class.} We \textcolor{black}{thus} compute analytically the critical line
for both models. In the case of MIPS, gives rise to a
reentrant phase diagram compatible with an inverse transition from liquid to
gas as the strength of the noise decreases. \textcolor{black}{However, in the
case of particles interacting through anisotropic potentials, } the field
theory acquires a term that, \textcolor{black}{in general, cannot
be canceled performing the expansion around the critical point.} In this case,
the \textcolor{black}{Ising} critical point might \textcolor{black}{be
replaced} by a first-order phase transition \textcolor{black}{region}
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
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
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
Generalized Fluctuation-Dissipation Relation and Effective Temperature upon Heating a Deeply Supercooled Liquid
We show that a generalized fluctuation-dissipation relation applies upon
instantaneously increasing the temperature of a deeply supercooled liquid. This
has the same two-step shape of the relation found upon cooling the liquid, but
with opposite violation, indicating an effective temperature that is lower than
bath temperature. We show that the effective temperature exhibits some sensible
time-dependence and that it retains its connection with the partitioned phase
space visited in ageing. We underline the potential relevance of our numerical
results for experimental studies of the fluctuation-dissipation relation in
glassy systems.Comment: 5 pages, 4 figure
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
Motility fractionation of bacteria by centrifugation
Centrifugation is a widespread laboratory technique used to separate mixtures
into fractions characterized by a specific size, weight or density. We
demonstrate that centrifugation can be also used to separate swimming cells
having different motility. To do this we study self-propelled bacteria under
the influence of an external centrifugal field. Using dynamic image correlation
spectroscopy we measure the spatially resolved motility of bacteria after
centrifugation. A significant gradient in swimming-speeds is observed for
increasing centrifugal speeds. Our results can be reproduced by a model that
treats bacteria as "hot" colloidal particles having a diffusion coefficient
that depends on the swimming speed.Comment: 7 pages, 5 figures (in press
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