Related papers: Continuum limit of nonlinear discrete systems with…
Different subtleties and problems associated with a nonrelativistic limit of the field theory to the Schroedinger theory are discussed. In this paper, we revisit different cases of the nonrelativistic limit of a real and complex scalar…
A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimensional, function space,…
We study a two-dimensional quaternary inhibitory system. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited…
We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by…
We examine lower order perturbations of the harmonic map prob- lem from $\mathbb{R}^2$ to $\mathbb{S}^2$ including chiral interaction in form of a helicity term that prefers modulation, and a potential term that enables decay to a uniform…
We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator plus an indefinite potential. On the reaction term we impose conditions only near zero. Using variational methods, together with truncation and…
Optical bound state in the continuum (BIC) is characterized by infinitely high quality factor resulting in drastic enhancement of light-matter interaction phenomena. We study the optical response of a one-dimensional photonic crystal slab…
We consider the following nonlinear Schrodinger equation [{l} \Delta u-(1+\delta V)u+f(u)=0 in \R^N, u>0 in \R^N, u\in H^1(\R^N).] where $V$ is a potential satisfying some decay condition and $ f(u)$ is a superlinear nonlinearity satisfying…
The approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) when the intensity of spin-spin interaction is $\sim 1/r^3$, where $r$ is a distance between those…
One- to three-dimensional hypercubic lattices half-filled with localized particles interacting via the long-range Coulomb potential are investigated numerically. The temperature dependences of specific heat, mean staggered occupation, and…
We establish the $\Gamma$-convergence of some energy functionals describing nonlocal attractive interactions in bounded domains. The interaction potential solves an elliptic equation (local or nonlocal) in the bounded domain and the primary…
For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior…
We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, discrete, and interface contributions. Our main estimate…
Infinite-dimensional linear systems with unbounded input and output operators are considered. For the purpose of finite-dimensional observer-based state feedback, an observer approximation scheme will be developed which can be directly…
The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying…
Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…
We prove the equivalence between the integral central limit theorem and the local central limit theorem for two-body potentials with long-range interactions on the lattice $\mathbb{Z}^d$ for $d\ge 1$. The spin space can be an arbitrary,…
In the present article, we provide analytic foundation of the following nonlinear elliptic system, called the \emph{Hamiltonian-perturbed contact instanton equation}, $$ (du - X_H \otimes \gamma)^{\pi(0,1)} = 0, \quad d(e^{g_{H,…
For systems of one-component interacting oscillators on the d-dimensional lattice, d>1, whose potential energy besides a large nearest-neighbour (n-n) ferromagnetic translation-invariant quadratic term contains small non-nearest-neighbour…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…