24 research outputs found
Toward a phenomenological approach to the clustering of heavy particles in turbulent flows
A simple model accounting for the ejection of heavy particles from the
vortical structures of a turbulent flow is introduced. This model involves a
space and time discretization of the dynamics and depends on only two
parameters: the fraction of space-time occupied by rotating structures of the
carrier flow and the rate at which particles are ejected from them. The latter
can be heuristically related to the response time of the particles and hence
measure their inertia. It is shown that such a model reproduces qualitatively
most aspects of the spatial distribution of heavy particles transported by
realistic flows. In particular the probability density function of the mass
in a cell displays an power-law behavior at small values and decreases faster
than exponentially at large values. The dependence of the exponent of the first
tail upon the parameters of the dynamics is explicitly derived for the model.
The right tail is shown to decrease as . Finally, the
distribution of mass averaged over several cells is shown to obey rescaling
properties as a function of the coarse-grain size and of the ejection rate of
the particles. Contrarily to what has been observed in direct numerical
simulations of turbulent flows (Bec et al., http://arxiv.org/nlin.CD/0608045),
such rescaling properties are only due in the model to the mass dynamics of the
particles and do not involve any scaling properties in the spatial structure of
the carrier flow.Comment: 16 pages, 8 figure
The number of potential winners in Bradley-Terry model in random environment
We consider a Bradley-Terry model in random environment where each player
faces each other once. More precisely the strengths of the players are assumed
to be random and we study the influence of their distributions on the
asymptotic number of potential winners.First we prove that under mild
assumptions, mainly on their moments, if the strengths are unbounded, the
asymptotic probability that the best player wins is 1. We also exhibit a
sufficient convexity condition to obtain the same result when the strengths are
bounded. When this last condition fails, the number of potential winners grows
at a rate depending on the tail of the distribution of strengths. We also study
the minimal strength required for an additional player to win in this last
case
Motility-induced phase separation of active particles in the presence of velocity alignment
Self-propelled particle (SPP) systems are intrinsically out of equilibrium
systems, where each individual particle converts energy into work to move in a
dissipative medium. When interacting through a velocity alignment mechanism,
and the medium acts as a momentum sink, even momentum is not conserved. In this
scenario, a mapping into an equilibrium system seems unlikely. Here, we show
that an entropy functional can be derived for SPPs with velocity alignment and
density-dependent speed, at least in the (orientationally) disordered phase.
This non-trivial result has important physical consequences. The study of the
entropy functional reveals that the system can undergo phase separation before
the orientational-order phase transition known to occur in SPP systems with
velocity alignment.Moreover, we indicate that the spinodal line is a function
of the alignment sensitivity and show that density fluctuations as well as the
critical spatial diffusion, that leads to phase separation, dramatically
increase as the orientational-order transition is approached.Comment: Published in J. Stat. Phy
Current fluctuations in periodically driven systems
Small nonequelibrium systems driven by an external periodic protocol can be
described by Markov processes with time-periodic transition rates. In general,
current fluctuations in such small systems are large and may play a crucial
role. We develop a theoretical formalism to evaluate the rate of such large
deviations in periodically driven systems. We show that the scaled cumulant
generating function that characterizes current fluctuations is given by a
maximal Floquet exponent. Comparing deterministic protocols with stochastic
protocols, we show that, with respect to large deviations, systems driven by a
stochastic protocol with an infinitely large number of jumps are equivalent to
systems driven by deterministic protocols. Our results are illustrated with
three case studies: a two-state model for a heat engine, a three-state model
for a molecular pump, and a biased random walk with a time-periodic affinity.Comment: 18 pages, 4 figure