Stochastic tools in turbulence:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, NY
Dover Publications
2007
|
| Edition: | Dover ed., 1. publ., unabridged republ. |
| Series: | Dover books on engineering
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references (p. 187-190) and index |
| Physical Description: | xi, 194 p. graph. Darst. |
| ISBN: | 9780486462707 0486462706 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic tools in turbulence |c John L. Lumley |
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Record in the Search Index
| _version_ | 1804138110286561280 |
|---|---|
| adam_text | Contents
Preface
Й.
1.
Probability Distributions and Densities
1.1
Definition of Probability
1
1.2
Formalizing the Definition
3
1.3
Measure and Lebesgue Integration
S
1.4
Distribution Function
7
1.5
The Probability Density Function
8
1.6
A Simple Example of the Distribution and Density Functions
10
1.7
Expected Values
U
1.8
Joint Distribution Functions
12
1.9
The Joint Density Function
13
.10
Expected Values
14
.11
Conditional Probabilities IS
.12
Conditional Expectations
16
.13
Statistical Independence and Lack of Correlation
16
.14
Change of Variable
17
2.
Moments, Characteristic Functions, and the
Gaussian Distribution
2.1
Moments Denned
19
2.2
Significance of the Moments
21
2.3
The Correlation Matrix and Principal Axes
24
2.4
The Characteristic Function
25
2.5
Properties of the Characteristic Function
25
2.6
Two Simple Examples
27
2.7
The Central-Limit Theorem for Independent Variables
30
2.8
The Gaussian Distribution from a More Physical Point of View
33
2.9
Moments of a Gaussian Distribution
37
2.10
The Jointly Normal Distribution
38
2.11
Cumulants
39
2.12
The Gram-Charlier Expansion
39
VÍ
CONTENTS
3.
Random Functions
3.1
Generalities: Multipoint Characteristic Functions
43
3.2
Statistics for Derivatives and Integrals
44
3.3
Processes and Characteristic Functionals: The Gaussian Process
47
3.4
Limit Processes of Random Functions
50
3.5
The Representation Problem
54
3.6
Finite Total Energy and Characteristic Eddies
57
3.7
Calculation of the Characteristic Eddies
59
3.8
Rate of Convergence of the Series of Eigenfunctions
60
3.9
Stationarity and the Ergodic Problem
62
3.10
Autocorrelations of Stationary Processes and Their Properties
68
3.11
Estimation by Time Averages
71
3.12
The Representation Problem for Stationary Processes: Spectra
76
3.13
Estimation by Time Averages with Zero Integral Scale
79
3.14
Another Type of Representation Theorem for Stationary Processes:
Characteristic Eddies
80
3.15
Alternate Approaches to Harmonic Decomposition for Stationary
Processes
82
3.16
A Central-Limit Theorem for Random Functions
84
4.
Random Processes in More Dimensions
4.1
Multidimensional Vector Fields of Finite Energy
95
4.2
Homogeneity, Averaging, and Ergodicity in Several Dimensions
96
4.3
The Homogeneous Scalar Field: One-Dimensional Spectra
98
4.4
The Homogeneous Scalar Field: The Three-Dimensional Spectrum
100
4.5
The Homogeneous Scalar Field: Consequences of Isotropy
100
4.6
The Homogeneous Scalar Field: General Form of the Spectra
102
4.7
The Solenoidal Homogeneous Vector Field: Implications of
Incompressibility
104
4.8
The Solenoidal Homogeneous Vector Field: One-Dimensional Spectra
107
4.9
The Solenoidal Homogeneous Vector Field: The Three-Dimensional
Spectrum
107
4.10
The Solenoidal Homogenous Vector Field: Consequences of Isotropy
108
4.11
The Solenoidal Homogeneous Vector Field: General Form of the
Spectra 111
4.12
Characteristic Eddies for a Homogeneous Vector Field
113
4.13
Incompletely Homogeneous Fields: Co- and Quadrature Spectra and
Coherence
114
4.14
Characteristic Eddies for an Incompletely Homogeneous Field
117
4.15
Multiple-Valued Functions
121
4.16
Distribution of Solutions for an Algebraic Equation
13°
Appendix
1.
Fourier Transforms
Al.l Fourier Transforms of Well-Behaved Functions I37
A1.2 The Inverse Transform
138
A1.3 The Convolution I»
CONTENTS VU
ЛІ
.4
Symmetry Properties
140
A1.5 Parseval s Relation
141
Al
.6
Relations among Derivatives
142
A1.7 Shift of Variables
142
A1.8 Multiple Variables
143
Appendix
2.
