Massive 3+1 Aharonov-Bohm fermions in an MIT cylinder

We study the effect of a background flux string on the vacuum energy of massive Dirac fermions in 3+1 dimensions confined to a finite spatial region through MIT boundary conditions. We treat two admissible self-adjoint extensions of the Hamiltonian. The external sector is also studied and unambiguous results for the Casimir energy of massive fermions in the whole space are obtained.Comment: 12 pages, 5 figures, LaTe

Multi-scale simulation method for electroosmotic flows

Electroosmotic transport in micro-and nano- channels has important applications in biological and engineering systems but is difficult to model because nanoscale structure near surfaces impacts flow throughout the channel. We develop an efficient multi-scale simulation method that treats near-wall and bulk subdomains with different physical descriptions and couples them through a finite overlap region. Molecular dynamics is used in the near-wall subdomain where the ion density is inconsistent with continuum models and the discrete structure of solvent molecules is important. In the bulk region the solvent is treated as a continuum fluid described by the incompressible Navier-Stokes equations with thermal fluctuations. A discrete description of ions is retained because of the low density of ions and the long range of electrostatic interactions. A stochastic Euler-Lagrangian method is used to simulate the dynamics of these ions in the implicit continuum solvent. The overlap region allows free exchange of solvent and ions between the two subdomains. The hybrid approach is validated against full molecular dynamics simulations for different geometries and types of flows