0 50 50 67 v 1 2 5 M ay 2 00 5 The geometry of the Mel ’ nikov “ function ”

50 50 67 v 2 2 6 M ay 2 00 5 Intersections of Lagrangian submanifolds and the Mel ’ nikov “ function ” Nicolas Roy

Abstract Wemake explicit the geometric content of Mel’nikov’s method for detecting heteroclinic points between transversally hyperbolic periodic orbits. After developing the general theory of intersections for pairs of family of Lagrangian submanifolds N ε , with N + 0 = N − 0 constrained to live in an auxiliary family of submanifolds, we explain how the heteroclinic orbits are detected by the ...

ar X iv : n uc l - th / 0 50 50 24 v 1 9 M ay 2 00 5 Structure of isomeric states in 66 As and 67 As

0 50 50 06 v 1 2 M ay 2 00 5 A derivation of the Boltzmann – Vlasov equation from multiple scattering using the Wigner function ∗

A derivation is given of the Boltzmann–Vlasov equation beginning from multiple scattering considerations. The motivation for the discussion, which is purely pedagogical in nature, is the current interest in understanding the origins of transport equations in terms of rigorous field-theory descriptions, or, as in this case, exact nonrelativistic formulations.

m at h - ph / 0 50 50 36 v 1 1 1 M ay 2 00 5 Droplet minimizers for the Cahn – Hilliard free energy functional

We prove theorems characterizing the minimizers in a model for condensation based on the Cahn–Hilliard free energy functional. In particular we exactly determine the critical density for droplet formation.

ar X iv : g r - qc / 0 50 51 30 v 1 2 6 M ay 2 00 5 An Exact Solution for Static Scalar Fields Coupled to Gravity in ( 2 + 1 ) - Dimensions

We obtain an exact solution for the Einstein’s equations with cosmological constant coupled to a scalar, static particle in static, ”spherically” symmetric background in 2 + 1 dimensions. ————————————————————————————