The noisy oscillator: the first hundred years, from Einstein until now
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 144 S. graph. Darst. |
| ISBN: | 9789812565129 9812565124 |
Staff View
MARC
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| 100 | 1 | |a Gitterman, Moshe |d 1931- |e Verfasser |0 (DE-588)140080287 |4 aut | |
| 245 | 1 | 0 | |a The noisy oscillator |b the first hundred years, from Einstein until now |c Moshe Gitterman |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2005 | |
| 300 | |a XIV, 144 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Bruit | |
| 650 | 4 | |a Mécanique statistique | |
| 650 | 4 | |a Oscillations | |
| 650 | 4 | |a Équations différentielles stochastiques | |
| 650 | 4 | |a Noise | |
| 650 | 4 | |a Oscillations | |
| 650 | 4 | |a Statistical mechanics | |
| 650 | 4 | |a Stochastic differential equations | |
| 650 | 0 | 7 | |a Nichtlineare Schwingung |0 (DE-588)4042100-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
1. Deterministic and random oscillators 1
1.1 Simple harmonic oscillator............. . 1
1.2 Damped harmonic oscillator............. 2
1.3 Driven harmonic oscillator.............. 2
1.4 Driven, damped harmonic oscillator......... 3
1.5 Nonlinear oscillator in a double-well potential ... 3
1.6 Nonlinear oscillator in a single-well potential .... 4
1.7 Harmonic oscillator with external noise....... 4
1.8 Brownian motion ................... 4
1.9 Harmonic oscillator with random frequency..... 5
1.10 Harmonic oscillator with random damping..... 6
2. White and colored noise 7
2.1 Dichotomous noise................... 8
2.2 White Poisson noise.................. 9
2.3 Shot noise ....................... 9
3. Brownian motion 11
3.1 In the beginning...................... 11
3.2 Fokker-Planck equation................ 13
3.2.1 Additive white noise.............. 13
3.2.2 Multiplicative white noise........... 15
XI
xii The noisy oscillator: the first hundred years, from Einstein until now
3.2.3 Colored noise: unified colored noise
approximation (UCNA)............ 18
3.3 Brownian motion and anomalous diffusion ..... 19
3.4 Brownian motion near the critical point....... 21
4. Overdamped harmonic oscillator with additive noise 25
4.1 Additive white noise.................. 26
4.2 Additive noise and periodic force........... 27
5. Overdamped harmonic oscillator with multiplicative noise 29
5.1 Multiplicative noise (shift of stable points)..... 29
5.2 Multiplicative and additive noises.......... 30
5.2.1 Two white noises ............... 31
5.2.2 Two correlated white noises......... 31
5.2.3 Two color dichotomous correlated noises . . 32
5.3 Multiplicative color noise and periodic signal
(stochastic resonance (SR)).............. 33
5.4 Stochastic resonance in a overdamped system with
signal-modulated noise................ 37
6. Overdamped single-well oscillator 41
6.1 Steady state...................... 42
6.1.1 White noises.................. 42
6.1.2 Multiplicative noise (gene selection)..... 44
6.1.3 Dichotomous noise............... 45
6.1.4 Poisson white noise.............. 46
6.2 Response to a periodic force
(noise-enhanced stability)............... 47
6.3 Piece-wise model of a metastable state ....... 51
6.4 Rectangular potential barrier (stabilization of
metastable state) ................... 54
7. Overdamped double-well oscillator 63
7.1 Steady state...................... 64
7.1.1 White noise .................. 64
7.1.2 Dichotomous noise................ 66
Contents xiii
7.2 Eigenfunction expansion of the
Fokker-Planck equation................ 67
7.3 Matrix continued fraction method.......... 68
7.4 Mean first-passage time................ 71
7.5 Response to a periodic force
(stochastic resonance)................. 73
7.6 Fluctuating potential barrier
(resonance activation)................. 78
7.6.1 Piece-wise linear potential.......... 79
7.6.2 Phenomenological model........... 81
7.6.3 Coherent stochastic resonance........ 82
8. Harmonic oscillator with additive noise 83
8.1 Internal and external noise.............. 83
8.2 White and dichotomous noise............. 84
8.3 Additive noise and parametric oscillations...... 86
9. Nonlinear oscillator with additive noise 89
9.1 Statistical linearization................ 89
9.2 Double-well oscillator with additive noise...... 91
9.3 Double-well oscillator driven by two periodic fields
(vibrational resonance)................ 92
10. Harmonic oscillator with random frequency 97
10.1 First moment for the random frequency....... 97
10.1.1 Force-free oscillator.............. 97
10.1.2 White noise.................. 97
10.1.3 Colored noise.................. 97
10.2 Driven oscillator.................... 99
10.3 Second moment for a random frequency....... 102
10.4 Maxwell equation with random
dielectric constant................... 104
10.4.1 Driven Maxwell equation........... 107
11. Harmonic oscillator with random damping 109
11.1 First moment for random damping.......... 109
xiv The noisy oscillator: the first hundred years, from Einstein until now
11.1.1 Force-free oscillator..............109
11.1.2 Driven oscillator................112
11.2 Second moment for random damping........116
11.3 Force-free oscillator..................120
11.3.1 White noise ..................120
11.3.2 Dichotomous noise...............120
11.4 Driven oscillator....................120
11.5 Second moments....................121
11.6 Correlation functions.................122
11.7 Periodically varying damping.............123
12. Nonlinear oscillator with multiplicative noise 125
12.1 Double-well potential (noise induced reentrant
transition).......................125
12.2 Duffing oscillator....................129
12.3 Van der Pol oscillator.................130
13. In the future ... 133
Bibliography 135
Index 143
|
| any_adam_object | 1 |
| author | Gitterman, Moshe 1931- |
| author_GND | (DE-588)140080287 |
| author_facet | Gitterman, Moshe 1931- |
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| author_sort | Gitterman, Moshe 1931- |
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| building | Verbundindex |
| bvnumber | BV035846746 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.23 QC174.8 |
| callnumber-search | QA274.23 QC174.8 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)62877310 (DE-599)HBZHT015025743 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV035846746 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:01Z |
| institution | BVB |
| isbn | 9789812565129 9812565124 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018704928 |
| oclc_num | 62877310 |
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| owner_facet | DE-29T DE-384 DE-83 DE-91G DE-BY-TUM |
| physical | XIV, 144 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Gitterman, Moshe 1931- Verfasser (DE-588)140080287 aut The noisy oscillator the first hundred years, from Einstein until now Moshe Gitterman New Jersey [u.a.] World Scientific 2005 XIV, 144 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bruit Mécanique statistique Oscillations Équations différentielles stochastiques Noise Statistical mechanics Stochastic differential equations Nichtlineare Schwingung (DE-588)4042100-4 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Oszillator (DE-588)4132814-0 gnd rswk-swf Rauschen (DE-588)4048606-0 gnd rswk-swf Harmonische Schwingung (DE-588)4159123-9 gnd rswk-swf Rauschen (DE-588)4048606-0 s Oszillator (DE-588)4132814-0 s Stochastische Differentialgleichung (DE-588)4057621-8 s Harmonische Schwingung (DE-588)4159123-9 s Nichtlineare Schwingung (DE-588)4042100-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018704928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gitterman, Moshe 1931- The noisy oscillator the first hundred years, from Einstein until now Bruit Mécanique statistique Oscillations Équations différentielles stochastiques Noise Statistical mechanics Stochastic differential equations Nichtlineare Schwingung (DE-588)4042100-4 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Oszillator (DE-588)4132814-0 gnd Rauschen (DE-588)4048606-0 gnd Harmonische Schwingung (DE-588)4159123-9 gnd |
| subject_GND | (DE-588)4042100-4 (DE-588)4057621-8 (DE-588)4132814-0 (DE-588)4048606-0 (DE-588)4159123-9 |
| title | The noisy oscillator the first hundred years, from Einstein until now |
| title_auth | The noisy oscillator the first hundred years, from Einstein until now |
| title_exact_search | The noisy oscillator the first hundred years, from Einstein until now |
| title_full | The noisy oscillator the first hundred years, from Einstein until now Moshe Gitterman |
| title_fullStr | The noisy oscillator the first hundred years, from Einstein until now Moshe Gitterman |
| title_full_unstemmed | The noisy oscillator the first hundred years, from Einstein until now Moshe Gitterman |
| title_short | The noisy oscillator |
| title_sort | the noisy oscillator the first hundred years from einstein until now |
| title_sub | the first hundred years, from Einstein until now |
| topic | Bruit Mécanique statistique Oscillations Équations différentielles stochastiques Noise Statistical mechanics Stochastic differential equations Nichtlineare Schwingung (DE-588)4042100-4 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Oszillator (DE-588)4132814-0 gnd Rauschen (DE-588)4048606-0 gnd Harmonische Schwingung (DE-588)4159123-9 gnd |
| topic_facet | Bruit Mécanique statistique Oscillations Équations différentielles stochastiques Noise Statistical mechanics Stochastic differential equations Nichtlineare Schwingung Stochastische Differentialgleichung Oszillator Rauschen Harmonische Schwingung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018704928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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