Related papers: Comment to "Thomson rings in a disk"
We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau-de Gennes model. The nematic is assumed to occupy the exterior of a ball of radius r_0, satisfy…
Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for…
We consider constellations of disks which are unions of disjoint hyperbolic disks in the unit disk with fixed radii and unfixed centers. We study the problem of maximizing the conformal capacity of a constellation with a fixed number of…
We analyse theoretically the possibilities of contactless control of in-gap states formed by a pair of electrons confined in a triangular quantum ring. The in-gap states are corner-localized states associated with two electrons occupying…
This note establishes, first of all, the monotonic increase with $N$ of the average $K$-body energy of classical $N$-body ground state configurations with $N\geq K$ monomers that interact solely through a permutation-symmetric $K$-body…
This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg-Landau energy. Denoting by $\varepsilon$ the length…
We provide a systematic test of empirical theories of covalent bonding in solids using an exact procedure to invert ab initio cohesive energy curves. By considering multiple structures of the same material, it is possible for the first time…
The quasi-harmonic model proposes that a crystal can be modeled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss' law shows that the ion-ion potential for a cubic Coulomb…
Non-gravitational feedback affects the nature of the intra-cluster medium (ICM). X-ray cooling of the ICM and in situ energy feedback from AGN's and SNe as well as {\it preheating} of the gas at epochs preceding the formation of clusters…
For general dimension $d$ we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. At the microscopic scale, i.e. after blow-up at the…
Given a positive definite kernel in a locally compact space, we study a minimal energy problem in the presence of an external field over the class of all nonnegative Radon measures that are supported by a given closed noncompact set,…
We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are $r$ and $R$, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is…
Using Monte Carlo simulations, we study the assembly of colloidal particles interacting via isotropic core-corona potentials in two dimensions and confined in a circular box. We explore the structural variety at low temperatures as function…
We prove that, in the large-dimension limit, the high-density correlation energy $\Ec$ of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by $\Ec \sim -1/(8D^2)$ for any…
Correlations lie at the heart of almost all scientific predictions. It is therefore of interest to ask whether there exist general limitations to the amount of correlations that can be created at a finite amount of invested energy. Within…
We consider the energy stored in a one-dimensional ballistic ring with a barrier subject to a linearly time-dependent magnetic flux. An exact analytic solution for the quantum dynamics of electrons in the ring is found for the case when the…
An effective pair potential for systems of uniformly charged lamellar colloids in the presence of an electrolytic solution of microscopic co- and counterions is derived. The charge distribution on the discs is expressed as a collection of…
Motivated by the discovery of extremely low energy collective modes in the fractional quantum Hall effect (Kang, Pinczuk {\em et al.}), with energies below the Zeeman energy, we study theoretically the spin reversed excitations for…
Effects of Coulomb interaction on persistent currents in disordered one-dimensional rings are numerically investigated. First of all effectiveness of the Hartree-Fock approximation is established on small systems. Then the calculations are…
A recent study [Phys. Rev. B 17 174111 (2022)] has hypothesized the assembly, along a specific type of one-dimensional defects of diamond, of chains of nitrogen-vacancy (NV) centers, potentially enabling the creation of qubit registers via…