Arnold diffusion for a complete family of perturbations

In this work we illustrate the Arnold diffusion in a concrete example — the a priori unstable Hamiltonian system of 2 + 1/2 degrees of freedom H(p, q, I, f, s) = p2/2+ cos q - 1 + I2/2 + h(q, f, s; e) — proving that for any small periodic perturbation of the form h(q, f, s; e) = e cos q (a00 + a10 cosf + a01 cos s) (a10a01 ¿ 0) there is global instability for the action. For the proof we apply a geometrical mechanism based on the so-called scattering map. This work has the following structure: In the first stage, for a more restricted case (I* ~ p/2µ, µ = a10/a01), we use only one scattering map, with a special property: the existence of simple paths of diffusion called highways. Later, in the general case we combine a scattering map with the inner map (inner dynamics) to prove the more general result (the existence of instability for any µ). The bifurcations of the scattering map are also studied as a function of µ. Finally, we give an estimate for the time of diffusion, and we show that this time is primarily the time spent under the scattering map.Peer ReviewedPostprint (published version

A Monte Carlo Model for Interrogation of Thick Cargos for Clandestine Fissionable Materials; Tests with 14-MeV Neutrons

A Monte Carlo model has been developed for interrogation of fissionable material embedded in thick cargos when high-energy {beta}-delayed {gamma} rays are detected following neutron-induced fission. The model includes the principal structural components of the laboratory, the neutron source and collimator assembly in which it resides, the assembly that represents cargo of given characteristics, a target of highly-enriched uranium (HEU) and large external plastic scintillators for photon detection. The ability of this model to reproduce experimental measurements was tested by comparing simulations with measurements of the number of induced fissions and the number of detected photons when the HUE target was irradiated with 14.25-MeV neutrons in the absence of any cargo and while embedded in assemblies of plywood and iron pipes. The simulations agreed with experimental measurements within a factor of about 2 for irradiation of the bare target and when the areal density of intervening cargo was 33 g cm{sup -2} (wood) and 61 g cm{sup -2} (steel pipes). This suggests that the model can permit exploration of a large range in parameter space with reasonable fidelity