The virial theorem with periodic boundary conditions

Molecular dynamics with helical periodic boundary conditions

Helical symmetry is often encountered in nature and thus also in molecular dynamics (MD) simulations. In many cases, an approximation based on infinite helical periodicity can save a significant amount of computer time. However, standard simulations with the usual periodic boundary conditions (PBC) are not easily compatible with it. In the present study, we propose and investigate an algorithm ...

Perturbation of Periodic Boundary-Conditions

Existence Theorem for First Order Ordinary Functional Differential Equations with Periodic Boundary Conditions

A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions

In this paper, one-dimensional (1D) nonlinear Schrödinger equation iut − uxx +mu+ g(u, ū) ū = 0, with Periodic Boundary Conditions is considered; m / ∈ 1 12Z is a real parameter and the nonlinearity g(u, ū)= ∑ j,l,j+l 4 ajlu j ū , aj l = alj ∈ R, a22 = 0 is a real analytic function in a neighborhood of the origin. The KAM machinery is adapted to fit the above equation so as to construct small-a...

Periodic boundary conditions on the pseudosphere

We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic pl...