The General Theory of Particle Mechanics
A Special Course
This book provides insights into the tight connection between fundamental math and mechanics, the basic grounding of physics. It demonstrates that quantum, classical, and relativistic mechanics, historically (and separately) formulated upon an experimental basis, can be regarded as links of a single theoretical chain readily extracted from a simple mathematical medium. It uses mathematical tools to endow formerly abstract entities, such as quantum wave-function and classical action function, with original and clear geometric images, strongly simplifying them. The book comprises the author’s lectures, manual texts, typical problems and tests, and…
Yefremov provides insights into the tight connection between fundamental math and mechanics, demonstrating that quantum, classical, and relativistic mechanics can be regarded as links of a single theoretical chain readily extracted from a simple mathematical medium.
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This book explores how we may overcome categorizations and opposites in how we explain all existence. It places such ideas into the context of existing complexity paradigms. Research into complex systems has revolutionized virtually all areas of inquiry over the past half century. The algorithms of non-linear systems research have enabled us to unify descriptions of the world that were distinct under traditional, reductionist explorations. It is the beauty of complexity that it brings together various scientific fields that, in the past, were treated as separate entities under specialized study.…
This book uses complexity research to overcome the categorizations and opposites that limit our descriptions of existence. It offers innovative philosophical insights to arrive at a unified vision of nature and society, governed by the same laws of non-linearity.
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This book explores statistical physics, with an emphasis on the distinct character of the statistical motion and difficult subjects, related, mainly, to condensed matter. It discusses the interaction problem in real gases, as well as dimensionality effects and melting. The book shows how to estimate easily the critical temperature of the Ising ferromagnets, the origin of the drag force, how to get an inverse-wind vortex in turbulence, the entropy of the earthquakes, and how the gas-liquid transition occurs. It also describes the hadronization of the quark-gluon plasma, the phase diagram…
This book explores statistical physics, focusing on subjects from condensed matter to black holes. It discusses gas-liquid transitions, the entropy of earthquakes, the hadronization of the quark-gluon plasma, and the phase diagram of quantum chromodynamics.
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This book presents the subject of physical kinetics from an original and unique angle, by deriving the Boltzmann equation from atomic motion, making extensive use of Landau’s concept of elementary excitations. It includes external forces, besides statistical motion, in its treatment of the subject wherever relevant. It also details the kinetic theory of classical gas and its transport, devoting special attention to the classical plasma. In addition, the book emphasises the role played by the anharmonic interactions in the lifetime of phonons, and presents the basic features of superconductivity and…
This book presents physical kinetics from a unique angle, deriving the Boltzmann equation from atomic motion using Landau’s elementary excitations. It details the kinetic theory of classical gas and plasma, the lifetime of phonons, and the features of superconductivity.
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This volume celebrates the over fifty-year career in non-equilibrium statistical physics of Professor Paolo Grigolini of the Center for Nonlinear Science at the University of North Texas. It begins by positioning Grigolini in a five-dimensional science-personality space with the following axes: Sleeper, Keeper, Leaper, Creeper and Reaper. This introduction to the person is followed by a sequence of papers in the various areas of science where his work has had impact, including subtle questions concerned with the connection between classical and quantum systems; a two-level atom coupled to a radiation…
Celebrating Paolo Grigolini’s 50-year legacy in non-equilibrium statistical physics. This collection explores his pioneering work on the quantum-classical connection, anomalous diffusion, and new methods for detecting scaling in time series.
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This book develops a theory of the nonlinear response of densely charged and neutral media to electric and electromagnetic fields and gradients of hydrodynamic variables. It considers phenomena related to the nonlinear response of the media to plasma echo, transformation of waves, and parametric and second harmonic generation of radiation, and determines exact expressions and calculation methods for Burnett transport coefficients describing heat, mass, momentum and charge flows. It also discusses the use of transport coefficients in hydrodynamic tasks outside the framework of Euler’s theorem on homogeneous functions. It analyses…
This book presents a theory of nonlinear response in charged media, yielding Burnett transport coefficients to model heat and mass flows. It applies these methods to extreme scenarios, from gas-phase nuclear reactors to a spacecraft landing on Mars. For specialists.
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Fractal Fluctuations and Climate Cycles in Atmospheric Flows
Order in Chaos
Within this book, the author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following: (i) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations; (ii) the probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean; (iii) fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies…
This book unveils a systems theory where fractal fluctuations are signatures of quantum-like chaos. Based on statistical physics, the model predicts a distribution that is near-normal for moderate events but exhibits a fat long tail associated with hazardous extreme events.
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