相关论文: Asymptotic Analysis of Second Order Nonlocal Cahn-…
We propose a simple nonlocal energy functional that is suitable for the continuum field characterization of nonperiodic and localized textures. The phenomenological functional is based on the pairwise direction-dependent interaction of…
We introduce a new type of local and microlocal asymptotic analysis in algebras of generalized functions, based on the presheaf properties of those algebras and on the properties of their elements with respect to a regularizing parameter.…
In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation with nonlocal memory effects. We analyze…
In this paper we study asymptotic behavior of $n$-superharmonic functions at isolated singularity using the Wolff potential and $n$-capacity estimates in nonlinear potential theory. Our results are inspired by and extend those of…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
We consider ensembles of Gaussian (Hermite) and Wishart (Laguerre) $N\times N$ hermitian matrices. We study the effect of finite rank perturbations of these ensembles by a source term. The rank $r$ of the perturbation corresponds to the…
Second-harmonic generation (SHG) is a direct measure of the strength of second-order nonlinear optical effects, which also include frequency mixing and parametric oscillations. Natural and artificial materials with broken…
A hierarchical model of interacting quantum particles performing anharmonic oscillations is studied in the Euclidean approach, in which the local Gibbs states are constructed as measures on infinite dimensional spaces. The local states…
Recently proposed nonlocal and nonperturbative late time behavior of the heat kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is dominated by two terms one of which represents a trivial covariantization of the…
We discuss the $\Gamma$-convergence, under the appropriate scaling, of the energy functional $$ \|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)dx,$$ with $s \in (0,1)$, where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in the…
Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $\mathbb{R}^n$. In particular, in the case when $n=2$ they obtained Gaussian…
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…
A double hybrid approximation using the Coulomb-attenuating method (CAM-DH) is derived within range-separated density-functional perturbation theory, in the spirit of a recent work by Cornaton {\it et al.} [Phys. Rev. A 88, 022516 (2013)].…
On a two-dimensional Riemannian manifold without boundary we consider the variational limit of a family of functionals given by the sum of two terms: a Ginzburg-Landau and a perimeter term. Our scaling allows low-energy states to be…
We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived…
The phase-field system is a nonlinear model that has significant applications in material sciences. In this paper, we are concerned with the uniqueness of determining the nonlinear energy potential in a phase-field system consisting of…
This work revolves around the rigorous asymptotic analysis of models in nonlocal hyperelasticity. The corresponding variational problems involve integral functionals depending on nonlocal gradients with a finite interaction range $\delta$,…
The paper is devoted to the linearization of the non linear Signorini functional in the incompressible case. The limit functional, in the sense of Gamma-convergence, may coincide with the expected one only in some particular cases.
We investigate a highly-nonlocal generalization of the Lindhard function, given by the jellium-with-gap model. We find a band-gap-dependent gradient expansion of the kinetic energy, which performs noticeably well for large atoms. Using the…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…