Related papers: Distributing points uniformly on the unit sphere u…
Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…
The search for optimal configurations of pointsets, the most notable examples being the problems of Kepler and Thompson, have an extremely rich history with diverse applications in physics, chemistry, communication theory, and scientific…
Nonlinear Thomson scattering of an electron motion in a combining field constituted by an elliptically polarized laser and a background magnetic field is investigated. The dependence of the electron trajectories, the fundamental frequency,…
A self-consistent kinetic theory of Thomson scattering of an electromagnetic field by a non-uniform plasma is derived. We draw the readers' attention to the inconsistency in recent results on the Thomson scattering in inhomogeneous plasma,…
Using numerical arguments we find that for $N$ = 306 a tetrahedral configuration ($T_h$) and for N=542 a dihedral configuration ($D_5$) are likely the global energy minimum for Thomson's problem of minimizing the energy of $N$ unit charges…
We consider random flights in $\mathbb{R}^d$ reflecting on the surface of a sphere $\mathbb{S}^{d-1}_R,$ with center at the origin and with radius $R,$ where reflection is performed by means of circular inversion. Random flights studied in…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
We discuss the conceptual design of a spatially-resolved spectroscopy system of Thomson scattering with high wavelength resolution capable of measuring the shape of electron velocity distribution functions in magnetically confined plasmas.…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
We consider point distributions in compact connected two-point homogeneous spaces (Riemannian symmetric spaces of rank one). All such spaces are known, they are the spheres in the Euclidean spaces, the real, complex and quaternionic…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…
We consider the problem of optimally insulating a given domain $\Omega$ of ${\mathbb{R}}^d$; this amounts to solve a nonlinear variational problem, where the optimal thickness of the insulator is obtained as the boundary trace of the…
A novel scheme is proposed to generate uniform relativistic electron layers for coherent Thomson backscattering. A few-cycle laser pulse is used to produce the electron layer from an ultra-thin solid foil. The key element of the new scheme…
Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
We propose a general design strategy based on genetic optimization to realize asymmetric reflectivity in periodic and non-periodic planar structures containing dielectric and gain-loss layers. By means of an optimization algorithm, it is…
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…