Noise-Induced Transitions

Noise-Induced Transitions PDF

Author: W. Horsthemke

Publisher: Springer Science & Business Media

Published: 2006-09-12

Total Pages: 322

ISBN-13: 3540368523

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The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during the last two decades. The behavior of far from equilibrium systems has received more and more attention and has been an extremely active and productive subject of research for physicists, chemists and biologists. Their studies have brought about a more unified vision of the laws which govern self-organization processes of physico-chemical and biological sys tems. A major achievement has been the extension of the notion of phase transi tion to instabilities which occur only in open nonlinear systems. The notion of phase transition has been proven fruitful in apphcation to nonequilibrium ins- bihties known for about eight decades, like certain hydrodynamic instabilities, as well as in the case of the more recently discovered instabilities in quantum optical systems such as the laser, in chemical systems such as the Belousov-Zhabotinskii reaction and in biological systems. Even outside the realm of natural sciences, this notion is now used in economics and sociology. In this monograph we show that the notion of phase transition can be extend ed even further. It apphes also to a new class of transition phenomena which occur only in nonequilibrium systems subjected to a randomly fluctuating en vironment.

Noise in Spatially Extended Systems

Noise in Spatially Extended Systems PDF

Author: Jordi Garcia-Ojalvo

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 314

ISBN-13: 1461215366

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Intended for graduates and researchers in physics, chemistry, biology, and applied mathematics, this book provides an up-to-date introduction to current research in fluctuations in spatially extended systems. It covers the theory of stochastic partial differential equations and gives an overview of the effects of external noise on dynamical systems with spatial degrees of freedom. Starting with a general introduction to noise-induced phenomena in dynamical systems, the text moves on to an extensive discussion of analytical and numerical tools needed to gain information from stochastic partial differential equations. It then turns to particular problems described by stochastic PDEs, covering a wide part of the rich phenomenology of spatially extended systems, such as nonequilibrium phase transitions, domain growth, pattern formation, and front propagation. The only prerequisite is a minimal background knowledge of the Langevin and Fokker-Planck equations.

Nonlinear Dynamics of Structures, Systems and Devices

Nonlinear Dynamics of Structures, Systems and Devices PDF

Author: Walter Lacarbonara

Publisher: Springer Nature

Published: 2020-01-29

Total Pages: 592

ISBN-13: 3030347133

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This first of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics of Structures, Systems and Devices. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume I include multi-scale dynamics: coexistence of multiple time/space scales, large system dynamics; dynamics of structures/industrial machines/equipment/facilities (e.g., cable transportation systems, suspension bridges, cranes, vehicles); nonlinear interactions: parametric vibrations with single/multi-frequency excitations, multiple external and autoparametric resonances in multi-dof systems; nonlinear system identification: parametric/nonparametric identification, data-driven identification; experimental dynamics: benchmark experiments, experimental methods, instrumentation techniques, measurements in harsh environments, experimental validation of nonlinear models; wave propagation, solitons, kinks, breathers; solution methods for pdes: Lie groups, Hirota’s method, perturbation methods, etc; nonlinear waves in media (granular materials, porous materials, materials with memory); composite structures: multi-layer, functionally graded, thermal loading; fluid/structure interaction; nonsmooth and retarded dynamics: systems with impacts, free play, stick-slip, friction hysteresis; nonlinear systems with time and/or space delays; stability of delay differential equations, differential-algebraic equations; space/time reduced-order modeling: enhanced discretization methods, center manifold reduction, nonlinear normal modes, normal forms; fractional-order systems; computational techniques: efficient algorithms, use of symbolic manipulators, integration of symbolic manipulation and numerical methods, use of parallel processors; and multibody dynamics: rigid and flexible multibody system dynamics, impact and contact mechanics, tire modeling, railroad vehicle dynamics, computational multibody dynamics.

