9,397 research outputs found
A Method to Extract Potentials from the Temperature Dependence of Langmuir Constants for Clathrate-Hydrates
It is shown that the temperature dependence of Langmuir constants contains
all the information needed to determine spherically averaged intermolecular
potentials. An analytical ``inversion'' method based on the standard
statistical model of van der Waals and Platteeuw is presented which extracts
cell potentials directly from experimental data. The method is applied to
ethane and cyclopropane clathrate-hydrates, and the resulting potentials are
much simpler and more meaningful than those obtained by the usual method of
numerical fitting with Kihara potentials.Comment: 33 pages, 7 figures, to appear in Physica
Rigorous results in space-periodic two-dimensional turbulence
We survey the recent advance in the rigorous qualitative theory of the 2d
stochastic Navier-Stokes system that are relevant to the description of
turbulence in two-dimensional fluids. After discussing briefly the
initial-boundary value problem and the associated Markov process, we formulate
results on the existence, uniqueness and mixing of a stationary measure. We
next turn to various consequences of these properties: strong law of large
numbers, central limit theorem, and random attractors related to a unique
stationary measure. We also discuss the Donsker-Varadhan and Freidlin-Wentzell
type large deviations, as well as the inviscid limit and asymptotic results in
3d thin domains. We conclude with some open problems
Large deviations and Gallavotti-Cohen principle for dissipative PDE's with rough noise
We study a class of dissipative PDE's perturbed by an unbounded kick force.
Under some natural assumptions, the restrictions of solutions to integer times
form a homogeneous Markov process. Assuming that the noise is rough with
respect to the space variables and has a non-degenerate law, we prove that the
system in question satisfies a large deviation principle in tau-topology. Under
some additional hypotheses, we establish a Gallavotti-Cohen type symmetry for
the rate function of an entropy production functional and the strict positivity
and finiteness of the mean entropy production in the stationary regime. The
latter result is applicable to PDE's with strong nonlinear dissipation.Comment: 47 pages; to appear in Communications in Mathematical Physic
Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
The Freidlin-Wentzell large deviation principle is established for the
distributions of stochastic evolution equations with general monotone drift and
small multiplicative noise. As examples, the main results are applied to derive
the large deviation principle for different types of SPDE such as stochastic
reaction-diffusion equations, stochastic porous media equations and fast
diffusion equations, and the stochastic p-Laplace equation in Hilbert space.
The weak convergence approach is employed in the proof to establish the Laplace
principle, which is equivalent to the large deviation principle in our
framework.Comment: 31 pages, published in Appl. Math. Opti
Large Deviations and Importance Sampling for Systems of Slow-Fast Motion
In this paper we develop the large deviations principle and a rigorous
mathematical framework for asymptotically efficient importance sampling schemes
for general, fully dependent systems of stochastic differential equations of
slow and fast motion with small noise in the slow component. We assume
periodicity with respect to the fast component. Depending on the interaction of
the fast scale with the smallness of the noise, we get different behavior. We
examine how one range of interaction differs from the other one both for the
large deviations and for the importance sampling. We use the large deviations
results to identify asymptotically optimal importance sampling schemes in each
case. Standard Monte Carlo schemes perform poorly in the small noise limit. In
the presence of multiscale aspects one faces additional difficulties and
straightforward adaptation of importance sampling schemes for standard small
noise diffusions will not produce efficient schemes. It turns out that one has
to consider the so called cell problem from the homogenization theory for
Hamilton-Jacobi-Bellman equations in order to guarantee asymptotic optimality.
We use stochastic control arguments.Comment: More detailed proofs. Differences from the published version are
editorial and typographica
Selection theorem for systems with inheritance
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic
systems is studied. A non-linear kinetic system with conservation of supports
for distributions has generically finite-dimensional asymptotics. Such systems
are apparent in many areas of biology, physics (the theory of parametric wave
interaction), chemistry and economics. This conservation of support has a
biological interpretation: inheritance. The finite-dimensional asymptotics
demonstrates effects of "natural" selection. Estimations of the asymptotic
dimension are presented. After some initial time, solution of a kinetic
equation with conservation of support becomes a finite set of narrow peaks that
become increasingly narrow over time and move increasingly slowly. It is
possible that these peaks do not tend to fixed positions, and the path covered
tends to infinity as t goes to infinity. The drift equations for peak motion
are obtained. Various types of distribution stability are studied: internal
stability (stability with respect to perturbations that do not extend the
support), external stability or uninvadability (stability with respect to
strongly small perturbations that extend the support), and stable realizability
(stability with respect to small shifts and extensions of the density peaks).
Models of self-synchronization of cell division are studied, as an example of
selection in systems with additional symmetry. Appropriate construction of the
notion of typicalness in infinite-dimensional space is discussed, and the
notion of "completely thin" sets is introduced.
Key words: Dynamics; Attractor; Evolution; Entropy; Natural selectionComment: 46 pages, the final journal versio
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