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Giving a detailed overview of the subject, this book takes in the results and methods that have arisen since the term 'self-organised criticality' was coined twenty years ago. Providing an overview of numerical and analytical methods, from their theoretical foundation to the actual application and implementation, the book is an easy access point to important results and sophisticated methods. Starting with the famous Bak-Tang-Wiesenfeld sandpile, ten key models are carefully defined, together with their results and applications. Comprehensive tables of numerical results are collected in one volume for the first time, making the information readily accessible to readers. Written for graduate students and practising researchers in a range of disciplines, from physics and mathematics to biology, sociology, finance, medicine and engineering, the book gives a practical, hands-on approach throughout. Methods and results are applied in ways that will relate to the reader's own research.

Scaling laws (Statistical physics) --- System Analysis --- Computer simulation --- System analysis. --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Physical laws --- Ranking and selection (Statistics) --- Statistical physics --- Computer simulation. --- Scaling laws (Statistical physics) - Computer simulation

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Investigation of the fractal and scaling properties of disordered systems has recently become a focus of great interest in research. Disordered or amorphous materials, like glasses, polymers, gels, colloids, ceramic superconductors and random alloys or magnets, do not have a homogeneous microscopic structure. The microscopic environment varies randomly from site to site in the system and this randomness adds to the complexity and the richness of the properties of these materials. A particularly challenging aspect of random systems is their dynamical behavior. Relaxation in disordered systems

Order-disorder models --- Scaling laws (Statistical physics) --- Statistical physics --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Physical laws --- Ranking and selection (Statistics) --- Coniglio, Antonio, --- Coniglio, A.

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This book is concerned with a leading-edge topic of great interest and importance, exemplifying the relationship between experimental research, material modeling, structural analysis and design. It focuses on the effect of structure size on structural strength and failure behaviour. Bazant's theory has found wide application to all quasibrittle materials, including rocks, ice, modern fiber composites and tough ceramics. The topic of energetic scaling, considered controversial until recently, is finally getting the attention it deserves, mainly as a result of Bazant's pioneering work. I

Engineering. --- Scaling laws (Statistical physics). --- Strength of materials. --- Structural analysis (Engineering). --- Civil Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Structural analysis (Engineering) --- Scaling laws (Statistical physics) --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Architectural engineering --- Engineering, Architectural --- Materials, Strength of --- Resistance of materials --- Structural mechanics --- Structures, Theory of --- Physical laws --- Ranking and selection (Statistics) --- Statistical physics --- Building materials --- Flexure --- Mechanics --- Testing --- Elasticity --- Graphic statics --- Strains and stresses --- Structural engineering

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The lace expansion is a powerful and flexible method for understanding the critical scaling of several models of interest in probability, statistical mechanics, and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models. Results include proofs of existence of critical exponents and construction of scaling limits. Often, the scaling limit is described in terms of super-Brownian motion.

Percolation (Statistical physics) --- Scaling laws (Statistical physics) --- Mathematical statistics. --- Probabilities. --- Percolation (Physique statistique) --- Lois d'échelle (Physique statistique) --- Statistique mathématique --- Probabilités --- Electronic books. -- local. --- Percolation (Statistical physics). --- Scaling laws (Statistical physics). --- Mathematical statistics --- Probabilities --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematical Statistics --- Atomic Physics --- Probability --- Statistical inference --- Statistics, Mathematical --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Statistical methods --- Mathematics. --- Combinatorics. --- Physics. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Combinations --- Chance --- Least squares --- Risk --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Combinatorics --- Algebra --- Mathematical analysis --- Math --- Science --- Physical laws --- Ranking and selection (Statistics) --- Statistical physics --- Statistics --- Sampling (Statistics) --- Lattice theory --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Mathematical physics. --- Physical mathematics

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Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.

Continuum mechanics. --- Scaling laws (Statistical physics). --- Calculus --- Atomic Physics --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Scaling laws (Statistical physics) --- Statistical mechanics. --- Micromechanics. --- Mechanics of continua --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Mathematics. --- Dynamics. --- Ergodic theory. --- Physics. --- Dynamical Systems and Ergodic Theory. --- Mathematical Methods in Physics. --- Composite materials --- Solid state physics --- Microstructure --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Mechanics --- Quantum statistics --- Statistical physics --- Thermodynamics --- Physical laws --- Ranking and selection (Statistics) --- Differentiable dynamical systems. --- Mathematical physics. --- Physical mathematics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Force and energy --- Statics