Related papers: Mathematical analysis of a thermodynamically consi…
Inelastic scattering techniques provide a powerful approach to studying electron and nuclear dynamics, via reconstruction of a propagator that quantifies the time evolution of a system. There is now growing interest in applying such methods…
We propose a systematic method of analyzing pseudopotential transferability based on linear-response properties of the free atom, including self-consistent chemical hardness and polarizability. Our calculation of hardness extends the…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…
Most mathematical models of the transport of charged species in battery electrodes require a constitutive relation describing intercalation of Lithium, which is a reversible process taking place on the interface between the electrolyte and…
Suppression of rectification at metal--Mott-insulator interfaces, which is previously shown by numerical solutions to the time-dependent Schr\"odinger equation and experiments on real devices, is reinvestigated theoretically by…
The structural evolution of laser-excited systems of gold has previously been measured through ultrafast MeV electron diffraction. However, there has been a long-standing inability of atomistic simulations to provide a consistent picture of…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…
We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…
The non-equilibrium dynamics of electrons is of a great experimental and theoretical value providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the…
An electro-chemo-mechanical phase-field formulation is developed to simulate pitting and stress corrosion in polycrystalline materials. The formulation incorporates dependencies of mechanical properties and corrosion potential on…
We study the low-energy behavior of metals coupled to gapless bosons. This problem arises in several contexts in modern condensed matter physics; we focus on the theory of metals near continuous quantum phase transitions (where the boson is…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
In this article the Butler-Volmer equation used in describing Lithium-ion (Li-ion) batteries is discussed. First, a complete mathematical model based on a macro-homogeneous approach developed by Neuman is presented. Two common mistakes…
An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The…
The Butler-Volmer (BV) equation links the current flux crossing an electrochemical interface to the electric potential drop across it with the assumption of Arrhenius kinetics and the Boltzmann factor. Applying the semilogarithmic Tafel…
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a…
In this paper, we demonstrate a set of fundamental conditions required for the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary Prandtl number. A specific collision operator form is then proposed that is in…
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution…
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and at a singular value of the temperature. To that end, we…