arXiv subjects
Publications and source records attributed to Hidetsugu Sakaguchi.
The aggregation dynamics of slime mold is studied using coupled equations of phase ϕand cell concentration n. Phase waves work as tactic signals for aggregation. Branching structures appear during the aggregation. A stationary branching pattern appears like a river network, if cells are uniformly supplied into the system.
Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all elements are statistically equivalent. A lognormal distribution describes well the nonstationary time evolution. If a nonlinear load corresponding to progressive taxation is introduced, a stationary distribution is obtained and disparity widening is suppressed.
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is derived using the Ott-Antonsen ansatz. The applicability of the ansatz is checked by the comparison of numerical results of the coupled oscillator system and the reduced low-dimensional equation. We investigate further several interesting phenomena in which mutual interactions between the fast and slow oscillators play an essential role. Fast oscillations appear intermittently as a result of excitatory interactions with slow oscillators in a certain parameter range. Slow oscillators experience an oscillator-death phenomenon owing to their interaction with fast oscillators. This oscillator death is explained as a result of saddle-node bifurcation in a simple phase equation obtained using the temporal average of the fast oscillations. Finally we show macroscopic synchronization of the order 1:m between the slow and fast oscillators.
We elaborate a model of the interferometer which, unlike previously studied ones, uses a local (delta-functional) nonlinear repulsive potential, embedded into a harmonic-oscillator trapping potential, as the splitter for the incident soliton. An estimate demonstrates that this setting may be implemented by means of the localized Feshbach resonance controlled by a focused laser beam. The same system may be realized as a nonlinear waveguide in optics. Subsequent analysis produces an exact solution for scattering of a plane wave in the linear medium on the delta-functional nonlinear repulsive potential, and an approximate solution for splitting of the incident soliton when the ambient medium is nonlinear. The most essential result, obtained by means of systematic simulations, is that the use of the nonlinear splitter provides the sensitivity of the soliton-based interferometer to the target, inserted into one of its arms, which is much higher than the sensitivity provided by the usual linear splitter.
An autoregressive model with a power-law type memory kernel is studied as a stochastic process that exhibits a self-affine-fractal-like behavior for a small time scale. We find numerically that the root-mean-square displacement for the time interval increases with a power law for small time but saturates at sufficiently large time. The exponent changes with the power exponent of the memory kernel.
A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear visco-elasticity. Several aftershocks are generated after the main shock owing to the damping of the additional visco-elastic force. Both the Gutenberg-Richter law and Omori's law are reproduced in a numerical simulation of the modified Carlson-Langer model on a critical percolation cluster of a square lattice.
The crystal size distribution in polynuclear growth is numerically studied using a coupled map lattice model. The width of the size distribution depends on c/D, where c is the growth rate at interface sites and $D$ is the diffusion constant. When c/D is sufficiently small, the width W increases linearly with c/D and saturates at large c/D. Monodisperse square and cubic crystals are obtained respectively on square and cubic lattices when c/D is sufficiently small for a small kinetic parameter b. The linear dependence of W on c/D in a parameter range of small c/D is explained by the eigenfunction for the first eigenvalue in a two-dimensional model and a mean-field model. For the mean-field model, the slope of the linear dependence is evaluated theoretically.
A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)^{1/3} for a fixed value of branching number, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number when the Peclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)^{1/3}.
In the Ginzburg-Landau equation, there are domain walls connecting two metastable states. The dynamics of domain walls has been intensively studied, but there remain still unsolved but crucial problems even for a single domain. We study the domain wall dynamics in three different Ginzburg-Landau-type equations satisfying conservation laws. In a modified $ϕ^4$ model satisfying the law of energy conservation and the Lorentz invariance, the motion of a domain wall is accelerated and the velocity approaches its maximum. In a one-dimensional model of eutectic growth, the order parameter is conserved and a domain wall connecting a metastable uniform state and a spatially periodic pattern appears. We try to find a selection rule for the wavelength of a spatially periodic pattern. In a model equation for martensitic transformation, a domain wall connecting a uniform metastable state and a zigzag structure appears which propagates at a high velocity.
It is commonly known that two-dimensional mean-field models of optical and matter waves with the cubic self-attraction cannot produce stable solitons in free space because of the occurrence of the collapse in the same setting. By means of the numerical analysis and variational approximation, we demonstrate that the two-component model of the Bose-Einstein condensate, with the spin-orbit Rashba coupling and cubic attractive interactions, gives rise to solitary-vortex complexes of two types: semi-vortices (SVs, with a vortex in one component and a fundamental soliton in the other), and mixed modes (MMs, with topological charges 0 and +1/-1 mixed in both components). These two- dimensional composite modes can be created using the trapping harmonic-oscillator (HO) potential, but remain stable in the free space, if the trap is gradually removed. The SVs and MMs realize the ground state of the system, provided that the self-attraction in the two components is, respectively, stronger or weaker than the cross-attraction between them. The SVs and MMs which are not the ground state are subject to a drift instability. In the free space (in the absence of the HO trap), modes of both types degenerate into unstable Townes solitons when their norms attain the respective critical values, while there is no lower existence threshold for the stable modes. Moving free-space stable solitons are also found in the present non-Galilean-invariant system, up to a critical velocity. Collisions between two moving solitons lead to their merger into a single one.
