Dynamical theory of dendritic growth in convective flow /

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Bibliographic Details
Author / Creator:Xu, Jian-Jun, 1940-
Imprint:Boston : Kluwer Academic, c2004.
Description:xii, 240 p. : ill. ; 25 cm.
Language:English
Series:Advances in mechanics and mathematics ; v. 7
Subject:Crystalline interfaces.
Solid-liquid interfaces.
Liquid-liquid interfaces.
Dendritic crystals.
Crystal growth.
Fluid dynamics.
Pattern formation (Physical sciences)
Crystal growth.
Crystalline interfaces.
Dendritic crystals.
Fluid dynamics.
Liquid-liquid interfaces.
Pattern formation (Physical sciences)
Solid-liquid interfaces.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/5172017
Hidden Bibliographic Details
ISBN:1402079249 (hardback : acid-free paper)
1402079257 (e-book)
Notes:Includes bibliographical references (p. [235]-238) and index.
Table of Contents:
  • Preface
  • 1.. Introduction
  • 1. Interfacial Pattern Formations in Dendritic Growth
  • 2. Dendritic Growth Interacting with Convective Flow
  • 3. Mathematical Formulation of the General Problem
  • 3.1. Scaling
  • 3.2. Macroscopic Transport Equations
  • 3.3. Interface Conditions
  • 2.. Interfacial Wave Theory of Dendritic Growth with No Convection
  • 1. Steady State of Dendritic Growth with Zero Surface Tension--Ivantsov's Solution
  • 2. The Basic State for Dendritic Growth with Nonzero Surface Tension
  • 3. Regular Perturbation Expansion of Axi-symmetric, Basic State of Dendritic Growth
  • 3.1. O([epsilon superscript 0])
  • 3.2. O([epsilon superscript 2])
  • 3.3. The Asymptotic Behavior of the Regular Perturbation Expansion Solution as [xi] to [infinity]
  • 3.4. Some Numerical Results of the Interface Shape Correction
  • 4. Global Interfacial Wave Instability
  • 5. Three-Dimensional, Linear Perturbed States Around the Axi-symmetric Basic State of Dendritic Growth
  • 6. Outer Solution in the Outer Region away from the Singular Points
  • 6.1. Zeroth-Order Approximation
  • 6.2. First-Order Approximation
  • 6.3. Singular Point [xi subscript c] of the Outer Solution and Stokes Phenomenon
  • 7. The Inner Solutions near the Singular Point [xi subscript c]
  • 8. Tip Inner Solution in the Tip Region
  • 9. Global Trapped-Wave (GTW) Modes and the Quantization Condition
  • 10. The Comparison of Theoretical Predictions with Experimental Data
  • 3.. Steady Dendritic Growth from Melt with Convective Flow
  • 1. Mathematical Formulation of Problem with Navier-Stokes Model
  • 4.. Steady Viscous Flow Past a Paraboloid of Revolution
  • 1. Mathematical Formulation of the Problem
  • 2. The Oseen Model Problem
  • 2.1. Laguerre Series Representation of Solutions
  • 2.2. Solution of the Oseen Model and the Paradox
  • 2.3. The Solution of Type (I)
  • 2.4. The Solution of Type (II)
  • 2.5. The Paradox of Oseen Model Solutions and Its Resolution
  • 2.6. Appendix (A)
  • 2.6.1. The Properties of Laguerre Functions
  • 2.6.2. Important Formulas
  • 2.6.3. The derivation of the solution {{A[subscript n], B[subscript n]}} for (4.44)
  • 2.6.4. The Determination of the Functions: {{A[subscript n,k]([tau]), A[subscript n,k]([tau]), B[subscript n,k]([tau]), B[subscript n,k]([tau])}}
  • 3. Uniformly Valid Asymptotic Solution for Steady Viscous Flow past a Slender Paraboloid of Revolution
  • 3.1. Mathematical Formulation of the Problem
  • 3.2. Laguerre Series Representation of Solutions
  • 3.3. Outer Asymptotic Expansion Solution in the Limit Re to 0
  • 3.3.1. Zeroth-Order Solution of Velocity Field O(v[subscript 0]([epsilon subscript 0]))
  • 3.4. Inner Asymptotic Expansion of the Solution
  • 3.4.1. The Zeroth-Order Inner Solution
  • 3.5. Matching Conditions of the Solutions
