Related papers: Conservation laws for a general Lorentz connection
This work describes underlying features of the universe such as fundamental constants and cosmological parameters, conservation laws, baryon and lepton asymmetries, etc. in the context of local gauge theories for fundamental forces under…
Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78, 531-676], we completely describe local conservation laws of second-order (1+1)-dimensional evolution equations up to contact equivalence. The possible dimensions of…
The exact global energy conservation laws for the full-$f$ and $\delta f$ formulations of the nonlinear electromagnetic gyrokinetic equations in general magnetic geometry are presented. In both formulations, the relation between…
We analyze the laws of conservation of momentum and angular momentum in classical electrodynamics of material media with bound charges, and explore the possibility to describe the properties of such media via a discrete set of point-like…
A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz…
We investigate conservation laws of diffusion-convection equations to construct first-order potential systems corresponding to these equations. We do two iterations of the construction procedure, looking, in the second step, for the…
By exploiting the mathematical analogy between the propagation of sound in a non-homogeneous potential flow and the propagation of a scalar field in a background gravitational field, various wave ``energy'' and wave ``momentum''…
Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations. Using group classification and Noether's theorem,…
We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for…
Maxwell's macroscopic equations combined with a generalized form of the Lorentz law of force are a complete and consistent set of equations. Not only are these five equations fully compatible with special relativity, they also conform with…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
The form of the energy-momentum tensor when a quasimonochromatic field propagates into and through an antireflection-coated, sourceless, transparent, continuous, linear magneto-dielectric medium, initially at rest in the local frame,…
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription…
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler-Korteweg system to conserve the total energy. The…
In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolution of the famous Onsager conjecture - which states…
An exact solution of Lorentz-Dirac equations where the energy conservation law is violated, is described herein for the case of two charges.
Using the maximal Lie algebra of point symmetries of a system of nonlinear equations used in geophysical fluid dynamics, two conservation laws are found in addition to the conservation of energy.
We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous…
Based on relativistic velocity addition and the conservation of momentum and energy, I present derivations of the expressions for the relativistic momentum and kinetic energy, and $E=mc^2$.
Angular momentum can be defined by rearranging the Komar surface integral in terms of a twist form, encoding the twisting around of space-time due to a rotating mass, and an axial vector. If the axial vector is a coordinate vector and has…