Publication Date:
2022-05-26
Description:
The explosive growth of dynamieal systems theory in the past two decades
stems in large part from the realization that it is applicable to many
natural phenomena. Indeed, much o f the theoretical development has been
sparked by numerical and laboratory experiments which exhibit ordered
sequences of behavior that call for a general framework of interpretation
We have been fortunate this summer to have had in residence both pioneers
and developers of dynamical systems theory and its applications to fluid
mechanics. Several recent texts contain the basic principles that Ed Spiegel
used as a springboard for five lectures in which he exposed us to elementary
examples of bifurcation and chaos, to symmetry breaking, normal forms and
temporal and spatial disorder, as well as to pertinent fluid mechanical and
astrophysical phenomena. Yves Pomeau continued the development with an
elegant summary of different types of intermittency . Stephan Fauve agree
to write up his impressive seminars on phase instability and turbulence as
an extension of the lecture series. Many of the remaining seminars introduced
new concepts in the theory, some with specific examples, others via
mathematical development, and still others through ways of interpreting the
data that emerge from calculations and experiments. As an outstanding
example of this, Albert Libchaber has demonstrated the fascinating correspondence
between the frequencies observed in one of his recent fluid mechanics
experiments and results from number theory relating the Fibonacci series to
the golden mean.
Description:
Office of Naval Research under contract NO0014-82-6-0079
and the National Science Foundation under Grants
MCS-82-000450 and DMS-85-04166.
Keywords:
Geophysics
;
Fluid dynamics
Repository Name:
Woods Hole Open Access Server
Type:
Technical Report
Format:
application/pdf
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