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We study $N$-particle systems in R^d whose interactions are governed by a hypersingular Riesz potential $|x-y|^{-s}$, $s>d$, and subject to an external field. We provide both macroscopic results as well as microscopic results in the limit…

Mathematical Physics · Physics 2017-11-09 Douglas P. Hardin , Thomas Leblé , Edward B. Saff , Sylvia Serfaty

We study a large family of Riesz-type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain…

Analysis of PDEs · Mathematics 2022-09-28 José A. Carrillo , Ruiwen Shu

We consider spin-half fermionic atoms with isotropic Rashba spin-orbit coupling in three directions. The interatomic potential is modeled by a square well potential. We derive the analytic form of the asymptotic wave-functions at short…

Quantum Gases · Physics 2013-03-19 Yuxiao Wu , Zhenhua Yu

The low-density expansions for the energy, chemical potential, and condensate depletion of the homogeneous dilute dipolar Bose gas are obtained by regularizing the dipole-dipole interaction at long distances. It is shown that the leading…

Quantum Gases · Physics 2020-01-01 Alexander Yu. Cherny

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

Probability · Mathematics 2021-06-09 Michael Röckner , Longjie Xie , Li Yang

We prove that, for a density of disorder $\rho$ small enough, a certain class of discrete random Schr\"odinger operators on $\Z^d$ with diluted potentials exhibits a Lifschitz behaviour from the bottom of the spectrum up to energies at a…

Mathematical Physics · Physics 2012-02-23 Francisco W. Hoecker-Escuti

We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the…

Analysis of PDEs · Mathematics 2023-11-27 Rupert L. Frank , Ryan W. Matzke

The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction-radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the…

Subcellular Processes · Quantitative Biology 2016-10-26 Sam Isaacson , Ava Mauro , Jay Newby

The Stretched Sierpinski Gasket (or Hanoi attractor) was subject of several prior works. In this work we use this idea of stretching self-similar sets to obtain non-self-similar ones. We are able to do this for a subset of the connected…

Spectral Theory · Mathematics 2018-09-28 Elias Hauser

The combination of density functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is…

Materials Science · Physics 2009-11-11 Paola Gori-Giorgi , Andreas Savin

In this paper, we provide modulated interaction energy estimates for the kernel $K(x) = |x|^{-\alpha}$ with $\alpha \in (0,d)$, and its applications to quantified asymptotic analyses for kinetic equations. The proof relies on a dimension…

Analysis of PDEs · Mathematics 2021-12-24 Young-Pil Choi , Jinwook Jung

Asymptotic Schur orthogonality relations are for irreducible unitary representations of locally compact groups that need not be discrete series, where $L^2$ pairing of matrix coefficients with respect to Haar measure is replaced by a limit…

Representation Theory · Mathematics 2025-06-24 Malay Mandal , Arghya Mondal

This paper investigates a system of nonlocal continuity equations modelling the interaction of two species coupled through Riesz-type potentials. The model incorporates self- and cross-interaction kernels of possibly different fractional…

Analysis of PDEs · Mathematics 2026-04-02 Simone Fagioli , Valeria Iorio

This paper investigates the principal spectral theory and the asymptotic behavior of the principal spectrum point for a class of time-periodic cooperative systems with nonlocal dispersal operators, incorporating both coupled and uncoupled…

Analysis of PDEs · Mathematics 2026-02-11 Hao Wu , Wan-Tong Li , Jian-Wen Sun , Hoang-Hung Vo

We use a Mellin-Barnes integral representation for the Lerch transcendent $\Phi(z,s,a)$ to obtain large $z$ asymptotic approximations. The simplest divergent asymptotic approximation terminates in the case that $s$ is an integer. For…

Classical Analysis and ODEs · Mathematics 2024-03-22 Adri B. Olde Daalhuis

We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces…

Group Theory · Mathematics 2007-05-23 G. C. Bell , A. N. Dranishnikov

The mean field properties and equation of state for asymmetric nuclear matter are studied by using a simple effective interaction which has a single finite range Gaussian term. The study of finite nuclei with this effective interaction is…

Nuclear Theory · Physics 2013-02-15 B. Behera , X. Vinas , M. Bhuyan , T. R. Routray , B. K. Sharma , S. K. Patra

In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic…

Analysis of PDEs · Mathematics 2012-05-08 Ivan Argatov

Range-separated density-functional theory is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into…

Chemical Physics · Physics 2015-02-20 Odile Franck , Bastien Mussard , Eleonora Luppi , Julien Toulouse

We derive an asymptotic expansion for two-dimensional displacement field associated to thin elastic inhomogeneities having no uniform thickness. Our derivation is rigorous and based on layer potential techniques. We extend these techniques…

Analysis of PDEs · Mathematics 2016-01-27 Jihene Lagha , Habib Zribi