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Takuma Akimoto

Publications and source records attributed to Takuma Akimoto.

63 records · Page 4Linked to original sources
arXiv2011

Dynamical Instability and Transport Coefficient in Deterministic Diffusion

We construct both normal and anomalous deterministic biased diffusions to obtain the Einstein relation for their time-averaged transport coefficients. We find that the difference of the generalized Lyapunov exponent between biased and unbiased deterministic diffusions is related to the normalized velocity based on the ensemble average. By Hopf's ergodic theorem, the ratios between the time-averaged velocity and the Lyapunov exponent for single trajectories converge to a universal constant, which is proportional to the strength of the bias. We confirm this theory using numerical simulations.

cond-mat.stat-mech↗
arXiv2011

Ultraslow Convergence to Ergodicity in Transient Subdiffusion

We investigate continuous time random walks with truncated $α$-stable trapping times. We prove distributional ergodicity for a class of observables; namely, the time-averaged observables follow the probability density function called the Mittag--Leffler distribution. This distributional ergodic behavior persists for a long time, and thus the convergence to the ordinary ergodicity is considerably slower than in the case in which the trapping-time distribution is given by common distributions. We also find a crossover from the distributional ergodic behavior to the ordinary ergodic behavior.

cond-mat.stat-mech↗
arXiv2010

Subexponential instability implies infinite invariant measure

We study subexponential instability to characterize a dynamical instability of weak chaos. We show that a dynamical system with subexponential instability has an infinite invariant measure, and then we present the generalized Lyapunov exponent to characterize subexponential instability.

cond-mat.stat-mech↗
arXiv2009

Characterization of intermittency in renewal processes: Application to earthquakes

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a new framework to understand a unified characterization of intermittency, and also present the Lyapunov exponent of renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency (JMA) catalog. We demonstrate that interevent times are not independent and identically distributed random variables by analyzing the return map of interevent times, but that there is a systematic change in conditional probability distribution functions of interevent times.

nlin.CD↗
arXiv2008

The Weibull - log Weibull Transition of the Inter-occurrence time statistics in the two-dimensional Burridge-Knopoff Earthquake model

In analyzing synthetic earthquake catalogs created by a two-dimensional Burridge-Knopoff model, we have found that a probability distribution of the interoccurrence times, the time intervals between successive events, can be described clearly by the superposition of the Weibull distribution and the log-Weibull distribution. In addition, the interoccurrence time statistics depend on frictional properties and stiffness of a fault and exhibit the Weibull - log Weibull transition, which states that the distribution function changes from the log-Weibull regime to the Weibull regime when the threshold of magnitude is increased. We reinforce a new insight into this model; the model can be recognized as a mechanical model providing a framework of the Weibull - log Weibull transition.

physics.geo-ph↗
arXiv2008

The Weibull - Log Weibull Distribution for Interoccurrence Times of Earthquakes

By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes --interoccurrence times-- can be described by the superposition of the Weibull distribution and the log-Weibull distribution. In particular, the distribution of large earthquakes obeys the Weibull distribution with the exponent $α_1 <1$, indicating the fact that the sequence of large earthquakes is not a Poisson process. It is found that the ratio of the Weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude. Our results infer that Weibull statistics and log-Weibull statistics coexist in the interoccurrence time statistics, and that the change of the distribution is considered as the change of the dominant distribution. In this case, the dominant distribution changes from the log-Weibull distribution to the Weibull distribution, allowing us to reinforce the view that the interoccurrence time exhibits the transition from the Weibull regime to the log-Weibull regime.

physics.geo-ph↗
arXiv2008

The Weibull - log Weibull transition of interoccurrence times for synthetic and natural earthquakes

We have studied interoccurrence time distributions by analyzing the synthetic and three natural catalogs of the Japan Meteorological Agency (JMA), the Southern California Earthquake Data Center (SCEDC), and Taiwan Central Weather Bureau (TCWB) and revealed the universal feature of the interoccurrence time statistics, Weibull - log Weibull transition. This transition reinforces the view that the interoccurrence time statistics possess Weibull statistics and log-Weibull statistics. Here in this paper, the crossover magnitude from the superposition regime to the Weibull regime $m_c^2$ is proportional to the plate velocity. In addition, we have found the region-independent relation, $m_c^2/m_{max} = 0.54 \pm 0.004$.

physics.geo-ph↗
arXiv2008

Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.

cond-mat.stat-mech↗