Analysis of the SDE/Monte Carlo Approach in Studying Nonlinear Systems: and its use in understanding the atmosphere's strange attractor associated with explosive baroclinic instability - Softcover

Fleming Rex J.

 
9783659715143: Analysis of the SDE/Monte Carlo Approach in Studying Nonlinear Systems: and its use in understanding the atmosphere's strange attractor associated with explosive baroclinic instability
Softcover
ISBN 10: 365971514X ISBN 13: 9783659715143
Verlag: LAP Lambert Academic Publishing, 2015

Inhaltsangabe

The reader is about to embark on a tutorial journey through a series of nonlinear dynamic systems that contain a rich tapestry of phenomena and solutions. The study of nonlinear systems can be greatly enhanced by the combined use of the stochastic dynamic equations and Monte Carlo calculations. When a dynamic system is forced and dissipative all the trajectories tend toward a bounded set of zero volume - often a strange attractor with a fractal dimension. The stochastic dynamic equations can directly reveal the statistical moments of the system, but their direct solution is inefficient, and they are not a closed set. The power of the combined method is that the time averaged Monte Carlo moments will agree exactly with equations described by the left hand side of the full stochastic dynamic equations set to zero - no closure is required. Every equation expresses an exact relationship among the variables. One is able to delve far deeper into the nature of the nonlinear systems. This tutorial exposition offers the tools for the past nonlinear modeling efforts in the traditional physical sciences and in various complex modeling problems in new fields of biology and health sciences.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

The reader is about to embark on a tutorial journey through a series of nonlinear dynamic systems that contain a rich tapestry of phenomena and solutions. The study of nonlinear systems can be greatly enhanced by the combined use of the stochastic dynamic equations and Monte Carlo calculations. When a dynamic system is forced and dissipative all the trajectories tend toward a bounded set of zero volume - often a strange attractor with a fractal dimension. The stochastic dynamic equations can directly reveal the statistical moments of the system, but their direct solution is inefficient, and they are not a closed set. The power of the combined method is that the time averaged Monte Carlo moments will agree exactly with equations described by the left hand side of the full stochastic dynamic equations set to zero - no closure is required. Every equation expresses an exact relationship among the variables. One is able to delve far deeper into the nature of the nonlinear systems. This tutorial exposition offers the tools for the past nonlinear modeling efforts in the traditional physical sciences and in various complex modeling problems in new fields of biology and health sciences.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
LAP Lambert Academic Publishing
Erscheinungsdatum
2015
Sprache
Englisch
ISBN 10 
365971514X
ISBN 13 
9783659715143
Einband
Tapa blanda
Anzahl der Seiten
144
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Verantwortliche Person
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