Koichiro Shida

Cluster formation by inelastically colliding particles in one-dimensional space

Inelastically colliding particles moving in one-dimensional space are found to form clusters, each of which consists of particles with identical coordinates and velocities. There exists a critical size of a cluster, above which the cluster grows indefinitely by absorbing a colliding particle as if the collision were completely inelastic (rebound coefficient e = 0. It is experimentally found that when e = 0, the expected number of n-particle clusters is 1n, and the average number of final clusters 〈M〉 is 〈M〉 = ΣNn 11n, where N is the number of the particles in the system.

An Inelastic Collision Model for the Evolution of "Planetary Rings"

We show that ringlets of a planet can be formed by inelastic collisions. If the collision law is v ′ =- e v ( v ′ and v are relative velocities after and before the collision), then the configuration of the particles evolves from a 3-dimensional torus to a 2-dimensional disc and finally to 1-dimensional sharp ringlets. The theory is also demonstrated and confirmed by numerical experiments. Velocity vectors of the particles tend equalize at collisions. This causes the angular momenta to equalize, and the orbits draw nearer. The above statement is rigorous in our special model, and applies qualitatively in the general inelastic collision model. It seems apparent that collisions diffuse a spatial pattern. But, on the contrary, ringlets are sharpened by inelastic collisions.

Maxwell's Thermal Creep in Two Space Dimensions

“Thermal Creep” is a steady streaming motion, induced by a temperature gradient parallel to a fluid boundary, in the absence of gravity. Thermal creep has been studied by Maxwell, analyzed by Kennard, and simulated by Ibsen, Soto, and Cordero. Here we report several two-dimensional simulations. We find that the creep velocity is sensitive to the imposed macroscopic boundary conditions and that the agreement with existing theoretical predictions is only semiquantitative.

1/ν velocity distribution of colliding particles in one-dimensional space

Colliding particles moving in one-dimensional space form clusters. When particles coalesce upon collisions, the velocity distribution of final clusters is 1/ν in the interval N−12 ⋘ν/σ⋘ 1, where σ is the initial rms velocity and N is the initial number of particles.

Formation of Sharp Ringlets by Inelastic Collisions

We investigate the possibility that the sharp ringlets observed around giant planets of the solar system are generated through inelastic collisions. First, a model is defined, and then ringlet formation is shown to occur under certain conditions on the rebound coefficients. A three-dimensional case with 2000-body was then simulated. If the condition is satisfied, particles under the gravitational influence of a planet are shown to evolve from a three-dimensional torus to a two-dimensional disc, and finally to one-dimensional ringlets. The form is thus simplified through inelastic collisions. This result is contrary to the common notion that collisions among the constituents of planetary rings would cause the rings to lose their sharp features.

The design of self tuning PID control system based on minimum variance control algorithm

In this paper, we proposes design method of self tuning PID control adapted for uncertainty of plant in control which characteristic change dynamicaly. In proposal method, characteristic polynomial was designed, and minimum variance control on basis of minimization of estimation example was used. Furthermore, self tuning PID control which used stabilization technique proposed. In range of characteristic change [ω,ϵ]= ± 50 % for nominal model, we compared it with a traditional method, and from simulation result gets possible to construct desirable control system. From simulation result of stabilization in incorrect identification, oscillation, emission were not examined characteristic change front and back, and the control that became stable was realized.