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Fundamentals of Stochastic Nature Sciences (Hardcover, 1st ed. 2017)
Loot Price: R4,088
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Fundamentals of Stochastic Nature Sciences (Hardcover, 1st ed. 2017)
Series: Understanding Complex Systems
Expected to ship within 12 - 17 working days
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This book addresses the processes of stochastic structure formation
in two-dimensional geophysical fluid dynamics based on statistical
analysis of Gaussian random fields, as well as stochastic structure
formation in dynamic systems with parametric excitation of positive
random fields f(r,t) described by partial differential equations.
Further, the book considers two examples of stochastic structure
formation in dynamic systems with parametric excitation in the
presence of Gaussian pumping. In dynamic systems with parametric
excitation in space and time, this type of structure formation
either happens - or doesn't! However, if it occurs in space, then
this almost always happens (exponentially quickly) in individual
realizations with a unit probability. In the case considered,
clustering of the field f(r,t) of any nature is a general feature
of dynamic fields, and one may claim that structure formation is
the Law of Nature for arbitrary random fields of such type. The
study clarifies the conditions under which such structure formation
takes place. To make the content more accessible, these conditions
are described at a comparatively elementary mathematical level by
employing ideas from statistical topography.
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