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Displaying 161 –
180 of
198
We consider the nearest-neighbor simple random walk on ℤd, d≥2, driven by a field of bounded random conductances ωxy∈[0, 1]. The conductance law is i.i.d. subject to the condition that the probability of ωxy>0 exceeds the threshold for bond percolation on ℤd. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2n-step return probability . We prove that is bounded by a random constant timesn−d/2 in d=2, 3, while it...
The accretive operators theory is employed for proving an existence theorem for the evolutive energy equations involving simultaneously conduction, stationary convection (in the sense that the velocity field is assumed to be time independent), and radiation. In doing that we need to use new existence results for elliptic linear problems with mixed boundary conditions and irregular data.
A computer aided method using symbolic computations that enables the calculation of the
source terms (Boltzmann) in Grad’s method of moments is presented. The method is extremely
powerful, easy to program and allows the derivation of balance equations to very high
moments (limited only by computer resources). For sake of demonstration the method is
applied to a simple case: the one-dimensional stationary granular gas under gravity. The
method should...
We illustrate how some interesting new variational principles can be
used for the numerical approximation of solutions to certain (possibly
degenerate) parabolic partial differential equations. One remarkable
feature of the algorithms presented here is that derivatives do not
enter into the variational principles, so, for example, discontinuous
approximations may be used for approximating the heat equation. We
present formulae for computing a Wasserstein metric which enters
into the variational...
We propose a new formulation of the 3D Boltzmann
non linear operator, without assuming Grad's angular cutoff
hypothesis, and
for intermolecular laws behaving as 1/rs, with s> 2. It involves
natural pseudo differential operators, under a form which is analogous
to the Landau operator. It may be used in the study of the
associated equations, and more precisely in the non homogeneous
framework.
Artificial neural networks (ANN) have received a great deal of attention in many fields of engineering and science. Inspired by the study of brain architecture, ANN represent a class of non-linear models capable of learning from data. ANN have been applied in many areas where statistical methods are traditionally employed. They have been used in pattern recognition, classification, prediction and process control. The purpose of this paper is to discuss ANN and compare them to non-linear time series...
Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex:...
Currently displaying 161 –
180 of
198