Continuous time random walk with jump length correlated with waiting time

A coupled continuous time random walk (CTRW) model is proposed, in which the jump length of a walker is correlated with waiting time. The power law distribution is chosen as the probability density function of waiting time and the Gaussian-like distribution as the probability density function of jump length. Normal diffusion, subdiffusion and superdiffusion can be realized within the present model. It is shown that the competition between long-tailed distribution and correlation of jump length and waiting time will lead to different diffusive behavior.     

Scale-Invariant Structure of the Seismic Kinetics in Strongly Nonequilibrium Medium

Results of the scaling analysis of the waiting time series for seismic events of the 2019 Ridgecrest earthquake sequence in East California have been presented. It has been shown that the waiting time series before a strong earthquake with a magnitude of M = 7.1 acquires a scale-invariant structure. A reason for the appearance of the statistical self-similarity in the waiting time series is the transition of the medium in the focal region to a strongly nonequilibrium state. The result can be interpreted as the appearance of a temporal dissipative structure in the process of seismic kinetics. It has been proposed to use the scaling analysis of the seismic kinetic data to monitor the current state of the seismogenerating medium.

     

等待点N=82附近核素β~-衰变寿命的研究

利用提出的远离稳定线附近的原子核β-衰变寿命的指数规律理论计算公式,对N=82附近快中子过程中等待点核素的β-衰变寿命进行了理论计算,比较了所获得的计算结果与最新的理论结果和实验结果并加以讨论.研究表明,相对于理论复杂和计算时间长的微观理论计算而言,利用考虑壳效应的远离稳定线的原子核β-衰变寿命指数规律理论计算公式能较快且准确地得出快中子俘获过程(R过程)等待点核素的β-衰变寿命.这能为R过程核素合成网络计算研究提供有效可靠的重要物理输入,并对今后天体中核素的合成研究具有重要意义.     

Exact results for the Barabási model of human dynamics

Human activity patterns display a bursty dynamics with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabási, Nature (London) 435, 207 (2005)]. In this Letter we obtain exact results for the Barabási model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.     

Fractional Fokker-Planck equations for subdiffusion with space- and time-dependent forces

We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.     

The return of the kink

We present a simple theory for the statistics of subsequent passages of kinks at a particular position along a fluctuating step on a crystal surface. Two situations are treated, namely one where the waiting time until the next passage is measured starting from the previous passage of a kink at the observation point, and one where the waiting time is measured starting from a random instant in time. In both cases the waiting time distribution is shown not to obey simple Poisson statistics. Monte Carlo simulations of kink motion show that Poisson statistics emerges for longer waiting times only when the creation and annihilation of kink-antikink pairs are explicitly included. Together, the theory and simulations provide an alternative interpretation of experimental results obtained by Giesen et al. with Scanning Tunneling Microscopy [M. Giesen-Seibert, H. Ibach, Surf. Sci. 316 (1994) 205].     

Nonrenewal statistics in the catalytic activity of enzyme molecules at mesoscopic concentrations

Recent fluorescence spectroscopy measurements of single-enzyme kinetics have shown that enzymatic turnovers form a renewal stochastic process in which the inverse of the mean waiting time between turnovers follows the Michaelis-Menten equation. We study enzyme kinetics at physiologically relevant mesoscopic concentrations using a master equation. From the exact solution of the master equation we find that the waiting times are neither independent nor identically distributed, implying that enzymatic turnovers form a nonrenewal stochastic process. The inverse of the mean waiting time shows strong departure from the Michaelis-Menten equation. The waiting times between consecutive turnovers are anticorrelated, where short intervals are more likely to be followed by long intervals and vice versa. Correlations persist beyond consecutive turnovers indicating that multiscale fluctuations govern enzyme kinetics.     

Effect of microscopic inhomogeneity of the medium on reaction-diffusion front velocity

A model of random walks on an inhomogeneous lattice is used to analyze the effect of microscopic inhomogeneity of the medium on reaction-diffusion front velocity. It is shown that the front velocity can be substantially higher on an inhomogeneous lattice as compared to that on a homogeneous one with the same onsite waiting time. The increase in velocity is due to a bias in the particle distribution between sites of different types toward those with shorter waiting times. The amount of bias depends on the rate of chemical reaction: the higher the rate, the stronger the bias. The front velocity also strongly depends on the reaction mechanism, more precisely, on how product particles are distributed between sites of different types.     

Asymptotic solutions of the continuous-time random walk model of diffusion

Asymptotic distributions of the Montroll-Weiss equation for the continuous-time random walk are investigated for long times. It is shown that, for a certain subclass of the hopping waiting time distributions belonging to the domain of attraction of stable distributions, these asymptotic distributions are of stable form. This indicates that the realm of applicability of the diffusion equation is limited. The Montroll-Weiss equation is rederived to include the influence of the initial waiting interval and the role of the stable distributions in physical problems is briefly discussed.     

