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Ideal gas in empty space
Nonlinear Science Abstracts
299
certain technical assumptions it is rig.o~roously shown by probabilistic techniques that falls-off faster than t - J ~ for any e>O , giving a continuous Fourier transform and line shape. An alternative expression is derived for the latter which explicitly displays its positivlty and which is a limit over increasing perturber numbers. In Part II this will serve as a starting point for a truncation expansion. Several open problems are pointed out which merit a rigorous investigation. JOURNAL: none given 143
(P6,TI2) NUMERICAL SOLUTION OF THE ZAKHAROV EQUATIONS, G. L. Payne, D. R. Nicholson, and R. M. Downie, Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242, USA. A new algorithm for the numerical solution of the Zakharov equations is presented. This algorithm is explicit and it is second-order accurate. The convergence of the algorithm is demonstrated by numerically solving the Zakharov equations for several test cases. JOURNAL: none given 144
(MI,13) CHAOTIC RESPONSE OF NONLINEAR OSCILLATORS, Kazuhisa Tomita, Department of Physics, Faculty of Science, University of Kyoto, Kyoto 606, JAPAN. A review is given of the chaotic response of nonlinear oscillators which is a typical example of chaotic, or turbulent phase, now attracting attention in various fields of research. Resorting to the quasi-one-dimensional character of the stroboscopic phase portrait of the chosen model, one-dimensional description and analysis have been presented at some length. This is the simplest case exhibiting chaos, and concepts and tools treating the problem are most abundant. Correlation spectra, invariant measure and Lyapunov number are all of use. In addition an example of statistical mechanics describing chaos is presented. The associated variational principle has some analogy with that in equilibrium statistical thermodynamics; however, the quantity to be maximized is the rate of information loss rather than the information loss itself. A typical example of the period doubling route to chaos is found in our model. The phenomenological renormalization theory is described which puts this route on a universal basis. Examples of more general two-dimensional stroboscopic portrait are given and discussed using the ocncept of homo- (and hetero-) clinicity. Two perturbation theoretic approaches are described to locate the onset of homoclinicity in the parameter space. JOURNAL: Physics Reports 86, No. 3 (1982) 113-167. 145
(P3,T5) PROPAGATION OF CHAOS AND BURGERS EQUATION, E. Gutkin, Columbia University; M. Kac, University of Southern California, USA. We establish a connection between the Burgers equation and the limit of a N-body problem when N + ~. Then we use this connection to linearize the Burgers equation. JOURNAL: none given 146
(P3,T9) IDEAL GAS IN EMPTY SPACE, L. Andrey, Department of Physics, University of Safarik-Moyzesova II, 040 00 Kosice, CZECHOSLOVAKIA. It is shown that an ideal gas in empty space is not recurrent in the sense of Poincare and Zermelo. The generalized Louville theorem is formulated in
299
certain technical assumptions it is rig.o~roously shown by probabilistic techniques that
(P6,TI2) NUMERICAL SOLUTION OF THE ZAKHAROV EQUATIONS, G. L. Payne, D. R. Nicholson, and R. M. Downie, Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242, USA. A new algorithm for the numerical solution of the Zakharov equations is presented. This algorithm is explicit and it is second-order accurate. The convergence of the algorithm is demonstrated by numerically solving the Zakharov equations for several test cases. JOURNAL: none given 144
(MI,13) CHAOTIC RESPONSE OF NONLINEAR OSCILLATORS, Kazuhisa Tomita, Department of Physics, Faculty of Science, University of Kyoto, Kyoto 606, JAPAN. A review is given of the chaotic response of nonlinear oscillators which is a typical example of chaotic, or turbulent phase, now attracting attention in various fields of research. Resorting to the quasi-one-dimensional character of the stroboscopic phase portrait of the chosen model, one-dimensional description and analysis have been presented at some length. This is the simplest case exhibiting chaos, and concepts and tools treating the problem are most abundant. Correlation spectra, invariant measure and Lyapunov number are all of use. In addition an example of statistical mechanics describing chaos is presented. The associated variational principle has some analogy with that in equilibrium statistical thermodynamics; however, the quantity to be maximized is the rate of information loss rather than the information loss itself. A typical example of the period doubling route to chaos is found in our model. The phenomenological renormalization theory is described which puts this route on a universal basis. Examples of more general two-dimensional stroboscopic portrait are given and discussed using the ocncept of homo- (and hetero-) clinicity. Two perturbation theoretic approaches are described to locate the onset of homoclinicity in the parameter space. JOURNAL: Physics Reports 86, No. 3 (1982) 113-167. 145
(P3,T5) PROPAGATION OF CHAOS AND BURGERS EQUATION, E. Gutkin, Columbia University; M. Kac, University of Southern California, USA. We establish a connection between the Burgers equation and the limit of a N-body problem when N + ~. Then we use this connection to linearize the Burgers equation. JOURNAL: none given 146
(P3,T9) IDEAL GAS IN EMPTY SPACE, L. Andrey, Department of Physics, University of Safarik-Moyzesova II, 040 00 Kosice, CZECHOSLOVAKIA. It is shown that an ideal gas in empty space is not recurrent in the sense of Poincare and Zermelo. The generalized Louville theorem is formulated in