Joint Wigner distribution for spin-1/2 particles

The Wigner distribution has proven to be a useful tool in many quantum problems requiring a joint distribution of position and momentum. In the present paper we develop a joint distribution for spin components within the spirit of the Wigner distribution. This distribution provides an insight into the quantum theory of measurement. We also discuss how one may write joint distributions for two arbitrary noncommuting operators.It is a pleasure to dedicate this paper to Professor John A. Wheeler—physicist, philosopher, poet—an inspiration to us all.Work supported by the Office of Naval Research.     

A circle map in a human heart

A circle is divided into two regions, a black one and a white one. Successive iterates of an invertible nonlinear circle map generate a symbolic string indicating whether each iterate is in the black or white region. A number of remarkable properties of the symbolic sequences are described. These properties were previously described for a linear circle map corresponding to a rigid rotation in the “gaps and steps” problem. These results have direct application to a cardiac arrhythmia, parasystole, that results from the competition between two pacemakers in the heart, one in the sinus mode and the other in the ventricles. The theoretical results are directly applicable to a clinical case of a young man who had frequent extra heartbeats.     

Prediction of yield and long‐term failure of oriented polypropylene: Kinetics and anisotropy

The time‐dependent yield and failure behavior of off‐axis loaded uniaxially oriented polypropylene tape is investigated. The yield and failure behavior is described with an anisotropic viscoplastic model. A viscoplastic flow rule is used with an equivalent stress, based on Hill's anisotropic yield criterion, and the Eyring flow theory combined with a critical equivalent strain definition. This model is based on factorization of the rate and draw ratio dependence and is capable of quantitatively predicting the rate, angle and draw ratio dependence of the yield stress as well as time‐to‐failure in various off‐axis tensile loading conditions characterized solely from the transverse direction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2026–2035, 2009     

A new wavelet multigrid method

The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.     

Conditional expectation values in quantum mechanics

The general question of defining the expectation value of an operator for a fixed value of another noncommuting observable is considered and explicit expressions are derived. Due to the noncommutivity of operators a unique definition is not possible, and we consider different possible expressions. Special cases which have previously been considered in the literature are shown to be derivable from the methods presented.In honor of Ilya Prigogine on the occasion of his 70th birthday.     

Controllability and asymptotic stabilization of the Camassa-Holm equation

We investigate the problems of exact controllability and asymptotic stabilization of the Camassa-Holm equation on the circle, by means of a distributed control. The results are global, and in particular the control prevents the solution from blowing up.     

Bemerkung über einen verzerrungssatz bei topologischen Abbildungen in der Hydromechanik

Ohne Zusammenfassung     

Untersuchungen über die Gestalt der Himmelskörper

Ohne Zusammenfassung