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Purcell's planar three-link microswimmer is a classic model of swimming in low-Reynolds-number fluid, inspired by motion of flagellated microorganisms. Many works analyzed this model, assuming that the two joint angles are directly…
Time optimal control problems for some non-smooth systems in general form are considered. The non-smoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus,…
The low-Reynolds-number Stokes flow driven by rotation of two parallel cylinders of equal unit radius is investigated by both analytical and numerical techniques. In Part I, the case of counter-rotating cylinders is considered. A numerical…
Interaction of motile microrganisms with a nearby solid substrate is a well studied phenomenon. However, the effects of hydrodynamic slippage on the substrate have received a little attention. In the present study, within the framework of…
Motivated by recent experiments on colloidal suspensions, we study analytically and numerically a microscopic model for self-propelled particles lacking alignment interactions. In this model, even for purely repulsive interactions, a…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
Wave turbulence is the study of the long-time statistical behaviour of equations describing a set of weakly non-linear interacting waves. Such a theory, which has a natural asymptotic closure, allows us to probe the nature of turbulence…
We present and analyze a theoretical model for the dynamics and interactions of "capillary surfers," which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. In our companion paper [1], we…
We investigate how dynamical decoupling methods may be used to manipulate the time evolution of quantum many-body systems. These methods consist of sequences of external control operations designed to induce a desired dynamics. The systems…
The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of…
This expository review is devoted to fish swimming and bird/insect flight. (i) The simple waving motion of an elongated flexible ribbon plate of constant width, immersed in a fluid at rest, propagating a wave distally down the plate to swim…
We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal…
Active matter has been the object of huge amount of research in recent years for its important fundamental and applicative properties. In this paper we investigate active suspensions of micro-swimmers through direct numerical simulation, so…
Conventionally, a microscopic particle that performs a reciprocal stroke cannot move through its environment. This is because at small scales, the response of simple Newtonian fluids is purely viscous and flows are time-reversible. We show…
We calculate the hydrodynamic force on a small spherical, unsteady squirmer moving with a time-dependent velocity in a fluid at rest, taking into account convective and unsteady fluid inertia effects in perturbation theory. Our results…
Turbulent flows, ubiquitous in nature and engineering, comprise fluctuations over a wide range of spatial and temporal scales. While flows with fluctuations in thermodynamic variables are much more common, much less is known about these…
A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…
An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium…
In this paper, the dynamics of nonholonomic systems on Lie groups with a left-invariant kinetic energy and left-invariant constraints are considered. Equations of motion form a closed system of differential equations on the corresponding…
Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…