Continuum Mechanics Applied Mathematics And Scientific Computing Godunov S Legacy
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Continuum Mechanics Applied Mathematics And Scientific Computing Godunov S Legacy
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Author : Gennadii V. Demidenko
language : en
Publisher: Springer Nature
Release Date : 2020-04-03
Continuum Mechanics Applied Mathematics And Scientific Computing Godunov S Legacy written by Gennadii V. Demidenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Science categories.
This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday. The contributions address those fields that Professor Godunov is most famous for: differential and difference equations, partial differential equations, equations of mathematical physics, mathematical modeling, difference schemes, advanced computational methods for hyperbolic equations, computational methods for linear algebra, and mathematical problems in continuum mechanics.
Modeling Biomaterials
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Author : Josef Málek
language : en
Publisher: Springer Nature
Release Date : 2022-01-21
Modeling Biomaterials written by Josef Málek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-21 with Mathematics categories.
The investigation of the role of mechanical and mechano-chemical interactions in cellular processes and tissue development is a rapidly growing research field in the life sciences and in biomedical engineering. Quantitative understanding of this important area in the study of biological systems requires the development of adequate mathematical models for the simulation of the evolution of these systems in space and time. Since expertise in various fields is necessary, this calls for a multidisciplinary approach. This edited volume connects basic physical, biological, and physiological concepts to methods for the mathematical modeling of various materials by pursuing a multiscale approach, from subcellular to organ and system level. Written by active researchers, each chapter provides a detailed introduction to a given field, illustrates various approaches to creating models, and explores recent advances and future research perspectives. Topics covered include molecular dynamics simulations of lipid membranes, phenomenological continuum mechanics of tissue growth, and translational cardiovascular modeling. Modeling Biomaterials will be a valuable resource for both non-specialists and experienced researchers from various domains of science, such as applied mathematics, biophysics, computational physiology, and medicine.
Advances In Numerical Methods For Hyperbolic Balance Laws And Related Problems
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Author : Giacomo Albi
language : en
Publisher: Springer Nature
Release Date : 2023-06-02
Advances In Numerical Methods For Hyperbolic Balance Laws And Related Problems written by Giacomo Albi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-02 with Mathematics categories.
A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers’ Conference “Numerical Aspects of Hyperbolic Balance Laws and Related Problems”, hosted at the University of Verona, Italy, in December 2021.
Classical And Relativistic Rational Extended Thermodynamics Of Gases
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Author : Tommaso Ruggeri
language : en
Publisher: Springer Nature
Release Date : 2021-04-22
Classical And Relativistic Rational Extended Thermodynamics Of Gases written by Tommaso Ruggeri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-22 with Mathematics categories.
Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book "Rational Extended Thermodynamics beyond the Monatomic Gas" by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. The book represents a valuable resource for applied mathematicians, physicists, and engineers, offering powerful models for many potential applications such as reentering satellites into the atmosphere, semiconductors, and nanoscale phenomena.
Property Preserving Numerical Schemes For Conservation Laws
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Author : Dmitri Kuzmin
language : en
Publisher: World Scientific
Release Date : 2023-08-28
Property Preserving Numerical Schemes For Conservation Laws written by Dmitri Kuzmin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
High-order numerical methods for hyperbolic conservation laws do not guarantee the validity of constraints that physically meaningful approximations are supposed to satisfy. The finite volume and finite element schemes summarized in this book use limiting techniques to enforce discrete maximum principles and entropy inequalities. Spurious oscillations are prevented using artificial viscosity operators and/or essentially nonoscillatory reconstructions.An introduction to classical nonlinear stabilization approaches is given in the simple context of one-dimensional finite volume discretizations. Subsequent chapters of Part I are focused on recent extensions to continuous and discontinuous Galerkin methods. Many of the algorithms presented in these chapters were developed by the authors and their collaborators. Part II gives a deeper insight into the mathematical theory of property-preserving numerical schemes. It begins with a review of the convergence theory for finite volume methods and ends with analysis of algebraic flux correction schemes for finite elements. In addition to providing ready-to-use algorithms, this text explains the design principles behind such algorithms and shows how to put theory into practice. Although the book is based on lecture notes written for an advanced graduate-level course, it is also aimed at senior researchers who develop and analyze numerical methods for hyperbolic problems.
Grid Generation Methods
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Author : Vladimir D. Liseikin
language : en
Publisher: Springer
Release Date : 2017-06-12
Grid Generation Methods written by Vladimir D. Liseikin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-12 with Science categories.
This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.
Discontinuous Galerkin Methods
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Author : Bernardo Cockburn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discontinuous Galerkin Methods written by Bernardo Cockburn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Multiscale Thermo Dynamics
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Author : Michal Pavelka
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06
Multiscale Thermo Dynamics written by Michal Pavelka and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-06 with Science categories.
One common feature of new emerging technologies is the fusion of the very small (nano) scale and the large scale engineering. The classical environment provided by single scale theories, as for instance by the classical hydrodynamics, is not anymore satisfactory. The main challenge is to keep the important details while still be able to keep the overall picture and simplicity. It is the thermodynamics that addresses this challenge. Our main reason for writing this book is to explain such general viewpoint of thermodynamics and to illustrate it on a very wide range of examples. Contents Levels of description Hamiltonian mechanics Irreversible evolution Reversible and irreversible evolution Multicomponent systems Contact geometry Appendix: Mathematical aspects
Continuum Mechanics Through The Twentieth Century
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Author : Gerard A Maugin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-08
Continuum Mechanics Through The Twentieth Century written by Gerard A Maugin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-08 with Science categories.
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.
A History Of Thermodynamics
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Author : Ingo Müller
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-16
A History Of Thermodynamics written by Ingo Müller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-16 with Science categories.
The most exciting and significant episode of scientific progress is the development of thermodynamics and electrodynamics in the 19th century and early 20th century. The nature of heat and temperature was recognized, the conservation of energy was discovered, and the realization that mass and energy are equivalent provided a new fuel, – and unlimited power. Much of this occurred in unison with the rapid technological advance provided by the steam engine, the electric motor, internal combustion engines, refrigeration and the rectification processes of the chemical industry. The availability of cheap power and cheap fuel has had its impact on society: Populations grew, the standard of living increased, the envir- ment became clean, traffic became easy, and life expectancy was raised. Knowledge fairly exploded. The western countries, where all this happened, gained in power and influence, and western culture – scientific culture – spread across the globe, and is still spreading. At the same time, thermodynamics recognized the stochastic and probabilistic aspect of natural processes. It turned out that the doctrine of energy and entropy rules the world; the first ingredient – energy – is deterministic, as it were, and the second – entropy – favours randomness. Both tendencies compete, and they find the precarious balance needed for stability and change alike.