Takuma Akimoto

Origin of subdiffusion of water molecules on cell membrane surfaces

Water molecules play an important role in providing unique environments for biological reactions on cell membranes. It is widely believed that water molecules form bridges that connect lipid molecules and stabilize cell membranes. Using all-atom molecular dynamics simulations, we show that translational and rotational diffusion of water molecules on lipid membrane surfaces exhibit subdiffusion and aging. Moreover, we provide evidence that both divergent mean trapping time (continuous-time random walk) and long-correlated noise (fractional Brownian motion) contribute to this subdiffusion. These results suggest that subdiffusion on cell membranes causes the water retardation, an enhancement of cell membrane stability, and a higher reaction efficiency.

Diffusive nature of xenon anesthetic changes properties of a lipid bilayer: molecular dynamics simulations.

Effects of general anesthesia can be controllable by the ambient pressure. We perform molecular dynamics simulations for a 1-palmitoyl-2-oleoyl phosphatidylethanolamine lipid bilayer with or without xenon molecules by changing the pressure to elucidate the mechanism of the pressure reversal of general anesthesia. According to the diffusive nature of xenon molecules in the lipid bilayer, a decrease in the orientational order of the lipid tails, an increase in the area and volume per lipid molecule, and an increase in the diffusivity of lipid molecules are observed. We show that the properties of the lipid bilayer with xenon molecules at high pressure come close to those without xenon molecules at 0.1 MPa. Furthermore, we find that xenon molecules are concentrated in the middle of the lipid bilayer at high pressures by the pushing effect and that the diffusivity of xenon molecules is suppressed. These results suggest that the pressure reversal originates from a jamming and suppression of the diffusivity of xenon molecules in lipid bilayers.

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 α1<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.

Distributional response to biases in deterministic superdiffusion.

We report on a novel response to biases in deterministic superdiffusion. For its reduced map, we show using infinite ergodic theory that the time-averaged velocity (TAV) is intrinsically random and its distribution obeys the generalized arcsine distribution. A distributional limit theorem indicates that the TAV response to a bias appears in the distribution, which is an example of what we term a distributional response induced by a bias. Although this response in single trajectories is intrinsically random, the ensemble-averaged TAV response is linear.

Distributional ergodicity in stored-energy-driven Lévy flights.

We study a class of random walk, the stored-energy-driven Lévy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean-square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean-square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of distributional ergodicity. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.

Size-dependent phase changes in water clusters

We investigate melting behavior of water clusters (H2O)N (N = 7, 8, 11, and 12) by using multicanonical-ensemble molecular dynamics simulations. Our simulations show that the melting behavior of water clusters is highly size dependent. Based on the computed canonical average of the potential energy and heat capacity CV, we conclude that (H2O)8 and (H2O)12 exhibit first-order-like phase change, while (H2O)7 and (H2O)11 exhibit continuous-like phase change. The melting temperature range for (H2O)8 and (H2O)12 can be defined based on the peak position of CV(T) and dCV(T)/dT (where T is the temperature). Moreover, for (H2O)8 and (H2O)12, the solid- and liquid-like phases separate temporally in the course of simulation. In contrast, no temporal separation of solid- and liquid-like phases is observed for (H2O)7 and (H2O)11. In light of the notable temporal separation of solid- and liquid-like phases for(H2O)8 and (H2O)12, an alternative computer approach for estimating the melting temperature range is proposed based on the time-dependent Lindemann parameters. We find that the melting temperature range estimated from both definitions is consistent with each other for (H2O)8 and (H2O)12 but not for (H2O)7 and (H2O)11. We also find that the melting behavior of small water clusters can be conveniently assessed if the energy differences of neighbor-sized clusters at zero temperature are known.

Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity.

The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long-time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.

Ergodic properties of continuous-time random walks: Finite-size effects and ensemble dependences

The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e., distributions of the first waiting time). Here, we consider two ensembles: the equilibrium and a typical non-equilibrium ensembles. For both ensembles, it is shown that the time-averaged mean square displacement (TAMSD) exhibits a crossover from normal to anomalous diffusion due to the spacial confinement and this crossover does not vanish even in the long measurement time limit. Moreover, for the non-equilibrium ensemble, we show that the probability density function of the diffusion constant of TAMSD follows the transient Mittag-Leffler distribution, and that scatter in the TAMSD shows a clear transition from weak ergodicity breaking (an irreproducible regime) to ordinary ergodic behavior (a reproducible regime) as the measurement time increases. This convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution; in other words, the weak ergodicity breaking persists for a long time. In addition, it is shown that, besides the TAMSD, a class of observables also exhibits this slow convergence to ergodicity. We also point out that, even though the system with the equilibrium initial ensemble shows no aging, its behavior is quite similar to that for the non-equilibrium ensemble.

Subexponential instability in one-dimensional maps implies infinite invariant measure

We characterize dynamical instability of weak chaos as subexponential instability. We show that a one-dimensional, conservative, ergodic measure preserving map with subexponential instability has an infinite invariant measure, and then we present a generalized Lyapunov exponent to characterize subexponential instability.

The Weibull-log Weibull transition of the interoccurrence 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.