TY  - BOOK
AU  - Kassner,Klaus
TI  - Pattern formation in diffusion-limited crystal growth
SN  - 9789812832023
AV  - QD921 .K34 1996eb
U1  - 548.5015118 22
PY  - 1996///
CY  - Singapore, River Edge, NJ
PB  - World Scientific
KW  - Crystal growth
KW  - Mathematical models
KW  - Pattern formation (Physical sciences)
KW  - Cristaux
KW  - Croissance
KW  - Modèles mathématiques
KW  - Formation des structures (Sciences physiques)
KW  - SCIENCE
KW  - Physics
KW  - Crystallography
KW  - bisacsh
KW  - fast
KW  - Kristallwachstum
KW  - gnd
KW  - Musterbildung
KW  - Kristalgroei
KW  - gtt
KW  - Electronic books
N1  - Includes bibliographical references (pages 247-258); 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
N2  - 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
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=565645
ER  -