Related papers: Generalized Four-momentum for Continuously Distrib…
The 4-D theory with connection components Gamma^k_{mn} as field variables and module of squared curvature |R^k_{lmn}R^{lmn}_k| as Lagrangian is described. The Maxwell equations, the Lorentz condition and the gravity field equation, that…
In this paper, it is proved that the teleparallel energy-momentum generalizes that of the ADM formalism. In doing so, it is shown that the teleparallel $4$-momentum can be made to coincide with that of the ADM approach whenever the ADM…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
A new theory for the dynamics of the magnetic particles and their magnetic moments in ferrofluids is developed. Based on a generalized Lagrangian formulation for the equations of motion of the colloidal particle, we introduce its…
We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of assuming any particular nature or…
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
We propose that the four-velocity of a Dirac particle is related to its relativistic wave function by $u^i=\bar{\psi}\gamma^i\psi/\bar{\psi}\psi$. This relativistic wave$-$particle duality relation is demonstrated for a free particle…
Generalized Lagrangian mean theories are used to analyze the interactions between mean flows and fluctuations, where the decomposition is based on a Lagrangian description of the flow. A systematic geometric framework was recently developed…
An exact description of the statistical motion of active particles in three dimension is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a non-local, in time and space, connecting (memory)…
We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
A new fourth partial derivative is introduced for the study of transport dynamics. It is a Lagrangian partial derivative following the path of diffusion, not the path of convection. Use of this derivative decouples the effect of diffusion…
In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the inclusion of irreversible phenomena in both discrete and…
Classical relativistic field theory is applied to perfect and magneto-hydrodynamic flows. The fields for Hamilton's principle are shown to be the Lagrangian coordinates of the fluid elements, which are potentials for the matter current…
We present an insightful ``derivation'' of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton's Law of motion…
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal…
I propose a model of mutually interacting particles on an M-dimensional unit sphere. I derive the dynamics of the particles by extending the dynamics of the Kuramoto-Sakaguchi model. The dynamics include a natural-frequency matrix, which…
We consider the Regge-Teitelboim model for a relativistic extended object embedded in a fixed background Minkowski spacetime, in which the dynamics is determined by an action proportional to the integral of the scalar curvature of the…
The deduction of a constant of motion, a Lagrangian, and a Hamiltonian for relativistic particle moving in a dissipative medium characterized by a force which depends on the square of the velocity of the particle is done. It is shown that…