# Active Biological Systems

**"Bifurcation of traveling waves in a Keller-Segel type free boundary model of cell motility”**(with J. Fuhrmann, V. Rybalko),*submitted,*(2017), pdf.**"Minimal Model of Directed Cell Motility on Patterned Substrates”**(with I. Aranson, M. Mizuhara),*submitted,*(2017), pdf.**"Flagella bending affects macroscopic properties of bacterial suspensions”**(with M. Potomkin, M. Tournus, and I. Aranson),*accepted to*__Journal of the Royal Society Interface__(2017), pdf.**"Effective rheological properties in semidilute bacterial suspensions"**(with M. Potomkin and S. D. Ryan),__Bulletin of Mathematical Biology__, 78(3), pp. 580-615 (2016), pdf.**"Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit"**(with M. Potomkin and V. Rybalko),__Comptes Rendus Mathematique__, 354(10), pp. 986-992 (2016), pdf.**"Sharp interface limit in a phase field model of cell motility”**(with V. Rybalko, M. Potomkin),*submitted*(2016), pdf.**"On an evolution equation in a cell motility model"**(with M.S. Mizuhara, V. Rybalko, L. Zhang),__Physica D__, 318-319, pp. 12-25 (2015), pdf.**"Flexibility of bacterial flagella in external shear results in complex swimming trajectories"**(with M. Tournus, A. Kirshtein, and I. Aranson),__Journal of the Royal Society Interface__12 (102) (2014), pdf.**"Collective dynamics in semidilute bacterial suspensions"**(with S.D. Ryan, A. Sokolov, I.S. Aranson),__New Journal of Physics__**15**105021 (2013), pdf.**"Effective viscosity of puller-like microswimmers: a renormalization approach"**(with S. Gluzman and D.A. Karpeev),__J. Royal Society Interface__**10**:89 (2013), pdf.**"A kinetic model for semi-dilute bacterial suspensions"**(with S.D. Ryan, B.M. Haines, D.A. Karpeev),__SIAM MMS__**11**:4, pp. 1176-1196 (2013), pdf.**"Collision of microswimmers in viscous fluid"**(with M. Potomkin, V. Gyrya, I. Aranson),__Physical Review E__**87**053005 (2013), pdf.**"Effective viscosity of bacterial suspensions: A three-dimensional PDE model with stochastic torque"**(with B.M. Haines, I.S. Aranson, D.A. Karpeev),__Comm. Pure Appl. Anal.__, v. 11(1), pp. 19-46 (2012), pdf.**"Viscosity of bacterial suspensions: Hydrodynamic interactions and self-induced noise"**(with S.D. Ryan, B.M. Haines, F. Ziebert, I.S. Aranson), Rapid Communication to__Phys. Rev. E__, 83 050904(R) (2011), pdf.**"Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations"**(with V. Gyrya, K. Lipnikov, I. Aranson),__J. Math. Biology__, v. 62 (5), pp. 707-740 (2011), pdf.**"A three-dimensional model for the effective viscosity of bacterial suspensions"**(with B.M. Haines, A. Sokolov, I.S. Aranson, D.A. Karpeev),__Physical Review E__, v. 80, pp.041922 (2009), pdf.**"A model of hydrodynamic interaction between swimming bacteria"**(with V.T. Gyrya, I.S. Aranson, D.A. Karpeev),__Bulletin of Mathematical Biology__v. 72, pp. 148-183 (2010), pdf.**"Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model"**(with B. Haines, I. Aronson, and D. Karpeev),__Physical Biology__, 5:4, 046003 (9pp) (2008), pdf.