Related papers: On equilibrium equations and their perturbations u…
The paper deals with electromagnetic perturbations of a central force problem of the form \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t} \bigl( \varphi(\dot{x}) \bigr) = V'(|x|) \dfrac{x}{|x|} + E_{\varepsilon}(t,x)+\dot{x} \wedge…
Euler-Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global…
A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid…
The boundary problem about behavior (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with specular boundary conditions is analytically solved. The kinetic equation of…
In our previous paper, based on the Carter & Quintana framework and the Damour-Soffel-Xu scheme, we deduced a complete and closed set of post-Newtonian dynamical equations for elastically deformable astronomical bodies. In this paper, we…
In this paper, first we present the variational formulation for a second strain gradient Euler-Bernoulli beam theory for the first time. The governing equation and associated classical and non-classical boundary conditions are obtained.…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
In 1933-1934 Born and Infeld constructed the first non-linear generalization of Maxwell's electrodynamics that turned out to be a remarkable theory in many respects. In 1935 Heisenberg and Euler computed a complete effective action…
In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is driven by the Baouendi-Grushin operator with variable…
Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…
We reexamine the energy-momentum tensor in classical electrodynamics from the perspective of spacetime-dependent translations, i.e., diffeomorphism invariance in flat spacetime. When energy-momentum is identified through local translations…
Soft dielectric elastomers that can exhibit extremely large deformations under the action of an electric field enable applications such as soft robotics, biomedical devices, energy harvesting among others. A key impediment in the use of…
We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via non-central two-body potentials as thermal averages of products of first and second partial derivatives of the…
In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the…
The mechanics of a flexible membrane decorated with a nematic liquid-crystal texture is considered in a variational framework. The variations on the splay, twist and the bend energy of the nematics are obtained from the local deformations…
We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…
This paper presents an alternative prerelativistic approach to the vacuum case of classical electrodynamics represented by vacuum Maxwell equations. Our view is based on the understanding that the corresponding differential equations should…