Pattern formation in diffusion-limited crystal growth /:
This book reviews the current state of the theory of pattern formation by a liquid-solid interface during crystal growth. It gives a pedagogical introduction to the subject, including experimental results, mathematical modeling and linear stability analysis. After highlighting the success of the the...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
©1996.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book reviews the current state of the theory of pattern formation by a liquid-solid interface during crystal growth. It gives a pedagogical introduction to the subject, including experimental results, mathematical modeling and linear stability analysis. After highlighting the success of the theory in resolving the selection problem of dendritic growth, various new directions of research are presented in which progress has been made recently. These are the formation of nondendritic seaweed-like structures, growth of lamellar eutectics and rapid solidification. The interplay between analytic methods on the one hand (scaling arguments, asymptotic analysis, similarity equation, Sivashinsky singular expansion) and numerical calculations on the other (Newton method, dynamical schemes) is emphasized. |
| Beschreibung: | 1 online resource (viii, 258 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 247-258). |
| ISBN: | 9789812832023 9812832025 |
Internformat
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| 505 | 0 | |a 1. Introduction -- 2. Experiments and growth mechanisms. 2.1. Free versus directional growth. 2.2. Growth mechanisms -- 3. Semimicroscopic growth models. 3.1. Diffusion-limited aggregation. 3.2. Particle models for crystal growth -- 4. Macroscopic continuum models. 4.1. Defining equations. 4.2. Boundary integral equation. 4.3. Characteristic solutions and stability considerations -- 5. Numerical approach. 5.1. Discretization. 5.2. Dynamical code. 5.3. Stationary code -- 6. Selection problems. 6.1. Solvability theory. 6.2. Numerical evidence. 6.3. Experimental evidence and discussion -- 7. Analytic theory of morphology diagram -- 8. Lamellar eutectics. 8.1. The Jackson-Hunt theory. 8.2. Numerical results for axisymmetric growth -- comparison with the Jackson-Hunt theory. 8.3. Parity breaking. 8.4. Similarity equation. 8.5. Consequences of similarity -- scaling laws. 8.6. Anisotropy effects. 8.7. Coupling between phase dynamics and tilt angle -- 9. Liquid crystals. 9.1. Local description. 9.2. Characteristic solutions and stability considerations. 9.3. Small aspect ratio: transition to chaos. 9.4. Amplitude equations -- phase chaos. 9.5. Intermediate aspect ratios -- 10. Conclusions and outlook. | |
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| _version_ | 1816882231672569856 |
| adam_text | |
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| author | Kassner, Klaus |
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| contents | 1. Introduction -- 2. Experiments and growth mechanisms. 2.1. Free versus directional growth. 2.2. Growth mechanisms -- 3. Semimicroscopic growth models. 3.1. Diffusion-limited aggregation. 3.2. Particle models for crystal growth -- 4. Macroscopic continuum models. 4.1. Defining equations. 4.2. Boundary integral equation. 4.3. Characteristic solutions and stability considerations -- 5. Numerical approach. 5.1. Discretization. 5.2. Dynamical code. 5.3. Stationary code -- 6. Selection problems. 6.1. Solvability theory. 6.2. Numerical evidence. 6.3. Experimental evidence and discussion -- 7. Analytic theory of morphology diagram -- 8. Lamellar eutectics. 8.1. The Jackson-Hunt theory. 8.2. Numerical results for axisymmetric growth -- comparison with the Jackson-Hunt theory. 8.3. Parity breaking. 8.4. Similarity equation. 8.5. Consequences of similarity -- scaling laws. 8.6. Anisotropy effects. 8.7. Coupling between phase dynamics and tilt angle -- 9. Liquid crystals. 9.1. Local description. 9.2. Characteristic solutions and stability considerations. 9.3. Small aspect ratio: transition to chaos. 9.4. Amplitude equations -- phase chaos. 9.5. Intermediate aspect ratios -- 10. Conclusions and outlook. |
| ctrlnum | (OCoLC)841810482 |
| dewey-full | 548.5015118 |
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| dewey-ones | 548 - Crystallography |
| dewey-raw | 548.5015118 |
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| discipline | Chemie / Pharmazie Physik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn841810482 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:19Z |
| institution | BVB |
| isbn | 9789812832023 9812832025 |
| language | English |
| oclc_num | 841810482 |
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| spelling | Kassner, Klaus. Pattern formation in diffusion-limited crystal growth / Klaus Kassner. Singapore ; River Edge, NJ : World Scientific, ©1996. 1 online resource (viii, 258 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 247-258). Print version record. 1. Introduction -- 2. Experiments and growth mechanisms. 2.1. Free versus directional growth. 2.2. Growth mechanisms -- 3. Semimicroscopic growth models. 3.1. Diffusion-limited aggregation. 3.2. Particle models for crystal growth -- 4. Macroscopic continuum models. 4.1. Defining equations. 4.2. Boundary integral equation. 4.3. Characteristic solutions and stability considerations -- 5. Numerical approach. 5.1. Discretization. 5.2. Dynamical code. 5.3. Stationary code -- 6. Selection problems. 6.1. Solvability theory. 