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The Stability of Cylindrical Pendant Drops.
The author considers the stability of certain liquid drops in a gravity field satisfying a mixed boundary condition. He also considers as special cases portions of cylinders that model either the zero gravity case or soap films with the same kind of boundary behavior.
| Call Number: | Libro Electrónico |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Providence :
American Mathematical Society,
2018.
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| Series: | Memoirs of the American Mathematical Society.
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| Subjects: | |
| Online Access: | Texto completo |
Table of Contents:
- Cover; Title page; Introduction; Chapter 1. Normalization, stability condition, and elementary properties; 1.1. ODEs for Cylindrical Profiles; 1.2. Elementary Properties; 1.3. Proofs of Elementary Properties; Chapter 2. One Parameter Families; Definition of â#x82;#x82;; 2.1. Continuous families; 2.2. Enclosed volume/cross-sectional area; 2.3. Smooth families; profile arclength; 2.4. More on enclosed volume; 2.5. Further properties of drop profiles; Chapter 3. Stability; 3.1. Separation of Variables; 3.2. Decomposition; 3.3. Secondary variational problems and PDE results; 3.4. Initial Stability.
- 3.5. Geometric interpretation of (H)3.6. Geometric interpretation of (V); initial stable families; 3.7. A surprise; Chapter 4. Infinitely long drops; Chapter 5. Zero gravity and soap bubbles; Chapter 6. Open problems; Appendix 1: Explicit formulas; Appendix 2: Sturm-Liouville Theory; Appendix 3: Elliptic integrals; Acknowledgement; Bibliography; Back Cover.