Aluminum foil interconnects for solar cell panels

Commercially available sonic welding system and a specially-designed tip bonds aluminum foil interconnects to titanium-silver solar cell contacts

Reconstruction of potential energy profiles from multiple rupture time distributions

We explore the mathematical and numerical aspects of reconstructing a potential energy profile of a molecular bond from its rupture time distribution. While reliable reconstruction of gross attributes, such as the height and the width of an energy barrier, can be easily extracted from a single first passage time (FPT) distribution, the reconstruction of finer structure is ill-conditioned. More careful analysis shows the existence of optimal bond potential amplitudes (represented by an effective Peclet number) and initial bond configurations that yield the most efficient numerical reconstruction of simple potentials. Furthermore, we show that reconstruction of more complex potentials containing multiple minima can be achieved by simultaneously using two or more measured FPT distributions, obtained under different physical conditions. For example, by changing the effective potential energy surface by known amounts, additional measured FPT distributions improve the reconstruction. We demonstrate the possibility of reconstructing potentials with multiple minima, motivate heuristic rules-of-thumb for optimizing the reconstruction, and discuss further applications and extensions.Comment: 20 pages, 9 figure

Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems

We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations. We can compute branches of solutions with limit points, bifurcation points, etc. Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations

Recurrence spectrum in smooth dynamical systems

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting

Development and optimization of pyrrone polymers, June 1966 - June 1967

Development and optimization of pyrrone polymer

On Urabe's criteria of isochronicity

We give a short proof of Urabe's criteria for the isochronicity of periodical solutions of the equation $\ddot{x}+g(x)=0$. We show that apart from the harmonic oscillator there exists a large family of isochronous potentials which must all be non-polynomial and not symmetric (an even function of the coordinate x).Comment: 8 page

Energy Gaps and Kohn Anomalies in Elemental Superconductors

The momentum and temperature dependence of the lifetimes of acoustic phonons in the elemental superconductors Pb and Nb was determined by resonant spin-echo spectroscopy with neutrons. In both elements, the superconducting energy gap extracted from these measurements was found to converge with sharp anomalies originating from Fermi-surface nesting (Kohn anomalies) at low temperatures. The results indicate electron many-body correlations beyond the standard theoretical framework for conventional superconductivity. A possible mechanism is the interplay between superconductivity and spin- or charge-density-wave fluctuations, which may induce dynamical nesting of the Fermi surface

On the Birth of Isolas

Isolas are isolated, closed curves of solution branches of nonlinear problems. They have been observed to occur in the buckling of elastic shells, the equilibrium states of chemical reactors and other problems. In this paper we present a theory to describe analytically the structure of a class of isolas. Specifically, we consider isolas that shrink to a point as a parameter τ of the problem, approaches a critical value τ_0. The point is referred to as an isola center. Equations that characterize the isola centers are given. Then solutions are constructed in a neighborhood of the isola centers by perturbation expansions in a small parameter ε that is proportional to (τ-τo), with a appropriately determined. The theory is applied to a chemical reactor problem