Running Boundary Condition

In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin. In this setting we find the renormalization group flow of U(2) family of boundary conditions exactly. We show that the well-known scale-independent subfamily of boundary conditions are realized as fixed points. We also discuss the duality between two distinct boundary conditions from the renormalization group point of view. Generalizations to conformal mechanics and quantum graph are also discussed.Comment: PTPTeX, 21 pages, 8 eps figures; typos corrected, references and an appendix adde

The Nahm Pole Boundary Condition

The Nahm pole boundary condition for certain gauge theory equations in four and five dimensions is defined by requiring that a solution should have a specified singularity along the boundary. In the present paper, we show that this boundary condition is elliptic and has regularity properties analogous to more standard elliptic boundary conditions. We also establish a uniqueness theorem for the solution of the relevant equations on a half-space with Nahm pole boundary conditions. These results are expected to have a generalization involving knots, with applications to the Jones polynomial and Khovanov homology.Comment: 60 pp, minor corrections in v.

Boundary condition at the junction

The quantum graph plays the role of a solvable model for a two-dimensional network. Here fitting parameters of the quantum graph for modelling the junction is discussed, using previous results of the second author.Comment: Replaces unpublished draft on related researc

Boundary Condition of Polyelectrolyte Adsorption

The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.Comment: 4 page

On open boundary conditions for three dimensional primitive equation ocean circulation models

An open boundary condition is constructed for three dimensional primitive equation ocean circulation models. The boundary condition utilises dominant balances in the governing equations to assist calculations of variables at the boundary. The boundary condition can be used in two forms. Firstly as a passive one in which there is no forcing at the boundary and phenomena generated within the domain of interest can propagate outwards without distorting the interior. Secondly as an active condition where a model is forced by the boundary condition. Three simple idealised tests are performed to verify the open boundary condition, (1) a passive condition to test the outflow of free Kelvin waves, (2) an active condition during the spin up phase of an ocean, (3) finally an example of the use of the condition in a tropical ocean