相关论文: Reciprocal Transformations in Relativistic Gasdyna…
A new method for the Lie group classification of differential equations is proposed. It is based of the determination of all possible cases of linear dependence of certain indeterminate appearing in the determining equations of symmetries…
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…
An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The microscopic deterministic mechanism of the irreversible equilibration process in…
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to…
Accurate accounting of particle number and 4-momentum in radiative transfer may be facilitated by the use of transport equations that allow transparent conversion between volume and surface integrals in both spacetime and momentum space.…
The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the…
To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…
We show that an increasingly strong thermal rectification effect occurs in the thermodynamic limit in a one-dimensional, graded rotor lattice with nearest-neighboring interactions only. The underlying mechanism is related to the transition…
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity.…
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of…
In this paper, the dynamics of nonholonomic systems on Lie groups with a left-invariant kinetic energy and left-invariant constraints are considered. Equations of motion form a closed system of differential equations on the corresponding…
Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities…
Lie point symmetries of the one-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates are considered. Complete Lie group classification of these equations reduced to a scalar second-order PDE is performed. The…
The radial neoclassical fluxes of electrons in the 1/nu regime are calculated with relativistic effects taken into account and compared with those in the non-relativistic approach. The treatment is based on the relativistic drift-kinetic…
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…
We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is…
We analyze a few illustrative examples of scenarios in which relativistic symmetries are deformed by Planck-scale effects in particle-type-dependent manner. The novel mathematical structures required by such scenarios are the mixing…
We obtain a covariant decomposition of the motion of a relativistic charged particle into parallel motion and perpendicular gyration, and transform to guiding-center coordinates using Lie transforms. The natural guiding-center Poisson…