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Long time tails and diffusion
Nonlinear science abstracts
421
387 (B8,T6) GLOBAL STABILITY IN POPULATION MODELS, J. R. Pounder and Thomas D. Rogers, Department of Mathematics, University of Alberta, Edmonton, Alberta, CANADA T6G 2Gl. If g is a continuous map of an interval, the recursion x +l = g(x,), n = 0, 1 . . . converges globally if and only if the equation has only?ixed points of g as roots. This leads to simple geometric conditions for global stability in discrete population models. Related conditions involving the Schwarzian derivative and curvature are discussed. JOURNAL: Mathematical Modelling, Vol. 3, pp. 207-214, 1982. 388
(P8,12) TOWARD A COMPREHENSIVE SEMICLASSICAL ERGODIC THEORY, Kenneth G. Kay, Department of Chemistry, Kansas State University, Manhattan, Kansas 66506, USA. We identify quantum dynamical conditions that tend, as n + 0; to the classical conditions of ergodicity, weak mixing, mixing, and absolutely continuous spectrum. We use these conditions to derive asymptotic properties of matrix wave-functions, elements, and energy levels of systems with various ergodic properties in the classical limit. Some of these properties are new while others modify older predictions of "quantum ergodic properties." Thus, the present work serves to extend, unify, and refine a number of pervious theories. One new prediction is that weak mixing leads to the Van Hove diagonal singularity condition for a certain class of operators. This result may have significant implications for the applicability of nonequilibrium statistical mechanics to finite systems. JOURNAL: J. Chem. Phys., to be published 389
(P3,15) DYNAMIC MONTE CARLO RENORMALIZATION GROUP, Naeem Jan, Physics Department, St Francis Xavier University, Antigonish, Nova Scotia B2G lC0, CANADA; L. Leo Moseley, Physics Department, University of the West BARBADOS; Indies, Cave Hill, Dietrich Stauffer, Institut fiir Theoretische Physik, Universitat, 5000 Kb'ln 41, FRG. A new and simple method for applying the idea of real space renormalization group theory to the analysis of Monte Carlo configurations is proposed and applied to the Glauber kinetic Ising model in two and three dimensions and to the Kawasaki model in two dimensions. The renormalization analysis takes only a small fraction of the computer time needed to produce the Monte Carlo configurations and the results are obtained as the system relaxes to its equilibrium state at Tc (the critical temperature). The values obtained for the dynamical critical exponent, z, are 2.12 (d=2) and 2.11 (d=3) for the Glauber model and 3.90 for the two dimensional Kawasaki model. These results are in good agreement with those obtained by other methods but with smaller error bars in three dimensions. JOURNAL: Journal of Statistical Physics 390 (P3) LONG TIME TAILS AND DIFFUSION, Ronald F. Fox, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA. The evidence for long time tails as a part of the velocity autocorrelation function for a classical particle is examined. Computer simulations, theoretical treatments, and light scattering experiments are discussed. It is argued that numerical error propagation in the computer simulations may give rise to long time tails as an artifact which is of hydrodynamic character. The theoretical treatments of physicists, whether
421
387 (B8,T6) GLOBAL STABILITY IN POPULATION MODELS, J. R. Pounder and Thomas D. Rogers, Department of Mathematics, University of Alberta, Edmonton, Alberta, CANADA T6G 2Gl. If g is a continuous map of an interval, the recursion x +l = g(x,), n = 0, 1 . . . converges globally if and only if the equation has only?ixed points of g as roots. This leads to simple geometric conditions for global stability in discrete population models. Related conditions involving the Schwarzian derivative and curvature are discussed. JOURNAL: Mathematical Modelling, Vol. 3, pp. 207-214, 1982. 388
(P8,12) TOWARD A COMPREHENSIVE SEMICLASSICAL ERGODIC THEORY, Kenneth G. Kay, Department of Chemistry, Kansas State University, Manhattan, Kansas 66506, USA. We identify quantum dynamical conditions that tend, as n + 0; to the classical conditions of ergodicity, weak mixing, mixing, and absolutely continuous spectrum. We use these conditions to derive asymptotic properties of matrix wave-functions, elements, and energy levels of systems with various ergodic properties in the classical limit. Some of these properties are new while others modify older predictions of "quantum ergodic properties." Thus, the present work serves to extend, unify, and refine a number of pervious theories. One new prediction is that weak mixing leads to the Van Hove diagonal singularity condition for a certain class of operators. This result may have significant implications for the applicability of nonequilibrium statistical mechanics to finite systems. JOURNAL: J. Chem. Phys., to be published 389
(P3,15) DYNAMIC MONTE CARLO RENORMALIZATION GROUP, Naeem Jan, Physics Department, St Francis Xavier University, Antigonish, Nova Scotia B2G lC0, CANADA; L. Leo Moseley, Physics Department, University of the West BARBADOS; Indies, Cave Hill, Dietrich Stauffer, Institut fiir Theoretische Physik, Universitat, 5000 Kb'ln 41, FRG. A new and simple method for applying the idea of real space renormalization group theory to the analysis of Monte Carlo configurations is proposed and applied to the Glauber kinetic Ising model in two and three dimensions and to the Kawasaki model in two dimensions. The renormalization analysis takes only a small fraction of the computer time needed to produce the Monte Carlo configurations and the results are obtained as the system relaxes to its equilibrium state at Tc (the critical temperature). The values obtained for the dynamical critical exponent, z, are 2.12 (d=2) and 2.11 (d=3) for the Glauber model and 3.90 for the two dimensional Kawasaki model. These results are in good agreement with those obtained by other methods but with smaller error bars in three dimensions. JOURNAL: Journal of Statistical Physics 390 (P3) LONG TIME TAILS AND DIFFUSION, Ronald F. Fox, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA. The evidence for long time tails as a part of the velocity autocorrelation function for a classical particle is examined. Computer simulations, theoretical treatments, and light scattering experiments are discussed. It is argued that numerical error propagation in the computer simulations may give rise to long time tails as an artifact which is of hydrodynamic character. The theoretical treatments of physicists, whether