Magnetic field dependence of charge density waves in PbTe

Previous work by the authors indicated the possible existence of charge density waves in PbTe in the presence of strong magnetic fields so that the extreme quantum limit conditions prevail. The present work follows the transition as the field is lowered so that successively higher Landau levels become occupied. The transition persists at increasingly lower temperatures, having a maximum value, T_cmax, identifiable with each value, N, of the last (partially) occupied Landau level.     

Making forecasts for chaotic physical processes

Making a prediction for a chaotic physical process involves specifying the probability associated with each possible outcome. Ensembles of solutions are frequently used to estimate this probability distribution. However, for a typical chaotic physical system and model of that system, no solution of remains close to for all time. We propose an alternative. This Letter shows how to inflate or systematically perturb the ensemble of solutions of so that some ensemble member remains close to for orders of magnitude longer than unperturbed solutions of . This is true even when the perturbations are significantly smaller than the model error.     

Synchrotron X‐ray CT characterization of titanium parts fabricated by additive manufacturing. Part I. Morphology

Synchrotron X‐ray tomography has been applied to the study of titanium parts fabricated by additive manufacturing (AM). The AM method employed here was the Arcam EBM^® (electron beam melting) process which uses powdered titanium alloy, Ti64 (Ti alloy with approximately 6%Al and 4%V), as the feed and an electron beam for the sintering/welding. The experiment was conducted on the Imaging and Medical Beamline of the Australian Synchrotron. Samples were chosen to examine the effect of build direction and complexity of design on the surface morphology and final dimensions of the piece.     

Using fractal to solve the multiple minima problem in molecular mechanics calculation

This article presents an approach using fractal to solve the multiple minima problem. We use the Newton–Raphson method of the MM3 molecular mechanics program to scan the conformational spaces of a model molecule and a real molecule. The results show each energy minimum, maximum point, and saddle point has a basin of initial points converging to it in conformational spaces. Points converging to different extrema are mixed, and form fractal structures around basin boundaries. Singular points seem to involve in the formation of fractal. When searching within a small region of fractal basin boundaries, the self‐similarity of fractal makes it possible to find all energy minima, maxima, and saddle points from which global minimum may be extracted. Compared with other methods, this approach is efficient, accurate, conceptually simple, and easy to implement. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1101–1108, 2000     

Finding safety in partially controllable chaotic systems

Many discrete-time dynamical systems have a region Q from which all or almost all trajectories leave, or at least they leave in the presence of perturbations that we call disturbances. We partially control systems so that despite disturbances the trajectories of a dynamical system stay in the region Q at least for some initial points in Q. The disturbances can be thought of as either noise or as purposeful, hostile efforts of an enemy to drive the trajectory out of the region. Our goal is to keep trajectories inside Q despite the disturbances and our partial control of chaos method succeeds.Surprisingly this goal can be achieved with a control whose maximum allowable size is smaller than the maximum allowed disturbance. A fundamental step towards this goal is to compute a set called the safe set that had, until now, been found only in certain very special situations.This paper provides a general algorithm for computing safe sets. The algorithm is able to compute the safe sets for a specified region in phase space, the maximum disturbance value, and the maximum allowed control. We call it the Sculpting Algorithm. Its operation is analogous to removing material while sculpting a statue. The algorithm sculpts the safe sets. Our Sculpting Algorithm is independent of the dimension and is fast for one- and two-dimensional dynamical systems. As examples, we apply the algorithm to two paradigmatic nonlinear dynamical systems, namely, the Hénon map and the Duffing oscillator.