Kinetic equations of soft active matter

1Gerasimenko, VI
2Fedchun, Yu.Yu.
1Institute of Mathematics of the NAS of Ukraine, Kyiv
2Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2014, 5:11-18
https://doi.org/10.15407/dopovidi2014.05.011
Section: Mathematics
Language: Ukrainian
Abstract: 

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.

Keywords: activity, kinetic equations, soft matter
References: 

1. Marchetti M. C., Joanny J. F., Ramaswamy S. et al. Rev. Mod. Phys., 2013, 85: 1143–1195. https://doi.org/10.1103/RevModPhys.85.1143
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. https://doi.org/10.1007/978-3-540-78362-6_4
4. Lachowicz M. Nonlinear Analysis: Real World Applications, 2011, 12: 2396–2408. https://doi.org/10.1016/j.nonrwa.2011.02.014
5. Gerasimenko V. I., Fedchun Yu. Yu. J. Coupled Syst. Multiscale Dyn., 2013, 1, No. 2: 273–279. https://doi.org/10.1166/jcsmd.2013.1018
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. https://doi.org/10.1007/978-94-011-5558-8
9. Gerasimenko V. I., Tsvir Zh. A. A. J. Phys. A: Math. Theor., 2010, 43, No. 48: 485203. https://doi.org/10.1088/1751-8113/43/48/485203
10. Gerasimenko V. I., Tsvir Zh. A. Physica A: Stat. Mech. Appl., 2012, 391, No. 24: 6362–6366. https://doi.org/10.1016/j.physa.2012.07.061