46 research outputs found
Uniform semiclassical wave function for coherent 2D electron flow
We find a uniform semiclassical (SC) wave function describing coherent
branched flow through a two-dimensional electron gas (2DEG), a phenomenon
recently discovered by direct imaging of the current using scanned probed
microscopy. The formation of branches has been explained by classical
arguments, but the SC simulations necessary to account for the coherence are
made difficult by the proliferation of catastrophes in the phase space. In this
paper, expansion in terms of "replacement manifolds" is used to find a uniform
SC wave function for a cusp singularity. The method is then generalized and
applied to calculate uniform wave functions for a quantum-map model of coherent
flow through a 2DEG. Finally, the quantum-map approximation is dropped and the
method is shown to work for a continuous-time model as well.Comment: 9 pages, 7 figure
Analytic solutions and Singularity formation for the Peakon b--Family equations
Using the Abstract Cauchy-Kowalewski Theorem we prove that the -family
equation admits, locally in time, a unique analytic solution. Moreover, if the
initial data is real analytic and it belongs to with , and the
momentum density does not change sign, we prove that the
solution stays analytic globally in time, for . Using pseudospectral
numerical methods, we study, also, the singularity formation for the -family
equations with the singularity tracking method. This method allows us to follow
the process of the singularity formation in the complex plane as the
singularity approaches the real axis, estimating the rate of decay of the
Fourier spectrum
Water waves generated by a moving bottom
Tsunamis are often generated by a moving sea bottom. This paper deals with
the case where the tsunami source is an earthquake. The linearized water-wave
equations are solved analytically for various sea bottom motions. Numerical
results based on the analytical solutions are shown for the free-surface
profiles, the horizontal and vertical velocities as well as the bottom
pressure.Comment: 41 pages, 13 figures. Accepted for publication in a book: "Tsunami
and Nonlinear Waves", Kundu, Anjan (Editor), Springer 2007, Approx. 325 p.,
170 illus., Hardcover, ISBN: 978-3-540-71255-8, available: May 200