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Supercell modelling of an electrical double layer (EDL) at electrified solid-electrolyte interfaces is a challenge. The net polarization of EDLs arising from the fixed chemical composition setup leads to uncompensated EDLs under periodic…
We derive the spectral decomposition of the Lippmann-Schwinger equation for electrodynamics, obtaining the fields as a sum of eigenmodes. The method is applied to cylindrical geometries.
We introduce the heat equation relative to a positive dd-bar-closed current and apply it to the invariant currents associated with Riemann surface laminations possibly with singularities. The main examples are holomorphic foliations by…
A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate,…
We propose an electro-hydrodynamics model to describe the dynamic evolution of a slender drop containing a dilute ionic surfactant on a naturally wettable surface, with a varying external electric field. This unified model reproduces…
The linear electromagnetic response of a uniform electron gas to a longitudinal electric field is determined, within the self-consistent-field theory, by the linear polarizability and the Lindhard dielectric function. Using the same…
A phenomenological theory of electric double layer polarization of blocking electrode is presented solving modified Debye-Falkenhagen (MDF) equation for potential, under the impedance boundary condition. The dynamic impedance and…
The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard…
We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface…
The hydrodynamic equation for the spatial and temporal evolution of the electron temperature T_e in the breakdown of the quantum Hall effect at even-integer filling factors in a uniform current density j is derived from the Boltzmann-type…
The description of a conducting medium in thermal equilibrium, such as an electrolyte solution or a plasma, involves nonlinear electrostatics, a subject rarely discussed in the standard electricity and magnetism textbooks. We consider in…
In this paper, we present the general governing equations of electrodynamics and continuum mechanics that need to be considered while mathematically modelling the behaviour of electromagnetic acoustic transducers (EMATs). We consider the…
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
Coupled elliptic quantum dots with different aspect ratios containing up to two electrons are studied using a model confinement potential in the presence of magnetic fields. Single and two particle Schroedinger equations are solved using…
Understanding the electrical double layer (EDL), i.e, the distribution of electrolyte at an electrified interface, in concentrated electrolytes is important for various technologies, such as supercapacitors, batteries and electrocatalysis.…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…
We generalize the Einstein photoelectric equation for the case that the matter is irradiated by the polychromatic light of blackbody, or, by the synchrotron radiation. The work function of the collective motion of photoelectrons is…
This article is the second of a three-part series that derives a self-consistent theoretical framework of the electromechanics of arbitrarily curved lipid membranes. Existing continuum theories commonly treat lipid membranes as strictly…
The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects…
The electrical double layer for three different topologies of nanopore electrodes is studied, i.e., the interior and exterior electrical double layers of planar, cylindrical and spherical nanopores immersed into a point-ions electrolyte,…