Kinetic equations of soft active matter

TitleKinetic equations of soft active matter
Publication TypeJournal Article
Year of Publication2014
AuthorsGerasimenko, VI, Fedchun, Yu.Yu.
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published5/2014

We construct a non-Markovian generalization of the kinetic equation for a system of interacting stochastic Markovian processes modeling the evolution of soft active matter. For such systems, we substantiate the kinetic equation in the mean field scaling limit and establish the property of the initial chaos to propagate in soft active matter.

Keywordsactivity, kinetic equations, soft matter

1. Marchetti M. C., Joanny J. F., Ramaswamy S. et al. Rev. Mod. Phys., 2013, 85: 1143–1195.
2. Bellouquid A., Delitala M. Mathematical modeling of complex biological systems: a kinetic theory approach. Boston: Birkhäuser, 2006.
3. Lachowicz M. Links between microscopic and macroscopic descriptions. In: Multiscale Problems in the Life Sciences. From Microscopic to Macroscopic. Berlin: Springer, 2008: 201–215.
4. Lachowicz M. Nonlinear Analysis: Real World Applications, 2011, 12: 2396–2408.
5. Gerasimenko V. I., Fedchun Yu. Yu. J. Coupled Syst. Multiscale Dyn., 2013, 1, No. 2: 273–279.
6. Gerasimenko V. I., Fedchun Yu. Yu. Proc. Inst. Math. NASU, 2012, 9, No. 2: 347–375.
7. Borgioli G., Gerasimenko V. I. Nuovo Cimento C., 2010, 33, No. 1: 71–78.
8. Cercignani C., Gerasimenko V. I., Petrina D. Ya. Many-particle dynamics and kinetic equations. Dordrecht: Kluwer, 1997.
9. Gerasimenko V. I., Tsvir Zh. A. A. J. Phys. A: Math. Theor., 2010, 43, No. 48: 485203.
10. Gerasimenko V. I., Tsvir Zh. A. Physica A: Stat. Mech. Appl., 2012, 391, No. 24: 6362–6366.