Yumino Hayase

Surface switching of rotating fluid in a cylinder

We study the surface shape of water in an open cylinder driven by constant rotation of the bottom. Around the critical Reynolds number for the laminar-turbulent transition, the surface deformation, which is of the order of the container size, shows an aperiodic switching phenomenon between an axisymmetric shape and a nonaxisymmetric shape. The axisymmetric shape is observed as a steady state when the Reynolds number is smaller than that in the switching region, while the nonaxisymmetric shape is observed as a (quasi-) periodic state in which the surface rotates at almost constant angular velocity when the Reynolds number is larger than that in the switching region. A detailed analysis for the surface shape suggests that the flow with the nonaxisymmetric shape is turbulent.

Collision and Self-Replication of Pulses in a Reaction Diffusion System

We study numerically, the collision and self-replication of pulses in a reaction-diffusion system of the activator-inhibitor type. We established the following new properties of pulse dynamics. Two propagating pulses result in a localized oscillatory domain after a head-on collision. However this domain is a transient one and disappears after one period leaving new pulses propagating outward. In another parameter regime, a traveling pulse breaks into a pair of pulses propagating in opposite directions.

Self-organized pulse generator

Abstract Numerical simulations of a reaction diffusion system of the Bonhoeffer-van der Pol type will be presented. The system admits a coesistence of a stable stationary solution and a stable limit cycle, which leads to the generation of a self-organized pulse generator. Pattern dynamics of the system are explored in one and two dimensional spaces.

OSCILLATING LOCALIZED STRUCTURES IN REACTION–DIFFUSION SYSTEMS

Oscillating localized structures are studied for a simple reaction–diffusion model from an analytical point of view. The result is a particle solution which acts as a source of traveling waves. The analytical expressions obtained are in good agreement with direct numerical simulations.

Lattice model of sweeping interface for drying process in water-granule mixture

Based on the invasion percolation model, a lattice model for the sweeping interface dynamics is constructed to describe the pattern forming process by a sweeping interface upon drying the water–granule mixture. The model is shown to produce labyrinthine patterns, that are highly branched without any loop structure in clusters as those found in the experiment [Yamazaki and Mizuguchi: J. Phys. Soc. Jpn. 69 (2000) 2387]. Resulting patterns undergo the percolation transition upon changing the initial granular density, but estimated critical exponents are different from those of the conventional percolation. Loopless structure of clusters in the patterns produced by the sweeping dynamics seems to influence the nature of the transition.

Phase field model for dynamics of sweeping interface

Motivated by the drying pattern experiment by Yamazaki and Mizuguchi [J. Phys. Soc. Jpn. 69 (2000) 2387], we propose the dynamics of sweeping interface, in which material distributed over a region is swept by a moving interface. A model based on a phase field is constructed and results of numerical simulations are presented for one and two dimensions. Relevance of the present model to the drying experiment is discussed.

Riddled-like Basin in Two-Dimensional Map for Bouncing Motion of an Inelastic Particle on a Vibrating Board

Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling bifurcation, we found peculiar behavior in the parameter region where two stable periodic attractors coexist. A typical orbit in the region goes through chaotic motion for an extended transient period before it converges into one of the two periodic attractors. The basin structure in this parameter region is almost riddling and the fractal dimension of the basin boundary is close to two, i.e., the dimension of the phase space.

Square-Hexagonal Transformation of Periodic Domain Structures in a Conserved System

In a previous paper [M. Matsushita and T. Ohta: J. Phys. Soc. Jpn. 67 (1998) 1973], the model equation for a structural phase transition between a hexagonal symmetry and a square symmetry has been introduced and numerical simulations have been carried in two dimensions where the order parameter is a non-conserved quantity. In the present paper, we extend the model equation for the conserved order parameter. The thermal random force is also taken into account. The kinetics of the structural transition is studied by analyzing the non-equilibrium scattering function of the domain structures and by evaluating the time-dependence of the volume fraction of one of the structures. The equilibrium phase diagram for domain structures is also derived by means of the single wave number approximation.

