相关论文: Studies on optimizing potential energy functions f…

We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of…

We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be viewed as a generalization of the Levenshtein bounds for…

We solve the Schr\"odinger wave equation for the generalized Morse and Cusp molecular potential models. In the limit of high temperature, at first, we need to calculate the canonical partition function which is basically used to study the…

We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the…

This is a review and tutorial paper which discusses the fundamental limitations on the maximal power which can be received, absorbed, and scattered by an electrically small electrically polarizable particle and infinite periodical arrays of…

The induced surface charges appear to diverge when dielectric particles form close contacts. Resolving this singularity numerically is prohibitively expensive because high spatial resolution is needed. We show that the strength of this…

Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to…

We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion…

Rigorous mathematical foundations of density functional theory are revisited, with some use of infinitesimal (nonstandard) methods. A thorough treatment is given of basic properties of internal energy and ground-state energy functionals…

Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and…

We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of points, which serve as multi-input generalizations of the…

A grand challenge in fundamental physics and practical applications is overcoming wave diffusion to deposit energy into a target region deep inside a diffusive system. While it is known that coherently controlling the incident wavefront…

The sum-utility maximization problem is known to be important in the energy systems literature. The conventional assumption to address this problem is that the utility is concave. But for some key applications, such an assumption is not…

A high-energy photon polarimeter for astrophysics studies in the energy range from 10 MeV to 800 MeV is considered. The proposed concept uses a stack of silicon micro-strip detectors where they play the roles of both a converter and a…

Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact…

Understanding a hadron's electric and magnetic polarizabilities allows one to access internal structural information. Traditionally, the external field two-point function method has been used to calculate polarizabilities. However, recent…

We investigate the possibility of electrostatic potential saturation, which may lead to the phenomenon of effective charge saturation. The system under study is a uniformly charged infinite plane immersed in an arbitrary electrolyte made up…

We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of…

We investigate strategies for estimating a depolarizing channel for a finite dimensional system. Our analysis addresses the double optimization problem of selecting the best input probe state and the measurement strategy that minimizes the…

We provide upper and lower bounds on the lowest free energy of a classical system at given one-particle density $\rho(x)$. We study both the canonical and grand-canonical cases, assuming the particles interact with a pair potential which…