Toshiya Iwai

Study of stochastic resonance by method of stochastic energetics

Stochastic resonance (SR) is numerically analyzed by the method of the stochastic energetics that enable us to analyze the energetics of non-equilibrium processes described by the Langevin equations. The work done by the external agent which drives the potential to fluctuate periodically is shown to be a good quantitative measure of SR. If the phase lag of the inter-well resonant motion before the periodic force is investigated, the good measure of SR can be devised by extracting the inter-well resonant motion. Thus, we numerically investigate the phase lag of the Brownian motion. The value of phase lag at the optimal noise intensity is found to depend on the frequency of the periodic force.

Numerical Analysis of Stochastic Resonance by Method of Stochastic Energetics.

Stochastic resonance (SR) is numerically analyzed by the method of stochastic energetics. The work done by the external agent which drives the potential to fluctuate periodically is shown to be a good quantitative measure to detect SR. On the other hand, signal-to-noise ratio (SNR) is shown to be not a good quantitative measure of SR by comparison with the work.

Simulation of Domain Growth in a System with Random Impurities

Domain growth in a system with random impurities for both conserved and nonconserved order parameter is investigated by means of the cell-dynamical system (CDS) method. We find the following. (i) The characteristic length in domain growth obeys l ( t )∼(log t ) α where α is smaller than the value predicted by Huse and Henley [Phys. Rev. Lett. 55 (1985) 2708]. (ii) The exponent α seems to depend on the impurity concentration and temperature. (iii) Dynamical scaling of the structure factor is satisfied and the form of the scaling function depends on the impurity concentration.

Vacancy-mediated phase separation of binary alloy

The most important element process of the phase separation of binary alloys is the vacancy diffusion mechanism. A set of phenomenological dynamical equations for the vacancy-mediated phase separation is formulated from a mean-field free energy and the numerical simulation of the model is performed. From numerical results, vacancies form clusters along phase boundaries between two degenerate stable domains. The width of the vacancy-cluster across the interface grows with the logarithmic function of time. If effects of vacancy-clusters are not dominant, the dynamics is not different from that by the exchange dynamics. If the effects are dominant, the characteristic length proportional to the average domain size grows with the logarithmic function of time. The analytical approach shows that the logarithmic growth of the characteristic length is related to the growth law of the width of the vacancy-cluster.

Surface critical field of superconducting superlattice I

Abstract We investigate the surface effects on the parallel critical field H c3 ( T ) and the pair function F 0 ( z ) of the superlattice with spatial variations of the BCS coupling constant and the diffusion constant. We make use of the lowest eigenvalues and eigenfunctions up to 30 to obtain the temperature dependence of the critical field. The effect of the BCS coupling constant appears significantly in our results. It is found that the positive curvature in H c3 (T) is related to the disappearance of the sub-peaks of F 0 ( z ).

Kink Dynamics in a One-Dimensional Non-Conserved TDGL System with a Quenched Impurity

Dynamics of a kink in the presence of a quenched impurity is investigated both analytically and numerically by making use of the time dependent Ginzburg-Landau equation for the case of a scalar order parameter in a one-dimensional system without the thermal noise. We find the following results in our model. (i) The interaction between the kink and the impurity is attractive. (ii) When the distance between the kink and the impurity is larger than the width of the kink, the motion of the kink is described by the logarithmic function of time. This is similar to the growth law of dynamics of kinks and anti-kinks [K. Kawasaki and T. Ohta: Physica 116A (1982) 573.]. (iii) When the distance between the kink and the impurity is small, the distance decreases exponentially with time and finally the kink is pinned by the impurity. (iv) When the distance between the kink and the impurity is large, the order parameter field has the spiky defect at the impurity position.

Stable states of superconducting superlattices

Abstract The temperature dependence of the upper critical field Hc2(T) perpendicular to the planes of the superconducting superlattice with magnetic layers is calculated. The results show that the phase difference ϕ(L) of the order parameter in one spatial period L changes from 0 to π with decreasing temperature for an appropriate set of the physical quantities. Further, we derive the analytic expression for the third-order term of the order parameter of the Ginzburg–Landau equation as the first step to study the stable state at (H,T) below Hc2(T).

Memory search model by chaotic neural netowork

P2-q13 Transition of information representation in a multistable attractor model of the prefrontal cortex Yuichi Katori 1,2 , Kazuhiro Sakamoto 3, Hajime Mushiake 3,4, Kazuyuki Aihara 1,2 1 Institute of Industrial Science, The University of Tokyo, Tokyo, Japan 2 Aihara Innovative Mathematical Modelling Project, JST, Tokyo, Japan 3 Research Institute of Electronic Communication, Tohoku University, Sendai, Japan 4 Department of Physiology, Tohoku University, School of medicine, Sendai, Japan

Domain growth in quenched random impurities

Domain growth in a system with quenched random impurities for the conserved scalar order parameter is investigated using a cell‐dynamics method. We find that the growth rate of domains are reduced due to the pinning by impurities.

Numerical Study of Ordering Processes in a One-Dimensional System with Quenched Impurities

Ordering processes in a one-dimensional system with quenched impurities and negligible thermal noise for the case of non-conserved order parameter is investigated numerically. We find the following results. (i) For a large impurity density, the average size of a stable domain, l ( t ), shows a crossover from the growth due to the drift motion, l ( t ) ∼ln t , at the early stage in our simulation to a slowing down of the growth at the late stage. The proportionality coefficient of this logarismic law is a decreasing function of the impurity density. (ii) Scaling property of the domain size distribution function is satisfied for the region of a large size and the scaled distribution function is independent of the impurity density.