Robert Finn
Equilibrium Capillary Surfaces
Robert Finn
Equilibrium Capillary Surfaces
- Gebundenes Buch
Produktdetails
- Grundlehren der mathematischen Wissenschaften Bd.284
- Verlag: Springer, Berlin
- 1986.
- Seitenzahl: 245
- Englisch
- Abmessung: 240mm
- Gewicht: 514g
- ISBN-13: 9783540961741
- ISBN-10: 3540961747
- Artikelnr.: 09232192
1 Introduction.- 1.1. Mean Curvature.- 1.2. Laplace's Equation.- 1.3. Angle of Contact.- 1.4. The Method of Gauss; Characterization of the Energies.- 1.5. Variational Considerations.- 1.6. The Equation and the Boundary Condition.- 1.7. Divergence Structure.- 1.8. The Problem as a Geometrical One.- 1.9. The Capillary Tube.- 1.10. Dimensional Considerations.- Notes to Chapter 1.- 2 The Symmetric Capillary Tube.- 2.1. Historical and General.- 2.2. The Narrow Tube; Center Height.- 2.3. The Narrow Tube; Outer Height.- 2.4. The Narrow Tube; Estimates Throughout the Trajectory.- 2.5. Height Estimates for Tubes of General Size.- 2.6. Meniscus Height; Narrow Tubes.- 2.7. Meniscus Height; General Case.- 2.8. Comparisons with Earlier Theories.- Notes to Chapter 2.- 3 The Symmetric Sessile Drop.- 3.1. The Correspondence Principle.- 3.2. Continuation Properties.- 3.3. Uniqueness and Existence.- 3.4. The Envelope.- 3.5. Comparison Theorems.- 3.6. Geometry of the Sessile Drop; Small Drops.- 3.7. Geometry of the Sessile Drop; Larger Drops.- Notes to Chapter 3.- 4 The Pendent Liquid Drop.- 4.1. Mise en Scène.- 4.2. Local Existence.- 4.3. Uniqueness.- 4.4. Global Behavior; General Remarks.- 4.5. Small u0 .- 4.6. Appearance of Vertical Points.- 4.7. Behavior for Large u0 .- 4.8. Global Behavior.- 4.9. Maximum Vertical Diameter.- 4.10. Maximum Diameter.- 4.11. Maximum Volume.- 4.12. Asymptotic Properties.- 4.13. The Singular Solution.- 4.14. Isolated Character of Global Solutions.- 4.15. Stability.- Notes to Chapter 4.- 5 Asymmetric Case; Comparison Principles and Applications.- 5.1. The General Comparison Principle.- 5.2. Applications.- 5.3. Domain Dependence.- 5.4. A Counterexample.- 5.5. Convexity.- Notes to Chapter 5.- 6 Capillary Surfaces Without Gravity.- 6.1. General Remarks.- 6.2. A Necessary Condition.- 6.3. Sufficiency Conditions.- 6.4. Sufficiency Conditions II.- 6.5. A Subsidiary Extremal Problem.- 6.6. Minimizing Sequences.- 6.7. The Limit Configuration.- 6.8. The FirstVariation.- 6.9. The Second Variation.- 6.10. Solution of the Jacobi Equation.- 6.11. Convex Domains.- 6.12. Continuous and Discontinuous Disappearance.- 6.13. An Example.- 6.14. Another Example.- 6.15. Remarks on the Extremals.- 6.16. Example 1.- 6.17. Example 2.- 6.18. Example 3.- 6.19. The Trapezoid.- 6.20. Tail Domains; A Counterexample.- 6.21. Convexity.- 6.22. A Counterexample.- 6.23. Transition to Zero Gravity.- Notes to Chapter 6.- 7 Existence Theorems.- 7.1. Choice of Venue.- 7.2. Variational Solutions.- 7.3. Generalized Solutions.- 7.4. Construction of a Generalized Solution.- 7.5. Proof of Boundedness.- 7.6. Uniqueness.- 7.7. The Variational Condition; Limiting Case.- 7.8. A Necessary and Sufficient Condition.- 7.9. A Limiting Configuration.- 7.10. The Case µ>µ0>1.- 7.11. Application: A General Gradient Bound.- Notes to Chapter 7.- 8 The Capillary Contact Angle.- 8.1. Everyday Experience.- 8.2. The Hypothesis.- 8.3. The Horizontal Plane; Preliminary Remarks.- 8.4. Necessityfor ?.- 8.5. Proof that ? is Monotone.- 8.6. Geometrically Imposed Stability Bounds.- 8.7. A Further Kind of Instability.- 8.8. The Inclined Plane; Preliminary Remarks.- 8.9. Integral Relations, and Impossibility of Constant Contact Angle.- 8.10. The Zero-Gravity Solution.- 8.11. Postulated Form for ?.- 8.12. Formal Analytical Solution.- 8.13. The Expansion; Leading Terms.- 8.14. Computer Calculations.- 8.15. Discussion.- 8.16. Further Discussion.- Notes to Chapter 8.- 9 Identities and Isoperimetric Relations.
