Related papers: Energetically-consistent collisional gyrokinetics
We study energy transport in a one-dimensional model of elastically colliding particles with alternate masses $m$ and $M$. In order to prevent total momentum conservation we confine particles with mass $M$ inside a cell of finite size. We…
The relativistic conservation law involving the center of energy is reviewed and illustrated using simple examples from classical electromagnetic theory. It is emphasized that this conservation law is parallel to the conservation laws for…
A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference…
We treat energy-momentum conservation laws as particular gauge conservation laws when generators of gauge transformations are horizontal vector fields on fibre bundles. In particular, the generators of general covariant transformations are…
Implications of noncommutative field theories with commutator of the coordinates of the form $[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu \nu}x^{\omega}$with nilpotent structure constants are investigated. It is shown that a free…
In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and…
We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the…
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on…
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the…
The Eulerian variational principle for the Vlasov-Poisson-Amp\`{e}re system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to…
Motivated by ultra-high-energy cosmic ray physics, we discuss all the possible alternatives to the familiar Lorentz transformations of the momentum and the energy of a particle. Starting from natural physical requirements, we exclude all…
Gauge invariant conservation laws for the linear and angular momenta are studied in a certain 2+1 dimensional first order dynamical model of vortices in superconductivity. In analogy with fluid vortices it is possible to express the linear…
In this note I sketch the work of Christiaan Huygens to develop a theory of motion and its application to elastic collisions. In this theory he uses the relativity of uniform linear motion to derive the conservation of momentum and kinetic…
We construct an action for the composite Dirac fermion consistent with symmetries of electrons projected to the lowest Landau level. First we construct a generalization of the $g=2$ electron that gives a smooth massless limit on any curved…
In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…
In this study I develop a novel action for lattice gauge theory for finite systems, which accommodates non-periodic boundary conditions, implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum…
Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy--momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity…
We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the…
The dynamics of classical field theories is usually governed by field equations, but when fields are constrained to bounded domains it is also dependent on its boundary conditions. Usually boundary conditions are constrained by the…
We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in…