Related papers: Synge's dynamic problem for two isolated point cha…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…
We discuss a set of novel discrete symmetries of a free N = 2 supersymmetric (SUSY) quantum mechanical system which is the limiting case of a widely-studied interacting SUSY model of a charged particle constrained to move on a sphere in the…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…
In this work, the synchronization problem of a master-slave system of autonomous ordinary differential equations (ODEs) is considered. Here, the systems are, chaotic with a nonlinearity represented by a piecewise linear function,…
We consider SDEs with (distributional) drift in negative Besov spaces and random initial condition and investigate them from two different viewpoints. In the first part we set up a martingale problem and show its well-posedness.We then…
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution…
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…
Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…
We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic…
We consider self-similar, radially symmetric solutions of the relativistic Euler equations with constitutive relations from relativistic kinetic theory, based on Synge energies for monatomic and its extension to diatomic gases. For the…
In the direct action form of classical EM we give the equation of motion for a classical massless bare charge without self-interaction in the presence of an external field. That equation permits superluminal speeds and time-reversals, and…
A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange…
When exploring equations of nonlinear electrodynamics in effective medium formed by mutually parallel external electric and magnetic fields, we come to special static axial-symmetric solutions of two types. The first are comprised of fields…
The increasing global spread of electric vehicles (EVs) has introduced significant interdependence between transportation and power networks. Most of the previous studies on coupled networks focus on the formation of equilibrium states…
The Maxwell-Lorentz theory of electrodynamics cannot readily be applied to a system of point charges: the electromagnetic field is not well-defined at the position of a point charge, an energy conservation argument is not obvious, an…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
Interatomic potentials which accurately describe long-range electrostatics require atom-centred charges. One such method to determine these atom-centred charges from density functional theory (DFT) calculations is the density-derived atomic…