Related papers: Thomson problem on a spherical cap
We study a generalized Thomson problem that appears in several condensed matter settings: identical point-charge particles can penetrate inside a homogeneously charged sphere, with global electro-neutrality. The emphasis is on scaling laws…
We discuss the basic principles of a self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in a disk geometry. Our approach is based on the cyclic symmetry and periodicity of the Coulomb…
We present a theoretical approach to study the dynamics of spherical, cylindrical and ellipsoidal charge distributions under their self-Coulomb field and a stochastic force due to collisions and random motions of charged particles. The…
We have found that the minimum energy configuration of $N=395$ charges confined in a disk and interacting via the Coulomb potential, reported by Cerkaski et al. in Ref.~\cite{Cerkaski15} is not a global minimum of the total electrostatic…
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…
The bulk distribution of the topological charge density, constructed via HP^1 sigma-model embedding method, is investigated. We argue that the specific pattern of leading power corrections to gluon condensate hints on a particular UV…
We analyzed the localized charge dynamics in the system of $N$ interacting single-level quantum dots (QDs) coupled to the continuous spectrum states in the presence of Coulomb interaction between electrons within the dots. Different dots…
We consider the minimal energy problem on the unit sphere $\mathbb S^2$ in the Euclidean space $\mathbb R^3$ immersed in an external field $Q$, where the charges are assumed to interact via Newtonian potential $1/r$, $r$ being the Euclidean…
We analyse charge inversion in colloidal systems at zero temperature using stability concepts, and connect this to the classical Thomson problem of arranging electrons on sphere. We show that for a finite microion charge, the globally…
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 evaluate, by means of variational calculations, the bound state energy E_B of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e^2 / r . The trial wave function involves three variational…
We study the behaviour of the minimal solution to the Gelfand problem on a spherical cap under the Dirichlet boundary conditions. The asymptotic behaviour of the solution is discussed as the cap approaches the whole sphere. The results are…
We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method,…
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an…
We show that topological waves at the interface between two magnetic domains in a graphene device are possible. First, we consider the case of a linear relation between the applied gate voltage and local density in the channel and,…
We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron…
Leveraging topological properties in the response of electromagnetic systems can greatly enhance their potential. Although the investigation of singularity-based electromagnetics and non-Hermitian electronics has considerably increased in…
The general formula for the interaction potential between two point electric charges which contains the lowest order corrections to the vacuum polarization is derived and investigated. Analytical derivation of this formula is based on the…
The one-component Coulomb gas on the sphere, consisting on $N$ unit charges interacting via a logarithmic potential, and in the presence of two external charges each of strength proportional to $N$, is considered. There are two spherical…
We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value…