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Complexity And Criticality (Paperback)
Loot Price: R1,423
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Complexity And Criticality (Paperback)
Series: Imperial College Press Advanced Physics Texts, 1
Expected to ship within 10 - 15 working days
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This book provides a challenging and stimulating introduction to
the contemporary topics of complexity and criticality, and explores
their common basis of scale invariance, a central unifying theme of
the book.Criticality refers to the behaviour of extended systems at
a phase transition where scale invariance prevails. The many
constituent microscopic parts bring about macroscopic phenomena
that cannot be understood by considering a single part alone. The
phenomenology of phase transitions is introduced by considering
percolation, a simple model with a purely geometrical phase
transition, thus enabling the reader to become intuitively familiar
with concepts such as scale invariance and renormalisation. The
Ising model is then introduced, which captures a thermodynamic
phase transition from a disordered to an ordered system as the
temperature is lowered in zero external field. By emphasising
analogies between percolation and the Ising model, the reader's
intuition of phase transitions is developed so that the underlying
theoretical formalism may be appreciated fully. These equilibrium
systems undergo a phase transition only if an external agent finely
tunes certain external parameters to particular values.Besides
fractals and phase transitions, there are many examples in Nature
of the emergence of such complex behaviour in slowly driven
non-equilibrium systems: earthquakes in seismic systems, avalanches
in granular media and rainfall in the atmosphere. A class of
non-equilibrium systems, not constrained by having to tune external
parameters to obtain critical behaviour, is addressed in the
framework of simple models, revealing that the repeated application
of simple rules may spontaneously give rise to emergent complex
behaviour not encoded in the rules themselves. The common basis of
complexity and criticality is identified and applied to a range of
non-equilibrium systems. Finally, the reader is invited to
speculate whether self-organisation in non-equilibrium systems
might be a unifying concept for disparate fields such as
statistical mechanics, geophysics and atmospheric physics.Visit for
animations for the models in the book (available for Windows and
Linux), solutions to exercises, as well as a list with corrections.
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