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An introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field.

Phase transformations (Statistical physics) --- Critical phenomena (Physics) --- Physics --- Physical Sciences & Mathematics --- Atomic Physics

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Interest in structures with nanometer-length features has significantly increased as experimental techniques for their fabrication have become possible. The study of phenomena in this area is termed nanoscience, and is a research focus of chemists, pure and applied physics, electrical engineers, and others. The reason for such a focus is the wide range of novel effects that exist at this scale, both of fundamental and practical interest, which often arise from the interaction between metallic nanostructures and light, and range from large electromagnetic field enhancements to extraordinary optical transmission of light through arrays of subwavelength holes. This dissertation is aimed at addressing some of the most fundamental and outstanding questions in nanoscience from a theoretical and computational perspective, specifically: · At the single nanoparticle level, how well do experimental and classical electrodynamics agree? · What is the detailed relationship between optical response and nanoparticle morphology, composition, and environment? · Does an optimal nanostructure exist for generating large electromagnetic field enhancements, and is there a fundamental limit to this? · Can nanostructures be used to control light, such as confining it, or causing fundamentally different scattering phenomena to interact, such as electromagnetic surface modes and diffraction effects? · Is it possible to calculate quantum effects using classical electrodynamics, and if so, how do they affect optical properties?

Critical phenomena (Physics). --- Nanoscience. --- Pattern formation (Physical sciences). --- Solid state physics. --- Nanoscience --- Chemistry --- Engineering & Applied Sciences --- Physics --- Physical Sciences & Mathematics --- Physical & Theoretical Chemistry --- Technology - General --- Atomic Physics --- Nano science --- Nanoscale science --- Nanosciences --- Chemistry. --- Chemistry, Physical and theoretical. --- Physics. --- Theoretical and Computational Chemistry. --- Theoretical, Mathematical and Computational Physics. --- Science --- Physical sciences --- Mathematical physics. --- Physical mathematics --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Mathematics

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The concept of ‘self-organized criticality’ (SOC) has been applied to a variety of problems, ranging from population growth and traffic jams to earthquakes, landslides and forest fires. The technique is now being applied to a wide range of phenomena in astrophysics, such as planetary magnetospheres, solar flares, cataclysmic variable stars, accretion disks, black holes and gamma-ray bursts, and also to phenomena in galactic physics and cosmology. Self-organized Criticality in Astrophysics introduces the concept of SOC and shows that, due to its universality and ubiquity, it is a law of nature. The theoretical framework and specific physical models are described, together with a range of applications in various aspects of astrophyics. The mathematical techniques, including the statistics of random processes, time series analysis, time scale and waiting time distributions, are presented and the results are applied to specific observations of astrophysical phenomena.

Astrophysics --- Nonlinear theories. --- Mathematics. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Critical phenomena (Physics) --- Self-organizing systems. --- Nonlinear systems. --- Systems, Nonlinear --- System theory --- Learning systems (Automatic control) --- Self-optimizing systems --- Cybernetics --- Intellect --- Learning ability --- Synergetics --- Phenomena, Critical (Physics) --- Astronomy. --- Physical geography. --- Astrophysics. --- Statistics. --- Statistical physics. --- Astronomy, Astrophysics and Cosmology. --- Complex Systems. --- Geophysics/Geodesy. --- Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Statistical Physics and Dynamical Systems. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Mathematical statistics --- Geography --- Dynamical systems. --- Geophysics. --- Space sciences. --- Statistics . --- Science and space --- Space research --- Cosmology --- Science --- Geological physics --- Terrestrial physics --- Earth sciences --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Self-organizing systems --- Nonlinear systems --- Nonlinear theories