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The book contains review articles on recent advances in
first-passage phenomena and applications contributed by leading
international experts. It is intended for graduate students and
researchers who are interested in learning about this intriguing
and important topic.
Aimed at graduate students, this book explores some of the core
phenomena in non-equilibrium statistical physics. It focuses on the
development and application of theoretical methods to help students
develop their problem-solving skills. The book begins with
microscopic transport processes: diffusion, collision-driven
phenomena, and exclusion. It then presents the kinetics of
aggregation, fragmentation and adsorption, where the basic
phenomenology and solution techniques are emphasized. The following
chapters cover kinetic spin systems, both from a discrete and a
continuum perspective, the role of disorder in non-equilibrium
processes, hysteresis from the non-equilibrium perspective, the
kinetics of chemical reactions, and the properties of complex
networks. The book contains 200 exercises to test students'
understanding of the subject. A link to a website hosted by the
authors, containing supplementary material including solutions to
some of the exercises, can be found at
www.cambridge.org/9780521851039.
First-passage properties underlie a wide range of stochastic
processes, such as diffusion-limited growth, neuron firing and the
triggering of stock options. This book provides a unified
presentation of first-passage processes, which highlights its
interrelations with electrostatics and the resulting powerful
consequences. The author begins with a presentation of fundamental
theory including the connection between the occupation and
first-passage probabilities of a random walk, and the connection to
electrostatics and current flows in resistor networks. The
consequences of this theory are then developed for simple,
illustrative geometries including the finite and semi-infinite
intervals, fractal networks, spherical geometries and the wedge.
Various applications are presented including neuron dynamics,
self-organized criticality, diffusion-limited aggregation, the
dynamics of spin systems and the kinetics of diffusion-controlled
reactions. First-passage processes provide an appealing way for
graduate students and researchers in physics, chemistry,
theoretical biology, electrical engineering, chemical engineering,
operations research and finance to understand all of these systems.
First-passage properties underlie a wide range of stochastic processes, such as diffusion-limited growth, neuron firing, and the triggering of stock options. This book provides a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The author begins with a modern presentation of fundamental theory including the connection between the occupation and first-passage probabilities of a random walk, and the connection to electrostatics and current flows in resistor networks. The consequences of this theory are then developed for simple, illustrative geometries including the finite and semi-infinite intervals, fractal networks, spherical geometries and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin systems, and the kinetics of diffusion-controlled reactions. Examples discussed include neuron dynamics, self-organized criticality, kinetics of spin systems, and stochastic resonance.
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