arXiv subjects
Publications and source records attributed to M. Sano.
In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non-attainability of the constants in the inequalities are also proved.
The experimental application of fluctuation theorem (FT) on nanometer to submicrometer sized systems has received thorough attention in the past several years. Nonetheless, the employment of FT on self-propelling objects has seldom been performed due to experimental difficulties. In this paper, we applied FT on a doublet that is comprised of asymmetrically coated self-propelling colloidal particles (Janus particles), which experiences a continuous rotation by applying AC electric field. We found that FT is valid for rotating self-propelling colloids by evaluating the estimated rotary torque to coincide with another form of torque estimation, which considers the rotation speed of the doublet and a simple Stokes equation.
We investigate the dynamical coupling between the motion and the deformation of a single self-propelled domain based on two different model systems in two dimensions. One is represented by the set of ordinary differential equations for the center of gravity and two tensor variables characterizing deformations. The other is an active cell model which has an internal mechanism of motility and is represented by the partial differential equation for deformations. Numerical simulations show a rich variety of dynamics, some of which are common to the two model systems. The origin of the similarity and the difference is discussed.
Collective behavior of active elements inspired by mass of biological organisms is addressed. Especially, two topics are focused on among amazing behaviors performed by colony of ants. First, task allocation phenomena are treated from the viewpoint of proportion regulation of population between different states. Using a dynamical model consisting of elements and external ``stock materials'', adaptability against various disturbances is numerically studied. In addition, a dynamical model for a colony ants interacting via two kind of pheromones is studied, in which simulated ants, as a mass, are shown to make an efficient foraging flexibly varying the foraging tactics according to feeding schedules. Finally, experiments are performed with robots moving in virtual pheromone fields simulated by CG and CCD camera feedback system. Trail formation processes are demonstrated by this multi-robot system.
Using ultrasonic velocimetry we measured the vertical profile of the velocity fluctuation in high Rayleigh number thermal convection in a cell with aspect ratio of 0.5, filled with a low Prandtl number fluid, mercury. Intriguing fluctuating dynamics of the mean flow and universal nature of the kinetic energy cascade are elucidated utilizing spectral decomposition and reconstruction. Scaling properties of the structure functions and the energy spectrum are directly calculated without the use of Taylor's frozen-flow hypothesis for the first time. Despite the complex nature of the mean flow, it is found that the energy cascade process exhibits universal laws in thermal turbulence.