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The theory of the inhomogeneous electron gas had its origin in the
Thomas Fermi statistical theory, which is discussed in the first
chapter of this book. This already leads to significant physical
results for the binding energies of atomic ions, though because it
leaves out shell structure the results of such a theory cannot
reflect the richness of the Periodic Table. Therefore, for a long
time, the earlier method proposed by Hartree, in which each
electron is assigned its own personal wave function and energy,
dominated atomic theory. The extension of the Hartree theory by
Fock, to include exchange, had its parallel in the density
description when Dirac showed how to incorporate exchange in the
Thomas-Fermi theory. Considerably later, in 1951, Slater, in an
important paper, showed how a result similar to but not identical
with that of Dirac followed as a simplification of the Hartree-Fock
method. It was Gombas and other workers who recognized that one
could also incorporate electron correlation consistently into the
Thomas-Fermi-Dirac theory by using uniform electron gas relations
locally, and progress had been made along all these avenues by the
1950s."
This volume is concerned with the theoretical description of
patterns and instabilities and their relevance to physics,
chemistry, and biology. More specifically, the theme of the work is
the theory of nonlinear physical systems with emphasis on the
mechanisms leading to the appearance of regular patterns of ordered
behavior and chaotic patterns of stochastic behavior. The aim is to
present basic concepts and current problems from a variety of
points of view. In spite of the emphasis on concepts, some effort
has been made to bring together experimental observations and
theoretical mechanisms to provide a basic understanding of the
aspects of the behavior of nonlinear systems which have a measure
of generality. Chaos theory has become a real challenge to
physicists with very different interests and also in many other
disciplines, of which astronomy, chemistry, medicine, meteorology,
economics, and social theory are already embraced at the time of
writing. The study of chaos-related phenomena has a truly
interdisciplinary charac ter and makes use of important concepts
and methods from other disciplines. As one important example, for
the description of chaotic structures the branch of mathematics
called fractal geometry (associated particularly with the name of
Mandelbrot) has proved invaluable. For the discussion of the
richness of ordered structures which appear, one relies on the
theory of pattern recognition. It is relevant to mention that, to
date, computer studies have greatly aided the analysis of
theoretical models describing chaos."
This volume is concerned with the theoretical description of
patterns and instabilities and their relevance to physics,
chemistry, and biology. More specifically, the theme of the work is
the theory of nonlinear physical systems with emphasis on the
mechanisms leading to the appearance of regular patterns of ordered
behavior and chaotic patterns of stochastic behavior. The aim is to
present basic concepts and current problems from a variety of
points of view. In spite of the emphasis on concepts, some effort
has been made to bring together experimental observations and
theoretical mechanisms to provide a basic understanding of the
aspects of the behavior of nonlinear systems which have a measure
of generality. Chaos theory has become a real challenge to
physicists with very different interests and also in many other
disciplines, of which astronomy, chemistry, medicine, meteorology,
economics, and social theory are already embraced at the time of
writing. The study of chaos-related phenomena has a truly
interdisciplinary charac ter and makes use of important concepts
and methods from other disciplines. As one important example, for
the description of chaotic structures the branch of mathematics
called fractal geometry (associated particularly with the name of
Mandelbrot) has proved invaluable. For the discussion of the
richness of ordered structures which appear, one relies on the
theory of pattern recognition. It is relevant to mention that, to
date, computer studies have greatly aided the analysis of
theoretical models describing chaos."
The theory of the inhomogeneous electron gas had its origin in the
Thomas Fermi statistical theory, which is discussed in the first
chapter of this book. This already leads to significant physical
results for the binding energies of atomic ions, though because it
leaves out shell structure the results of such a theory cannot
reflect the richness of the Periodic Table. Therefore, for a long
time, the earlier method proposed by Hartree, in which each
electron is assigned its own personal wave function and energy,
dominated atomic theory. The extension of the Hartree theory by
Fock, to include exchange, had its parallel in the density
description when Dirac showed how to incorporate exchange in the
Thomas-Fermi theory. Considerably later, in 1951, Slater, in an
important paper, showed how a result similar to but not identical
with that of Dirac followed as a simplification of the Hartree-Fock
method. It was Gombas and other workers who recognized that one
could also incorporate electron correlation consistently into the
Thomas-Fermi-Dirac theory by using uniform electron gas relations
locally, and progress had been made along all these avenues by the
1950s."
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