Related papers: On the passage from atomistic systems to nonlinear…
Interaction of the superconducting condensate with deformations of the crystal lattice is formulated assuming the electrostatic potential of Bernoulli type and the effect of strain on material parameters. In the isotropic approximation it…
We derive a time-dependent density functional theory appropriate for calculating the near-edge X-ray absorption spectrum in molecules and condensed matter. The basic assumption is to increase the space of many-body wave functions from one…
In this paper, a phenomenological theory of saturated ferromagnetoelastic conductors is established using a multi-continuum model and the classical laws of mechanics, thermodynamics and electromagnetics. The theory is nonlinear and is valid…
Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and…
The exact nonlinear response of noninteracting (Bloch) electrons is examined within a nonequilibrium formalism on the infinite-dimensional hypercubic lattice. We examine the effects of a spatially uniform, but time-varying electric field…
We consider a quasilinear system of hyperbolic equations that describes plane one-dimensional non-relativistic oscillations of electrons in a cold plasma with allowance for electron-ion collisions. Accounting for collisions leads to the…
In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…
Density functional theory provides the most widespread framework for the realistic description of the electronic structure of solids, but the description of strongly-correlated systems has remained so far elusive. Here we consider a…
We consider the geometry of the space of Borel measures endowed with a distance that is defined by generalizing the dynamical formulation of the Wasserstein distance to concave, nonlinear mobilities. We investigate the energy landscape of…
We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic…
A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel-Kontorova…
The multiphase Whitham modulation equations with $N$ phases have $2N$ characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for coalescence, where two characteristics change from…
This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal effects within a macroscopic continuum. The nonlocal…
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee the convergence of the hybrid scheme to the solution of the…
We develop an analytic and environment-dependent interatomic potential for the overlap repulsion in solid argon, based on an approximate treatment of the non-orthogonal Tight-Binding theory for the closed-shell systems. The present model…
We derive a non-perturbative, closed, analytic equation for the non-linear power spectrum of cosmic density fluctuations. This result is based on our kinetic field theory (KFT) of cosmic structure formation and on evaluating particle…
The question of whether features and behaviors that are characteristic to completely integrable systems persist in the transition to non-integrable settings is a central one in the field of nonlinear dispersive equations. In this work, we…