Interfacial wave theory of pattern formation: selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1998
|
| Series: | Springer series in synergetics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 296 S. Ill., graph. Darst. |
| ISBN: | 3540631453 |
Staff View
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| 245 | 1 | 0 | |a Interfacial wave theory of pattern formation |b selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables |c Jian-Jun Xu |
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Record in the Search Index
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| adam_text | JIAN-JUN XU INTERFACIAL WAVE THEORY OF PATTERN FORMATION SELECTION OF
DENDRITIC GROWTH AND VISCOUS FINGERING IN HELE-SHAW FLOW WITH 83 FIGURES
AND 11 TABLES SPRINGER TABLE OF CONTENTS 1. INTRODUCTION . . . 1 1.1
INTERFACIAL PATTERN FORMATIONS IN DENDRITE GROWTH AND HELE-SHAW FLOW 1
1.2 A BRIEF REVIEW OF THE THEORIES OF FREE DENDRITE GROWTH 9 1.2.1
MAXIMUM VELOCITY PRINCIPLE (1976) 9 1.2.2 MARGINAL STABILITY HYPOTHESIS
(1978) 10 1.2.3 MICROSCOPIC SOLVABILITY CONDITION (MSC) THEORY
(1986-1990S) 11 1.2.4 INTERFACIAL WAVE (IFW) THEORY (1990) 12 1.3
MACROSCOPIC CONTINUUM MODEL 13 1.3.1 MACROSCOPIC TRANSPORT EQUATIONS 14
1.3.2 THE INTERFACE CONDITIONS 16 1.3.3 THE SCALING AND THE
DIMENSIONLESS SYSTEM 21 REFERENCES 24 2. UNIDIRECTIONAL SOLIDIFICATION
AND THE MULLINS-SEKERKA INSTABILITY. 27 2.1 SOLIDIFICATION WITH PLANAR
INTERFACE FROM A PURE MELT 27 2.1.1 BASIC STEADY STATE SOLUTION 28 2.1.2
UNSTEADY PERTURBED SOLUTIONS AND MULLINS-SEKERKA; INSTABILITY 29 2.1.3
ASYMPTOTIC SOLUTIONS IN THE LONG-WAVELENGTH REGIME, K = O(E) 38 2.1.4
ASYMPTOTIC SOLUTIONS IN THE EXTREMELY SHORT-WAVELENGTH REGIME, K = O(^)
42 2.2 UNIDIRECTIONAL SOLIDIFICATION FROM A BINARY MIXTURE 48 2.2.1
MATHEMATICAL FORMULATION OF THE PROBLEM 48 2.2.2 BASIC STEADY STATE 50
2.2.3 UNSTEADY PERTURBED SOLUTIONS 52 2.2.4 ASYMPTOTIC SOLUTIONS IN THE
LONG-WAVELENGTH REGIME, K = O(E) 60 2.2.5 ASYMPTOTIC SOLUTIONS IN THE
EXTREMELY SHORT-WAVELENGTH REGIME, {K = O( ); G = O(J)} 62 2.2.6 SOME
REMARKS ON UNIDIRECTIONAL SOLIDIFICATION 66 REFERENCES : 67 X TABLE OF
CONTENTS 3. MATHEMATICAL FORMULATION OF FREE DENDRITE GROWTH FROM A PURE
MELT 69 3.1 THREE-DIMENSIONAL AXIALLY SYMMETRIC FREE DENDRITE GROWTH 70
3.2 TWO-DIMENSIONAL FREE DENDRITE GROWTH 75 REFERENCE 78 4. STEADY STATE
OF DENDRITE GROWTH WITH ZERO SURFACE TENSION AND ITS REGULAR
PERTURBATION EXPANSION 79 4.1 THE IVANTSOV SOLUTION AND UNSOLVED
FUNDAMENTAL PROBLEMS . 79 4.2 THREE-DIMENSIONAL AXIALLY SYMMETRIC STEADY
NEEDLE GROWTH 81 4.2.1 MATHEMATICAL FORMULATION 81 4.2.2 THE REGULAR
PERTURBATION EXPANSION SOLUTIONS (RPE) AS - 0 82 4.2.3 THE ASYMPTOTIC
BEHAVIOR OF THE REGULAR PERTURBATION EXPANSION SOLUTION AS * OO 92
4.3 TWO-DIMENSIONAL, STEADY NEEDLE CRYSTAL GROWTH 94 4.3.1 MATHEMATICAL
FORMULATION OF TWO-DIMENSIONAL NEEDLE GROWTH 94 4.3.2 THE REGULAR
PERTURBATION EXPANSION SOLUTION AS E - 0 95 4.3.3 ASYMPTOTIC BEHAVIOR
OF THE REGULAR PERTURBATION EXPANSION SOLUTION AS * » OO 100 4.4
SUMMARY AND DISCUSSION 101 REFERENCES 103 5. THE STEADY STATE FOR
DENDRITE GROWTH WITH NONZERO SURFACE TENSION 105 5.1 THE NASH-GLICKSMAN
PROBLEM AND THE CLASSIC NEEDLE CRYSTAL SOLUTION 105 5.2 THE GEOMETRIC
MODEL AND SOLUTIONS OF THE NEEDLE CRYSTAL FORMATION PROBLEM 108 5.2.1
GEOMETRIC MODEL OF DENDRITE GROWTH 108 5.2.2 THE SEGUR-KRUSKAL PROBLEM
109 5.2.3 NONCLASSIC STEADY NEEDLE GROWTH PROBLEM ILL 5.2.4 NEEDLE
CRYSTAL FORMATION PROBLEM 118 5.3 THE NONCLASSIC STEADY STATE OF
DENDRITIC GROWTH WITH NONZERO SURFACE TENSION 120 5.3.1 THE COMPLETE
MATHEMATICAL FORMULATION FOR FREE DENDRITE GROWTH 120 REFERENCES 123 6.
GLOBAL INTERFACIAL WAVE INSTABILITY OF DENDRITE GROWTH FROM A PURE MELT
125 6.1 LINEAR PERTURBED SYSTEM AROUND THE BASIC STATE OF
THREE-DIMENSIONAL DENDRITE GROWTH 126 TABLE OF CONTENTS XI 6.2 OUTER
SOLUTION IN THE OUTER REGION AWAY FROM THE TIP 128 6.2.1 ZEROTH-ORDER
APPROXIMATION , 131 6.2.2 FIRST-ORDER APPROXIMATION 134 6.2.3 SINGULAR
POINT C OF THE OUTER SOLUTION 138 6.3 THE INNER SOLUTIONS NEAR THE
SINGULAR POINT C 142 6.4 TIP INNER SOLUTION IN THE TIP REGION 152 6.5
GLOBAL TRAPPED-WAVE MODES AND THE QUANTIZATION CONDITION 154 6.6 GLOBAL
INTERFACIAL WAVE INSTABILITY OF TWO-DIMENSIONAL DENDRITE GROWTH 161 6.7
THE COMPARISON OF THEORETICAL PREDICTIONS WITH EXPERIMENTAL DATA 172
REFERENCES 179 7. THE EFFECT OF SURFACE TENSION ANISOTROPY AND
LOW-FREQUENCY INSTABILITY ON DENDRITE GROWTH 181 7.1 LINEAR PERTURBED
SYSTEM AROUND THE BASIC STATE 183 7.2 MULTIPLE VARIABLE EXPANSION
SOLUTION IN THE OUTER REGION ... 184 7.3 THE INNER EQUATION NEAR THE
SINGULAR POINT C 187 7.3.1 CASE I: A 0 = O(L) 191 7.3.2 CASE II: | O |
1 192 7.3.3 A BRIEF SUMMARY 195 7.4 MATCHING CONDITIONS 197 7.5 THE
SPECTRA OF EIGENVALUES AND INSTABILITY MECHANISMS 197 7.5.1 THE GLOBAL
TRAPPED-WAVE INSTABILITY ....:* 198 7.5.2 THE LOW-FREQUENCY INSTABILITY
204 7.6 LOW-FREQUENCY.INSTABILITY FOR AXIALLY SYMMETRIC DENDRITE GROWTH
208 7.7 THE SELECTION CONDITIONS FOR DENDRITE GROWTH 209 REFERENCES 212
8. THREE-DIMENSIONAL DENDRITE GROWTH FROM BINARY MIXTURES 213 8.1
MATHEMATICAL FORMULATION OF THE PROBLEM 214 8.2 BASIC STATE SOLUTION FOR
THE CASE OF ZERO SURFACE TENSION.... 215 8.3 LINEAR PERTURBED SYSTEM FOR
THE CASE OF NONZERO SURFACE TENSION 216 8.4 THE MVE SOLUTIONS IN THE
OUTER REGION 220 8.4.1 THE ZEROTH-ORDER APPROXIMATION 220 8.4.2 THE
FIRST-ORDER APPROXIMATION 222 8.5 THE INNER SOLUTIONS NEAR THE SINGULAR
POINT C 226 8.6 GLOBAL MODES AND THE QUANTIZATION CONDITION 229 8.7
COMPARISONS OF THEORETICAL RESULTS WITH EXPERIMENTAL DATA . 238
REFERENCES 241 XII TABLE OF CONTENTS 9. VISCOUS FINGERING IN A HELE-SHAW
CELL 243 9.1 INTRODUCTION 243 9.2 MATHEMATICAL FORMULATION OF THE
PROBLEM 249 9.3 THE SMOOTH FINGER SOLUTION WITH ZERO SURFACE TENSION 251
9.4 FORMULATION OF THE GENERAL PROBLEM IN CURVILINEAR COORDINATES (,
77) AND THE BASIC STATE SOLUTIONS 254 9.5 THE LINEAR PERTURBED SYSTEM
AND THE OUTER SOLUTIONS 257 9.6 THE INNER EQUATION NEAR THE SINGULAR
POINT C 265 9.6.1 CASE I: A O =0(1) 269 9.6.2 CASE II: A Q 1
270 9.7 EIGENVALUES SPECTRA AND INSTABILITY MECHANISMS 272 9.7.1 THE
SPECTRUM OF COMPLEX EIGENVALUES AND GTW INSTABILITY 273 9.7.2 THE
SPECTRUM OF REAL EIGENVALUES AND THE LF INSTABILITY 276 9.8 FINGERING
FLOW WITH A NOSE BUBBLE 280 9.8.1 THE BASIC STATE OF FINGER FORMATION
WITH A NOSE BUBBLE AND ITS LINEAR PERTURBATION 280 9.8.2 THE
QUANTIZATION CONDITIONS FOR THE SYSTEM WITH A NOSE BUBBLE 283 9.9 THE
SELECTION CRITERIA OF FINGER SOLUTIONS 287 REFERENCES 289 BIBLIOGRAPHY
291 INDEX 293
|
| any_adam_object | 1 |
| author | Xu, Jian-Jun |
| author_facet | Xu, Jian-Jun |
| author_role | aut |
| author_sort | Xu, Jian-Jun |
| author_variant | j j x jjx |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.417 |
| dewey-search | 530.417 |
