Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1

Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1

Author: Valery I. Klyatskin

Publisher: Springer

Published: 2014-07-14

Total Pages: 423

ISBN-13: 331907587X

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This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.


Book Synopsis Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1 by : Valery I. Klyatskin

Download or read book Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1 written by Valery I. Klyatskin and published by Springer. This book was released on 2014-07-14 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2

Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2

Author: Valery I. Klyatskin

Publisher: Springer

Published: 2014-07-14

Total Pages: 489

ISBN-13: 331907590X

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In some cases, certain coherent structures can exist in stochastic dynamic systems almost in every particular realization of random parameters describing these systems. Dynamic localization in one-dimensional dynamic systems, vortexgenesis (vortex production) in hydrodynamic flows, and phenomenon of clustering of various fields in random media (i.e., appearance of small regions with enhanced content of the field against the nearly vanishing background of this field in the remaining portion of space) are examples of such structure formation. The general methodology presented in Volume 1 is used in Volume 2 Coherent Phenomena in Stochastic Dynamic Systems to expound the theory of these phenomena in some specific fields of stochastic science, among which are hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics. The material of this volume includes particle and field clustering in the cases of scalar (density field) and vector (magnetic field) passive tracers in a random velocity field, dynamic localization of plane waves in layered random media, as well as monochromatic wave propagation and caustic structure formation in random media in terms of the scalar parabolic equation.


Book Synopsis Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2 by : Valery I. Klyatskin

Download or read book Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2 written by Valery I. Klyatskin and published by Springer. This book was released on 2014-07-14 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: In some cases, certain coherent structures can exist in stochastic dynamic systems almost in every particular realization of random parameters describing these systems. Dynamic localization in one-dimensional dynamic systems, vortexgenesis (vortex production) in hydrodynamic flows, and phenomenon of clustering of various fields in random media (i.e., appearance of small regions with enhanced content of the field against the nearly vanishing background of this field in the remaining portion of space) are examples of such structure formation. The general methodology presented in Volume 1 is used in Volume 2 Coherent Phenomena in Stochastic Dynamic Systems to expound the theory of these phenomena in some specific fields of stochastic science, among which are hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics. The material of this volume includes particle and field clustering in the cases of scalar (density field) and vector (magnetic field) passive tracers in a random velocity field, dynamic localization of plane waves in layered random media, as well as monochromatic wave propagation and caustic structure formation in random media in terms of the scalar parabolic equation.

Principles of Statistical Radiophysics 3

Principles of Statistical Radiophysics 3

Author: Sergei M. Rytov

Publisher: Springer

Published: 1989-07-14

Total Pages: 239

ISBN-13: 9783540178293

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Principles of Statistical Radiophysics is a four-volume series that introduces the newcomer to the theory of random functions. It aims at providing the background necessary to understand papers and monographs on the subject and to carry out independent research in the fields where fluctuations are of importance, e.g. radiophysics, optics, astronomy, and acoustics. Volume 3, Elements of Random Fields, gives the basic mathematical definitions, general properties and specific forms of random fields, the generalization from correlation theory to random fields. It deals with stochastic partial differential equations, wave scattering at a chaotic screen, single scattering in random media and thermal fluctuations and radiation of electromagnetic fields.


Book Synopsis Principles of Statistical Radiophysics 3 by : Sergei M. Rytov

Download or read book Principles of Statistical Radiophysics 3 written by Sergei M. Rytov and published by Springer. This book was released on 1989-07-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principles of Statistical Radiophysics is a four-volume series that introduces the newcomer to the theory of random functions. It aims at providing the background necessary to understand papers and monographs on the subject and to carry out independent research in the fields where fluctuations are of importance, e.g. radiophysics, optics, astronomy, and acoustics. Volume 3, Elements of Random Fields, gives the basic mathematical definitions, general properties and specific forms of random fields, the generalization from correlation theory to random fields. It deals with stochastic partial differential equations, wave scattering at a chaotic screen, single scattering in random media and thermal fluctuations and radiation of electromagnetic fields.

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Author: Gregory S. Chirikjian

Publisher: Springer Science & Business Media

Published: 2011-11-15

Total Pages: 460

ISBN-13: 0817649433

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This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.


