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Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.

7495.27 Р.

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A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.

10268.42 Р.

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This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the Helmholtz-Hodge decomposition plays an important role.

10048.72 Р.

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Mechanics and Physics of Porous Solids addresses the mechanics and physics of deformable porous materials whose porous space is filled by one or several fluid mixtures interacting with the solid matrix. Coussy uses the language of thermodynamics to frame the discussion of this topic and bridge the gap between physicists and engineers, and organises the material in such a way that individual phases are explored, followed by coupled problems of increasing complexity. This structure allows the reader to build a solid understanding of the physical processes occurring in the fluids and then porous solids. Mechanics and Physics of Porous Solids offers a critical reference on the physics of multiphase porous materials – key reading for engineers and researchers in structural and material engineering, concrete, wood and materials science, rock and soil mechanics, mining and oil prospecting, biomechanics.

12057.62 Р.

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Mechanics and Physics of Porous Solids addresses the mechanics and physics of deformable porous materials whose porous space is filled by one or several fluid mixtures interacting with the solid matrix. Coussy uses the language of thermodynamics to frame the discussion of this topic and bridge the gap between physicists and engineers, and organises the material in such a way that individual phases are explored, followed by coupled problems of increasing complexity. This structure allows the reader to build a solid understanding of the physical processes occurring in the fluids and then porous solids. Mechanics and Physics of Porous Solids offers a critical reference on the physics of multiphase porous materials – key reading for engineers and researchers in structural and material engineering, concrete, wood and materials science, rock and soil mechanics, mining and oil prospecting, biomechanics.

11623.19 Р.

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Research in nano and cell mechanics has received much attention from the scientific community as a result of society needs and government initiatives to accelerate developments in materials, manufacturing, electronics, medicine and healthcare, energy, and the environment. Engineers and scientists are currently engaging in increasingly complex scientific problems that require interdisciplinary approaches. In this regard, studies in this field draw from fundamentals in atomistic scale phenomena, biology, statistical and continuum mechanics, and multiscale modeling and experimentation. As a result, contributions in these areas are spread over a large number of specialized journals, which prompted the Editors to assemble this book. Nano and Cell Mechanics: Fundamentals and Frontiers brings together many of the new developments in the field for the first time, and covers fundamentals and frontiers in mechanics to accelerate developments in nano- and bio-technologies. Key features: • Provides an overview of recent advances in nano and cell mechanics. • Covers experimental, analytical, and computational tools used to investigate biological and nanoscale phenomena. • Covers fundamentals and frontiers in mechanics to accelerate developments in nano- and bio-technologies. • Presents multiscale-multiphysics modeling and experimentation techniques. • Examines applications in materials, manufacturing, electronics, medicine and healthcare. Nano and Cell Mechanics: Fundamentals and Frontiers is written by internationally recognized experts in theoretical and applied mechanics, applied physics, chemistry, and biology. It is an invaluable reference for graduate students of nano- and bio-technologies, researchers in academia and industry who are working in nano and cell mechanics, and practitioners who are interested in learning about the latest analysis tools. The book can also serve as a text for graduate courses in theoretical and applied mechanics, mechanical engineering, materials science, and applied physics.

12373.78 Р.

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A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.

9373.54 Р.

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This book deals with the mechanics and physics of fractures at various scales. Based on advanced continuum mechanics of heterogeneous media, it develops a rigorous mathematical framework for single macrocrack problems as well as for the effective properties of microcracked materials. In both cases, two geometrical models of cracks are examined and discussed: the idealized representation of the crack as two parallel faces (the Griffith crack model), and the representation of a crack as a flat elliptic or ellipsoidal cavity (the Eshelby inhomogeneity problem). The book is composed of two parts: – The first part deals with solutions to 2D and 3D problems involving a single crack in linear elasticity. Elementary solutions of cracks problems in the different modes are fully worked. Various mathematical techniques are presented, including Neuber-Papkovitch displacement potentials, complex analysis with conformal mapping and Eshelby-based solutions. – The second part is devoted to continuum micromechanics approaches of microcracked materials in relation to methods and results presented in the first part. Various estimates and bounds of the effective elastic properties are presented. They are considered for the formulation and application of continuum micromechanics-based damage models.

10873.3 Р.

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This book is intended to help the reader understand impact phenomena as a focused application of diverse topics such as rigid body dynamics, structural dynamics, contact and continuum mechanics, shock and vibration, wave propagation and material modelling. It emphasizes the need for a proper assessment of sophisticated experimental/computational tools promoted widely in contemporary design. A unique feature of the book is its presentation of several examples and exercises to aid further understanding of the physics and mathematics of impact process from first principles, in a way that is simple to follow.

8998.6 Р.

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A concise introductory course text on continuum mechanics Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally. This book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics. A concise introductory course text on continuum mechanics Covers the fundamentals of continuum mechanics Uses modern tensor notation Contains problems and accompanied by a companion website hosting solutions Suitable as a textbook for introductory graduate courses for students in mechanical and civil engineering

6970.21 Р.

