71,294 research outputs found
Collision number statistics for transport processes
Many physical observables can be represented as a particle spending some
random time within a given domain. For a broad class of transport-dominated
processes, we detail how it is possible to express the moments of the number of
particle collisions in an arbitrary volume in terms of repeated convolutions of
the ensemble equilibrium distribution. This approach is shown to generalize the
celebrated Kac formula for the moments of residence times, which is recovered
in the diffusion limit. Some practical applications are illustrated for
bounded, unbounded and absorbing domains.Comment: 4 pages, 4 figure
Burgers velocity fields and dynamical transport processes
We explore a connection of the forced Burgers equation with the
Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of
deterministic external forces. This entails an exploration of the consistency
conditions that allow to interpret dispersion of passive contaminants in the
Burgers flow as a Markovian diffusion process. In general, the usage of a
continuity equation , where
stands for the Burgers field and is the
density of transported matter, is at variance with the explicit diffusion
scenario. Under these circumstances, we give a complete characterisation of the
diffusive matter transport that is governed by Burgers velocity fields. The
result extends both to the approximate description of the transport driven by
an incompressible fluid and to motions in an infinitely compressible medium.Comment: Latex fil
Transport Processes in Metal-Insulator Granular Layers
Tunnel transport processes are considered in a square lattice of metallic
nanogranules embedded into insulating host to model tunnel conduction in real
metal/insulator granular layers. Based on a simple model with three possible
charging states (, or 0) of a granule and three kinetic processes
(creation or recombination of a pair, and charge transfer) between
neighbor granules, the mean-field kinetic theory is developed. It describes the
interplay between charging energy and temperature and between the applied
electric field and the Coulomb fields by the non-compensated charge density.
The resulting charge and current distributions are found to be essentially
different in the free area (FA), between the metallic contacts, or in the
contact areas (CA), beneath those contacts. Thus, the steady state dc transport
is only compatible with zero charge density and ohmic resistivity in FA, but
charge accumulation and non-ohmic behavior are \emph{necessary} for conduction
over CA. The approximate analytic solutions are obtained for characteristic
regimes (low or high charge density) of such conduction. The comparison is done
with the measurement data on tunnel transport in related experimental systems.Comment: 10 pages, 11 figures, 1 reference corrected, acknowlegments adde
Lagrangian coherent structures and plasma transport processes
A dynamical system framework is used to describe transport processes in
plasmas embedded in a magnetic field. For periodic systems with one degree of
freedom the Poincar\'e map provides a splitting of the phase space into regions
where particles have different kinds of motion: periodic, quasi-periodic or
chaotic. The boundaries of these regions are transport barriers; i.e., a
trajectory cannot cross such boundaries during the whole evolution of the
system. Lagrangian Coherent Structure (LCS) generalize this method to systems
with the most general time dependence, splitting the phase space into regions
with different qualitative behaviours. This leads to the definition of
finite-time transport barriers, i.e. trajectories cannot cross the barrier for
a finite amount of time. This methodology can be used to identify fast
recirculating regions in the dynamical system and to characterize the transport
between them
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