Inhaltsangabe
Excerpt from Dynamics of Nonlinear Stochastic Systems
The closed statistical equations which characterize the models are obtained by averaging over an ensemble of realizations of the collection of coupled sys tems. When iteration expansions are generated for the averages of basic interest, it is found, using the collective representation, that the random couplings result in the cancellation of large classes of terms of all orders. The remain ing terms are identical with corresponding ones in the expansion.for the true problem (zero couplings). Although still of all orders, they have a sufficiently simple structure that their sum represents the exact solution of closed integral equations.
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Dynamics of Nonlinear Stochastic Systems (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book introduces a method for treating complex nonlinear stochastic systems, which is relevant for both the quantum-mechanical many-body problem and turbulence theory. The technique involves replacing the true problem by models that lead to closed equations for correlation functions and averaged Green's functions. Remarkably, solutions for these models are exact descriptions of possible dynamical systems, providing certain consistency properties inherent to the true problem. For example, spectral components of Green's functions that must be positive-definite in the true problem are automatically so in the models. These properties are often absent in truncated perturbation expansions, which the author shows can exhibit pathological characteristics and lead to physically unacceptable results. The author applies the method to a linear oscillator with random frequency parameter and demonstrates that the model solutions converge rapidly to the exact solution for the true problem. They also formulate stochastic models for the Schrodinger equation of a particle in a random potential and for Burgers' analog to turbulence dynamics, obtaining closed model equations that determine the average Green's function, the amplitude of the mean field, and the covariance of the fluctuating field. These insights suggest a potentially valuable application of this method: it could help assess the validity of partial summations of perturbation series in analogous situations. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781334016905_0
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