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This textbook takes the reader on a tour of the most important
landmarks of theoretical physics: classical, quantum, and
statistical mechanics, relativity, electrodynamics, as well as the
most modern and exciting of all: elementary particles and the
physics of fractals. The second edition has been supplemented with
a new chapter devoted to concise though complete presentation of
dynamical systems, bifurcations and chaos theory. The treatment is
confined to the essentials of each area, presenting all the central
concepts and equations at an accessible level. Chapters 1 to 4
contain the standard material of courses in theoretical physics and
are supposed to accompany lectures at the university; thus they are
rather condensed. They are supposed to fill one year of teaching.
Chapters 5 and 6, in contrast, are written less condensed since
this material may not be part of standard lectures and thus could
be studied without the help of a university teacher. An appendix on
elementary particles lies somewhere in between: It could be a
summary of a much more detailed course, or studied without such a
course. Illustrations and numerous problems round off this unusual
textbook. It will ideally accompany the students all along their
course in theoretical physics and prove indispensable in preparing
and revising the exams. It is also suited as a reference for
teachers or scientists from other disciplines who are interested in
the topic.
Proceedings of the NATO Advanced Study Institute, Cargese, Corsica,
France, 18-31 July, 1988"
Phase transitions are involved in phenomena ranging from the
initial stages of the creation of the Universe to the existence of
biological objects. It is natural to as whether any phenomena
analogous to phase transitions are possible in disordered
substances like liquids and glasses. The possibility of such
transitions is still very much a matter of debate. Neither the
nature nor the features of transformations in liquids and glasses
are yet clear, nor is the nature of the order parameters.
Investigations in recent years have shown that transformations in
liquids and glasses lead to a drastic change of their physical
properties and short-range order structure.
The papers collected here contribute to a better understanding of
the physics of disordered systems and phase transformations in
them. An unambiguous identification of transitions in liquids and
glasses requires further high-precision experimental study of the
thermodynamic and structural properties in the vicinity of
transitions in order to test existing theoretical models and
develop new, more accurate ones.
We have shown that simple power-law dynamics is expected for
flexible fractal objects. Although the predicted behavior is well
established for linear polymers, the situationm is considerably
more complex for colloidal aggregates. In the latter case, the
observed K-dependence of (r) can be explained either in terms of
non-asymptotic hydrodynamics or in terms of weak power-law
polydispersity. In the case of powders (alumina, in particular)
apparent fractal behavior seen in static scattering is not found in
the dynamics. ID. W. Schaefer, J. E. Martin, P. Wiitzius, and D. S.
Cannell, Phys. Rev. Lett. 52,2371 (1984). 2 J. E. Martin and D. W.
Schaefer, Phys. Rev. Lett. 5:1,2457 (1984). 3 D. W. Schaefer and C.
C. Han in Dynamic Light Scattering, R. Pecora ed, Plenum, NY, 1985)
p. 181. 4 P. Sen, this book. S J. E. Martin and B. J. Ackerson,
Phys. Rev. A :11, 1180 (1985). 6 J. E. Martin, to be published. 7
D. A. Weitz, J. S. Huang, M. Y. Lin and J. Sung, Phys. Rev. Lett.
53,1657 (1984) . 8 J. E. Martin, D. W. Schaefer and A. J. Hurd, to
be published; D. W. Schaefer, K. D. Keefer, J. E. Martin, and A. J.
Hurd, in Physics of Finely Divided Matter, M. Daoud, Ed., Springer
Verlag, NY, 1985. 9 D. W. Schaefer and A. J. Hurd, to be published.
lOJ. E. Martin, J. Appl. Cryst. (to be published).
Topics of complex system physics and their interdisciplinary
applications to different problems in seismology, biology, economy,
sociology, energy and nanotechnology are covered in this new work
from renowned experts in their fields. Inparticular, contributed
papers contain original results on network science, earthquake
dynamics, econophysics, sociophysics, nanoscience and biological
physics. Most of the papers use interdisciplinary approaches based
on statistical physics, quantum physics and other topics of complex
system physics.Papers on econophysics and sociophysics are focussed
on societal aspects of physics such as, opinion dynamics, public
debates and financial and economic stability. This work will be of
interest to statistical physicists, economists, biologists,
seismologists and all scientists working in interdisciplinary
topics of complexity."