A simple one-dimensional mechanical model is proposed for splitting instability in swollen membranes. The splitting instability occurs by ring constriction. The bifurcation can be both subcritical and supercritical, depending on the slenderness of spheroidal membranes. The lower critical point is estimated theoretically for the simplest circular system. Necking instability occurs in a spheroidal membrane when the twist angle in the boundary conditions is increased.
Attraction of the quantum particle to the center in the 3D space with potential V/r^2 gives rise to the quantum collapse, i.e., nonexistence of the ground state (GS) when the attraction strength exceeds a critical value (V = 1/8, in the present notation). Recently, we have demonstrated that the quantum collapse is suppressed, and the GS is restored, if repulsive interactions between particles in the quantum gas are taken into account, in the mean-field approximation. This setting can be realized in a gas of dipolar molecules attracted to the central charge, with dipole-dipole interactions taken into regard too. Here we analyze this problem for a binary gas. GSs supported by the repulsive interactions are constructed in a numerical form, as well as by means of analytical approximations for both miscible and immiscible binary systems. In particular, the Thomas-Fermi (TF) approximation is relevant if V is large enough. It is found that the GS of the miscible binary gas, both balanced and imbalanced, features a weak phase transition at another critical value, V = 1/2. The transition is characterized by an analyticity-breaking change in the structure of the wave functions at small r. To illustrate the generic character of the present phenomenology, we also consider the binary system with the attraction between the species (rather than repulsion), in the case when the central potential pulls a single component only.
The Carlson-Langer model is a deterministic model of earthquakes. There were many investigations of this model, but its complicated spatio-temporal dynamics is not yet completely understood. We again study the model equation numerically, and obtain two new results. Firstly, we try to understand the complicated dynamics from the viewpoint of spatio-temporal intermittency. We study the intermittent dynamics of a two-block system using a one-dimensional map, which is useful for understanding an intermittent spatio-temporal chaos in larger systems. Large slips occur intermittently after repeated small slips when the parameter of the velocity weakening friction is large. Small slips reduce the spatial irregularity of block displacement, and large slips occur on a relatively flat configuration of blocks. Secondly, we study the effect of spatial heterogeneity such as asperity using percolation clusters. We show the numerical results of the slip-size distribution in the block-spring model on percolation clusters, and find that the b parameter for the magnitude distribution is close to 2/3 when the velocity weakening parameter is intermediate.
Shock waves propagate in falling coupled harmonic oscillators. The bottom end of coupled harmonic oscillators does not fall downwards until a shock wave reaches the bottom end. The exact solution can be expressed by the Fourier series expansion, and an approximate solution can be expressed by the integral of the Airy function. The width of the shock wave increases slowly in accordance with a power law.
A phase model with feedback control is studied as a dynamical model of power grids. As an example, we study a model network corresponding to the power grid in the Kyushu region. The standard frequency is maintained by the mutual synchronization and the feedback control. Electric failures are induced by an overload. We propose a local feedback method in which the strength of feedback control is proportional to the magnitude of generators. We find that the electric failures do not occur until the utilization ratio is close to 1 under this feedback control. We also find that the temporal response for the time-varying input power is suppressed under this feedback control. We explain the mechanisms using the corresponding global feedback method.
We introduce a three-dimensional (3D) model of optical media with the quadratic ($χ^{(2)}$) nonlinearity and an effective 2D isotropic harmonic-oscillator (HO) potential. While it is well known that 3D χ^2 solitons with embedded vorticity ("vortical light bullets") are unstable in the free space, we demonstrate that they have a broad stability region in the present model, being supported by the HO potential against the splitting instability. The shape of the vortical solitons may be accurately predicted by the variational approximation (VA). They exist above a threshold value of the total energy (norm) and below another critical value, which determines a stability boundary. The existence threshold vanishes is a part of the parameter space, depending on the mismatch parameter, which is explained by means of the comparison with the 2D counterpart of the system. Above the stability boundary, the vortex features shape oscillations, periodically breaking its axisymmetric form and restoring it. Collisions between vortices moving in the longitudinal direction are studied too. The collision is strongly inelastic at relatively small values of the velocities, breaking the two colliding vortices into three, with the same vorticity. The results suggest a possibility of the creation of stable 3D optical solitons with the intrinsic vorticity.
A model of clustering dynamics is proposed for a population of spatially distributed active rotators. A transition from excitable to oscillatory dynamics is induced by the increase of the local density of active rotators. It is interpreted as dynamical quorum sensing. In the oscillation regime, phase waves propagate without decay, which generates an effectively long-range interaction in the clustering dynamics. The clustering process becomes facilitated and only one dominant cluster appears rapidly as a result of the dynamical quorum sensing. An exact localized solution is found to a simplified model equation, and the competitive dynamics between two localized states is studied numerically.
Three dimensional dendrites are studied with a coupled map lattice model. We study the fractal dimensions, the f(α) spectrum, the size distribution of sidebranches, and the envelope formed by sidebranches.