Tensors
A2.1 Transformation Properties: Co-and
Contravariant
Indices
145
A2.2 The Metric Tensor: Changing Indices
147
A2.3 Cartesian Systems, Numerical Tensors, and Tensor Densities
149
A2.4 Differentiation
152
A2.5 Eigenvalues and Eigenvectors: Representations
153
A2.6 Principal Invariants, The Cayley-Hamilton Theorem, and Inverses
156
Appendix
3.
Theory of Generalized Functions
A3.1 Generalities
159
A3.2 Linear Continuous Functionate
160
A3.3 Addition and Multiplication by a Constant and by a Function
161
A3.4 Convergence of Sequences of Generalized Functions
162
A3.5 Differentiation and Integration of Generalized Functions
162
A3.6 Support of a Generalized Function
164
A3.7 Direct Product of Generalized Functions
164
A3.8 Convolutions of Generalized Functions
164
A3.9 Fourier Transforms of Generalized Functions
166
A3.10 Several Variables
167
A3.11 Effect of a Shift of Variables
167
A3.12 Asymptotic Behavior of Generalized Functions
168
A3.13 Fourier Transforms of Generalized Functions Defined on the Space
of Bounded, Infinitely Differentiable Functions
172
A3.14 The Fourier Transform of the Convolution
174
A3.15 Behavior of the Fourier Transform
175
A3.16
The Kernel Theorem
176
A3.17 Representations of Generalized Functions of Finite Total Energy
176
Appendix
4.
Invariant Theory, Isotropy, and Axisymmetry
A4.1
Invariance
under Transformation Groups
179
A4.2 Independent Invariants of Tensors of Various Orders
180
A4.3 Representations of Tensor Functions—A General Method
182
A4.4 Tensor Constants and Functions of a Scalar
183
A4.5 Tensor Functions of a Vector
183
A4.6 Tensor Functions of a Tensor of Second Rank
184
References
187
Index
191
Stochastic
Tools
IN TURBULENCE
JOHN L. LUMLEY
his accessible treatment offers the mathematical tools for
describing and solving problems related to stochastic vector
fields. Advanced undergraduates and graduate students will
find its use of generalized functions a relatively simple method of
resolving mathematical questions. It will prove a valuable reference
for applied mathematicians and professionals in the fields of aerospace,
¡¡chemical, civil, and nuclear engineering.
і
The author, Professor Emeritus of Engineering at Cornell University, j
starts with a survey of probability distributions and densities and
proceeds to examinations of moments, characteristic functions, and
the Gaussian distribution; random functions; and random processes
in more dimensions. Extensive appendixes
—
which include informa¬
tion on Fouriertransforms, tensors, generalized functions, and invari¬
ant theory
—
contribute toward making this volume mathematically
self-contained.
Dover
(2007)
unabridged
republication
of the edition published by
Academic Press, New York,
1970.
208pp. 53s
χ
8V2. Paperbound.
See every Dover book in print at www.doverpublications.com
|
| adam_txt |
Contents
Preface
Й.
1.
Probability Distributions and Densities
1.1
Definition of Probability
1
1.2
Formalizing the Definition
3
1.3
Measure and Lebesgue Integration
S
1.4
Distribution Function
7
1.5
The Probability Density Function
8
1.6
A Simple Example of the Distribution and Density Functions
10
1.7
Expected Values
U
1.8
Joint Distribution Functions
12
1.9
The Joint Density Function
13
.10
Expected Values
14
.11
Conditional Probabilities IS
.12
Conditional Expectations
16
.13
Statistical Independence and Lack of Correlation
16
.14
Change of Variable
17
2.
Moments, Characteristic Functions, and the
Gaussian Distribution
2.1
Moments Denned
19
2.2
Significance of the Moments
21
2.3
The Correlation Matrix and Principal Axes
24
2.4
The Characteristic Function
25
2.5
Properties of the Characteristic Function
25
2.6
Two Simple Examples
27
2.7
The Central-Limit Theorem for Independent Variables
30
2.8
The Gaussian Distribution from a More Physical Point of View
33
2.9
Moments of a Gaussian Distribution
37
2.10
The Jointly Normal Distribution
38
2.11
Cumulants
39
2.12
The Gram-Charlier Expansion
39
VÍ
CONTENTS
3.