Proceedings of the NATO Advanced Study Institute on Propagation of
Correlations in Constrained Systems, Cargese, Corsica, France, July
2-14, 1990"
This textbook takes the reader on a tour of the most important
landmarks of theoretical physics: classical, quantum, and
statistical mechanics, relativity, electrodynamics, as well as the
most modern and exciting of all: elementary particles and the
physics of fractals. The second edition has been supplemented with
a new chapter devoted to concise though complete presentation of
dynamical systems, bifurcations and chaos theory. The treatment is
confined to the essentials of each area, presenting all the central
concepts and equations at an accessible level. Chapters 1 to 4
contain the standard material of courses in theoretical physics and
are supposed to accompany lectures at the university; thus they are
rather condensed. They are supposed to fill one year of teaching.
Chapters 5 and 6, in contrast, are written less condensed since
this material may not be part of standard lectures and thus could
be studied without the help of a university teacher. An appendix on
elementary particles lies somewhere in between: It could be a
summary of a much more detailed course, or studied without such a
course. Illustrations and numerous problems round off this unusual
textbook. It will ideally accompany the students all along their
course in theoretical physics and prove indispensable in preparing
and revising the exams. It is also suited as a reference for
teachers or scientists from other disciplines who are interested in
the topic.
Topics of complex system physics and their interdisciplinary
applications to different problems in seismology, biology, economy,
sociology, energy and nanotechnology are covered in this new work
from renowned experts in their fields. Inparticular, contributed
papers contain original results on network science, earthquake
dynamics, econophysics, sociophysics, nanoscience and biological
physics. Most of the papers use interdisciplinary approaches based
on statistical physics, quantum physics and other topics of complex
system physics.Papers on econophysics and sociophysics are focussed
on societal aspects of physics such as, opinion dynamics, public
debates and financial and economic stability. This work will be of
interest to statistical physicists, economists, biologists,
seismologists and all scientists working in interdisciplinary
topics of complexity."
Phase transitions are involved in phenomena ranging from the
initial stages of the creation of the Universe to the existence of
biological objects. It is natural to as whether any phenomena
analogous to phase transitions are possible in disordered
substances like liquids and glasses. The possibility of such
transitions is still very much a matter of debate. Neither the
nature nor the features of transformations in liquids and glasses
are yet clear, nor is the nature of the order parameters.
Investigations in recent years have shown that transformations in
liquids and glasses lead to a drastic change of their physical
properties and short-range order structure.
The papers collected here contribute to a better understanding of
the physics of disordered systems and phase transformations in
them. An unambiguous identification of transitions in liquids and
glasses requires further high-precision experimental study of the
thermodynamic and structural properties in the vicinity of
transitions in order to test existing theoretical models and
develop new, more accurate ones.
From Newton to Mandelbrot takes the student on a tour of the most
important landmarks of theoretical physics: classical, quantum, and
statistical mechanics, relativity, electrodynamics, and, the most
modern and exciting of all, the physics of fractals. The treatment
is confined to the essentials of each area, and short computer
programs, numerous problems, and beautiful color illustrations
round off this unusual textbook. Ideally suited for a one-year
course in theoretical physics it will also prove useful in
preparing and revising for exams. This edition is corrected and
includes a new appendix on elementary particle physics, answers to
all short questions, and a diskette where a selection of executable
programs exploring the fractal concept can be found.
Nature is full of spidery patterns: lightning bolts, coastlines,
nerve cells, termite tunnels, bacteria cultures, root systems,
forest fires, soil cracking, river deltas, galactic distributions,
mountain ranges, tidal patterns, cloud shapes, sequencing of
nucleotides in DNA, cauliflower, broccoli, lungs, kidneys, the
scraggly nerve cells that carry signals to and from your brain, the
branching arteries and veins that make up your circulatory system.
These and other similar patterns in nature are called natural
fractals or random fractals. This chapter contains activities that
describe random fractals. There are two kinds of fractals:
mathematical fractals and natural (or random) fractals. A
mathematical fractal can be described by a mathematical formula.
Given this formula, the resulting structure is always identically
the same (though it may be colored in different ways). In contrast,
natural fractals never repeat themselves; each one is unique,
different from all others. This is because these processes are
frequently equivalent to coin-flipping, plus a few simple rules.
