# Survival of a walker in gated trapping systems

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We consider an affine Euclidean lattice and record the directions of all lattice vectors of length at most T. StroÂ¨mbergsson and the second author proved in [Ann. Math. 173 (2010), 1949-2033] that the distribution of gaps between the lattice directions has a limit as T tends to infinity. For...

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We use sums over Bessel functions of the first kind to derive a convenient form of the Poisson summation identity relating sums over direct lattices in two dimensions to sums over reciprocal lattices. After three simple examples of the use of the identity, we consider sums over complex powers of...

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We consider cohomological and Poisson structures associated with the special tautological subbundles $$TB_{W_{1,2, \ldots n} }$$ for the Birkhoff strata of the Sato Grassmannian. We show that the tangent bundles of $$TB_{W_{1,2, \ldots n} }$$ are isomorphic to the linear spaces of...

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Distributions of the electrostatic potential, electric field strength, and electron concentration for a strained semiconductor quantum dot (QD) have been calculated within the nonlinear Poisson model with allowance for the deformation potential that arises due to a lattice misfit between the QD...

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We consider the interactions of finite dipoles in a doubly periodic domain. A finite dipole is a pair of equal and opposite strength point vortices separated by a finite distance. The dynamics of multiple finite dipoles in an unbounded inviscid fluid was first proposed by Tchieu, Kanso, and...