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Author: Carlo Cercignani
Publisher: Birkhäuser
ISBN: 3034888104
Category : Mathematics
Languages : en
Pages : 192
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Book Description
This is an introductory text, in two parts, on scaling limits and modelling in equations of mathematical physics. The first part is concerned with basic concepts of the kinetic theory of gases which is not only important in its own right but also as a prototype of a mathematical construct central to the theory of non-equilibrium phenomena in large systems. It also features a very readable historic survey of the field. The second part dwells on the role of integrable systems for modelling weakly nonlinear equations which contain the effects of both dispersion and nonlinearity. Starting with a historical introduction to the subject and a description of numerical techniques, it proceeds to a discussion of the derivation of the Korteweg de Vries and nonlinear Schrödinger equations, followed by a careful treatment of the inverse scattering theory for the Schrödinger operator. The book provides an up-to-date and detailed overview to this very active area of research and is intended as an accessible introduction for non-specialists and graduate students in mathematics, physics and engineering.
Author: Carlo Cercignani
Publisher: Birkhäuser
ISBN: 3034888104
Category : Mathematics
Languages : en
Pages : 192
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Book Description
This is an introductory text, in two parts, on scaling limits and modelling in equations of mathematical physics. The first part is concerned with basic concepts of the kinetic theory of gases which is not only important in its own right but also as a prototype of a mathematical construct central to the theory of non-equilibrium phenomena in large systems. It also features a very readable historic survey of the field. The second part dwells on the role of integrable systems for modelling weakly nonlinear equations which contain the effects of both dispersion and nonlinearity. Starting with a historical introduction to the subject and a description of numerical techniques, it proceeds to a discussion of the derivation of the Korteweg de Vries and nonlinear Schrödinger equations, followed by a careful treatment of the inverse scattering theory for the Schrödinger operator. The book provides an up-to-date and detailed overview to this very active area of research and is intended as an accessible introduction for non-specialists and graduate students in mathematics, physics and engineering.
Author: Gerard G. Emch
Publisher: Springer Science & Business Media
ISBN: 3662048868
Category : Science
Languages : en
Pages : 707
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Book Description
This book is devoted to a thorough analysis of the role that models play in the practise of physical theory. The authors, a mathematical physicist and a philosopher of science, appeal to the logicians’ notion of model theory as well as to the concepts of physicists.
Author: Radyadour Kh. Zeytounian
Publisher: Springer Science & Business Media
ISBN: 3642207456
Category : Technology & Engineering
Languages : en
Pages : 283
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Book Description
This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.
Author: Professor of Theoretical Mechanics Carlo Cercignani
Publisher:
ISBN: 9783034888110
Category :
Languages : en
Pages : 204
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Book Description
This is an introductory text, in two parts, on scaling limits and modelling in equations of mathematical physics. The first part is concerned with basic concepts of the kinetic theory of gases which is not only important in its own right but also as a prototype of a mathematical construct central to the theory of non-equilibrium phenomena in large systems. It also features a very readable historic survey of the field. The second part dwells on the role of integrable systems for modelling weakly nonlinear equations which contain the effects of both dispersion and nonlinearity. Starting with a historical introduction to the subject and a description of numerical techniques, it proceeds to a discussion of the derivation of the Korteweg de Vries and nonlinear Schrodinger equations, followed by a careful treatment of the inverse scattering theory for the Schrodinger operator. The book provides an up-to-date and detailed overview to this very active area of research and is intended as an accessible introduction for non-specialists and graduate students in mathematics, physics and engineering.
Author: Elliott H. Lieb
Publisher: Springer Science & Business Media
ISBN: 9783764373368
Category : Science
Languages : en
Pages : 220
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Book Description
This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.
Author: Guido Schneider
Publisher: American Mathematical Soc.
ISBN: 1470436132
Category : Mathematics
Languages : en
Pages : 593
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Book Description
This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.
Author: Jacek Banasiak
Publisher: Springer Science & Business Media
ISBN: 1846281539
Category : Mathematics
Languages : en
Pages : 443
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Book Description
This book deals mainly with modelling systems that change with time. The evolution equations that it describes can be found in a number of application areas, such as kinetics, fragmentation theory and mathematical biology. This will be the first self-contained account of the area.
Author: Randall J. LeVeque
Publisher: Springer Science & Business Media
ISBN: 9783764327231
Category : Mathematics
Languages : en
Pages : 238
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Book Description
These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave structure of solutions to the Riemann problem. The emphasis is on tools and techniques that are indispensable in developing good numerical methods for discontinuous solutions. Part II is devoted to the development of high resolution shock-capturing methods, including the theory of total variation diminishing (TVD) methods and the use of limiter functions. The book is intended for a wide audience, and will be of use both to numerical analysts and to computational researchers in a variety of applications.
Author: Yangang Liu
Publisher: John Wiley & Sons
ISBN: 1119528941
Category : Science
Languages : en
Pages : 483
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Book Description
Improving weather and climate prediction with better representation of fast processes in atmospheric models Many atmospheric processes that influence Earth’s weather and climate occur at spatiotemporal scales that are too small to be resolved in large scale models. They must be parameterized, which means approximately representing them by variables that can be resolved by model grids. Fast Processes in Large-Scale Atmospheric Models: Progress, Challenges and Opportunities explores ways to better investigate and represent multiple parameterized processes in models and thus improve their ability to make accurate climate and weather predictions. Volume highlights include: Historical development of the parameterization of fast processes in numerical models Different types of major sub-grid processes and their parameterizations Efforts to unify the treatment of individual processes and their interactions Top-down versus bottom-up approaches across multiple scales Measurement techniques, observational studies, and frameworks for model evaluation Emerging challenges, new opportunities, and future research directions The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.
Author: Yong Zhu
Publisher: Cambridge Int Science Publishing
ISBN: 1898326312
Category : Atmospheric physics
Languages : en
Pages : 648
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Book Description
Annotation This book introduces a new science, large-scale inhomogeneous thermodynamics, to study the inhomogeneous thermodynamic systems.