Nature is full of random fractals. In this book you will explore a
few of the many random fractals in Nature. Branching, scraggly
nerve cells are important to life (one of the patterns on the
preceding pages). We cannot live without them. How do we describe a
nerve cell? How do we classify different nerve cells? Each
individual nerve cell is special, unique, different from every
other nerve cell. And yet our eye sees that nerve cells are similar
to one another.
Proceedings of the NATO Advanced Study Institute on Propagation of
Correlations in Constrained Systems, Cargese, Corsica, France, July
2-14, 1990
Proceedings of the NATO Advanced Study Institute, Cargese, Corsica,
France, 18-31 July, 1988
We have shown that simple power-law dynamics is expected for
flexible fractal objects. Although the predicted behavior is well
established for linear polymers, the situationm is considerably
more complex for colloidal aggregates. In the latter case, the
observed K-dependence of (r) can be explained either in terms of
non-asymptotic hydrodynamics or in terms of weak power-law
polydispersity. In the case of powders (alumina, in particular)
apparent fractal behavior seen in static scattering is not found in
the dynamics. ID. W. Schaefer, J. E. Martin, P. Wiitzius, and D. S.
Cannell, Phys. Rev. Lett. 52,2371 (1984). 2 J. E. Martin and D. W.
Schaefer, Phys. Rev. Lett. 5:1,2457 (1984). 3 D. W. Schaefer and C.
C. Han in Dynamic Light Scattering, R. Pecora ed, Plenum, NY, 1985)
p. 181. 4 P. Sen, this book. S J. E. Martin and B. J. Ackerson,
Phys. Rev. A :11, 1180 (1985). 6 J. E. Martin, to be published. 7
D. A. Weitz, J. S. Huang, M. Y. Lin and J. Sung, Phys. Rev. Lett.
53,1657 (1984) . 8 J. E. Martin, D. W. Schaefer and A. J. Hurd, to
be published; D. W. Schaefer, K. D. Keefer, J. E. Martin, and A. J.
Hurd, in Physics of Finely Divided Matter, M. Daoud, Ed., Springer
Verlag, NY, 1985. 9 D. W. Schaefer and A. J. Hurd, to be published.
lOJ. E. Martin, J. Appl. Cryst. (to be published).
Statistical physics concepts such as stochastic dynamics, short-
and long-range correlations, self-similarity and scaling, permit an
understanding of the global behavior of economic systems without
first having to work out a detailed microscopic description of the
system. This pioneering text explores the use of these concepts in
the description of financial systems, the dynamic new specialty of
econophysics. The authors illustrate the scaling concepts used in
probability theory, critical phenomena, and fully-developed
turbulent fluids and apply them to financial time series. They also
present a new stochastic model that displays several of the
statistical properties observed in empirical data. Physicists will
find the application of statistical physics concepts to economic
systems fascinating. Economists and other financial professionals
will benefit from the book's empirical analysis methods and
well-formulated theoretical tools that will allow them to describe
systems composed of a huge number of interacting subsystems.
Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling, permit an understanding of the global behavior of economic systems without first having to work out a detailed microscopic description of the system. This pioneering text explores the use of these concepts in the description of financial systems, the dynamic new specialty of econophysics. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully-developed turbulent fluids and apply them to financial time series. They also present a new stochastic model that displays several of the statistical properties observed in empirical data. Physicists will find the application of statistical physics concepts to economic systems fascinating. Economists and other financial professionals will benefit from the book's empirical analysis methods and well-formulated theoretical tools that will allow them to describe systems composed of a huge number of interacting subsystems.
Do the movements of animals, including humans, follow patterns that
can be described quantitatively by simple laws of motion? If so,
then why? These questions have attracted the attention of
scientists in many disciplines, and stimulated debates ranging from
ecological matters to queries such as 'how can there be free will
if one follows a law of motion?' This is the first book on this
rapidly evolving subject, introducing random searches and foraging
in a way that can be understood by readers without a previous
background on the subject. It reviews theory as well as experiment,
addresses open problems and perspectives, and discusses
applications ranging from the colonization of Madagascar by
Austronesians to the diffusion of genetically modified crops. The
book will interest physicists working in the field of anomalous
diffusion and movement ecology as well as ecologists already
familiar with the concepts and methods of statistical physics.
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