Related papers: On the Minimax Spherical Designs
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
We investigate the effect of linear diffusion and interactions with the domain boundary on swarm equilibria by analyzing critical points of the associated energy functional. Through this process we uncover two properties of energy…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
Locating the global minimum of a complex potential energy surface is facilitated by considering a homotopy, namely a family of surfaces that interpolate continuously from an arbitrary initial potential to the system under consideration.…
We study numerical integration on the unit sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by…
We present a general framework to construct symmetric, well-conditioned, cross-element compatible nodal distributions that can be used for high-order and high-dimensional finite elements. Starting from the inherent symmetries of an element…
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross-Pitaevskii and Kohn-Sham equation arising in computational physics and chemistry. These problems characterize critical points of energy…
Scientific machine learning (SciML) is a relatively new field that aims to solve problems from different fields of natural sciences using machine learning tools. It is well-documented that the optimizers commonly used in other areas of…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…
A quantum Monte Carlo method of determining Jastrow-Slater wave functions for which the energy is stationary with respect to variations in the single-particle orbitals is presented. A potential is determined by a least-squares fitting of…
The scission of a nucleus into two fragments is at present the least understood part of the fission process, though the most important for the formation of the observables. To investigate the potential energy landscape at the largest…
As the world is transitioning towards highly renewable energy systems, advanced tools are needed to analyze such complex networks. Energy system design is, however, challenged by real-world objective functions consisting of a blurry mix of…
We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular…
It turned out that the set of the fixed points is not necessarily the same as the set of the local minima of the energy functional. It depends on the diagonal elements of the connection matrix. The simple method which allows to cut off…
We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
A new method for approximating Skyrme solutions is developed. It consists of cutting sections out of the Skyrme crystal and smoothly interpolating between the boundary and spatial infinity. Several field configurations are constructed, and…
We present an algorithm for producing discrete distributions with a prescribed nearest-neighbor distance function. Our approach is a combination of quasi-Monte Carlo (Q-MC) methods and weighted Riesz energy minimization: the initial…