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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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Operational research. Game theory --- Engineering mathematics. --- Mathematical analysis. --- Scaling laws (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) --- Statistical physics --- Advanced calculus --- Analysis (Mathematics) --- Algebra --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- 517.1 Mathematical analysis --- Scaling laws (Statistical physics). --- Engineering mathematics --- 517.1. --- 517.1

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Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modelling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modelling and understanding the atmosphere. This synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also valuable for graduate students in atmospheric dynamics and physics, meteorology, oceanography and climatology.

Meteorology --- Atmospheric physics --- Fractals --- Scaling laws (Statistical physics) --- Meteorology. --- Atmospheric physics. --- Fractals. --- 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 --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Aerophysics --- Meteorology, Physical --- Physical meteorology --- Atmospheric science --- Aerology

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Scaling laws (Statistical physics) --- Soil physics --- 551.3 --- 551.3 External geodynamics (exogenous processes) --- External geodynamics (exogenous processes) --- Agricultural physics --- Soil mechanics --- 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

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Computational chemistry methods have become increasingly important in recent years, as manifested by their rapidly extending applications in a large number of diverse fields. The ever-increasing size of the systems one wants to study leads to the development and application of methods, which provide satisfactory answers at a manageable computational cost. An important variety of computational techniques for large systems are represented by the linear-scaling techniques, that is, by methods where the computational cost scales linearly with the size of the system. This monograph is a collection of chapters, which report the state-of-the-art developments and applications of many important classes of linear-scaling methods. Linear-Scaling Techniques in Computational Chemistry and Physics: Methods and Applications serves as a handbook for theoreticians who are involved in the development of new and efficient computational methods as well as for scientists who use the tools of computational chemistry and physics in their research.

Chemistry -- Data processing. --- Chemistry -- Mathematics. --- Mathematical physics. --- Physics -- Data processing. --- Chemistry --- Physical Sciences & Mathematics --- Chemistry - General --- Physical & Theoretical Chemistry --- Scaling laws (Statistical physics) --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Chemistry. --- Chemistry, Physical and theoretical. --- Physics. --- Theoretical and Computational Chemistry. --- Theoretical, Mathematical and Computational Physics. --- Physical laws --- Ranking and selection (Statistics) --- Statistical physics --- Physical sciences --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Physical mathematics --- Physics --- Mathematics