148 research outputs found
Flocking with discrete symmetry: the 2d Active Ising Model
We study in detail the active Ising model, a stochastic lattice gas where
collective motion emerges from the spontaneous breaking of a discrete symmetry.
On a 2d lattice, active particles undergo a diffusion biased in one of two
possible directions (left and right) and align ferromagnetically their
direction of motion, hence yielding a minimal flocking model with discrete
rotational symmetry. We show that the transition to collective motion amounts
in this model to a bona fide liquid-gas phase transition in the canonical
ensemble. The phase diagram in the density/velocity parameter plane has a
critical point at zero velocity which belongs to the Ising universality class.
In the density/temperature "canonical" ensemble, the usual critical point of
the equilibrium liquid-gas transition is sent to infinite density because the
different symmetries between liquid and gas phases preclude a supercritical
region. We build a continuum theory which reproduces qualitatively the behavior
of the microscopic model. In particular we predict analytically the shapes of
the phase diagrams in the vicinity of the critical points, the binodal and
spinodal densities at coexistence, and the speeds and shapes of the
phase-separated profiles.Comment: 20 pages, 25 figure
Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both
self-propel at fixed speed along a body-axis that reorients
either through slow angular diffusion (ABPs) or sudden complete randomisation
(RTPs). We compare the physics of these two model systems both at microscopic
and macroscopic scales. Using exact results for their steady-state distribution
in the presence of external potentials, we show that they both admit the same
effective equilibrium regime perturbatively that breaks down for stronger
external potentials, in a model-dependent way. In the presence of collisional
repulsions such particles slow down at high density: their propulsive effort is
unchanged, but their average speed along becomes . A
fruitful avenue is then to construct a mean-field description in which
particles are ghost-like and have no collisions, but swim at a variable speed
that is an explicit function or functional of the density . We give
numerical evidence that the recently shown equivalence of the fluctuating
hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to
microscopic models of ABPs and RTPs interacting with repulsive forces.Comment: 32 pages, 6 figure
When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
Active Brownian particles (ABPs, such as self-phoretic colloids) swim at
fixed speed along a body-axis that rotates by slow angular
diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with
constant \u until a random tumble event suddenly decorrelates the
orientation. We show that when the motility parameters depend on density
but not on , the coarse-grained fluctuating hydrodynamics of
interacting ABPs and RTPs can be mapped onto each other and are thus strictly
equivalent. In both cases, a steeply enough decreasing causes phase
separation in dimensions , even when no attractive forces act between
the particles. This points to a generic role for motility-induced phase
separation in active matter. However, we show that the ABP/RTP equivalence does
not automatically extend to the more general case of \u-dependent motilities
A numerical approach to large deviations in continuous-time
We present an algorithm to evaluate the large deviation functions associated
to history-dependent observables. Instead of relying on a time discretisation
procedure to approximate the dynamics, we provide a direct continuous-time
algorithm, valuable for systems with multiple time scales, thus extending the
work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)).
The procedure is supplemented with a thermodynamic-integration scheme, which
improves its efficiency. We also show how the method can be used to probe large
deviation functions in systems with a dynamical phase transition -- revealed in
our context through the appearance of a non-analyticity in the large deviation
functions.Comment: Submitted to J. Stat. Mec
Duality and fluctuation relations for statistics of currents on cyclic graphs
We consider stochastic motion of a particle on a cyclic graph with
arbitrarily periodic time dependent kinetic rates. We demonstrate duality
relations for statistics of currents in this model and in its continuous
version of a diffusion in one dimension. Our duality relations are valid beyond
detailed balance constraints and lead to exact expressions that relate
statistics of currents induced by dual driving protocols. We also show that
previously known no-pumping theorems and some of the fluctuation relations,
when they are applied to cyclic graphs or to one dimensional diffusion, are
special consequences of our duality.Comment: 2 figure, 6 pages (In twocolumn). Accepted by JSTA
The New Fe4a2o9 (A=Nb Or Ta) Magnetoelectric Oxides: on the Peculiar Role of Divalent Iron in the "429" Corundum Derivatives
Lattice Models of Nonequilibrium Bacterial Dynamics
We study a model of self propelled particles exhibiting run and tumble
dynamics on lattice. This non-Brownian diffusion is characterised by a random
walk with a finite persistence length between changes of direction, and is
inspired by the motion of bacteria such as E. coli. By defining a class of
models with multiple species of particle and transmutation between species we
can recreate such dynamics. These models admit exact analytical results whilst
also forming a counterpart to previous continuum models of run and tumble
dynamics. We solve the externally driven non-interacting and zero-range
versions of the model exactly and utilise a field theoretic approach to derive
the continuum fluctuating hydrodynamics for more general interactions. We make
contact with prior approaches to run and tumble dynamics off lattice and
determine the steady state and linear stability for a class of crowding
interactions, where the jump rate decreases as density increases. In addition
to its interest from the perspective of nonequilibrium statistical mechanics,
this lattice model constitutes and efficient tool to simulate a class of
interacting run and tumble models relevant to bacterial motion, so long as
certain conditions (that we derive) are met.Comment: 33 pages, 12 figure
Zero-range processes with saturated condensation: the steady state and dynamics
We study a class of zero-range processes in which the real-space condensation
phenomenon does not occur and is replaced by a saturated condensation: that is,
an extensive number of finite-size "condensates" in the steady state. We
determine the conditions under which this occurs, and investigate the dynamics
of relaxation to the steady state. We identify two stages: a rapid initial
growth of condensates followed by a slow process of activated evaporation and
condensation. We analyze these nonequilibrium dynamics with a combination of
meanfield approximations, first-passage time calculations and a
fluctuation-dissipation type approach.Comment: 21 pages, 12 figure
Entropy production and fluctuation relations for a KPZ interface
We study entropy production and fluctuation relations in the restricted
solid-on-solid growth model, which is a microscopic realization of the KPZ
equation. Solving the one dimensional model exactly on a particular line of the
phase diagram we demonstrate that entropy production quantifies the distance
from equilibrium. Moreover, as an example of a physically relevant current
different from the entropy, we study the symmetry of the large deviation
function associated with the interface height. In a special case of a system of
length L=4 we find that the probability distribution of the variation of height
has a symmetric large deviation function, displaying a symmetry different from
the Gallavotti-Cohen symmetry.Comment: 21 pages, 5 figure
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