Continuum Modeling In The Physical Sciences

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Continuum Modeling in the Physical Sciences

Author : E. van Groesen
Publisher : SIAM
ISBN 13 : 9780898718249
Total Pages : 238 pages
Book Rating : 4.7/5 (182 download)

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Book Synopsis Continuum Modeling in the Physical Sciences by : E. van Groesen

Download or read book Continuum Modeling in the Physical Sciences written by E. van Groesen and published by SIAM. This book was released on 2007-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling - the ability to apply mathematical concepts and techniques to real-life systems has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the challenging problems sections found at the ends of several chapters.

Continuum Methods of Physical Modeling

Author : Kolumban Hutter
Publisher : Springer Science & Business Media
ISBN 13 : 3662064022
Total Pages : 645 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Continuum Methods of Physical Modeling by : Kolumban Hutter

Download or read book Continuum Methods of Physical Modeling written by Kolumban Hutter and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.

Mathematical Modeling in Continuum Mechanics

Author : Roger Temam
Publisher : Cambridge University Press
ISBN 13 : 1139443216
Total Pages : 356 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Mathematical Modeling in Continuum Mechanics by : Roger Temam

Download or read book Mathematical Modeling in Continuum Mechanics written by Roger Temam and published by Cambridge University Press. This book was released on 2005-05-19 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Continuum Mechanics

Author : Myron B. Allen, III
Publisher : John Wiley & Sons
ISBN 13 : 1118909348
Total Pages : 291 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Continuum Mechanics by : Myron B. Allen, III

Download or read book Continuum Mechanics written by Myron B. Allen, III and published by John Wiley & Sons. This book was released on 2015-07-13 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continuum Mechanics

Author : Antonio Romano
Publisher : Springer Science & Business Media
ISBN 13 : 0817648704
Total Pages : 353 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Continuum Mechanics by : Antonio Romano

Download or read book Continuum Mechanics written by Antonio Romano and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.

Continuum Mechanics Through the Twentieth Century

Author : Gerard A Maugin
Publisher : Springer Science & Business Media
ISBN 13 : 9400763530
Total Pages : 321 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Continuum Mechanics Through the Twentieth Century by : Gerard A Maugin

Download or read book Continuum Mechanics Through the Twentieth Century written by Gerard A Maugin and published by Springer Science & Business Media. This book was released on 2013-04-08 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.

Continuum Modeling

Author : Adrian Muntean
Publisher : Springer
ISBN 13 : 3319221329
Total Pages : 83 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Continuum Modeling by : Adrian Muntean

Download or read book Continuum Modeling written by Adrian Muntean and published by Springer. This book was released on 2015-08-09 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes. The focus of this presentation lies on many practical examples covering aspects such as coupled flow, diffusion and reaction in porous media or microwave heating of a pizza, as well as traffic issues in bacterial colonies and energy harvesting from geothermal wells. The target audience comprises primarily graduate students in pure and applied mathematics as well as working practitioners in engineering who are faced by nonstandard rheological topics like those typically arising in the food industry.

Continuum Solvation Models in Chemical Physics

Author : Benedetta Mennucci
Publisher : John Wiley & Sons
ISBN 13 : 9780470515228
Total Pages : 636 pages
Book Rating : 4.5/5 (152 download)

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Book Synopsis Continuum Solvation Models in Chemical Physics by : Benedetta Mennucci

Download or read book Continuum Solvation Models in Chemical Physics written by Benedetta Mennucci and published by John Wiley & Sons. This book was released on 2008-02-28 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the theory and applications of continuum solvation models. The main focus is on the quantum-mechanical version of these models, but classical approaches and combined or hybrid techniques are also discussed. Devoted to solvation models in which reviews of the theory, the computational implementation Solvation continuum models are treated using the different points of view from experts belonging to different research fields Can be read at two levels: one, more introductive, and the other, more detailed (and more technical), on specific physical and numerical aspects involved in each issue and/or application Possible limitations or incompleteness of models is pointed out with, if possible, indications of future developments Four-colour representation of the computational modeling throughout.

