Related papers: Electrostatic problems with a rational constraint …
Equations of motion of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles…
We show that certain mixed displacement/traction problems (including live pressure tractions) of nonlinear elastostatics that are solved by a homogeneous deformation, admit no other classical equilibrium solution under suitable constitutive…
In the stationary case, atomistic interaction energies can be proved to $\Gamma$-converge to classical elasticity models in the simultaneous atomistic-to-continuum and linearization limit [19],[40]. The aim of this note is that of extending…
Several families of nonlinear field equations are known to possess space- localized singularity-free solutions which describe fields with finite Hermitian norms. This paper studies the interaction of such fields with given electromagnetic…
Tensegrity mechanisms are composed of rigid and tensile parts that are in equilibrium. They are interesting alternative designs for some applications, such as modelling musculo-skeleton systems. Tensegrity mechanisms are more difficult to…
For a given polynomial $P$ with simple zeros, and a given semiclassical weight $w$, we present a construction that yields a linear second-order differential equation (ODE), and in consequence, an electrostatic model for zeros of $P$. The…
In this paper, we study the regularity of solutions to uniformly degenerate elliptic equations in bounded domains under the condition that the characteristic polynomials have varying characteristic exponents.
In this paper we have obtained some dynamics equations, in the presence of nonlinear nonholonomic constraints and according to a lagrangian and some Chetaev-like conditions. Using some natural regular conditions, a simple form of these…
We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
By requiring the linear differential operator in Newton's law of motion to be self adjoint, we obtain the field equation for the linear theory, which is the classical electrodynamics. In the process, we are also led to a fundamental…
In this work we investigate the presence of electrically charged structures that are localized in two and three spatial dimensions. We use the Maxwell-scalar Lagrangian to describe several systems with distinct interactions for the scalar…
We study a covariant classical model of neutral point particles with magnetic moment interacting with external electromagnetic fields. Classical dynamical equations which reproduce a correct behavior in the non-relativistic limit are…
We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains $\Omega$, of solutions of degenerate elliptic equations depending also on the nonlinear gradient term $H$, in term of the size of $\Omega$,…
A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, the dynamics of the charged particle is described by an implicit ordinary second order differential…
The band structure of the Lam\'e equation, viewed as a one-dimensional Schr\"odinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion…
The study shows that errors exist in the derivation of equilibrium equations in terms of displacement. It is discovered that when the equilibrium equations in terms of displacement are derived, the variation of the differential order of…
Motion of a charged particle in uniform magnetic field has been studied in detail, classically as well as quantum mechanically. However, classical dynamics of a charged particle in non-uniform magnetic field is solvable only for some…
In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters…
The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In…