This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz–Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.

A comprehensive and unified introduction to describing and understanding complex interacting systems.

This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.

This book presents studies of complexity in the context of nonequilibrium phenomena using theory, modeling, simulations, and experiments, both in the laboratory and in nature.

This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

REVIEWS IN COMPUTATIONAL CHEMISTRY THE LATEST VOLUME IN THE REVIEWS IN COMPUTATIONAL CHEMISTRY SERIES, THE INVALUABLE REFERENCE TO METHODS AND TECHNIQUES IN COMPUTATIONAL CHEMISTRY Reviews in Computational Chemistry reference texts assist researchers in selecting and applying new computational chemistry methods to their own research. Bringing together writings from leading experts in various fields of computational chemistry, Volume 32 covers topics including global structure optimization, time-dependent density functional tight binding calculations, non-equilibrium self-assembly, cluster prediction, and molecular simulations of microphase formers and deep eutectic solvents. In keeping with previous books in the series, Volume 32 uses a non-mathematical style and tutorial-based approach that provides students and researchers with easy access to computational methods outside their area of expertise. The chapters comprising Volume 32 are connected by two themes: methods that can be broadly applied to a variety of systems, and special considerations required when modeling specific system types. Each in-depth chapter contains background and theory, strategies for using the methods correctly, mini-tutorials and best practices, and critical literature reviews highlighting advanced applications. Essential reading for both newcomers and experts in the area of molecular modeling, this state-of-the-art resource: Covers topics such as non-deterministic global optimization (NDGO) approaches and excited-state dynamics calculations Contains a detailed overview of deep eutectic solvents (DESs) and simulation methods Presents methodologies for investigating chemical systems that form microphases with periodic morphologies such as lamellae and cylinders Features step-by-step tutorials on applying techniques to probe and understand the chemical dynamics exhibited in a system Includes detailed subject indices on each volume in the series and up-to-date compendiums of molecular modeling software, services, programs, suppliers, and other useful information Reviews in Computational Chemistry, Volume 32 is a must-have guide for computational chemists, theoretical chemists, pharmaceutical chemists, biological chemists, chemical engineers, researchers in academia and industry, and graduate students involved in molecular modeling.