Five- and Six-armed Brittle Stars Make Different Currents in the Disk

Physiological experiments and mathematical models have supported that neuronal activity is crucial for coordinating rhythmic movements of animals. On the other hand, robotics studies have suggested the importance of physical properties made by body structure. However, it remains unclear how morphology affects movement coordination in animals independent of neuronal activity. To begin to understand this issue, this study reports a rhythmic movement in the green brittle star. We found this animal moved five radially symmetric parts in a well-ordered unsynchronized pattern. We explained the coordinated pattern without considering neuronal activity, by building a phenomenological model where internal fluid flows between the body parts. Changing the number of body parts from five to six simulated a synchronized pattern, which is also demonstrated by a rare individual with six symmetric parts. This model suggests the different number in morphology changes the symmetry of the fluid flow, leading to the different synchronization patterns.Many researchers have explained how animals generate rhythmic movement. Physiological experiments and mathematical models have supported a crucial role of oscillatory neuronal activities, while robotics researches have suggested the importance of physical communication. However, it remains unclear how physical communication functions in animals. As a solution, we focused on individual difference in the number of radially symmetric arms and unique movement in brittle stars. We found that the green brittle star shrank and expanded interradii (parts of the disk partitioned by neighbor arms) with a rhythmic pattern. The movement among the interradii was unsynchronized in five-armed individuals but synchronized in a six-armed individual. To explain the relation between the pumping pattern and the body structure, we built a phenomenological model where internal fluid flows between the interradii. Based on the model, an interradius in five-armed ones makes an asymmetric flow into either neighbor, whereas that in six-armed ones makes symmetric flows into both neighbors.Physiological experiments and mathematical models have supported that neuronal activity is crucial for coordinating rhythmic movements in animals. On the other hand, robotics studies have suggested the importance of physical properties made by body structure, i.e. morphology. However, it remains unclear how morphology affects movement coordination in animals, independent of neuronal activity. To begin to understand this issue, our study reports a rhythmic movement in the green brittle star. We found this animal moved five radially symmetric parts in a well-ordered unsynchronized pattern. We built a phenomenological model where internal fluid flows between the five body parts to explain the coordinated pattern without considering neuronal activity. Changing the number of the body parts from five to six, we simulated a synchronized pattern, which was demonstrated also by an individual with six symmetric parts. Our model suggests a different number in morphology makes a different fluid flow, leading to a different synchronization pattern in the animal.

Individual Differences in the Pattern of Coordination in Brittle Stars with Five and Six Arms

Physiological experiments and mathematical models have supported that neuronal activity is crucial for coordinating rhythmic movements of animals. On the other hand, robotics studies have suggested the importance of physical properties made by body structure. However, it remains unclear how morphology affects movement coordination in animals independent of neuronal activity. To begin to understand this issue, this study reports a rhythmic movement in the green brittle star. We found this animal moved five radially symmetric parts in a well-ordered unsynchronized pattern. We explained the coordinated pattern without considering neuronal activity, by building a phenomenological model where internal fluid flows between the body parts. Changing the number of body parts from five to six simulated a synchronized pattern, which is also demonstrated by a rare individual with six symmetric parts. This model suggests the different number in morphology changes the symmetry of the fluid flow, leading to the different synchronization patterns.Many researchers have explained how animals generate rhythmic movement. Physiological experiments and mathematical models have supported a crucial role of oscillatory neuronal activities, while robotics researches have suggested the importance of physical communication. However, it remains unclear how physical communication functions in animals. As a solution, we focused on individual difference in the number of radially symmetric arms and unique movement in brittle stars. We found that the green brittle star shrank and expanded interradii (parts of the disk partitioned by neighbor arms) with a rhythmic pattern. The movement among the interradii was unsynchronized in five-armed individuals but synchronized in a six-armed individual. To explain the relation between the pumping pattern and the body structure, we built a phenomenological model where internal fluid flows between the interradii. Based on the model, an interradius in five-armed ones makes an asymmetric flow into either neighbor, whereas that in six-armed ones makes symmetric flows into both neighbors.Physiological experiments and mathematical models have supported that neuronal activity is crucial for coordinating rhythmic movements in animals. On the other hand, robotics studies have suggested the importance of physical properties made by body structure, i.e. morphology. However, it remains unclear how morphology affects movement coordination in animals, independent of neuronal activity. To begin to understand this issue, our study reports a rhythmic movement in the green brittle star. We found this animal moved five radially symmetric parts in a well-ordered unsynchronized pattern. We built a phenomenological model where internal fluid flows between the five body parts to explain the coordinated pattern without considering neuronal activity. Changing the number of the body parts from five to six, we simulated a synchronized pattern, which was demonstrated also by an individual with six symmetric parts. Our model suggests a different number in morphology makes a different fluid flow, leading to a different synchronization pattern in the animal.