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The Stability of Cylindrical Pendant Drops.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2018Copyright date: ©2017Edition: 1st edDescription: 1 online resource (122 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470442026
Subject(s): Genre/Form: Additional physical formats: Print version:: The Stability of Cylindrical Pendant DropsDDC classification:
  • 530.4/27
LOC classification:
  • QC156 .M338 2017
Online resources:
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 ₂ -- 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.
Summary: 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.
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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 ₂ -- 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.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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