Accuracy of the IOS approximation for highly inelastic R-T collisional energy transfer

Rate constants for rotational excitation of CO by collisions with He atoms computed within the infinite order sudden (IOS) approximation are compared with accurate quantum (coupled-states) and classical trajectory values. Taking the IOS energy as the initial kinetic energy for upward. 0 → J, transitions is found to overestimate the rates, especially for higher J (larger inelasticity). Taking the IOS energy as the initial energy for downward, J → 0, transitions underestimates the rates by a comparable amount. The geometric average of IOS rates computed in these two ways is found to provide accurate values.     

Symbolic extensions and smooth dynamical systems

Let f:XX be a homeomorphism of the compact metric space X. A symbolic extension of (f,X) is a subshift on a finite alphabet (g,Y) which has f as a topological factor. We show that a generic C¹ non-hyperbolic (i.e., non-Anosov) area preserving diffeomorphism of a compact surface has no symbolic extensions. For r>1, we exhibit a residual subset of an open set of C^r diffeomorphisms of a compact surface such that if , then any possible symbolic extension has topological entropy strictly larger than that of f. These results complement the known fact that any C diffeomorphism has symbolic extensions with the same entropy. We also show that C^r generically on surfaces, homoclinic closures which contain tangencies of stable and unstable manifolds have Hausdorff dimension two.     

Performance Analysis of Cyclical Simulated Annealing Algorithms

Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms for addressing intractable discrete optimization problems. Measures for assessing the finite-time performance of GHC algorithms have been developed using this framework, including the expected number of iterations to visit a predetermined objective function value level. This paper analyzes how the expected number of iterations to visit a predetermined objective function value level can be estimated for cyclical simulated annealing. Cyclical simulated annealing uses a cooling schedule that cycles through a set of temperature values. Computational results with traveling salesman problem instances taken from TSPLIB show how the expected number of iterations to visit solutions with predetermined objective function levels can be estimated for cyclical simulated annealing.AMS 2000 Subject Classification 90-08 Computational Methods: Local Search, 90C59 Heuristics: Simulated Annealing     

Products of Toeplitz operators

A sufficient condition is found for the product of two Toeplitz operators to be a compact perturbation of a Toeplitz operator. The condition, which comprehends all previously known sufficient conditions, is shown to be necessary under additional hypotheses. The question whether the condition is necessary in general is left open.     

On a generalization of Chen's iterated integrals

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In this paper, Chen's iterated integrals are generalized by interpolation of functions of the positive integer number of times which particular forms are iterated in integrals along specific paths, to certain complex values. These generalized iterated integrals satisfy both an additive iterative property and comultiplication formula. In a particular example, a (non-classical) multiplicative iterative property is also shown to hold. After developing this theory in the first part of the paper we discuss various applications, including the expression of certain zeta functions as complex iterated integrals (from which an obstruction to the existence of a contour integration proof of the functional equation for the Dedekind zeta function emerges); a way of thinking about complex iterated derivatives arising from a reformulation of a result of Gel'fand and Shilov in the theory of distributions; and a direct topological proof of the monodromy of polylogarithms.

Video

For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=dsVvo7s8BYU.     

The imprint of genius

Marconis transmission of wireless waves across the Atlantic in 1901 suggested that there was a ‘Heaviside layer’ in the high atmosphere to reflect them, but it was not until 1924 that experiments clearly demonstrated the layers existence. Between then and about 1935 wireless waves were used to elucidate the structure of the layer and the upper atmosphere.

It is shown why the proof of the layers existence was delayed so long, and how some doubtful suggestions about it were occasionally made: it is suggested that Appleton and the early workers in England conducted their experiments with a belief in the importance of ‘style in physics’, assisted, no doubt, by financial stringency.