Modeling Phase Transitions in the Brain

Modeling Phase Transitions in the Brain PDF

Author: D. Alistair Steyn-Ross

Publisher: Springer Science & Business Media

Published: 2010-03-14

Total Pages: 325

ISBN-13: 1441907963

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Foreword by Walter J. Freeman. The induction of unconsciousness using anesthetic agents demonstrates that the cerebral cortex can operate in two very different behavioral modes: alert and responsive vs. unaware and quiescent. But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts. Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle. The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states. Modeling Phase Transitions in the Brain contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band Hopf oscillations, gap-junction-moderated Turing structures, and Hopf-Turing interactions leading to cortical waves.

Noise-Induced Phenomena in the Environmental Sciences

Noise-Induced Phenomena in the Environmental Sciences PDF

Author: Luca Ridolfi

Publisher: Cambridge University Press

Published: 2011-06-20

Total Pages: 327

ISBN-13: 1139498258

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Randomness is ubiquitous in nature. Random drivers are generally considered a source of disorder in environmental systems. However, the interaction between noise and nonlinear dynamics may lead to the emergence of a number of ordered behaviors (in time and space) that would not exist in the absence of noise. This counterintuitive effect of randomness may play a crucial role in environmental processes. For example, seemingly 'random' background events in the atmosphere can grow into larger instabilities that have great effects on weather patterns. This book presents the basics of the theory of stochastic calculus and its application to the study of noise-induced phenomena in environmental systems. It will be an invaluable reference text for ecologists, geoscientists and environmental engineers interested in the study of stochastic environmental dynamics.

Noise-Induced Phenomena in Slow-Fast Dynamical Systems

Noise-Induced Phenomena in Slow-Fast Dynamical Systems PDF

Author: Nils Berglund

Publisher: Springer Science & Business Media

Published: 2006-02-07

Total Pages: 283

ISBN-13: 1846281865

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Stochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.

Quantitative Physiology

Quantitative Physiology PDF

Author: Shangbin Chen

Publisher: Springer Nature

Published: 2021-02-09

Total Pages: 246

ISBN-13: 9813340339

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Stephen Hawking says that the 21st century will be the century of complexity and indeed now systems biology or medicine means dealing with complexity. Both the genome and physiome have emerged in studying complex physiological systems. Computational and mathematical modeling has been regarded as an efficient tool to boost the understanding about living systems in normal or pathophysiological states. Covering applied methodology, basic case studies and complex applications, this volume provides researchers with an overview of modeling and computational studies of physiology (i.e. quantitative physiology), which is becoming an increasingly important branch of systems biology. This book aims to build multi-scale models to investigate functions in living systems and explain how biomolecules, cells, organs, organ systems and organisms carry out the chemical or physical functions. Some of the models addressed are related to gene expression, calcium signalling, neural activity, blood dynamics and bone mechanics. Combining theory and practice, with extensive use of MATLAB, this book is designed to establish a paradigm for quantitative physiology by integrating biology, mathematics, physics and informatics etc. To benefit from this book, the readers are expected to have a background in general physiology and mathematics

Noise-Induced Phenomena in the Environmental Sciences

Noise-Induced Phenomena in the Environmental Sciences PDF

Author: Luca Ridolfi

Publisher: Cambridge University Press

Published: 2018-03-01

Total Pages: 325

ISBN-13: 9781108446785

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Randomness is ubiquitous in nature. Random drivers are generally considered a source of disorder in environmental systems. However, the interaction between noise and nonlinear dynamics may lead to the emergence of a number of ordered behaviors (in time and space) that would not exist in the absence of noise. This counterintuitive effect of randomness may play a crucial role in environmental processes. For example, seemingly "random" background events in the atmosphere can grow into larger instabilities that have great effects on weather patterns. This book presents the basics of the theory of stochastic calculus and its application to the study of noise-induced phenomena in environmental systems. It will be an invaluable reference text for ecologists, geoscientists, and environmental engineers interested in the study of stochastic environmental dynamics.

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