Aspects of electrostatics in BTZ geometries

Some graph theoretic aspects of finite geometries

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical ha...

Winding tachyons in BTZ

Analysing closed string tachyon condensation will improve our understanding of spacetime in string theory. We study the string spectrum on a BTZ black hole spacetime supported by NS-NS flux, which provides a calculable example where we would expect to find a quasi-localised tachyon. We find that there is a winding tachyon when the black hole horizon is smaller than the string scale, as expected...

Several Aspects of Antimatroids and Convex Geometries Master's Thesis

Convexity is important in several elds, and we have some theories on it. In this thesis, we discuss a kind of combinatorial convexity, in particular, antimatroids and convex geometries. An antimatroid is a combinatorial abstraction of convexity. It has some di erent origins; by Dilworth in lattice theory, by Edelman and Jamison in the notions of convexity, by Korte{Lov asz who were motivated by...

Electrostatics Modes in Mono-Layered Graphene

In this paper, we investigated the corrected plasmon dispersion relation for graphene in presence of a constant magnetic field which it includes a quantum term arising from the collective electron density wave interference effects. By using quantum hydrodynamic plasma model which incorporates the important quantum statistical pressure and electron diffraction force, the longitudinal plasmons ar...