Fluid Mixtures and Applications to Biological Systems

Chapter

Abstract

We apply the free energy principle to fluid systems, where the components react with each other. As example we treat the predator-prey system and cyclic reactions. We deal with the polymerization of actin filaments and with the general diffusion limit.

Keywords

Free Energy Actin Filament Momentum Equation Fractional Density Objective Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Wir möchten uns an dieser Stelle bei der DFG bedanken, die in den Sonderforschungsbereichen SBF123 “Stochastische Mathematische Modelle”, SFB72 “Approximation und Mathematische Optimierung”, SFB256 “Nichtlineare Partielle Differentialgleichungen” und SFB611 “Singuläre Phänomene und Skalierung in mathematischen Modellen” für eine ausgezeichnete Umgebung für Mathematiker gesorgt hat. Dies hat uns das systematische Forschen auf dem Gebiet der Partiellen Differentialgleichungen erst ermöglicht.

References

  1. 1.
    Alt, W.: Nonlinear hyperbolic systems of generalized Navier-Stokes type for interactive motion in biology. In: Hildebrandt, S., Karcher, H. (eds.) Geometric Analysis and Nonlinear Partial Differential Equations, pp. 431–461. Springer, Berlin/New York (2003)CrossRefGoogle Scholar
  2. 2.
    Alt, H.W.: The entropy principle for interfaces. Solids and fluids. Adv. Math. Sci. Appl. 19, 585–663 (2009)MathSciNetMATHGoogle Scholar
  3. 3.
    Alt, H.W., Alt, W.: Phase boundary dynamics: transition between ordered and disordered lipid monolayers. Interfaces Free Bound. 11, 1–36 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Alt, H.W., Witterstein, G.: Distributional equation in the limit of phase transition. Interfaces Free Bound. 13, 531–554 (2011)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Alt, H.W., Witterstein, G.: Free energy identity in the limit of phase transitions. Adv. Math. Sci. Appl. (2013, submitted)Google Scholar
  6. 6.
    Chatelain, C., Balois, T., Ciarletta, P., Ben Amar, M.: Emergence of microstructural patterns in skin cancer: a phase separation analysis in a binary mixture. New J. Phys. 13, 115013 (2011)CrossRefGoogle Scholar
  7. 7.
    de Groot, S.R., Mazur, P.: Non-Equilibrium Thermodynamics. North-Holland, Amsterdam (1962)Google Scholar
  8. 8.
    Metzler, W.: Dynamische Systeme in der Ökologie. Mathematische Modelle und Simulationen. Teubner, Stuttgart (1987) (In particular: Kap. 6 Räuber-Beute-Systeme)Google Scholar
  9. 9.
    Müller, I.: Thermodynamics of mixtures of non-viscous fluids (Chap.  6). In: Thermodynamics. Pitman, Boston (1985)Google Scholar
  10. 10.
    Rajagopal, K.R., Johnson, G., Massoudi, M.: Averaged Equations for an Isothermal, Developing Flow of a Fluid-Solid Mixture. DOE/PETC/TR-96/2 (Mar 1996)Google Scholar
  11. 11.
    Wikipedia: Lotka-Volterra equation. http://en.wikipedia.org/wiki/Lotka-Volterra_equation
  12. 12.
    Wittenfeld, A., Ryskin, A., Alt, W.: Modeling and simulation of lipid monolayers as surfactant in lung alveoli. This volume, pp. 171–189 (2013) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Zentrum für MathematikTechnische Universität MünchenGarchingGermany
  2. 2.Abteilung Theoretische Biologie, Institut für Zelluläre und Molekulare BotanikRheinische Friedrich-Wilhelms-Universität BonnBonnGermany

Personalised recommendations