| dewey-sort | 3530.417 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:09:16Z |
| institution | BVB |
| isbn | 3540631453 |
| language | German |
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| physical | XII, 296 S. Ill., graph. Darst. |
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| spelling | Xu, Jian-Jun Verfasser aut Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables Jian-Jun Xu Berlin [u.a.] Springer 1998 XII, 296 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics Dendritische Struktur (DE-588)4313407-5 gnd rswk-swf Musterbildung (DE-588)4137934-2 gnd rswk-swf Dendritische Kristallisation (DE-588)4149070-8 gnd rswk-swf Kristallwachstum (DE-588)4123579-4 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Hele-Shaw-Strömung (DE-588)4485695-7 gnd rswk-swf Grenzfläche (DE-588)4021991-4 gnd rswk-swf Kristallwachstum (DE-588)4123579-4 s Dendritische Struktur (DE-588)4313407-5 s Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Grenzfläche (DE-588)4021991-4 s Musterbildung (DE-588)4137934-2 s Dendritische Kristallisation (DE-588)4149070-8 s Hele-Shaw-Strömung (DE-588)4485695-7 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007670256&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xu, Jian-Jun Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables Dendritische Struktur (DE-588)4313407-5 gnd Musterbildung (DE-588)4137934-2 gnd Dendritische Kristallisation (DE-588)4149070-8 gnd Kristallwachstum (DE-588)4123579-4 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Hele-Shaw-Strömung (DE-588)4485695-7 gnd Grenzfläche (DE-588)4021991-4 gnd |
| subject_GND | (DE-588)4313407-5 (DE-588)4137934-2 (DE-588)4149070-8 (DE-588)4123579-4 (DE-588)4126141-0 (DE-588)4485695-7 (DE-588)4021991-4 |
| title | Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables |
| title_auth | Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables |
| title_exact_search | Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables |
| title_full | Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables Jian-Jun Xu |
| title_fullStr | Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables Jian-Jun Xu |
| title_full_unstemmed | Interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables Jian-Jun Xu |
| title_short | Interfacial wave theory of pattern formation |
| title_sort | interfacial wave theory of pattern formation selection of dentritic growth and viscous fingerings in hele shaw flow with 11 tables |
| title_sub | selection of dentritic growth and viscous fingerings in Hele-Shaw flow ; with 11 tables |
| topic | Dendritische Struktur (DE-588)4313407-5 gnd Musterbildung (DE-588)4137934-2 gnd Dendritische Kristallisation (DE-588)4149070-8 gnd Kristallwachstum (DE-588)4123579-4 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Hele-Shaw-Strömung (DE-588)4485695-7 gnd Grenzfläche (DE-588)4021991-4 gnd |
| topic_facet | Dendritische Struktur Musterbildung Dendritische Kristallisation Kristallwachstum Nichtlineare Dynamik Hele-Shaw-Strömung Grenzfläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007670256&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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