Anomalously slow cross symmetry phase relaxation, thermalized non-equilibrated matter and quantum computing beyond the quantum chaos border.
Application of accretive operators theory to evolutive combined conduction, convection and radiation.
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.
Application of the Method of Generating Functions to the Derivation of Grad’s N-Moment Equations for a Granular Gas
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...
Approximation in the sense of Kato for the transport problem.
Approximation of crystalline dendrite growth in two space dimensions.
Approximation of parabolic equations using the Wasserstein metric
Approximation of Parabolic Equations Using the Wasserstein Metric
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...
Artificial neural networks. A review from physical and mathematical points of view
Artificial neural networks in time series forecasting: a comparative analysis
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 behaviour of a transport equation
We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation . We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.
Asymptotic self-similar blow-up for a model of aggregation
In this article we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see e.g. M. P. Brenner et al. 1999, Nonlinearity 12, 1071-1098); one type is self-similar, and may be viewed as a trade-off between diffusion...
Asymptotic stability of an equilibrium for the gas dynamics model of charge transport in semiconductors.
Asymptotic stability of the extended Tjon-Wu model.
Attractors of semigroups associated with nonlinear systems for diffusive phase separation.
Averaged large deviations for random walk in a random environment
In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ℤd with d≥1, and gives a variational formula for the corresponding rate function Ia. Under Sznitman’s transience condition (T), we show that Ia is strictly convex and analytic on a non-empty open set , and that the true velocity of the particle is an element (resp. in the boundary) of when the walk is non-nestling...
Billiards: models with chaotic dynamics.
Boundary value problems for the stationary Vlasov-Maxwell system.
Breaking the symmetry of a circular system of coupled harmonic oscillators.
Brownian fluctuations of the interface in the D=1 Ginzburg-Landau equation with noise
Capacity bounds for the CDMA system and a neural network: a moderate deviations approach
We study two systems that are based on sums of weakly dependent Bernoulli random variables that take values ± 1 with equal probabilities. We show that already one step of the so-called soft decision parallel interference cancellation, used in the third generation of mobile telecommunication CDMA, is able to considerably increase the number of users such a system can host. We also consider a variant of the well-known Hopfield model of neural networks. We show that this variant proposed by Amari...