American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 862-867. doi: 10.3934/proc.2005.2005.862

Comments on radially symmetric liquid bridges with inflected profiles

Thomas I. Vogel 1,

1. 

Department of Mathematics, Texas A&M University, College Station, TX 77843, United States

Received  September 2004 Revised  February 2005 Published  September 2005

For a liquid bridge between parallel planes which makes equal contact angles with those planes, it is already known that a pitchfork bifurcation occurs when there is an inflection in the profile curve. A geometrical argument is outlined to give an alternate and more elementary proof of this fact. In contrast to the behavior of liquid bridges between parallel planes, it is shown that a liquid bridge between spheres exists which is stable and has two inflections. Along the way, a result relating stability and \(dH/dV\) for a family of capillary surfaces is established.
Keywords: stability, inflections., capillarity.
Mathematics Subject Classification: Primary: 53A10, 49Q1.
Citation: Thomas I. Vogel. Comments on radially symmetric liquid bridges with inflected profiles. Conference Publications, 2005, 2005 (Special) : 862-867. doi: 10.3934/proc.2005.2005.862
[1]

Franco Obersnel, Pierpaolo Omari. Multiple bounded variation solutions of a capillarity problem. Conference Publications, 2011, 2011 (Special) : 1129-1137. doi: 10.3934/proc.2011.2011.1129
[2]

Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra. Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks & Heterogeneous Media, 2013, 8 (4) : 969-984. doi: 10.3934/nhm.2013.8.969
[3]

Franco Obersnel, Pierpaolo Omari. Existence, regularity and boundary behaviour of bounded variation solutions of a one-dimensional capillarity equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 305-320. doi: 10.3934/dcds.2013.33.305
[4]

Jin Lai, Huanyao Wen, Lei Yao. Vanishing capillarity limit of the non-conservative compressible two-fluid model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1361-1392. doi: 10.3934/dcdsb.2017066
[5]

Bettina Klaus, Frédéric Payot. Paths to stability in the assignment problem. Journal of Dynamics & Games, 2015, 2 (3&4) : 257-287. doi: 10.3934/jdg.2015004
[6]

Jan Boman, Vladimir Sharafutdinov. Stability estimates in tensor tomography. Inverse Problems & Imaging, 2018, 12 (5) : 1245-1262. doi: 10.3934/ipi.2018052
[7]

Ramon Quintanilla, Reinhard Racke. Stability in thermoelasticity of type III. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 383-400. doi: 10.3934/dcdsb.2003.3.383
[8]

Guillaume Bal, Olivier Pinaud, Lenya Ryzhik. On the stability of some imaging functionals. Inverse Problems & Imaging, 2016, 10 (3) : 585-616. doi: 10.3934/ipi.2016013
[9]

Luis D'Alto, Martin Corless. Incremental quadratic stability. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 175-201. doi: 10.3934/naco.2013.3.175
[10]

Jinpeng An. Hölder stability of diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 315-329. doi: 10.3934/dcds.2009.24.315
[11]

Andrey V. Kremnev, Alexander S. Kuleshov. Nonlinear dynamics and stability of the skateboard. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 85-103. doi: 10.3934/dcdss.2010.3.85
[12]

Siniša Slijepčević. Stability of invariant measures. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1345-1363. doi: 10.3934/dcds.2009.24.1345
[13]

Jean Lerbet, Noël Challamel, François Nicot, Félix Darve. Kinematical structural stability. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 529-536. doi: 10.3934/dcdss.2016010
[14]

Yanfang Li, Zhuangyi Liu, Yang Wang. Weak stability of a laminated beam. Mathematical Control & Related Fields, 2018, 8 (3&4) : 789-808. doi: 10.3934/mcrf.2018035
[15]

E. Cabral Balreira, Saber Elaydi, Rafael Luís. Local stability implies global stability for the planar Ricker competition model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 323-351. doi: 10.3934/dcdsb.2014.19.323
[16]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655
[17]

Frédéric Mazenc, Michael Malisoff, Patrick D. Leenheer. On the stability of periodic solutions in the perturbed chemostat. Mathematical Biosciences & Engineering, 2007, 4 (2) : 319-338. doi: 10.3934/mbe.2007.4.319
[18]

Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure & Applied Analysis, 2006, 5 (3) : 515-528. doi: 10.3934/cpaa.2006.5.515
[19]

Carlos Arnoldo Morales, M. J. Pacifico. Lyapunov stability of $\omega$-limit sets. Discrete & Continuous Dynamical Systems - A, 2002, 8 (3) : 671-674. doi: 10.3934/dcds.2002.8.671
[20]

PaweŁ Hitczenko, Georgi S. Medvedev. Stability of equilibria of randomly perturbed maps. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 369-381. doi: 10.3934/dcdsb.2017017

 Impact Factor: 

Tools

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences