Related papers: Exactly Solvable Dielectrics, Radiation Induced Fo…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
We consider a model of an elastic body immersed between two layers of incompressible viscous fluid. The elastic displacement $w$ is governed by the damped wave equation $w_{tt} + \alpha w_t + \Delta w =0$ without any stabilization terms,…
In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form.…
The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon…
We determine the invariant expression of the force density that the electromagnetic field exerts on dipolar matter and construct the non-symmetric energy-momentum tensor of the electromagnetic field in matter which is consistent with that…
In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations [Gopalakrishnan J., Lederer P., and Sch\"oberl J., A mass conserving mixed stress formulation for the Stokes equations, IMA…
Using the Green function integral representation the Dyson-Schwinger equations are solved directly in Minkowski space. Essential ideas of the spectral techniques are discussed and applied on two renormalizable models: the Yukawa theory with…
Using well-known mathematical foundations of the elasticity theory, a mathematical model for two solutes transport in a poroelastic material (soft tissue is a typical example) is suggested. It is assumed that molecules of essentially…
We present a microscopic model of a charge carrier transfer under an action of a constant electric field in a complex medium. Generalizing previous theoretical approaches, we model the dynamical environment hindering the carrier motion by…
A discussion is given on the interpretation and physical importance of the Minkowski momentum in macroscopic electrodynamics (essential for the Abraham-Minkowski problem). We focus on the following two facets: (1) Adopting a simple…
This paper is a continuation of a recent one in which, apparently for the first time, the existence of polaritons in ionic crystals was proven in a microscopic electrodynamic theory. This was obtained through an explicit computation of the…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…
The three-dimensional axisymmetric Boussinesq problem of an isotropic half-space subjected to a concentrated normal quasi-static load is studied within the framework of linear dipolar gradient elasticity. Our main concern is to determine…
Based upon our compact group approach and the Hashin-Shtrikman variational theorem, we propose a new solution, which effectively incorporates many-particle effects in concentrated systems, to the problem of the effective quasistatic…
Exact equations describing flexoelectric deformation in solids, derived previously within the framework of a continuum media theory, are partial differential equations of the fourth order. They are too complex to be used in the cases…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
Positive semi-definite expressions for the time-domain macroscopic energy density in passive, spatially nondispersive, dipolar continua are derived from the underlying microscopic Maxwell equations satisfied by classical models of discrete…