Filtering complex turbulent systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 357 S. zahlr. graph. Darst. |
| ISBN: | 9781107016668 |
Internformat
MARC
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| 020 | |a 9781107016668 |c (hbk.) |9 978-1-107-01666-8 | ||
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| 100 | 1 | |a Majda, Andrew |d 1949- |e Verfasser |0 (DE-588)135598788 |4 aut | |
| 245 | 1 | 0 | |a Filtering complex turbulent systems |c Andrew J. Majda ; John Harlim |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a VII, 357 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Filterung |g Stochastik |0 (DE-588)4121267-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Turbulenztheorie |0 (DE-588)4186472-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexes System |0 (DE-588)4114261-5 |2 gnd |9 rswk-swf |
| 653 | |a Filters and filtration--Mathematics. | ||
| 653 | |a Turbulence. | ||
| 653 | |a Numerical analysis. | ||
| 689 | 0 | 0 | |a Komplexes System |0 (DE-588)4114261-5 |D s |
| 689 | 0 | 1 | |a Turbulenztheorie |0 (DE-588)4186472-4 |D s |
| 689 | 0 | 2 | |a Filterung |g Stochastik |0 (DE-588)4121267-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Harlim, John |e Verfasser |0 (DE-588)1022751417 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894491&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024894491 | ||
Datensatz im Suchindex
| _version_ | 1804149037489717248 |
|---|---|
| adam_text | Contents
Preface
page jx
1
Introduction and overview: Mathematical strategies for filtering
turbulent systems
1
1.1
Turbulent dynamical systems and basic filtering
3
1.2
Mathematical guidelines for filtering turbulent dynamical systems
9
1.3
Filtering turbulent dynamical systems
11
Part I Fundamentals
13
2
Filtering a stochastic complex scalar: The prototype test problem
15
2.1
Kalman
filter: One-dimensional complex variable
15
2.2
Filtering stability
20
2.3
Model error
23
3
The
Kalman
filter for vector systems: Reduced filters and
a three-dimensional toy model
30
3.1
The classical TV-dimensional
Kalman
filter
30
3.2
Filter stability
32
3.3
Example: A three-dimensional toy model with a single observation
33
3.4
Reduced filters for large systems
39
3.5
A priori covariance stability for the unstable mode filter given
strong observability
43
4
Continuous and discrete Fourier series and numerical discretization
47
4.1
Continuous and discrete Fourier series
47
4.2
Aliasing
49
4.3
Differential and difference operators
52
4.4
Solving initial value problems
53
4.5
Convergence of the difference operator
55
vi
Contents
Part II Mathematical guidelines for filtering turbulent signals
59
5
Stochastic models for turbulence
61
5.1
The stochastic test model for turbulent signals
61
5.2
Turbulent signals for the damped forced advection-diffusion equation
65
5.3
Statistics of turbulent solutions in physical space
66
5.4
Turbulent Rossby waves
68
Appendix A: Temporal correlation function for each Fourier mode
70
Appendix B: Spatio-temporal correlation function
71
6
Filtering turbulent signals: Plentiful observations
72
6.1
A mathematical theory for Fourier filter reduction
73
6.2
Theoretical guidelines for filter performance under mesh refinement
for turbulent signals
77
6.3
Discrete filtering for the stochastically forced dissipative advection
equation
81
7
Filtering turbulent signals: Regularly spaced sparse observations
94
7.1
Theory for filtering sparse regularly spaced observations
94
7.2
Fourier domain filtering for sparse regular observations
99
7.3
Approximate filters in the Fourier domain
102
7.4
New phenomena and filter performance for sparse regular
observations
107
8
Filtering linear stochastic PDE models with instability and model error
116
8.1
Two-state continuous-time Markov process
117
8.2
Idealized spatially extended turbulent systems with instability
119
8.3
The mean stochastic model for filtering
123
8.4
Numerical performance of the filters with and without model error
127
Part III Filtering turbulent nonlinear dynamical systems
131
9
Strategies for filtering nonlinear systems
133
9.1
The extended
Kalman
filter
134
9.2
The ensemble
Kalman
filter
136
9.3
The ensemble square-root filters
139
9.4
Ensemble filters on the Lorenz-63 model
143
9.5
Ensemble square-root filters on stochastically forced linear systems
149
9.6
Advantages and disadvantages with finite ensemble strategies
151
10
Filtering prototype nonlinear slow-fast systems
153
10.1
The nonlinear test model for filtering slow-fast systems with strong
fast forcing: An overview
153
10.2
Exact solutions and exactly solvable statistics in the nonlinear test
