Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field

Using a Ginzburg-Landau model, we study the vortex behavior of a rectangular thin film superconductor subjected to an applied current fed into a portion of the sides and an applied magnetic field directed orthogonal to the film. Through a center manifold reduction we develop a rigorous bifurcation theory for the appearance of periodic solutions in certain parameter regimes near the normal state. The leading order dynamics yield in particular a motion law for kinematic vortices moving up and down the center line of the sample. We also present computations that reveal the co-existence and periodic evolution of kinematic and magnetic vortices

Electronic polarization in pentacene crystals and thin films

Electronic polarization is evaluated in pentacene crystals and in thin films on a metallic substrate using a self-consistent method for computing charge redistribution in non-overlapping molecules. The optical dielectric constant and its principal axes are reported for a neutral crystal. The polarization energies P+ and P- of a cation and anion at infinite separation are found for both molecules in the crystal's unit cell in the bulk, at the surface, and at the organic-metal interface of a film of N molecular layers. We find that a single pentacene layer with herring-bone packing provides a screening environment approaching the bulk. The polarization contribution to the transport gap P=(P+)+(P-), which is 2.01 eV in the bulk, decreases and increases by only ~ 10% at surfaces and interfaces, respectively. We also compute the polarization energy of charge-transfer (CT) states with fixed separation between anion and cation, and compare to electroabsorption data and to submolecular calculations. Electronic polarization of ~ 1 eV per charge has a major role for transport in organic molecular systems with limited overlap.Comment: 10 revtex pages, 6 PS figures embedde

Time integration and steady-state continuation for 2d lubrication equations

Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. In both algorithms a Cayley transform is employed to overcome numerical problems resulting from scale separation in space and time. An adaptive time-step allows to study the dynamics close to hetero- or homoclinic connections. The developed framework is employed on the one hand to analyse different phases of the dewetting of a liquid film on a horizontal homogeneous substrate. On the other hand, we consider the depinning of drops pinned by a wettability defect. Time-stepping and path-following are used in both cases to analyse steady-state solutions and their bifurcations as well as dynamic processes on short and long time-scales. Both examples are treated for two- and three-dimensional physical settings and prove that the developed algorithms are reliable and efficient for 1d and 2d lubrication equations, respectively.Comment: 33 pages, 16 figure

Metastability of solitary roll wave solutions of the St. Venant equations with viscosity

We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallow-water flow down an incline, and related models. Our main result is to exhibit examples of metastable solitary waves for the St. Venant equations, with stable point spectrum indicating coherence of the wave profile but unstable essential spectrum indicating oscillatory convective instabilities shed in its wake. We propose a mechanism based on ``dynamic spectrum'' of the wave profile, by which a wave train of solitary pulses can stabilize each other by de-amplification of convective instabilities as they pass through successive waves. We present numerical time evolution studies supporting these conclusions, which bear also on the possibility of stable periodic solutions close to the homoclinic. For the closely related viscous Jin-Xin model, by contrast, for which the essential spectrum is stable, we show using the stability index of Gardner--Zumbrun that solitary wave pulses are always exponentially unstable, possessing point spectra with positive real part.Comment: 42 pages, 9 figure

Pattern formation in annular convection

This study of spatio-temporal pattern formation in an annulus is motivated by two physical problems on vastly different scales. The first is atmospheric convection in the equatorial plane between the warm surface of the Earth and the cold tropopause, modeled by the two dimensional Boussinesq equations. The second is annular electroconvection in a thin semetic film, where experiments reveal the birth of convection-like vortices in the plane as the electric field intensity is increased. This is modeled by two dimensional Navier-Stokes equations coupled with a simplified version of Maxwell's equations. The two models share fundamental mathematical properties and satisfy the prerequisites for application of O(2)-equivariant bifurcation theory. We show this can give predictions of interesting dynamics, including stationary and spatio-temporal patterns