Mathematical Modelling of Continuum Physics

Author : Angelo Morro
Publisher : Springer Nature
ISBN 13 : 3031208145
Total Pages : 1018 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Mathematical Modelling of Continuum Physics by : Angelo Morro

Download or read book Mathematical Modelling of Continuum Physics written by Angelo Morro and published by Springer Nature. This book was released on 2023-03-19 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive and self-contained treatment of continuum physics, illustrating a systematic approach to the constitutive equations for wide-ranging classes of materials. Derivations of results are detailed through careful proofs, and the contents have been developed to ensure a self-contained and consistent presentation. Part I reviews the kinematics of continuous bodies and illustrates the general setting of balance laws. Essential preliminaries to continuum physics – such as reference and current configurations, transport relations, singular surfaces, objectivity, and objective time derivatives – are covered in detail. A chapter on balance equations then develops the balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the balance laws in electromagnetism. Part II is devoted to the general requirements on constitutive models, emphasizing the application of objectivity and consistency with the second law of thermodynamics. Common models of simple materials are then reviewed, and in this framework, detailed descriptions are given of solids (thermoelastic, elastic, and dissipative) and fluids (elastic, thermoelastic, viscous, and Newtonian). A wide of variety of constitutive models are investigated in Part III, which consists of separate chapters focused on several types of non-simple materials: materials with memory, aging and higher-order grade materials, mixtures, micropolar media, and porous materials. The interaction of the electromagnetic field with deformation is also examined within electroelasticity, magnetoelasticity, and plasma theory. Hysteretic effects and phase transitions are considered in Part IV. A new approach is established by treating entropy production as a constitutive function in itself, as is the case for entropy and entropy flux. This proves to be conceptually and practically advantageous in the modelling of nonlinear phenomena, such as those occurring in hysteretic continua (e.g., plasticity, electromagnetism, and the physics of shape memory alloys). Mathematical Modelling of Continuum Physics will be an important reference for mathematicians, engineers, physicists, and other scientists interested in research or applications of continuum mechanics.

Modeling Materials

Author : Ellad B. Tadmor
Publisher : Cambridge University Press
ISBN 13 : 1139500651
Total Pages : 789 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Modeling Materials by : Ellad B. Tadmor

Download or read book Modeling Materials written by Ellad B. Tadmor and published by Cambridge University Press. This book was released on 2011-11-24 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: Material properties emerge from phenomena on scales ranging from Angstroms to millimeters, and only a multiscale treatment can provide a complete understanding. Materials researchers must therefore understand fundamental concepts and techniques from different fields, and these are presented in a comprehensive and integrated fashion for the first time in this book. Incorporating continuum mechanics, quantum mechanics, statistical mechanics, atomistic simulations and multiscale techniques, the book explains many of the key theoretical ideas behind multiscale modeling. Classical topics are blended with new techniques to demonstrate the connections between different fields and highlight current research trends. Example applications drawn from modern research on the thermo-mechanical properties of crystalline solids are used as a unifying focus throughout the text. Together with its companion book, Continuum Mechanics and Thermodynamics (Cambridge University Press, 2011), this work presents the complete fundamentals of materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.

Physical Foundations of Continuum Mechanics

Author : A. Ian Murdoch
Publisher : Cambridge University Press
ISBN 13 : 1139788787
Total Pages : 439 pages
Book Rating : 4.1/5 (397 download)

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Book Synopsis Physical Foundations of Continuum Mechanics by : A. Ian Murdoch

Download or read book Physical Foundations of Continuum Mechanics written by A. Ian Murdoch and published by Cambridge University Press. This book was released on 2012-10-22 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ian Murdoch's Physical Foundations of Continuum Mechanics will interest engineers, mathematicians, and physicists who study the macroscopic behaviour of solids and fluids or engage in molecular dynamical simulations. In contrast to standard works on the subject, Murdoch's book examines physical assumptions implicit in continuum modelling from a molecular perspective. In so doing, physical interpretations of concepts and fields are clarified by emphasising both their microscopic origin and sensitivity to scales of length and time. Murdoch expertly applies this approach to theories of mixtures, generalised continua, fluid flow through porous media, and systems whose molecular content changes with time. Elements of statistical mechanics are included, for comparison, and two extensive appendices address relevant mathematical concepts and results. This unique and thorough work is an authoritative reference for both students and experts in the field.