model
159
10.3
Nonlinear extended
Kalman
filter (NEKF)
171
10.4
Experimental designs
174
Contents
vii
10.5 Filter
performance I77
10.6
Summary 19O
11
Filtering turbulent nonlinear dynamical systems by finite
ensemble methods
192
11.1
The L-96 model
192
11.2
Ensemble square-root filters on the L-96 model
195
11.3
Catastrophic filter divergence
200
11.4
The two-layer quasi-geostrophic model
204
11.5
Local least-square EAKF on the QG model
210
12
Filtering turbulent nonlinear dynamical systems by linear
stochastic models
214
12.1
Linear stochastic models for the L-96 model
215
12.2
Filter performance with plentiful observation
220
12.3
Filter performance with regularly spaced sparse observations
223
13
Stochastic parametrized extended
Kalman
filter for filtering turbulent
signals with model error
236
13.1
Nonlinear filtering with additive and multiplicative biases:
One-mode prototype test model
238
13.2
Filtering spatially extended turbulent systems with SPEKF
251
13.3
Application of SPEKF to the two-layer QG model
263
Appendix
269
14
Filtering turbulent tracers from partial observations: An exactly
solvable test model
276
14.1
Model description
278
14.2
System statistics
279
14.3
Nonlinear extended
Kalman
filter
292
14.4
Filter performance
297
15
The search for efficient skillful particle filters for high-dimensional
turbulent dynamical systems
316
15.1
The basic idea of a particle filter
317
15.2
Innovative particle filter algorithms
319
15.3
Filter performance on the L-63 model
326
15.4
Filter performance on the L-96 model
339
15.5
Discussion
346
References
349
Index
356
|
| any_adam_object | 1 |
| author | Majda, Andrew 1949- Harlim, John |
| author_GND | (DE-588)135598788 (DE-588)1022751417 |
| author_facet | Majda, Andrew 1949- Harlim, John |
| author_role | aut aut |
| author_sort | Majda, Andrew 1949- |
| author_variant | a m am j h jh |
| building | Verbundindex |
| bvnumber | BV040037757 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)796198013 (DE-599)OBVAC08964423 |
| dewey-full | 660.2842450151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 660 - Chemical engineering |
| dewey-raw | 660.2842450151 |
| dewey-search | 660.2842450151 |
| dewey-sort | 3660.2842450151 |
| dewey-tens | 660 - Chemical engineering |
| discipline | Chemie / Pharmazie Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040037757 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:16:39Z |
| institution | BVB |
| isbn | 9781107016668 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024894491 |
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| owner_facet | DE-703 DE-83 DE-824 DE-384 DE-11 DE-1043 |
| physical | VII, 357 S. zahlr. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Majda, Andrew 1949- Verfasser (DE-588)135598788 aut Filtering complex turbulent systems Andrew J. Majda ; John Harlim 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2012 VII, 357 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Filterung Stochastik (DE-588)4121267-8 gnd rswk-swf Turbulenztheorie (DE-588)4186472-4 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf Filters and filtration--Mathematics. Turbulence. Numerical analysis. Komplexes System (DE-588)4114261-5 s Turbulenztheorie (DE-588)4186472-4 s Filterung Stochastik (DE-588)4121267-8 s DE-604 Harlim, John Verfasser (DE-588)1022751417 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894491&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Majda, Andrew 1949- Harlim, John Filtering complex turbulent systems Filterung Stochastik (DE-588)4121267-8 gnd Turbulenztheorie (DE-588)4186472-4 gnd Komplexes System (DE-588)4114261-5 gnd |
| subject_GND | (DE-588)4121267-8 (DE-588)4186472-4 (DE-588)4114261-5 |
| title | Filtering complex turbulent systems |
| title_auth | Filtering complex turbulent systems |
| title_exact_search | Filtering complex turbulent systems |
| title_full | Filtering complex turbulent systems Andrew J. Majda ; John Harlim |
| title_fullStr | Filtering complex turbulent systems Andrew J. Majda ; John Harlim |
| title_full_unstemmed | Filtering complex turbulent systems Andrew J. Majda ; John Harlim |
| title_short | Filtering complex turbulent systems |
| title_sort | filtering complex turbulent systems |
| topic | Filterung Stochastik (DE-588)4121267-8 gnd Turbulenztheorie (DE-588)4186472-4 gnd Komplexes System (DE-588)4114261-5 gnd |
| topic_facet | Filterung Stochastik Turbulenztheorie Komplexes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894491&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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