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An appealing and engaging introduction to Continuum Mechanics in Biosciences This book presents the elements of Continuum Mechanics to people interested in applications to biological systems. It is divided into two parts, the first of which introduces the basic concepts within a strictly one-dimensional spatial context. This policy has been adopted so as to allow the newcomer to Continuum Mechanics to appreciate how the theory can be applied to important issues in Biomechanics from the very beginning. These include mechanical and thermodynamical balance, materials with fading memory and chemically reacting mixtures. In the second part of the book, the fully fledged three-dimensional theory is presented and applied to hyperelasticity of soft tissue, and to theories of remodeling, aging and growth. The book closes with a chapter devoted to Finite Element analysis. These and other topics are illustrated with case studies motivated by biomedical applications, such as vibration of air in the air canal, hyperthermia treatment of tumours, striated muscle memory, biphasic model of cartilage and adaptive elasticity of bone. The book offers a challenging and appealing introduction to Continuum Mechanics for students and researchers of biomechanics, and other engineering and scientific disciplines. Key features: Explains continuum mechanics using examples from biomechanics for a uniquely accessible introduction to the topic Moves from foundation topics, such as kinematics and balance laws, to more advanced areas such as theories of growth and the finite element method.. Transition from a one-dimensional approach to the general theory gives the book broad coverage, providing a clear introduction for beginners new to the topic, as well as an excellent foundation for those considering moving to more advanced application

10346.21 Р.

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A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.

9973.3 Р.

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Computational methods for the modeling and simulation of the dynamic response and behavior of particles, materials and structural systems have had a profound influence on science, engineering and technology. Complex science and engineering applications dealing with complicated structural geometries and materials that would be very difficult to treat using analytical methods have been successfully simulated using computational tools. With the incorporation of quantum, molecular and biological mechanics into new models, these methods are poised to play an even bigger role in the future. Advances in Computational Dynamics of Particles, Materials and Structures not only presents emerging trends and cutting edge state-of-the-art tools in a contemporary setting, but also provides a unique blend of classical and new and innovative theoretical and computational aspects covering both particle dynamics, and flexible continuum structural dynamics applications. It provides a unified viewpoint and encompasses the classical Newtonian, Lagrangian, and Hamiltonian mechanics frameworks as well as new and alternative contemporary approaches and their equivalences in [start italics]vector and scalar formalisms[end italics] to address the various problems in engineering sciences and physics. Highlights and key features Provides practical applications, from a unified perspective, to both particle and continuum mechanics of flexible structures and materials Presents new and traditional developments, as well as alternate perspectives, for space and time discretization Describes a unified viewpoint under the umbrella of Algorithms by Design for the class of linear multi-step methods Includes fundamentals underlying the theoretical aspects and numerical developments, illustrative applications and practice exercises The completeness and breadth and depth of coverage makes Advances in Computational Dynamics of Particles, Materials and Structures a valuable textbook and reference for graduate students, researchers and engineers/scientists working in the field of computational mechanics; and in the general areas of computational sciences and engineering.

15324.84 Р.

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Alongside a thorough definition of basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of quantum mechanics and information theory combined in one text. It deals with important topics hardly found in regular textbooks, including the Robertson-Schrodinger relation, incompatibility between angle and angular momentum, «dispersed indeterminacy», interaction-free measurements, «submissive quantum mechanics», and many others. With its in-depth discussion of key concepts complete with problems and exercises, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and an essential reference for physics students and physics professionals.

8319.76 Р.

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Build an intuitive understanding of the principles behind quantum mechanics through practical construction and replication of original experiments With easy-to-acquire, low-cost materials and basic knowledge of algebra and trigonometry, Exploring Quantum Physics through Hands-on Projects takes readers step by step through the process of re-creating scientific experiments that played an essential role in the creation and development of quantum mechanics. Presented in near chronological order—from discoveries of the early twentieth century to new material on entanglement—this book includes question- and experiment-filled chapters on: Light as a Wave Light as Particles Atoms and Radioactivity The Principle of Quantum Physics Wave/Particle Duality The Uncertainty Principle Schrödinger (and his Zombie Cat) Entanglement From simple measurements of Planck's constant to testing violations of Bell's inequalities using entangled photons, Exploring Quantum Physics through Hands-on Projects not only immerses readers in the process of quantum mechanics, it provides insight into the history of the field—how the theories and discoveries apply to our world not only today, but also tomorrow. By immersing readers in groundbreaking experiments that can be performed at home, school, or in the lab, this first-ever, hands-on book successfully demystifies the world of quantum physics for all who seek to explore it—from science enthusiasts and undergrad physics students to practicing physicists and engineers.

6141.61 Р.

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Quantum Physics for Scientists and Technologists is a self-contained, comprehensive review of this complex branch of science. The book demystifies difficult concepts and views the subject through non-physics fields such as computer science, biology, chemistry, and nanotechnology. It explains key concepts and phenomena in the language of non-physics majors and with simple math, assuming no prior knowledge of the topic. This cohesive book begins with the wavefunction to develop the basic principles of quantum mechanics such as the uncertainty principle and wave-particle duality. Comprehensive coverage of quantum theory is presented, supported by experimental results and explained through applications and examples without the use of abstract and complex mathematical tools or formalisms. From there, the book: Takes the mystery out of the Schrodinger equation, the fundamental equation of quantum physics, by applying it to atoms Shows how quantum mechanics explains the periodic table of elements Introduces the quantum mechanical concept of spin and spin quantum number, along with Pauli's Exclusion Principle regarding the occupation of quantum states Addresses quantum states of molecules in terms of rotation and vibration of diatomic molecules Explores the interface between classical statistical mechanics and quantum statistical mechanics Discusses quantum mechanics as a common thread through different fields of nanoscience and nanotechnology Each chapter features real-world applications of one or more quantum mechanics principles. «Study Checkpoints» and problems with solutions are presented throughout to make difficult concepts easy to understand. In addition, pictures, tables, and diagrams with full explanations are used to present data and further explain difficult concepts. This book is designed as a complete course in quantum mechanics for senior undergraduates and first-year graduate students in non-physics majors. It also applies to courses such as modern physics, physical chemistry and nanotechnology. The material is also accessible to scientists, engineers, and technologists working in the fields of computer science, biology, chemistry, engineering, and nanotechnology.

10812.96 Р.

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