2,211 research outputs found
Diffusion, subdiffusion, and trapping of active particles in heterogeneous media
We study the transport properties of a system of active particles moving at
constant speed in an heterogeneous two-dimensional space. The spatial
heterogeneity is modeled by a random distribution of obstacles, which the
active particles avoid. Obstacle avoidance is characterized by the particle
turning speed . We show, through simulations and analytical
calculations, that the mean square displacement of particles exhibits two
regimes as function of the density of obstacles and . We find
that at low values of , particle motion is diffusive and characterized
by a diffusion coefficient that displays a minimum at an intermediate obstacle
density . We observe that in high obstacle density regions and for
large values, spontaneous trapping of active particles occurs. We show
that such trapping leads to genuine subdiffusive motion of the active
particles. We indicate how these findings can be used to fabricate a filter of
active particles.Comment: to appear in Phys. Rev. Let
A spatial capture-recapture model for territorial species
Advances in field techniques have lead to an increase in spatially-referenced
capture-recapture data to estimate a species' population size as well as other
demographic parameters and patterns of space usage. Statistical models for
these data have assumed that the number of individuals in the population and
their spatial locations follow a homogeneous Poisson point process model, which
implies that the individuals are uniformly and independently distributed over
the spatial domain of interest. In many applications there is reason to
question independence, for example when species display territorial behavior.
In this paper, we propose a new statistical model which allows for dependence
between locations to account for avoidance or territorial behavior. We show via
a simulation study that accounting for this can improve population size
estimates. The method is illustrated using a case study of small mammal
trapping data to estimate avoidance and population density of adult female
field voles (Microtus agrestis) in northern England
Random walks and polymers in the presence of quenched disorder
After a general introduction to the field, we describe some recent results
concerning disorder effects on both `random walk models', where the random walk
is a dynamical process generated by local transition rules, and on `polymer
models', where each random walk trajectory representing the configuration of a
polymer chain is associated to a global Boltzmann weight. For random walk
models, we explain, on the specific examples of the Sinai model and of the trap
model, how disorder induces anomalous diffusion, aging behaviours and Golosov
localization, and how these properties can be understood via a strong disorder
renormalization approach. For polymer models, we discuss the critical
properties of various delocalization transitions involving random polymers. We
first summarize some recent progresses in the general theory of random critical
points : thermodynamic observables are not self-averaging at criticality
whenever disorder is relevant, and this lack of self-averaging is directly
related to the probability distribution of pseudo-critical temperatures
over the ensemble of samples of size . We describe the
results of this analysis for the bidimensional wetting and for the
Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S.,
France, November 200
Dynamic social learning under graph constraints
We introduce a model of graph-constrained dynamic choice with reinforcement
modeled by positively -homogeneous rewards. We show that its empirical
process, which can be written as a stochastic approximation recursion with
Markov noise, has the same probability law as a certain vertex reinforced
random walk. We use this equivalence to show that for , the
asymptotic outcome concentrates around the optimum in a certain limiting sense
when `annealed' by letting slowly
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