6.2. Numerical evidence. 6.3. Experimental evidence and discussion -- 7. Analytic theory of morphology diagram -- 8. Lamellar eutectics. 8.1. The Jackson-Hunt theory. 8.2. Numerical results for axisymmetric growth -- comparison with the Jackson-Hunt theory. 8.3. Parity breaking. 8.4. Similarity equation. 8.5. Consequences of similarity -- scaling laws. 8.6. Anisotropy effects. 8.7. Coupling between phase dynamics and tilt angle -- 9. Liquid crystals. 9.1. Local description. 9.2. Characteristic solutions and stability considerations. 9.3. Small aspect ratio: transition to chaos. 9.4. Amplitude equations -- phase chaos. 9.5. Intermediate aspect ratios -- 10. Conclusions and outlook. This book reviews the current state of the theory of pattern formation by a liquid-solid interface during crystal growth. It gives a pedagogical introduction to the subject, including experimental results, mathematical modeling and linear stability analysis. After highlighting the success of the theory in resolving the selection problem of dendritic growth, various new directions of research are presented in which progress has been made recently. These are the formation of nondendritic seaweed-like structures, growth of lamellar eutectics and rapid solidification. The interplay between analytic methods on the one hand (scaling arguments, asymptotic analysis, similarity equation, Sivashinsky singular expansion) and numerical calculations on the other (Newton method, dynamical schemes) is emphasized. Crystal growth Mathematical models. Pattern formation (Physical sciences) http://id.loc.gov/authorities/subjects/sh99003331 Cristaux Croissance Modèles mathématiques. Formation des structures (Sciences physiques) SCIENCE Physics Crystallography. bisacsh Crystal growth Mathematical models fast Pattern formation (Physical sciences) fast Kristallwachstum gnd http://d-nb.info/gnd/4123579-4 Musterbildung gnd http://d-nb.info/gnd/4137934-2 Kristalgroei. gtt Print version: Kassner, Klaus. Pattern formation in diffusion-limited crystal growth. Singapore ; River Edge, NJ : World Scientific, ©1996 9810215320 (DLC) 96210415 (OCoLC)35838059 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=565645 Volltext |
| spellingShingle | Kassner, Klaus Pattern formation in diffusion-limited crystal growth / 1. Introduction -- 2. Experiments and growth mechanisms. 2.1. Free versus directional growth. 2.2. Growth mechanisms -- 3. Semimicroscopic growth models. 3.1. Diffusion-limited aggregation. 3.2. Particle models for crystal growth -- 4. Macroscopic continuum models. 4.1. Defining equations. 4.2. Boundary integral equation. 4.3. Characteristic solutions and stability considerations -- 5. Numerical approach. 5.1. Discretization. 5.2. Dynamical code. 5.3. Stationary code -- 6. Selection problems. 6.1. Solvability theory. 6.2. Numerical evidence. 6.3. Experimental evidence and discussion -- 7. Analytic theory of morphology diagram -- 8. Lamellar eutectics. 8.1. The Jackson-Hunt theory. 8.2. Numerical results for axisymmetric growth -- comparison with the Jackson-Hunt theory. 8.3. Parity breaking. 8.4. Similarity equation. 8.5. Consequences of similarity -- scaling laws. 8.6. Anisotropy effects. 8.7. Coupling between phase dynamics and tilt angle -- 9. Liquid crystals. 9.1. Local description. 9.2. Characteristic solutions and stability considerations. 9.3. Small aspect ratio: transition to chaos. 9.4. Amplitude equations -- phase chaos. 9.5. Intermediate aspect ratios -- 10. Conclusions and outlook. Crystal growth Mathematical models. Pattern formation (Physical sciences) http://id.loc.gov/authorities/subjects/sh99003331 Cristaux Croissance Modèles mathématiques. Formation des structures (Sciences physiques) SCIENCE Physics Crystallography. bisacsh Crystal growth Mathematical models fast Pattern formation (Physical sciences) fast Kristallwachstum gnd http://d-nb.info/gnd/4123579-4 Musterbildung gnd http://d-nb.info/gnd/4137934-2 Kristalgroei. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh99003331 http://d-nb.info/gnd/4123579-4 http://d-nb.info/gnd/4137934-2 |
| title | Pattern formation in diffusion-limited crystal growth / |
| title_auth | Pattern formation in diffusion-limited crystal growth / |
| title_exact_search | Pattern formation in diffusion-limited crystal growth / |
| title_full | Pattern formation in diffusion-limited crystal growth / Klaus Kassner. |
| title_fullStr | Pattern formation in diffusion-limited crystal growth / Klaus Kassner. |
| title_full_unstemmed | Pattern formation in diffusion-limited crystal growth / Klaus Kassner. |
| title_short | Pattern formation in diffusion-limited crystal growth / |
| title_sort | pattern formation in diffusion limited crystal growth |
| topic | Crystal growth Mathematical models. Pattern formation (Physical sciences) http://id.loc.gov/authorities/subjects/sh99003331 Cristaux Croissance Modèles mathématiques. Formation des structures (Sciences physiques) SCIENCE Physics Crystallography. bisacsh Crystal growth Mathematical models fast Pattern formation (Physical sciences) fast Kristallwachstum gnd http://d-nb.info/gnd/4123579-4 Musterbildung gnd http://d-nb.info/gnd/4137934-2 Kristalgroei. gtt |
| topic_facet | Crystal growth Mathematical models. Pattern formation (Physical sciences) Cristaux Croissance Modèles mathématiques. Formation des structures (Sciences physiques) SCIENCE Physics Crystallography. Crystal growth Mathematical models Kristallwachstum Musterbildung Kristalgroei. |
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