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Deterministic Chaos Theory and Its Applications to Materials Science

Published online by Cambridge University Press:  29 November 2013

Alan J. Markworth ,
John Stringer  and
Roger W. Rollins
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Over the past 30 years or so, some fascinating new developments have taken place in a field that is now called “nonlinear science.” These developments have been of such magnitude that historian Alan Beyerchen concluded “There is every reason to believe that the westernized world is in the early stages of an intellectual transformation of major proportions, perhaps as significant as the emergence of the modern worldview in the fifteenth through seventeenth centuries.”

These new developments are rooted in work conducted by mathematician Jules Henri Poincaré around the turn of the century. He carried out some calculations regarding planetary orbits and demonstrated the possibility of erratic or “chaotic” dynamical behavior. What is particularly interesting about such behavior is that it is exhibited by deterministic systems, that is, systems that have no stochastic (noisy) character of any kind. Little was done with Poincaré's findings until the 1960s when new work in nonlinear science, based on numerical models, led to the discovery of amazingly complex behavior that can be exhibited even by very simple deterministic systems. Since that time, the discipline has grown enormously and has been applied in practically every area of science and engineering, as well as in other diverse areas such as the financial market, political science, economics, and even Adlerian psychology.

Type
Technical Features
Information
MRS Bulletin , Volume 20 , Issue 7 , July 1995 , pp. 20 - 28
Copyright
Copyright © Materials Research Society 1995

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