Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra

We derive a lower bound for energies of harmonic maps of convex polyhedra in $\R^3$ to the unit sphere $S^2,$ with tangent boundary conditions on the faces. We also establish that $C^\infty$ maps, satisfying tangent boundary conditions, are dense with respect to the Sobolev norm, in the space of continuous tangent maps of finite energy.Comment: Acknowledgment added, typos removed, minor correction

Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media

We analyze frequency conversion and its control among three light waves using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understand the fully nonlinear dynamics. The Poincaré sphere has been used in the same way to visualize polarization dynamics. A geometric understanding of control strategies that enhance energy transfer among interacting waves is introduced, and the quasi-phase-matching strategy that uses microstructured quadratic materials is illustrated in this setting for both type I and II second-harmonic generation and for parametric three-wave interactions

Domain wall motion in ferromagnetic nanowires driven by arbitrary time-dependent fields: An exact result

We address the dynamics of magnetic domain walls in ferromagnetic nanowires under the influence of external time-dependent magnetic fields. We report a new exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the case of soft ferromagnetic wires and nanostructures with uniaxial anisotropy. The solution holds for applied fields with arbitrary strength and time dependence. We further extend this solution to applied fields slowly varying in space and to multiple domain walls.Comment: 3 pages, 1 figur

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

U.S. households' access to and use of electronic banking. 1989-2007

Nationwide surveys show that consumers are increasingly embracing technology to make payments and manage their personal finances. However, only about one in two consumers could be considered a heavy user of electronic banking. This article examines changes over time in consumers’ access to, adoption of, and attitudes toward various e-banking products and services and looks at several emerging technologies.Consumers' preferences ; Electronic funds transfers