Random Functions
3.1
Generalities: Multipoint Characteristic Functions
43
3.2
Statistics for Derivatives and Integrals
44
3.3
Processes and Characteristic Functionals: The Gaussian Process
47
3.4
Limit Processes of Random Functions
50
3.5
The Representation Problem
54
3.6
Finite Total Energy and Characteristic Eddies
57
3.7
Calculation of the Characteristic Eddies
59
3.8
Rate of Convergence of the Series of Eigenfunctions
60
3.9
Stationarity and the Ergodic Problem
62
3.10
Autocorrelations of Stationary Processes and Their Properties
68
3.11
Estimation by Time Averages
71
3.12
The Representation Problem for Stationary Processes: Spectra
76
3.13
Estimation by Time Averages with Zero Integral Scale
79
3.14
Another Type of Representation Theorem for Stationary Processes:
Characteristic Eddies
80
3.15
Alternate Approaches to Harmonic Decomposition for Stationary
Processes
82
3.16
A Central-Limit Theorem for Random Functions
84
4.
Random Processes in More Dimensions
4.1
Multidimensional Vector Fields of Finite Energy
95
4.2
Homogeneity, Averaging, and Ergodicity in Several Dimensions
96
4.3
The Homogeneous Scalar Field: One-Dimensional Spectra
98
4.4
The Homogeneous Scalar Field: The Three-Dimensional Spectrum
100
4.5
The Homogeneous Scalar Field: Consequences of Isotropy
100
4.6
The Homogeneous Scalar Field: General Form of the Spectra
102
4.7
The Solenoidal Homogeneous Vector Field: Implications of
Incompressibility
104
4.8
The Solenoidal Homogeneous Vector Field: One-Dimensional Spectra
107
4.9
The Solenoidal Homogeneous Vector Field: The Three-Dimensional
Spectrum
107
4.10
The Solenoidal Homogenous Vector Field: Consequences of Isotropy
108
4.11
The Solenoidal Homogeneous Vector Field: General Form of the
Spectra 111
4.12
Characteristic Eddies for a Homogeneous Vector Field
113
4.13
Incompletely Homogeneous Fields: Co- and Quadrature Spectra and
Coherence
114
4.14
Characteristic Eddies for an Incompletely Homogeneous Field
117
4.15
Multiple-Valued Functions
121
4.16
Distribution of Solutions for an Algebraic Equation
13°
Appendix
1.
Fourier Transforms
Al.l Fourier Transforms of Well-Behaved Functions I37
A1.2 The Inverse Transform
138
A1.3 The Convolution I»
CONTENTS VU
ЛІ
.4
Symmetry Properties
140
A1.5 Parseval's Relation
141
Al
.6
Relations among Derivatives
142
A1.7 Shift of Variables
142
A1.8 Multiple Variables
143
Appendix
2.
Tensors
A2.1 Transformation Properties: Co-and
Contravariant
Indices
145
A2.2 The Metric Tensor: Changing Indices
147
A2.3 Cartesian Systems, Numerical Tensors, and Tensor Densities
149
A2.4 Differentiation
152
A2.5 Eigenvalues and Eigenvectors: Representations
153
A2.6 Principal Invariants, The Cayley-Hamilton Theorem, and Inverses
156
Appendix
3.
Theory of Generalized Functions
A3.1 Generalities
159
A3.2 Linear Continuous Functionate
160
A3.3 Addition and Multiplication by a Constant and by a Function
161
A3.4 Convergence of Sequences of Generalized Functions
162
A3.5 Differentiation and Integration of Generalized Functions
162
A3.6 Support of a Generalized Function
164
A3.7 Direct Product of Generalized Functions
164
A3.8 Convolutions of Generalized Functions
164
A3.9 Fourier Transforms of Generalized Functions
166
A3.10 Several Variables
167
A3.11 Effect of a Shift of Variables
167
A3.12 Asymptotic Behavior of Generalized Functions
168
A3.13 Fourier Transforms of Generalized Functions Defined on the Space
of Bounded, Infinitely Differentiable Functions
172
A3.14 The Fourier Transform of the Convolution
174
A3.15 Behavior of the Fourier Transform
175
A3.16
The Kernel Theorem
176
A3.17 Representations of Generalized Functions of Finite Total Energy
176
Appendix
4.
