Related papers: Application of the $j$-subgradient in a problem of…
The paper is concerned with a system of linear hyperbolic differential equations on a network coupled through general transmission conditions of Kirchhoff's type at the nodes. We discuss the reduction of such a problem to a system of…
Electrical transients enabled by optical excitation and electric detection provide a distinctive opportunity to study the charge transport, recombination and even the hysteresis of a solar cell in a much wider time window ranging from…
We consider a class of nonlinear non-diagonal elliptic systems with $p$-growth and establish the $L^q$-integrability for all $q\in [p,p+2]$ of any weak solution provided the corresponding right hand side belongs to the corresponding…
Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relations. For elliptic problems, the cornerstone in the scheme…
We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
A review of the present state of investigations of the pseudospin-electron model (PEM), which is used in the theory of strongly correlated electron systems, is given. The model is used to describe the systems with the locally anharmonic…
In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the…
We study a phenomenological electropermeabilization model in a periodic medium representing biological tissue. Starting from a cell-level model describing the electric potential and the degree of porosity, we perform dimension analysis to…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
Examples of scalar conserved currents are presented for trigonometric, hyperbolic and elliptic versions of the Hubbard model with non-nearest neighbour variable range hopping. They support for the first time the hypothesis about the…
In this paper, the inherent gradient flow structures of thermo-poro-visco-elastic processes in porous media are examined for the first time. In the first part, a modelling framework is introduced aiming for describing such processes as…
We present a microscopic theory for the description of the bias-controlled operation of an exciton-polariton-based heterostructure, in particular, the polariton laser. Combining together the Poisson equations for the scalar electric…
In this paper we study the pseudomonotone equilibrium problem. We consider a new inertial condition for the subgradient extragradient method with self-adaptive step size for approximating a solution of the equilibrium problem in a real…
The problem of electron-proton scattering is handed over both the elastic and inelastic scattering. Two models are presented in this sense. The first, depends on the multi photon exchange ladder diagram, where the transition matrix is…
We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We…
We consider an almost complex structure J on CP2, or more generally an elliptic structure E which is tamed by the standard symplectic structure. An E-curve is a surface tangent to E (this generalizes the notion of J(holomorphic)-curve), and…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…