Related papers: Minimum energy configurations of repelling particl…
In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit…
The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…
The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as…
We report on a study of a finite system of classical confined particles in two-dimensions in the presence of a uniform magnetic field and interacting via a two-body repulsive potential. We develop a simple analytical method of analysis to…
Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…
We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction $D/r^3$ favors an equilateral triangular arrangement of the molecules, which…
We have studied the general properties of the energy thresholds of stability for a three-particle system with short-range interaction. A wide region of the interaction constants and various ratios of the masses of particles are considered.…
We study a system of particles in two dimensions interacting via a dipolar long-range potential $D/r^3$ and subject to a square-lattice substrate potential $V({\bf r})$ with amplitude $V$ and lattice constant $b$. The isotropic interaction…
We explore the minimum energy configurations of repelling particles distributed over n possible locations forming a toric grid. We conjecture that the most energy-efficient way to distribute n/2 particles over this space is to place them in…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
The low-energy properties of two-dimensional ensembles of dipole-coupled magnetic nanoparticles are studied as function of structural disorder and particle coverage. Already small deviations from a square particle arrangement lift the…
We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the…
Consider a collection of particles interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at unit separation. For a range of exponents corresponding to mild…
We report calculations of the ground state energies and geometries for clusters of different sizes (up to 80 particles), where individual particles interact simultaneously via a short-ranged attractive -modeled with a generalization of the…
The lowest adiabatic potential expressed in hyperspherical coordinates is estimated for two boson systems in an external harmonic trap. Corresponding conditions for stability are investigated and the related structures are extracted for…
Densities of particles on $\Rn$ which interact pairwise through an attractive-repulsive power-law potential $W_{\al,\bt}(x) = |x|^\al/\al-|x|^\bt/\bt$ have often been used to explain patterns produced by biological and physical systems. In…
In addition to the conventional renormalized--coupling--constant picture, point interactions in dimension two and three are shown to model within a suitable energy range scattering on localized potentials, both attractive and repulsive.
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a…