粘弾性体中を遊泳するマイクロマシン

Microswimmers are tiny machines that swim in a fluid, such as sperm cells or motile bacteria, and they are expected to be applied to microfluidics and microsystems. By transforming chemical energy into mechanical work, microswimmers change their shape and move in viscous environments. Over the length scale of microswimmers, the fluid forces acting on them are governed by the effect of viscous dissipation. According to Purcell\u27s scallop theorem, time-reversal body motion cannot be used for locomotion in a Newtonian fluid. As one of the simplest models exhibiting broken time-reversal symmetry, Najafi and Golestanian proposed a three-sphere swimmer, in which three in-line spheres are linked by two arms of varying length. First, we discuss the locomotion of a three-sphere microswimmer in a viscoelastic medium and propose a new type of active microrheology. We derive a relation that connects the average swimming velocity and the frequency-dependent viscosity of the surrounding medium. In this relation, the viscous contribution can exist only when the time-reversal symmetry is broken, whereas the elastic contribution is present only when the structural symmetry of the swimmer is broken. Purcell\u27s scallop theorem breaks down for a three-sphere swimmer in a viscoelastic medium. Next, we discuss the dynamics of a generalized three-sphere microswimmer in which the spheres are connected by two elastic springs. The natural length of each spring is assumed to undergo a prescribed cyclic change. We analytically obtain the average swimming velocity as a function of the frequency of cyclic change in the natural length. In the low-frequency region, the swimming velocity increases with frequency, and its expression reduces to that of the original three-sphere model by Najafi and Golestanian. Conversely, in the high-frequency region, the average velocity decreases with increasing frequency. Such behavior originates from the intrinsic spring relaxation dynamics of an elastic swimmer moving in a viscous fluid. Finally, we discuss the directional motion of an elastic three-sphere micromachine in which the spheres are in equilibrium with independent heat baths having different temperatures. Even in the absence of prescribed motion of the springs, such a micromachine can gain a net motion due purely to thermal fluctuations. A relation connecting the average velocity and the temperatures of the spheres is analytically obtained. This velocity can also be expressed in terms of average heat flows in the steady state. Our model suggests a new mechanism for locomotion of micromachines in nonequilibrium biological systems.首都大学東京, 2018-03-25, 修士（理学）首都大学東

Most probable path of an active Brownian particle

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager--Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the $\ell$ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter

Localization and diffusion of tracer particles in viscoelastic media with active force dipoles

Optical tracking in vivo experiments reveal that diffusion of particles in biological cells is strongly enhanced in the presence of ATP and the experimental data for animal cells could previously be reproduced within a phenomenological model of a gel with myosin motors acting within it [EPL 110, 48005 (2015)]. Here, the two-fluid model of a gel is considered where active macromolecules, described as force dipoles, cyclically operate both in the elastic and the fluid components. Through coarse-graining, effective equations of motions for tracer particles displaying local deformations and local fluid flows are derived. The equation for deformation tracers coincides with the earlier phenomenological model and thus confirms it. For flow tracers, diffusion enhancement caused by active force dipoles in the fluid component, and thus due to metabolic activity, is found. The latter effect may explain why ATP-dependent diffusion enhancement could also be observed in bacteria that lack molecular motors in their skeleton or when the activity of myosin motors was chemically inhibited