Related papers: An energy method for averaging lemmas
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
A physically-based method to derive well-posed instances of the two-fluid transport equations for two-phase flow, from the Hamilton principle, is presented. The state of the two-fluid flow is represented by the superficial velocity and the…
We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries,…
This paper addresses the problem of the separation of rotational and internal motion. It introduces the concept of average angular velocity as the moment of inertia weighted average of particle angular velocities. It extends and elucidates…
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of…
Recent results on the fluid dynamic limits of the Boltzmann equation based on the DiPerna-Lions theory of renormalized solutions are reviewed in this paper, with an emphasis on regimes where the velocity field behaves to leading order like…
We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…
In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a mapping of the original model to a simpler…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
The kinetic theory of gases, including Granular Gases, is based on the Boltzmann equation. Many properties of the gas, from the characteristics of the velocity distribution function to the transport coefficients may be expressed in terms of…
We provide a new proof of the known partial regularity result for the optimal transportation map (Brenier map) between two sets. Contrary to the existing regularity theory for the Monge-Amp{\`e}re equation, which is based on the maximum…
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence…
In the present work, we adopt the idea of velocity averaging lemma to establish regularity for stationary linearized Boltzmann equations in a bounded convex domain. Considering the incoming data, with three iterations, we establish…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
The possible functional forms of the effective conductivity sigma_{eff} of the randomly inhomogeneous two-phase system at arbitrary values of concentrations are discussed. A new functional equation, generalizing the duality relation, is…
We present a new view for duality in classical electromagnetic theory, based on the physical properties of a dual theory, eliminating the problems of the usual treatment of the subject.