Mathematical Modeling in Science and Engineering

Author : Ismael Herrera
Publisher : John Wiley & Sons
ISBN 13 : 1118207203
Total Pages : 259 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Mathematical Modeling in Science and Engineering by : Ismael Herrera

Download or read book Mathematical Modeling in Science and Engineering written by Ismael Herrera and published by John Wiley & Sons. This book was released on 2012-03-19 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: A powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as: Mechanics of classical and non-classical continuous systems Solute transport by a free fluid Flow of a fluid in a porous medium Multiphase systems Enhanced oil recovery Fluid mechanics Throughout the text, diagrams are provided to help readers visualize and better understand complex mathematical concepts. A set of exercises at the end of each chapter enables readers to put their new modeling skills into practice. There is also a bibliography in each chapter to facilitate further investigation of individual topics. Mathematical Modeling in Science and Engineering is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.

Continuum Mechanics Modeling of Material Behavior

Author : Martin H. Sadd
Publisher : Academic Press
ISBN 13 : 0128116498
Total Pages : 432 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Continuum Mechanics Modeling of Material Behavior by : Martin H. Sadd

Download or read book Continuum Mechanics Modeling of Material Behavior written by Martin H. Sadd and published by Academic Press. This book was released on 2018-03-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance. The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Offers a thorough, concise and organized presentation of continuum mechanics formulation Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study Features extensive use of exercises, providing more material for student engagement and instructor presentation

Fields, Flows and Waves

Author : David F. Parker
Publisher : Springer Science & Business Media
ISBN 13 : 1447100190
Total Pages : 276 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Fields, Flows and Waves by : David F. Parker

Download or read book Fields, Flows and Waves written by David F. Parker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to the use of mathematics in describing collective phenomena in physics and biology. Derived from a course of innovative lectures, the book shows students early in their studies how many of the topics they have encountered – partial differential equations, differential equations, Fourier series, and linear algebra – are useful in constructing, analysing and interpreting phenomena present in the real world. Throughout, ideas are developed using worked examples and exercises with solution. The text does not assume a strong background in physics.

Improvements in Continuum Modeling for Biomolecular Systems*Project Supported by the National Natural Science Foundation of China (Grant No. 91230106) and the Chinese Academy of Sciences Program for Cross & Cooperative Team of the Science & Technology Innovation

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Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (15 download)

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Book Synopsis Improvements in Continuum Modeling for Biomolecular Systems*Project Supported by the National Natural Science Foundation of China (Grant No. 91230106) and the Chinese Academy of Sciences Program for Cross & Cooperative Team of the Science & Technology Innovation by :

Download or read book Improvements in Continuum Modeling for Biomolecular Systems*Project Supported by the National Natural Science Foundation of China (Grant No. 91230106) and the Chinese Academy of Sciences Program for Cross & Cooperative Team of the Science & Technology Innovation written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson– Boltzmann (PB)/Poisson–Nernst–Planck (PNP) equations has made great contributions towards simulation of these processes. However, the model has shortcomings in its commonly used form and cannot capture (or cannot accurately capture) some important physical properties of the biological systems. Considerable efforts have been made to improve the continuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecular systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.

Mathematical Methods in Continuum Mechanics of Solids

Author : Martin Kružík
Publisher : Springer
ISBN 13 : 3030020657
Total Pages : 617 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Mathematical Methods in Continuum Mechanics of Solids by : Martin Kružík

Download or read book Mathematical Methods in Continuum Mechanics of Solids written by Martin Kružík and published by Springer. This book was released on 2019-03-02 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.

Fundamentals of Continuum Mechanics

Author : Stephen Bechtel
Publisher : Academic Press
ISBN 13 : 0123948347
Total Pages : 347 pages
Book Rating : 4.1/5 (239 download)

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Book Synopsis Fundamentals of Continuum Mechanics by : Stephen Bechtel

Download or read book Fundamentals of Continuum Mechanics written by Stephen Bechtel and published by Academic Press. This book was released on 2014-12-02 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. - Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics - Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures - Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors' own research