Syuji Miyazaki

Kyoto University | Kyodai · Graduate School of Informatics

Nearest-neighbor-spacing distributions of people sitting along the west bank of the Kamogawa River flowing through the central part of Kyoto City are derived, based on a dual partitioning process with a fixed ratio. The theoretical asymmetric bell-shaped distribution is compared with previous measurements. This was performed as an advanced study of...

We theoretically derived the critical behaviors of the asymmetric granular Maxwell's demon phenomenon by introducing a symmetry-breaking parameter. This symmetry breaking can be realized experimentally by forming an angle between the vibration and vertical directions. The values of the conventional critical exponents β, γ, and δ were determined , a...

In a previous study of Dettmann and Georgiou, it was considered such a situation that point-wise particles repeatedly and elastically collided with the wall of a container without any particle-particle collision and eventually escaped through a small window from the container, which can be modeled by an open billiard. In the present study, point-wi...

We extended a network model of scientific paradigm shifts proposed by S. Bornholdt et al. (2011) to one of prevailing trends, such as music CDs. A mean-field state-update rule was replaced by a local state-update rule that depends only on nearest neighbors of a small-world network. Then, we used the extended model to establish a connection between...

Conducting thin rods with a length of half the wavelength of microwaves produced by the kitchen microwave oven, such as dress pins or mechanical pencil leads, absorb microwaves efficiently. Electrons in rods accelerated by microwaves are emitted from both ends of the rods, collide with surrounding gas molecules, and create plasma. Spectra with a si...

Identical granular particles in multiple compartments on a vertically shaking table may show an aggregation phenomenon termed granular Maxwell's demon for a suitable choice of parameters. Vertically vibrated binary granular particles may yield granular Maxwell's demon or the granular clock. Horizontally vibrated binary granular particles may form s...

The Collatz tree, or the directed graph of the 3x + 1 problem, was demonstrated to be decomposed into three different subgraphs. An arbitrary positive integer is assigned uniquely to a specific position of the nodes of either of the three subgraphs. The manner of connecting a specific subgraph to its neighboring subgraphs is explicitly given. A com...

In this study, we propose a consensus model with nontrivial behaviors. This model uses the prospect theory to describe the human decision-making process in considerable detail, which enables realistic and diverse behaviors. Under the proposed model, the equilibrium states were analyzed based on two settings. In one of the settings, we confirmed mar...

Shizuo Ishiguro, the father of Nobel Prize-winning British novelist Kazuo Ishiguro, studied various sea-level changes, such as seiche, also known as abiki in the Nagasaki dialect, and the 1953 North Sea Flood, with his pioneering use of an analog computer in the 50s and 60s. Note that pioneering studies by Lorenz and Ueda using digital and analog c...

Following Fujisaka's basic idea, large deviation statistics characterizing temporal fluctuations are calculated based on Mori's projection-operator method. It is shown that this calculation will overcome the finite-sample effect studied by Nakao et al. due to the finiteness of the length of time series, of the time span of the local average, or of...

The relaxation and hysteresis of a periodically forced Swift-Hohenberg (SH) equation as a phenomenological model for the magnetic domains of a garnet thin film in an oscillating magnetic field are studied. It is already known that the unforced SH equation settles down to a single type of spatial structure called a stripe pattern, and that the relax...

Random walk on a real social networking service consisting of 2271 nodes is analyzed on the basis of the statistical-thermodynamics formalism to find phase transitions in network structure. Each phase can be related to a characteristic local structure of the network such as a cluster or a hub. For this purpose, the generalized transition matrix is...

Various synchronizations and related phenomena in discrete-time coupled chaotic rotors are studied. For unidirectional and bidirectional couplings, various dynamical forms of chaotic phase synchronization (CPS) and their relation to the Lyapunov spectra are shown. For a small positive maximum Lyapunov exponent of the coupled element in the case of...

An approximate calculation method of time correlations by use of delayed coordinate is proposed. For a solvable piecewise linear hyperbolic chaotic map, this approximation is compared with the exact calculation, and an exponential convergence for the maximum time delay M is found. By use of this exponential convergence, the exact result for M → ∞ i...

Spectral properties of the transition matrix of a small-world network model are studied, and how those properties are relevant to the network structure is elucidated. The distribution of the nearest neighbor eigenvalue spacings changes from a level-crossing to an avoided-crossing type as the rewiring probability p is varied from 0 to 1, which agree...

It is shown that the large-deviation statistical quantities of the discrete-time, finite-state Markov process P_{n+1};{(j)}= summation _{k=1};{N}H_{jk}P_{n};{(k)} , where P_{n};{(j)} is the probability for the j state at the time step n and H_{jk} is the transition probability, completely coincide with those from the Kalman map corresponding to the...

A directed network such as the WWW can be represented by a transition matrix. Comparing this matrix to a Frobenius-Perron matrix of a chaotic piecewise-linear one-dimensional map whose domain can be divided into Markov subintervals, we are able to relate the network structure itself to chaotic dynamics. Just like various large-deviation properties...

A chaotic piecewise linear map whose statistical properties are identical to those of a random walk on directed graphs such as the world wide web (WWW) is constructed, and the dynamic quantity is analyzed in the framework of large deviation statistics. Gibbs measures include the weight factor appearing in the weighted average of the dynamic quantit...

Let us define this adjacency matrix A, where Aij is equal to unity if the node j is linked to i. If not, Aij is equal to zero. In the case of undirected network, Aij = Aji = 1 holds if the nodes i and j are linked to each other. If not, Aij is equal to zero. Transition matrix H can be derived straightforwardly from the adjacency matrix. The element...

