Related papers: Lower semicontinuity in $GSBD$ for nonautonomous s…
Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex geometries. Two key properties for non-conforming methods to…
We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an…
The paper combines two topics belonging to the general theme of the spontaneous symmetry breaking (SSB) in systems including two basic competing ingredients: the self-focusing cubic nonlinearity and a double-well-potential (DWP) structure.…
We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…
Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $\phi(v; \cdot)$ be the density of the absolutely…
We have developed a new type of self-consistent scheme within the $GW$ approximation, which we call quasiparticle self-consistent $GW$ (QS$GW$). We have shown that QS$GW$ rather well describes energy bands for a wide-range of materials,…
Unconditional guaranteed lower and upper eigenvalue bounds are mandatory for the understanding of the Schr\"odinger eigenvalue spectrum and its spectral gaps. While upper eigenvalue bounds are naturally induced by conforming…
A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system…
We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…
For algebro-geometric study of J-stability, a variant of K-stability, we prove a decomposition formula of non-archimedean $\mathcal{J}$-energy of $n$-dimensional varieties into $n$-dimensional intersection numbers rather than…
In the nonconvex case solutions of rate-independent systems may develop jumps as a function of time. To model such jumps, we adopt the philosophy that rate independence should be considered as limit of systems with smaller and smaller…
In this paper we introduce a new semicontinuity notion, which is weaker than upper semicontinuity, and assures the closedness of the sets $G(y)=\{x\in K: f(x,y)\not\in -\inte C\}.$ Furhter, this semicontinuity is also closed under addition.…
A semiconductor nanowire based superconductor-normal-superconductor (SNS) junction is modeled theoretically. A magnetic field is applied along the nanowire axis, parallel to the current. The Bogoliubov-de Gennes equations for Andreev bound…
In this work, we develop a level-set subdifferential error bound condition aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It…
The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…
The notion of Inertial Balanced Viscosity (IBV) solution to rate-independent evolutionary processes is introduced. Such solutions are characterized by an energy balance where a suitable, rate-dependent, dissipation cost is optimized at jump…
We derive novel concentration inequalities for the operator norm of the sum of self-adjoint operators that do not explicitly depend on the underlying dimension of the operator, but rather an intrinsic notion of it. Our analysis leads to…
We present a comprehensive convergence analysis for Self-Consistent Field (SCF) iteration to solve a class of nonlinear eigenvalue problems with eigenvector-dependency (NEPv). Using a tangent-angle matrix as an intermediate measure for…
Consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a new $W^{1,1}-$trace estimate for the diffuse boundary…
First-principles methods have recently established themselves in the field of photocathode research to provide microscopic, quantum-mechanical characterization of relevant materials for electron sources. While most of the existing studies…