  • 3.6. Skin Friction at the Surface of a Paraboloid
  • 3.7. Appendix (B)
  • 3.7.1. Asymptotic behavior of the outer solution [psi subscript 0] in the limit [tau] to 0
  • 3.7.2. Determination of the special outer solution [psi]*[subscript 0]
  • 5.. Asymptotic Solution of Dendritic Growth in External Flow (I)
  • 1. Mathematical Formulation of the Problem
  • 2. Laguerre Series Representation of Solutions
  • 3. Asymptotic Expansion Form of the Solution as [epsilon subscript 0] to 0
  • 3.1. Leading-Order Solutions of Flow Field
  • 3.2. Zeroth-Order Solution of Temperature Field O(1)
  • 3.3. First Order Solution of Temperature Field O([epsilon subscript 0])
  • 6.. Asymptotic Solution of Dendritic Growth in External Flow (II)
  • 1. Laguerre Series Representation of Solutions
  • 2. Asymptotic Expansion Forms of the Solution for the Flow Field
  • 2.1. Outer Expansion Form of the Solution
  • 2.2. Inner Expansion Form of the Solution
  • 3. Leading-Order Asymptotic Solutions of Flow Field
  • 3.1. Zeroth-Order Outer Solution of the Velocity Field
  • 3.2. First Sequence of Inner Solutions of the Velocity Field
  • 3.3. Second Sequence of Inner Solutions of the Velocity Field
  • 3.4. Matching Conditions for Leading-Order Solutions of the Flow Field
  • 4. Asymptotic Expansion Solution of the Temperature Field
  • 4.1. First Sequence of Solutions of the Temperature Field
  • 4.2. Second Sequence of Solutions of the Temperature Field
  • 5. A Brief Summary
  • 7.. Steady Dendritic Growth with Natural Convection (I)
  • 1. Mathematical Formulation of The Problem
  • 2. Laguerre Series Representation of Solutions
  • 3. Asymptotic Expansion Solution with Small Buoyancy Effect
  • 3.1. Zeroth-Order Solution of the Temperature Field O(1)
  • 3.2. Zeroth-Order Solution of the Velocity Field O([epsilon subscript 0])
  • 3.3. First-Order Solution of the Temperature Field O([epsilon subscript 0])
  • 4. Summary
  • 8.. Steady Dendritic Growth with Natural Convection (II)
  • 1. Laguerre Series Representation and Asymptotic Forms of Solutions
  • 1.1. Laguerre Series Representation of the Solution
  • 1.2. Outer Expansion Form of the Solution
  • 1.3. Inner Expansion Form of the Solution
  • 2. Leading-Order Asymptotic Expansion Solutions
  • 2.1. Leading-Order Asymptotic Expansion Solution of the Temperature Field
  • 2.2. Leading-Order Inner Solutions of the Velocity Field O([epsilon superscript 2 subscript 2])
  • 2.3. Leading-Order Outer Solutions of the Velocity Field O(v[subscript 0]([epsilon subscript 2]))
  • 2.4. Matching Conditions for the Leading Order Solutions of the Flow Field
  • 3. First-Order Asymptotic Expansion Solutions
  • 3.1. First-Order Asymptotic Solution for the Temperature Field
  • 4. Summary of the Results
  • 9.. Stability and Selection of Dendritic Growth with Convective Flow
  • 1. Basic Steady State Solution
  • 1.1. Convection Flow Field Induced by Uniform External Flow
  • 1.2. Convection Flow Field Induced by Buoyancy Effect
  • 1.3. Convection Motion Induced by Density Change During Phase Transition
  • 1.4. More General Steady State Solutions with Nearly Paraboloid Interface
  • 2. Linear Perturbed System around the Basic Steady State Solution
  • 3. Outer Expansion Solution
  • 3.1. Zeroth-Order Multiple Variables Expansion (MVE) Solutions
  • 3.2. First-Order Approximation
  • 4. Stability Criterion and Selection Condition of Tip Velocity
  • 5. Some Special Cases
  • 5.1. Convection Motion Induced by Uniform External Flow with Pr [double greater-than sign] 1
  • 5.2. Convection Motion Induced by Buoyancy Effect with Pr [double greater-than sign] 1
  • 5.3. Convection Motion Induced by Density Change During Phase Transition
  • 6. A Summary
  • 10.. Concluding Remark
  • References