9 research outputs found
A hierarchy of models related to nanoflows and surface diffusion
In last years a great interest was brought to molecular transport problems at
nanoscales, such as surface diffusion or molecular flows in nano or
sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V.
Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to
analyze the mechanisms that determine mobility of molecules in nanoscale
channels. This approach proved to be remarkably useful to give new insight on
these issues, such as density dependence of the diffusion coefficient. In this
paper we revisit these works to derive the kinetic and diffusion models
introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M.
Beenakker by using classical tools of kinetic theory such as scaling and
systematic asymptotic analysis. Some results are extended to less restrictive
hypothesis
Long Term Object Drift Forecast in the Ocean With Tide and
In this paper, we propose a new method to forecast the drift of objects in near coastal ocean on a period of several weeks. The proposed approach consists in estimating the probability of events linked to the drift using Monte Carlo simulations. It couples an averaging method which permits to decrease the computational cost and a statistical method in order to take into account the variability of meteorological loading factors
Gyro-gauge-independent formulation of the guiding-center reduction to arbitrary order in the Larmor radius
Large time dynamics of a classical system subject to a fast varying force
International audienceWe investigate the asymptotic behavior of solutions to a kinetic equation describing the evolution of particles subject to the sum of a fixed, confining, Hamiltonian, and a small, time-oscillating, perturbation. The equation also involves an interaction operator which acts as a relaxation in the energy variable. This paper aims at providing a classical counterpart to the derivation of rate equations from the atomic Bloch equations. In the present classical setting, the homogenization procedure leads to a diffusion equation in the energy variable, rather than a rate equation, and the presence of the relaxation operator regularizes the limit process, leading to finite diffusion coefficients. The key assumption is that the time-oscillatory perturbation should have well-defined long time averages: our procedure includes general "ergodic" behaviors, amongst which periodic, or quasi-periodic potentials only are a particular case
Theory of Transport Processes and the Method of the Nonequilibrium Statistical Operator
The aim of this review is to provide better understanding of a few approaches
that have been proposed for treating nonequilibrium (time-dependent) processes
in statistical mechanics with the emphasis on the inter-relation between
theories. The ensemble method, as it was formulated by J. W. Gibbs, have the
great generality and the broad applicability to equilibrium statistical
mechanics. Different macroscopic environmental constraints lead to different
types of ensembles, with particular statistical characteristics. In the present
work, the statistical theory of nonequilibrium processes which is based on
nonequilibrium ensemble formalism is discussed. The kinetic approach to dynamic
many-body problems, which is important from the point of view of the
fundamental theory of irreversibility, is alluded to. The emphasis is on the
method of the nonequilibrium statistical operator (NSO) developed by D. N.
Zubarev. The NSO method permits one to generalize the Gibbs ensemble method to
the nonequilibrium case and to construct a nonequilibrium statistical operator
which enables one to obtain the transport equations and calculate the transport
coefficients in terms of correlation functions, and which, in the case of
equilibrium, goes over to the Gibbs distribution. Although some space is
devoted to the formal structure of the NSO method, the emphasis is on its
utility. Applications to specific problems such as the generalized transport
and kinetic equations, and a few examples of the relaxation and dissipative
processes, which manifest the operational ability of the method, are
considered.Comment: This submission has been removed by arXiv admin because the files
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