Invariant Theory, Isotropy, and Axisymmetry
A4.1
Invariance
under Transformation Groups
179
A4.2 Independent Invariants of Tensors of Various Orders
180
A4.3 Representations of Tensor Functions—A General Method
182
A4.4 Tensor Constants and Functions of a Scalar
183
A4.5 Tensor Functions of a Vector
183
A4.6 Tensor Functions of a Tensor of Second Rank
184
References
187
Index
191
Stochastic
Tools
IN TURBULENCE
JOHN L. LUMLEY
"his accessible treatment offers the mathematical tools for
describing and solving problems related to stochastic vector
fields. Advanced undergraduates and graduate students will
find its use of generalized functions a relatively simple method of
resolving mathematical questions. It will prove a valuable reference
for applied mathematicians and professionals in the fields of aerospace,
¡¡chemical, civil, and nuclear engineering.
і
The author, Professor Emeritus of Engineering at Cornell University, \j
starts with a survey of probability distributions and densities and
proceeds to examinations of moments, characteristic functions, and
the Gaussian distribution; random functions; and random processes
in more dimensions. Extensive appendixes
—
which include informa¬
tion on Fouriertransforms, tensors, generalized functions, and invari¬
ant theory
—
contribute toward making this volume mathematically
self-contained.
Dover
(2007)
unabridged
republication
of the edition published by
Academic Press, New York,
1970.
208pp. 53s
χ
8V2. Paperbound.
See every Dover book in print at www.doverpublications.com |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Lumley, John L. 1930-2015 |
| author_GND | (DE-588)12273985X |
| author_facet | Lumley, John L. 1930-2015 |
| author_role | aut |
| author_sort | Lumley, John L. 1930-2015 |
| author_variant | j l l jl jll |
| building | Verbundindex |
| bvnumber | BV035128857 |
| callnumber-first | Q - Science |
| callnumber-label | QA913 |
| callnumber-raw | QA913 |
| callnumber-search | QA913 |
| callnumber-sort | QA 3913 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 4300 |
| classification_tum | MTA 309f |
| ctrlnum | (OCoLC)124075018 (DE-599)BVBBV035128857 |
| dewey-full | 532/.0527 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0527 |
| dewey-search | 532/.0527 |
| dewey-sort | 3532 3527 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | Dover ed., 1. publ., unabridged republ. |
| format | Book |
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| id | DE-604.BV035128857 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:23:55Z |
| indexdate | 2024-07-09T21:22:59Z |
| institution | BVB |
| isbn | 9780486462707 0486462706 |
| language | English |
| lccn | 2007019198 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016796393 |
| oclc_num | 124075018 |
| open_access_boolean | |
| owner | DE-703 DE-91 DE-BY-TUM |
| owner_facet | DE-703 DE-91 DE-BY-TUM |
| physical | xi, 194 p. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Dover Publications |
| record_format | marc |
| series2 | Dover books on engineering |
| spelling | Lumley, John L. 1930-2015 Verfasser (DE-588)12273985X aut Stochastic tools in turbulence John L. Lumley Dover ed., 1. publ., unabridged republ. Mineola, NY Dover Publications 2007 xi, 194 p. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dover books on engineering Includes bibliographical references (p. 187-190) and index Turbulence Stochastic processes Stochastik (DE-588)4121729-9 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 s Stochastik (DE-588)4121729-9 s DE-604 http://www.loc.gov/catdir/enhancements/fy0730/2007019198-d.html Publisher description Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016796393&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016796393&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Lumley, John L. 1930-2015 Stochastic tools in turbulence Turbulence Stochastic processes Stochastik (DE-588)4121729-9 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4117265-6 |
| title | Stochastic tools in turbulence |
| title_auth | Stochastic tools in turbulence |
| title_exact_search | Stochastic tools in turbulence |
| title_exact_search_txtP | Stochastic tools in turbulence |
| title_full | Stochastic tools in turbulence John L. Lumley |
| title_fullStr | Stochastic tools in turbulence John L. Lumley |
| title_full_unstemmed | Stochastic tools in turbulence John L. Lumley |
| title_short | Stochastic tools in turbulence |
| title_sort | stochastic tools in turbulence |
| topic | Turbulence Stochastic processes Stochastik (DE-588)4121729-9 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| topic_facet | Turbulence Stochastic processes Stochastik Turbulente Strömung |
| url | http://www.loc.gov/catdir/enhancements/fy0730/2007019198-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016796393&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016796393&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lumleyjohnl stochastictoolsinturbulence |