We consider a variational model for charge density $u\in{-1,1}$ on (hyper)plane, with short-range attraction coming from the interfacial energy and long-range repulsion electrostatic energy. This competition leads to pattern formation. prove that is (asymptotically) equidistributed at scales large compared scale of pattern. follow strategy laid out by Alberti, Choksi Otto (2009). The challenge ...

A self-consistent numerical model for silicon-based field effect nanowire biosensors is developed to study the impact of various surface-related physical and chemical processes, including transport of semiconductor carriers and electrolyte mobile ions, protonation and deprotonation of surface charge groups, and charges, and orientations and surface binding dynamics of immobilized biomolecules. ...

We examine the possibility that gauge field configurations on stacks of parallel Dp-branes support topological solitons. We give an exhaustive list of possible soliton charges for p ≤ 6. We also discuss how configurations carrying the soliton charges can be constructed from intersecting branes.

The $T\bar{T}$ deformed 2D CFTs correspond to AdS$_3$ gravity with Dirichlet boundary condition at finite cutoff or equivalently a mixed spatial infinity. In this work, we use the latter perspective and Chern-Simons formalism of construct surface charges associated algebra in theories. Starting from Ba\~nados geometry, obtain gauge fields for which are parametrized by two independent charges. W...