A dynamical monte carlo algorithm for master equations with time-dependent transition rates

A Monte Carlo algorithm for simulating master equations with time-dependent transition rates is described. It is based on a waiting time image, and takes into account that the system can become frozen when the transition rates tend to zero fast enough in time. An analytical justification is provided. The algorithm reduces to the Bortz-Kalos-Lebowitz one when the transition rates are constant. Since the exact evaluation of waiting times is rather involved in general, a simple and efficient iterative method for accurately calculating them is introduced. As an example, the algorithm is applied to a one-dimensional Ising system with Glauber dynamics. It is shown that it reproduces the exact analytical results, being more efficient than the direct implementation of the Metropolis algorithm     

Boiling-up of superheated water and water solutions under ultrasound influence

Boiling-up kinetics of superheated distilled water and sodium chloride solution in a glass cell at atmospheric pressure and low superheating of 15–35 °C has been studied far from the boundary of attainable superheating in the area of heterogeneous nucleation. Temperature dependences of average waiting time of superheated liquids boiling-up have been studied experimentally under natural conditions and in the ultrasonic field Waiting time of boiling-up at these temperatures reaches 1000 s, and average time is 600 s. Empirical distribution functions have been found with the use of the waiting time samples obtained by the method of order statistics. Omega-square goodness-of-fit test has shown that they disagree with exponential distribution describing stationary random process of supercritical embryo generation separating the system to macroscopic phases. Thus, it is shown that this random process is not stationary, consequently, nucleation rate to be depending on time.     

Excess noise in a hopping model for a resistor with quenched disorder

We consider a model for independent charged particles, hopping on a lattice with static disorder in the waiting times. The excess current noise is calculated and shown to be related to resistance noise and arising from mobility fluctuations. It is also related to the four point super-Burnett-function. The strength of the noise is calculated at small frequencies for weak disorder (classical long time tails) and for strong disorder, when it may behave like I/f. In that case the Hooge factor equals the fraction of deep trapping centers.     

Some properties of the asymptotic solutions of the Montroll-Weiss equation

Curves of asymptotic probability densities appropriate to the continuous time random walk model of Montroll and Weiss are presented and are calculated numerically using the fast Fourier transform. The behavior of the moments is briefly discussed and it is shown that the Einstein formula relating the diffusion and mobility coefficients can be generalized to include the case where the mean waiting time between hops is infinite.     

Influence of soundscape and interior design on anxiety and perceived tranquillity of patients in a healthcare setting

Tranquillity characterized by a pleasant but calming environment is often to be found in natural environments where man-made noise is at a low level though natural sounds can be relatively high. Numerous studies have shown a link between such restorative environments and hospital recovery rates, stress reduction, longevity, pain relief and even how the brain processes auditory signals. In hospitals and primary care facilities there is a need to improve patient waiting rooms as current designs are largely based solely on medical need. There are often long waits in such spaces and patients are coping with the stress and anxiety caused by their medical condition. Attention should therefore be given to creating “restorative environment” as a component to their medical treatment. The study describes the effects of introducing natural sounds and large images of natural landscapes into a waiting room in a student health center. Using self reported levels of anxiety and tranquillity it was possible to assess the impact that these targeted auditory and visual interventions had in affecting the quality of the patient experience. Following the changes results show that levels of reported tranquillity were significantly improved but there were smaller change in reported reductions in anxiety.     

Waiting time distributions in financial markets

We study waiting time distributions for data representing two completely different financial markets that have dramatically different characteristics. The first are data for the Irish market during the 19th century over the period 1850 to 1854. A total of 10 stocks out of a database of 60 are examined. The second database is for Japanese yen currency fluctuations during the latter part of the 20th century (1989-1992). The Irish stock activity was recorded on a daily basis and activity was characterised by waiting times that varied from one day to a few months. The Japanese yen data was recorded every minute over 24 hour periods and the waiting times varied from a minute to a an hour or so. For both data sets, the waiting time distributions exhibit power law tails. The results for Irish daily data can be easily interpreted using the model of a continuous time random walk first proposed by Montroll and applied recently to some financial data by Mainardi, Scalas and colleagues. Yen data show a quite different behaviour. For large waiting times, the Irish data exhibit a cut off; the Yen data exhibit two humps that could arise as result of major trading centres in the World. Received 31 December 2001     

Asymmetrical Diffusion-Induced Directional Motion

Competition between anomalous diffusion and normal diffusion along two different directions of the track for a Brownian motor, combined with a periodic potential flashing, can lead to a macroscopic motion. The current is calculated analytically by using the Astumian-Bier‘s approach of the step number per cycle. It is shown that the direction of current occurs reversal for different waiting times of the potential off and the magnitude of current is prominently enhanced. Moreover, a thermal “green“ noise is proposed to produce the ballistic diffusion, numerical simulations for the average velocity of the particle in the presence of ballistic and normal diffusions support the present theoretical findings.     

Electron waiting times for the mesoscopic capacitor

We evaluate the distribution of waiting times between electrons emitted by a driven mesoscopic capacitor. Based on a wave packet approach we obtain analytic expressions for the electronic waiting time distribution and the joint distribution of subsequent waiting times. These semi-classical results are compared to a full quantum treatment based on Floquet scattering theory and good agreement is found in the appropriate parameter ranges. Our results provide an intuitive picture of the electronic emissions from the driven mesoscopic capacitor and may be tested in future experiments.