Related papers: An energy method for averaging lemmas
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
A classical Lagrangian model of the Pauli potential is introduced. It is shown that the kinematic kinetic energy ($\sum \frac{1}{2} m v^2$) in the model approximately reproduces the energy of a free Fermi gas at low temperatures and at…
A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the…
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the optimal exchange problem are proved in case of completely…
We generalise the celebrated semiclassical wavepacket approach from the adiabatic to the non-adiabatic regime. A unified description covering both of these regimes is particularly desired for systems with spatially varying band structures…
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
This paper presents a pure complementary energy variational method for solving anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconex partial…
We introduce a general and systematic theoretical framework for Operational Dynamic Modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of…
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time-evolutions of…
The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the…
Mean force kinetic theory is used to evaluate the electrical conductivity, thermal conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity of a two-component (ion-electron) plasma. Results are compared with…
The transport phenomena of a nonequilibrium lattice gas system are investigated. We consider a simple system that consists of two particles interacting repulsively and the potential forces acting on these particles. Under an external…
The exponential moving average (EMA) is a commonly used statistic for providing stable estimates of stochastic quantities in deep learning optimization. Recently, EMA has seen considerable use in generative models, where it is computed with…
We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…
We discuss first-order and second-order regularization effects for solutions to the classical heat equation. In particular we propose a global approach to study smoothing effects of Hamilton-Li-Yau type: such approach is nonlinear in spirit…
This dissertation is about the study of three important issues in the theory of relativistic fluid dynamics: the stability of dissipative fluid dynamics, the shear viscosity, and fluid dynamics with triangle anomaly.(1)The second order…
We study the two-dimensional gravity water waves with a one-dimensional interface with small initial data. Our main contributions include the development of two novel localization lemmas and a Transition-of-Derivatives method, which enable…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas…
We provide a consistent description of the kinetic equation with triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an…