1 Introduction.- 1.1. Mean Curvature.- 1.2. Laplace's Equation.- 1.3. Angle of Contact.- 1.4. The Method of Gauss; Characterization of the Energies.- 1.5. Variational Considerations.- 1.6. The Equation and the Boundary Condition.- 1.7. Divergence Structure.- 1.8. The Problem as a Geometrical One.- 1.9. The Capillary Tube.- 1.10. Dimensional Considerations.- Notes to Chapter 1.- 2 The Symmetric Capillary Tube.- 2.1. Historical and General.- 2.2. The Narrow Tube; Center Height.- 2.3. The Narrow Tube; Outer Height.- 2.4. The Narrow Tube; Estimates Throughout the Trajectory.- 2.5. Height Estimates for Tubes of General Size.- 2.6. Meniscus Height; Narrow Tubes.- 2.7. Meniscus Height; General Case.- 2.8. Comparisons with Earlier Theories.- Notes to Chapter 2.- 3 The Symmetric Sessile Drop.- 3.1. The Correspondence Principle.- 3.2. Continuation Properties.- 3.3. Uniqueness and Existence.- 3.4. The Envelope.- 3.5. Comparison Theorems.- 3.6. Geometry of the Sessile Drop; Small Drops.- 3.7. Geometry of the Sessile Drop; Larger Drops.- Notes to Chapter 3.- 4 The Pendent Liquid Drop.- 4.1. Mise en Scène.- 4.2. Local Existence.- 4.3. Uniqueness.- 4.4. Global Behavior; General Remarks.- 4.5. Small u0 .- 4.6. Appearance of Vertical Points.- 4.7. Behavior for Large u0 .- 4.8. Global Behavior.- 4.9. Maximum Vertical Diameter.- 4.10. Maximum Diameter.- 4.11. Maximum Volume.- 4.12. Asymptotic Properties.- 4.13. The Singular Solution.- 4.14. Isolated Character of Global Solutions.- 4.15. Stability.- Notes to Chapter 4.- 5 Asymmetric Case; Comparison Principles and Applications.- 5.1. The General Comparison Principle.- 5.2. Applications.- 5.3. Domain Dependence.- 5.4. A Counterexample.- 5.5. Convexity.- Notes to Chapter 5.- 6 Capillary Surfaces Without Gravity.- 6.1. General Remarks.- 6.2. A Necessary Condition.- 6.3. Sufficiency Conditions.- 6.4. Sufficiency Conditions II.- 6.5. A Subsidiary Extremal Problem.- 6.6. Minimizing Sequences.- 6.7. The Limit Configuration.- 6.8. The FirstVariation.- 6.9. The Second Variation.- 6.10. Solution of the Jacobi Equation.- 6.11. Convex Domains.- 6.12. Continuous and Discontinuous Disappearance.- 6.13. An Example.- 6.14. Another Example.- 6.15. Remarks on the Extremals.- 6.16. Example 1.- 6.17. Example 2.- 6.18. Example 3.- 6.19. The Trapezoid.- 6.20. Tail Domains; A Counterexample.- 6.21. Convexity.- 6.22. A Counterexample.- 6.23. Transition to Zero Gravity.- Notes to Chapter 6.- 7 Existence Theorems.- 7.1. Choice of Venue.- 7.2. Variational Solutions.- 7.3. Generalized Solutions.- 7.4. Construction of a Generalized Solution.- 7.5. Proof of Boundedness.- 7.6. Uniqueness.- 7.7. The Variational Condition; Limiting Case.- 7.8. A Necessary and Sufficient Condition.- 7.9. A Limiting Configuration.- 7.10. The Case µ>µ0>1.- 7.11. Application: A General Gradient Bound.- Notes to Chapter 7.- 8 The Capillary Contact Angle.- 8.1. Everyday Experience.- 8.2. The Hypothesis.- 8.3. The Horizontal Plane; Preliminary Remarks.- 8.4. Necessityfor ?.- 8.5. Proof that ? is Monotone.- 8.6. Geometrically Imposed Stability Bounds.- 8.7. A Further Kind of Instability.- 8.8. The Inclined Plane; Preliminary Remarks.- 8.9. Integral Relations, and Impossibility of Constant Contact Angle.- 8.10. The Zero-Gravity Solution.- 8.11. Postulated Form for ?.- 8.12. Formal Analytical Solution.- 8.13. The Expansion; Leading Terms.- 8.14. Computer Calculations.- 8.15. Discussion.- 8.16. Further Discussion.- Notes to Chapter 8.- 9 Identities and Isoperimetric Relations.