D. A. Karpeev

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We derive the effective viscosity of dilute suspensions of swimming bacteria from the microscopic details of the interaction of an elongated body with the background flow. An individual bacterium propels itself forward by rotating its flagella and reorients itself randomly by tumbling. Due to the bacterium's asymmetric shape, interactions with a prescribed(More)
Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this,(More)
We present a PDE model for dilute suspensions of swimming bacteria in a three-dimensional Stokesian fluid. This model is used to calculate the statistically-stationary bulk deviatoric stress and effective viscosity of the suspension from the microscopic details of the interaction of an elongated body with the background flow. A bacterium is modeled as an(More)
Suspensions of self-propelled microscopic particles, such as swimming bacteria, exhibit collective motion leading to remarkable experimentally-observable macroscopic properties. Rigorous mathematical analysis of this emergent behavior can provide significant insight into the mechanisms behind these experimental observations; however, there are many(More)
We propose and study a model of molecular motor-induced ordering in a cytoskeletal filament solution for the semidilute case. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. In the semidilute regime multiple motors can bind a filament to several others and, for a critical motor density, induce a transition(More)
Effective viscosity (EV) of suspensions of puller-like microswimmers (pullers), for example Chlamydamonas algae, is difficult to measure or simulate for all swimmer concentrations. Although there are good reasons to expect that the EV of pullers is similar to that of passive suspensions, analytical determination of the passive EV for all concentrations(More)
This paper summarizes the results of numerical simulations of the interaction of a pair of biofilaments mediated by a molecular motor. The filaments are modeled as flexible rods, and the results are applicable to microtubules, which are relatively stiff, as well as to much softer filaments, such as actin. The results provide insight into the effects of(More)
We use a probabilistic model of microtubule interaction via molecular motors to study microtubule bundle interaction. Our model indicates that initially disordered systems of interacting polar rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and(More)
We study the dynamics and interaction of two swimming bacteria, modeled by self-propelled dumbbell-type structures. We focus on alignment dynamics of a coplanar pair of elongated swimmers, which propel themselves either by "pushing" or "pulling" both in three- and quasi-two-dimensional geometries of space. We derive asymptotic expressions for the dynamics(More)
E ective viscosity (EV) of suspensions of puller-like microswimmers (pullers), such as the Chlamydamonas algae, is di cult to measure or to simulate for all swimmer concentrations. Although there are good reasons to expect that the EV of pullers is similar to that of passive suspensions, analytic determination of the passive EV for all concentrations(More)