Related papers: Hydrodynamic approximation for the nonlinear respo…
In these notes, we describe the strategy for the derivation of the hydrodynamic limit for a family of long range interacting particle systems of exclusion type with symmetric rates. For $m \in \mathbb{N}:=\{1, 2, \ldots\}$ fixed, the…
The surface energy, the one-particle distribution function of electrons, etc. of a semi-bounded metal within the framework of the semi-infinite jellium are calculated. The influence of the potential barrier height on these characteristics…
The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(\nu e^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck…
Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a…
The motion of the charged particles in graphen in the frame of the quantum non-local hydrodynamic description is considered. It is shown as results of the mathematical modeling that the mentioned motion is realizing in the soliton forms.…
In this paper we dwell over the study of the boundary layer problem in a hydrodynamical description of the electrons in gated graphene. It has been verified experimentally that this fluid can display non-Poiseuille like flow as reproduced…
In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this paper, we develop an…
Electrostatics in the solution phase is governed by free electrical charges such as ions, as well as by bound charges that arise when a polarizable medium responds to an applied field. In a local medium, described by a constant dielectric…
We consider the derivation and numerical solution of the flow of passive and active polar liquid crystals, whose molecular orientation is subjected to a tangential anchoring on an evolving curved surface. The underlying passive model is a…
Can we avoid molecular dynamics simulations to estimate the electrostatic interaction between charged objects separated by a nanometric distance in water? To answer this question, we develop a continuous model for the dielectric properties…
We present real-time time-dependent density-functional-theory calculations of the electronic stopping power for negative and positive projectiles (electrons, protons, antiprotons and muons) moving through liquid water. After correction for…
We develop a thermodynamic description of particles held at a fixed surface potential. This system is of particular interest in view of the continuing controversy over the possibility of a fluid-fluid phase separation in aqueous colloidal…
We investigate the linear and non-linear optical response of two-dimensional (2D) interacting electron fluids confined by a strong non-parabolic potential. We show that such fluids may exhibit higher-harmonic spectra under realistic…
We study the mobility of a charged colloidal particle in a constant homogeneous electric field by means of computer simulations. The simulation method combines a lattice Boltzmann scheme for the fluid with standard Langevin dynamics for the…
We study the thermodynamic behavior of nonpolar liquid mixtures in the vicinity of curved charged objects, such as electrodes or charged colloids. For small enough charge on the object, or equivalently, small potential, the…
We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is…
Due to the many unique transport properties of Weyl semimetals, they are promising materials for modern electronics. We investigate the electrons in the strong coupling approximation near Weyl points based on their representation as…
Nonlinear electrokinetic phenomena, where electrically driven fluid flows depend nonlinearly on the applied voltage, are commonly encountered in aqueous suspensions of colloidal particles. A prime example is the induced-charge…
The position-dependent exact-exchange energy per particle $\varepsilon_x(z)$ (defined as the interaction between a given electron at $z$ and its exact-exchange hole) at metal surfaces is investigated, by using either jellium slabs or the…
By constructing a hydrodynamic canonical formalism, we show that the occurrence of an arbitrary density-dependent gauge potential in the meanfield Hamiltonian of a Bose-condensed fluid invariably leads to nonlinear flow-dependent terms in…