A chaotic piecewise linear map whose statistical properties are identical to those of a random walk on directed graphs such as the world wide web (WWW) is constructed, and the dynamic quantity is analyzed in the framework of large deviation statistics. Gibbs measures include the weight factor appearing in the weighted average of the dynamic quantit...

The nonperturbative non-Gaussian characteristics of diffusive motion are examined in the framework of the large deviation statistical theory, where simple extended mapping models showing chaotic diffusion are taken as an example. Furthermore, by rigorously solving the large deviation statistical quantities, it is found that the same type of anomalo...

A directed network such as the WWW can be represented by a transition matrix. Comparing this matrix to a Frobenius-Perron matrix of a chaotic piecewise-linear one-dimensional map whose domain can be divided into Markov subintervals, we are able to relate the network structure itself to chaotic dynamics. Just like various large-deviation properties...

Crossover between ballistic motion and normal diffusion is studied based on the continuous-time random walk (CTRW) approach in order to analyze universal properties of strongly correlated motion and the decay process of correlation in deterministic diffusion. There exists a characteristic time scale tau. For the time region t ≪ tau, ballistic mo...

A directed network such as the WWW can be represented by a transition matrix. Comparing this matrix to a Frobenius-Perron matrix of a chaotic piecewise-linear one-dimensional map whose domain can be divided into Markov subintervals, we are able to relate the network structure itself to chaotic dynamics. Just like various large-deviation properties...

Anomalous diffusion found in fluid systems is studied. Diffusion constants and mean square displacements are analytically obtained on the basis of the continuous-time random walk (CTRW) velocity model, and the values are compared with those obtained from model simulations employing dissipative dynamics describing oscillating convection flows. Good...

Synchronization of three-coupled chaotic oscillators was studied with the use of a coupled map system derived for interacting kicked relaxators. Partial synchronization (PS), in which two of the three were synchronized, was observed in addition to complete synchronization. An intermittency associated with the breakdown of the PS, seemingly differen...

Anomalous diffusion caused by modulational intermittency, which is also known as on-off intermittency, is studied on the basis of the continuous-time random walk (CTRW) approach. There exists a characteristic time scale τ. For the time region t ≪ τ, anomalous subdiffusion is observed, which is followed by normal diffusion for t ≫ τ. Higher-order mo...

Statistical properties and scale invariances of on-off diffusion, which is an anomalous transport phenomenon caused by on-off intermittency, are studied on the basis of the continuous-time random walk (CTRW) approach. The anomalous production of heat is also analyzed. Scaling functions of the time evolution of the mean square displacement and the p...

The mean square distance sigma2(t) of the diffusion induced by on-off intermittency is derived based on the continuous-time random walk theory. It obeys a scaling law sigma2(t)=2Dt phi(t/tau) with diffusion constant D and characteristic time tau, which is confirmed by the use of numerical iterations of a specific periodic map. The scaling function...

The power spectrum of the solvable on-off intermittency model previously introduced by the authors is analytically derived. A scaling law holds in the neighborhood of the critical point. Its universality is numerically confirmed for coupled maps and a stochastic model.

On-off intermittency observed in three types of spatially extended dynamical systems is reported. This is done by examining the linear stability of spatially synchronized state under a spatially inhomogeneous fluctuation. When the system size slightly exceeds the critical size and a single inhomogeneous mode becomes unstable, systems exhibit typica...

A solvable three-dimensional deterministic map that shows on-off intermittency is derived from a coupled mapping system. The distribution of an on-off variable, that of laminar duration, and the mean laminar duration are analytically obtained. The map enables us to discuss the probability measure on the attractor, which also gives the singularity s...

A four-dimensional Poincaré map is obtained from a coupling between a pair of nonlinear oscillators and it shows on-off intermittency under proper conditions. The power spectrum, and the distribution of on-off variable and that of laminar duration are numerically obtained and compared with analytical results of the multiplicative noise model, which...

The quantized center-of-mass dynamics of two-level atoms in a periodically modulated standing-wave laser field is analyzed, including the decohering effect of spontaneous emission. Under conditions appropriate for the occurrence of dynamical localization as determined in previous work, we predict a random diffusive motion of dynamically localized d...

We discuss the quasienergy-band structure for a periodically driven system with translational symmetry. The parameter is so fixed that a bounded fully developed chaotic region is surrounded by regular orbits. Due to the periodicity both in space and in time, eigenvalues of the Floquet operator (quasienergies) form band structures. Its two distinct...

The paper considers the dynamics of a particle in a periodically- space- and time-dependent potential under the condition of chaos. In the classical approach the distribution function for the particle position is shown to obey a diffusion law. We study the process of diffusion in the quantum case. It is found that quantum interference effects cause...

Just after a band crisis, a new type of q-phase transition occurs, and the fluctuation spectrum of coarse-grained local expansion rates has a remarkable linear part. As the crisis point is approached from above, the deviation from the linear part obeys a dynamic scaling law.

On the basis of the statistical-mechanical formalism, the q-phase transition for the fluctuation spectrum of coarse-grained local expansion rates of nearby orbits is rigorously derived at the band-crisis point when approached from above, and the critical scaling laws in the vicinity of the crisis point are presented. The implications and the nature...

The definition of the fluctuation spectrum of local expansion rates of nearby orbits is extended to a global region of phase space. It contains information on repellers as well as attractors coexisting in the region. Lyapunov exponents of attractors and repellers, the escape rates for repellers and some structures of these invariant sets are repres...

Various synchronizations and related phenomena in discrete-time coupled chaotic rotors are studied by use of numerical simulations. There exist multiple attractors with different long-time averages of the phase difference. Self-similar and complex structures of the basin in the phase space are observed. The relaxation times to attractors of the com...