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Galilean Mechanics and Thermodynamics of Continua

Author: Géry de Saxcé

Publisher: John Wiley & Sons

Published: 2016-01-07

Total Pages: 446

ISBN-13: 1119058031

This title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity. Based on the notion of affine tensors, a simple generalization of the classical tensors, this approach allows gathering the usual mechanical entities — mass, energy, force, moment, stresses, linear and angular momentum — in a single tensor. Starting with the basic subjects, and continuing through to the most advanced topics, the authors' presentation is progressive, inductive and bottom-up. They begin with the concept of an affine tensor, a natural extension of the classical tensors. The simplest types of affine tensors are the points of an affine space and the affine functions on this space, but there are more complex ones which are relevant for mechanics − torsors and momenta. The essential point is to derive the balance equations of a continuum from a unique principle which claims that these tensors are affine-divergence free.

Galilean Mechanics and Thermodynamics of Continua

Author: Géry de Saxcé

Publisher: John Wiley & Sons

Published: 2016-02-08

Total Pages: 446

ISBN-13: 1848216424

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Thermomechanics of Continua

Author: Krzysztof Wilmanski

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 284

ISBN-13: 3642589340

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The notion of continuum thermodynamics, adopted in this book, is primarily understood as a strategy for development of continuous models of various physical systems. The examples of such a strategy presented in the book have both the classical character (e. g. thermoelastic materials, viscous fluids, mixtures) and the extended one (ideal gases, Maxwellian fluids, thermoviscoelastic solids etc. ). The latter has been limited intentionally to non-relativistic models; many important relativistic applications of the true extended thermodynamics will not be considered but can be found in the other sources. The notion of extended thermodynamics is also adopted in a less strict sense than suggested by the founders. For instance, in some cases we allow the constitutive dependence not only on the fields themselves but also on some derivatives. In this way, the new thermodynamical models may have some features of the usual nonequilibrium models and some of those of the extended models. This deviation from the strategy of extended thermodynamics is motivated by practical aspects; frequently the technical considerations of extended thermodynamics are so involved that one can no longer see important physical properties of the systems. This book has a different form from that usually found in books on continuum mechanics and continuum thermodynamics. The presentation of the formal structure of continuum thermodynamics is not always as rigorous as a mathematician might anticipate and the choice of physical subjects is too disperse to make a physicist happy.

The Mechanics and Thermodynamics of Continua

Author: Morton E. Gurtin

Publisher: Cambridge University Press

Published: 2010-04-19

Total Pages: 721

ISBN-13: 1139482157

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The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Introduction to Relativistic Continuum Mechanics

Author: Giorgio Ferrarese

Publisher: Springer

Published: 2007-09-30

Total Pages: 340

ISBN-13: 3540731687

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This mathematically-oriented introduction takes the point of view that students should become familiar, at an early stage, with the physics of relativistic continua and thermodynamics within the framework of special relativity. Therefore, in addition to standard textbook topics such as relativistic kinematics and vacuum electrodynamics, the reader will be thoroughly introduced to relativistic continuum and fluid mechanics. There is emphasis on the 3+1 splitting technique.

Differential Geometrical Theory of Statistics

Author: Frédéric Barbaresco

Publisher: MDPI

Published: 2018-04-06

Total Pages: 473

ISBN-13: 3038424242

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This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy

Geometric Structures of Statistical Physics, Information Geometry, and Learning

Author: Frédéric Barbaresco

Publisher: Springer Nature

Published: 2021-06-27

Total Pages: 466

ISBN-13: 3030779572

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Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.

Frontiers In Entropy Across The Disciplines - Panorama Of Entropy: Theory, Computation, And Applications

Author: M Zuhair Nashed

Publisher: World Scientific

Published: 2022-08-30

Total Pages: 757

ISBN-13: 9811259410

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Frontiers in Entropy Across the Disciplines presents a panorama of entropy emphasizing mathematical theory, physical and scientific significance, computational methods, and applications in mathematics, physics, statistics, engineering, biomedical signals, and signal processing.In the last century classical concepts of entropy were introduced in the areas of thermodynamics, information theory, probability theory, statistics, dynamical systems, and ergodic theory. During the past 50 years, dozens of new concepts of entropy have been introduced and studied in many disciplines. This volume captures significant developments in this arena. It features expository, review, and research papers by distinguished mathematicians and scientists from many disciplines. The level of mathematics ranges from intermediate level to research level. Each chapter contains a comprehensive list of references. Topics include entropy and society, entropy and time, Souriau entropy on symplectic model of statistical physics, new definitions of entropy, geometric theory of heat and information, maximum entropy in Bayesian networks, maximum entropy methods, entropy analysis of biomedical signals (review and comparison of methods), spectral entropy and its application to video coding and speech coding, a comprehensive review of 50 years of entropy in dynamics, a comprehensive review on entropy, entropy-like quantities and applications, topological entropy of multimodal maps, entropy production in complex systems, entropy production and convergence to equilibrium, reversibility and irreversibility in entropy, nonequilibrium entropy, index of various entropy, entropy and the greatest blunder ever.

Rheology, Physical and Mechanical Behavior of Materials 1

Author: Maurice Leroy

Publisher: John Wiley & Sons

Published: 2023-11-28

Total Pages: 356

ISBN-13: 1394255616

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This book studies the flow of materials and the influence of strain rates on the relationship between imposed stresses and the dynamic deformations obtained. It provides applications for shaping, molecular molding, shrink-fit assembly and welding, including details of the various specific processes for implementation at high strain rates, illustrated by numerous industrial examples. Rheology, Physical and Mechanical Behavior of Materials 1 presents analyses of plasticity mechanisms at microscopic and macroscopic scales, and of the various forms of stressstrain behavior laws according to working speeds, mechanisms, athermics, viscoplasticity and formability limits at types and speeds of change. It is aimed at researchers involved in the mechanics of deformable media, as well as industrial design and manufacturing departments

Models, Simulation, and Experimental Issues in Structural Mechanics

Author: Michel Frémond

Publisher: Springer

Published: 2017-01-21

Total Pages: 267

ISBN-13: 3319488848

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This book offers valuable insights and provides effective tools useful for imagining, creating, and promoting novel and challenging developments in structural mechanics. It addresses a wide range of topics, such as mechanics and geotechnics, vibration and damping, damage and friction, experimental methods, and advanced structural materials. It also discusses analytical, experimental and numerical findings, focusing on theoretical and practical issues and innovations in the field. Collecting some of the latest results from the Lagrange Laboratory, a European scientific research group, mainly consisting of Italian and French engineers, mechanicians and mathematicians, the book presents the most recent example of the long-term scientific cooperation between well-established French and Italian Mechanics, Mathematics and Engineering Schools. It is a valuable resource for postgraduate students, researchers and practitioners dealing with theoretical and practical issues in structural engineering.