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The Resource Distributions in the physical and engineering sciences, Volume 3, Random and anomalous fractional dynamics in continuous media, Alexander I. Saichev, Wojbor A. Woyczyński

Distributions in the physical and engineering sciences, Volume 3, Random and anomalous fractional dynamics in continuous media, Alexander I. Saichev, Wojbor A. Woyczyński

Creator
Author
Contributor
Summary
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.--
Language
eng
Work
Publication
Extent
1 online resource (xx, 403 pages)
Contents
  • Introduction to Volume 3
  • Notation
  • Basic Distributional Tools for Probability Theory
  • Random Distributions: Generalized Stochastic Processes
  • Dynamical and Statistical Characteristics of Random Fields and Waves
  • Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows
  • Probability Distributions of Passive Tracers in Randomly Moving Media
  • Levy Processes and Their Generalized Derivatives
  • Linear Anomalous Fractional Dynamics in Continuous Media
  • Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media
  • Appendix A: Basic Facts About Distributions
  • Bibliography
  • Index
Isbn
9783319925868
Instance
Label
Distributions in the physical and engineering sciences, Volume 3, Random and anomalous fractional dynamics in continuous media
Title
Distributions in the physical and engineering sciences
Title number
Volume 3
Title part
Random and anomalous fractional dynamics in continuous media
Statement of responsibility
Alexander I. Saichev, Wojbor A. Woyczyński
Title variation
Random and anomalous fractional dynamics in continuous media
Creator
Contributor
Author
Subject
Language
eng
Summary
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.--
Member of
Assigning source
Provided by publisher
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Saichev, A. I
Dewey number
515/.782
Illustrations
illustrations
Index
index present
LC call number
QA324
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1943-
http://library.link/vocab/relatedWorkOrContributorName
Woyczyński, W. A.
Series statement
Applied and numerical harmonic analysis,
http://library.link/vocab/subjectName
Theory of distributions (Functional analysis)
Label
Distributions in the physical and engineering sciences, Volume 3, Random and anomalous fractional dynamics in continuous media, Alexander I. Saichev, Wojbor A. Woyczyński
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction to Volume 3 -- Notation -- Basic Distributional Tools for Probability Theory -- Random Distributions: Generalized Stochastic Processes -- Dynamical and Statistical Characteristics of Random Fields and Waves -- Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows -- Probability Distributions of Passive Tracers in Randomly Moving Media -- Levy Processes and Their Generalized Derivatives -- Linear Anomalous Fractional Dynamics in Continuous Media -- Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media -- Appendix A: Basic Facts About Distributions -- Bibliography -- Index
Dimensions
unknown
Extent
1 online resource (xx, 403 pages)
File format
unknown
Form of item
online
Isbn
9783319925868
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-92586-8
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1048355092
  • (OCoLC)1048355092
Label
Distributions in the physical and engineering sciences, Volume 3, Random and anomalous fractional dynamics in continuous media, Alexander I. Saichev, Wojbor A. Woyczyński
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction to Volume 3 -- Notation -- Basic Distributional Tools for Probability Theory -- Random Distributions: Generalized Stochastic Processes -- Dynamical and Statistical Characteristics of Random Fields and Waves -- Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows -- Probability Distributions of Passive Tracers in Randomly Moving Media -- Levy Processes and Their Generalized Derivatives -- Linear Anomalous Fractional Dynamics in Continuous Media -- Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media -- Appendix A: Basic Facts About Distributions -- Bibliography -- Index
Dimensions
unknown
Extent
1 online resource (xx, 403 pages)
File format
unknown
Form of item
online
Isbn
9783319925868
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-92586-8
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1048355092
  • (OCoLC)1048355092

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