Minimal Hypersurfaces Over Soft Obstacles

Abstract

Partial' cross sections for single electron capture in low to intermediate energy collisions of Ar6+ with He have been calculated in a simple two-electron atomic expansion. The calculated results are in good agreement at high energies with experimental results based on translational energy spectroscopy. At lower energies there is a 30% deviation in the 4p cross section and the comparison with the 3d cross section becomes poor. To understand this discrepancy, theoretical energy gain spectra have been deduced. Contributions from individual final states are well resolved at high energies, but there is a significant spectral overlap at lower energies, implying that a standard analysis of experimental spectra may lead to inaccuracies in the determination of partial cross sections. The observed deviation between theory and experiment may be attributed to this effect.

The N-membrane problem with nonlocal constraints

“…Physically (2.2) models the position of an elastic membrane to which a vertical force f is applied and which is constrained to stay above an obstacle represented by the function ψ. When an elastic membrane is constrained to lye above, or below, an incompressible liquid of fixed volume, then the constraint can be "softened," according to the terminology introduced by Titov [8]. Introducing for a ∈ R…”