arXiv subjects

Tim LaFave Jr

Publications and source records attributed to Tim LaFave Jr.

3 recordsLinked to original sources

arXiv2014

Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure

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 discrete geometries of neighboring $N-1$ systems. These non-uniformities yield electron energy pairs, intra-subshell pattern similarities with empirical ionization energy, and a salient pattern that coincides with size-normalized empirical ionization energies. Spatial symmetry limitations on discrete charges constrained to a spherical volume are conjectured as underlying physical mechanisms responsible for shell-filling patterns in atomic electronic structure and the Periodic Law.

physics.class-ph↗

arXiv2014

Discrete Transformations in the Thomson Problem

A significantly lower upper limit to minimum energy solutions of the electrostatic Thomson Problem is reported. A point charge is introduced to the origin of each $N$-charge solution. This raises the total energy by $N$ as an upper limit to each $(N+1)$-charge solution. Minimization of energy to $U(N+1)$ is well fit with $-0.5518(3/2)\sqrt N+1/2$ for up to $N=500$. The energy distribution due to this displacement exhibits correspondences with shell-filling behavior in atomic systems. This work may aid development of more efficient and innovative numerical search algorithms to obtain $N$-charge configurations having global energy minima and yield new insights to atomic structure.

physics.class-ph↗

arXiv2012

Discrete Charge Dielectric Model of Electrostatic Energy

Studies on nanoscale materials merit careful development of an electrostatics model concerning discrete point charges within dielectrics. The discrete charge dielectric model treats three unique interaction types derived from an external source: Coulomb repulsion among point charges, direct polarization between point charges and their associated surface charge elements, and indirect polarization between point charges and surface charge elements formed by other point charges. The model yields the potential energy, U(N), stored in a general $N$ point charge system differing from conventional integral formulations, $1/2\int{\bm E}\cdot{\bm D}dV$ and $1/2\intρΦdV$, in a manner significant to the treatment of few electron systems.

physics.class-ph↗