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Author: Gennadii V. Demidenko
Publisher: Springer Nature
ISBN: 3030388700
Category : Science
Languages : en
Pages : 378
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Book Description
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.
Author: Gennadii V. Demidenko
Publisher: Springer Nature
ISBN: 3030388700
Category : Science
Languages : en
Pages : 378
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Book Description
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.
Author: Alexander Domoshnitsky
Publisher: Springer Nature
ISBN: 9811662975
Category : Mathematics
Languages : en
Pages : 265
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Book Description
This book discusses delay and integro-differential equations from the point of view of the theory of functional differential equations. This book is a collection of selected papers presented at the international conference of Functional Differential Equations and Applications (FDEA-2019), 7th in the series, held at Ariel University, Israel, from August 22–27, 2019. Topics covered in the book include classical properties of functional differential equations as oscillation/non-oscillation, representation of solutions, sign properties of Green's matrices, comparison of solutions, stability, control, analysis of boundary value problems, and applications. The primary audience for this book includes specialists on ordinary, partial and functional differential equations, engineers and doctors dealing with modeling, and researchers in areas of mathematics and engineering.
Author: Josef Málek
Publisher: Springer Nature
ISBN: 3030880842
Category : Mathematics
Languages : en
Pages : 281
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Book Description
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.
Author: Tommaso Ruggeri
Publisher: Springer Nature
ISBN: 3030591441
Category : Mathematics
Languages : en
Pages : 675
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Book Description
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.
Author: Giacomo Albi
Publisher: Springer Nature
ISBN: 3031298756
Category : Mathematics
Languages : en
Pages : 241
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Book Description
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.
Author: Dmitri Kuzmin
Publisher: World Scientific
ISBN: 9811278202
Category : Mathematics
Languages : en
Pages : 491
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: KARAN S. SURANA
Publisher: CRC Press
ISBN: 9780367612962
Category :
Languages : en
Pages : 536
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Book Description
This book explores the foundation of continuum mechanics and constitutive theories of materials using understandable notations. Written using clear language to explore this mathematically demanding area of mechanical engineering, the book provides a thorough guide to continuum mechanics. Updated throughout for the second edition, the book adds new material aimed at defining classical continuum mechanics, discussing its limitations, and illustrating key concepts. New to the second edition is a chapter on advanced topics in classical continuum mechanics, defining and illustrating the type of physics that can be considered under calculus of variations and energy methods. Placing special emphasis on both matrix and vector notations, it presents material using these notations whenever possible. Establishing the tensorial nature of strain measures and influence of rotation of frames on various measures, the book illustrates the physical meaning of the components of strains, presents the polar decomposition of deformation, and provides the definitions and measures of stress. The book will be of interest to graduate students, with the objective of preparing them for advanced research or for advanced applications of continuum mechanics. Additionally, the new edition includes a solutions manual, aiding lecturers and those pursuing self-study.
Author: Vladimir N. Kukudzhanov
Publisher: Walter de Gruyter
ISBN: 3110273381
Category : Science
Languages : en
Pages : 447
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Book Description
This work focuses on computational methods in continuum thermomechanics. The text is based on the author's lectures, which ensures a didactical and coherent buildup. The main emphasis is put on the presentation of ideas and qualitative considerations, illustrated by specific examples and applications. Conditions and explanations that are essential for the practical application of methods are discussed thoroughly.
Author: E.F. Toro
Publisher: Springer Science & Business Media
ISBN: 1461506638
Category : Computers
Languages : en
Pages : 1050
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Book Description
This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.
