Related papers: On the connected-charges Thomson problem
The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the…
We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is…
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…
Determination of the classical ground state arrangement of $N$ charges on the surface of a sphere (Thomson's problem) is a challenging numerical task. For special values of $N$ we have obtained using the ring removal method of Toomre, low…
We examine the regime between crystalline and amorphous packings of anisotropic objects on surfaces of different genus by continuously varying their size distribution or shape from monodispersed spheres to bidispersed mixtures or…
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 topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological…
We investigate the low-energy configurations of N mutually repelling charges confined to a spherical cap and interacting via the Coulomb potential. In the continuum limit, this problem was solved by Lord Kelvin, who found a non-uniform…
General topological principles how to transfer the planar orders onto a sphere are considered. Formation of extended topological defects (ETDs), which have a reconstructed inner structure surrounded by perfect initial order, is discussed.…
We show that topological defects in an ion-doped nematic liquid crystal can be used to manipulate the surface charge distribution on chemically homogeneous, charge-regulating external surfaces, using a minimal theoretical model. In…
Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
We report the existence of topologically charged nodal surface, a band degeneracy on a two-dimensional surface in momentum space that is topologically charged. We develop a Hamiltonian for such charged nodal surface, and show that such a…
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…
Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the…
We investigate the problem of the electron interacting with the charge induced on the metal or dielectric surface. We show that the interaction between the electron and the induced surface charge leads to the lateral confinement of the…
Central heavy-ion collisions may induce sizeable fluctuations of the topological charge. This effect is expected to distort the dispersion relation for the hadron masses. We construct a general setup for a compact description of this…
Nominally identical materials exchange net electric charge during contact through a mechanism that is still debated. `Mosaic models', in which surfaces are presumed to consist of a random patchwork of microscopic donor/acceptor sites, offer…
We consider the coupling of scalar topological matter to (2+1)-dimensional gravity. The matter fields consist of a 0-form scalar field and a 2-form tensor field. We carry out a canonical analysis of the classical theory, investigating its…
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…