Book Synopsis Stochastic Models, Information Theory, and Lie Groups, Volume 2 by : Gregory S. Chirikjian

Download or read book Stochastic Models, Information Theory, and Lie Groups, Volume 2 written by Gregory S. Chirikjian and published by Springer Science & Business Media. This book was released on 2011-11-15 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Fluvial Hydrodynamics

Fluvial Hydrodynamics

Author: Subhasish Dey

Publisher: Springer

Published: 2014-08-22

Total Pages: 706

ISBN-13: 3642190626

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The state-of-the-art in fluvial hydrodynamics can be examined only through a careful exploration of the theoretical development and applied engineering technology. The book is primarily focused, since most up-to-date research findings in the field are presented, on the research aspects that involve a comprehensive knowledge of sediment dynamics in turbulent flows. It begins with the fundamentals of hydrodynamics and particle motion followed by turbulence characteristics related to sediment motion. Then, the sediment dynamics is analysed from a classical perspective by applying the mean bed shear approach and additionally incorporating a statistical description for the role of turbulence. The work finally examines the local scour problems at hydraulic structures and scale models. It is intended to design as a course textbook in graduate / research level and a guide for the field engineers as well, keeping up with modern technological developments. Therefore, as a simple prerequisite, the background of the readers should have a basic knowledge in hydraulics in undergraduate level and an understanding of fundamentals of calculus.


Book Synopsis Fluvial Hydrodynamics by : Subhasish Dey

Download or read book Fluvial Hydrodynamics written by Subhasish Dey and published by Springer. This book was released on 2014-08-22 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The state-of-the-art in fluvial hydrodynamics can be examined only through a careful exploration of the theoretical development and applied engineering technology. The book is primarily focused, since most up-to-date research findings in the field are presented, on the research aspects that involve a comprehensive knowledge of sediment dynamics in turbulent flows. It begins with the fundamentals of hydrodynamics and particle motion followed by turbulence characteristics related to sediment motion. Then, the sediment dynamics is analysed from a classical perspective by applying the mean bed shear approach and additionally incorporating a statistical description for the role of turbulence. The work finally examines the local scour problems at hydraulic structures and scale models. It is intended to design as a course textbook in graduate / research level and a guide for the field engineers as well, keeping up with modern technological developments. Therefore, as a simple prerequisite, the background of the readers should have a basic knowledge in hydraulics in undergraduate level and an understanding of fundamentals of calculus.

Magnetohydrodynamic Stability of Tokamaks

Magnetohydrodynamic Stability of Tokamaks

Author: Hartmut Zohm

Publisher: John Wiley & Sons

Published: 2015-02-09

Total Pages: 254

ISBN-13: 3527412328

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This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.


Book Synopsis Magnetohydrodynamic Stability of Tokamaks by : Hartmut Zohm

Download or read book Magnetohydrodynamic Stability of Tokamaks written by Hartmut Zohm and published by John Wiley & Sons. This book was released on 2015-02-09 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.

Number Theory

Number Theory

Author: Henri Cohen

Publisher: Springer Science & Business Media

Published: 2007-05-23

Total Pages: 673

ISBN-13: 0387499229

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The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.


Book Synopsis Number Theory by : Henri Cohen

Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2007-05-23 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Stochastic Models, Information Theory, and Lie Groups, Volume 1

Stochastic Models, Information Theory, and Lie Groups, Volume 1

Author: Gregory S. Chirikjian

Publisher: Springer Science & Business Media

Published: 2009-09-02

Total Pages: 397

ISBN-13: 0817648038

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This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.


Book Synopsis Stochastic Models, Information Theory, and Lie Groups, Volume 1 by : Gregory S. Chirikjian

Download or read book Stochastic Models, Information Theory, and Lie Groups, Volume 1 written by Gregory S. Chirikjian and published by Springer Science & Business Media. This book was released on 2009-09-02 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

A Textbook of Magnetohydrodynamics

A Textbook of Magnetohydrodynamics

Author: John Arthur Shercliff

Publisher:

Published: 1965

Total Pages: 294

ISBN-13:

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Book Synopsis A Textbook of Magnetohydrodynamics by : John Arthur Shercliff

Download or read book A Textbook of Magnetohydrodynamics written by John Arthur Shercliff and published by . This book was released on 1965 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interpolation and Extrapolation Optimal Designs V1

Interpolation and Extrapolation Optimal Designs V1

Author: Giorgio Celant

Publisher: John Wiley & Sons

Published: 2016-03-31

Total Pages: 254

ISBN-13: 111929228X

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This book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields. In this volume, the authors emphasize the importance of problems associated with the construction of design. After a brief introduction on how the theory of optimal designs meets the theory of the uniform approximation of functions, the authors introduce the basic elements to design planning and link the statistical theory of optimal design and the theory of the uniform approximation of functions. The appendices provide the reader with material to accompany the proofs discussed throughout the book.


Book Synopsis Interpolation and Extrapolation Optimal Designs V1 by : Giorgio Celant

Download or read book Interpolation and Extrapolation Optimal Designs V1 written by Giorgio Celant and published by John Wiley & Sons. This book was released on 2016-03-31 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields. In this volume, the authors emphasize the importance of problems associated with the construction of design. After a brief introduction on how the theory of optimal designs meets the theory of the uniform approximation of functions, the authors introduce the basic elements to design planning and link the statistical theory of optimal design and the theory of the uniform approximation of functions. The appendices provide the reader with material to accompany the proofs discussed throughout the book.