相关论文: Solution to the Thomson problem for Clifford tori …
In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract…
We investigate the classical ground state of a large number of charges confined inside a disk and interacting via the Coulomb potential. By realizing the important role that the peripheral charges play in determining the lowest energy…
The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other…
Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…
We give a rigorous computer-assisted proof that the triangular bi-pyramid is the unique configuration of 5 points on the 2-sphere that globally minimizes the Coulomb (1/r) potential. We also prove the same result for the (1/r^2) potential.…
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it $\Omega$ (the $S^{d-1}-$ sphere, in our…
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…
In this paper we construct entire solutions $u_{\varepsilon}$ to the Cahn-Hilliard equation $-\varepsilon^{2}\Delta(-\varepsilon^{2}\Delta u+W^{'}(u))+W^{"}(u)(-\varepsilon^{2}\Delta u+W^{'}(u))=0$, under the volume constraint…
The Poisson problem consists in finding an immersed surface $\Sigma\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a…
We give a description of numerical Newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical Newton algorithm on a sphere…
The Willmore Problem seeks the surface in $\mathbb S^3\subset\mathbb R^4$ of a given topological type minimizing the squared-mean-curvature energy $W = \int |\mathbf{H}_{\mathbb{R}^4}|^2 = \operatorname{area} + \int H_{\mathbb{S}^3}^2$. The…
We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which…
Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate the combined effects of the geometry of…
The classical Thomson problem of $n$ charged particles confined to the surface of a sphere of radius $a$ is analyzed within the Darwin approximation of electrodynamics. For $n<n_c(a)$ the ground state corresponds to a hexagonal Wigner…
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…
To advance Thomson problem we generalize physical principles suggested by Caspar and Klug (CK) to model icosahedral capsids. Proposed simplest distortions of the CK spherical arrangements yield new-type trial structures very close to the…
We propose a simple direct-sum method for the efficient evaluation of lattice sums in periodic solids. It consists of two main principles: i) the creation of a supercell that has the topology of a Clifford torus, which is a flat, finite and…
This paper is dedicated to the exploration of the conformal Willmore functional for surfaces within 4-dimensional conformal manifolds. We provide a detailed calculation of both the first and second variations, and present the Euler-Lagrange…
We construct embedded Willmore tori with small area constraint in Riemannian three-manifolds under some curvature condition used to prevent M\"obius degeneration. The construction relies on a Lyapunov-Schmidt reduction; to this aim we…
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…