First-passage time distributions for subdiffusion in confined geometry

In this Letter, we derive a relationship between the moments of the first-passage time for a random walk and the first-passage time density for subdiffusive processes modeled by continuous-time random walks. In particular, we show that the exact long-time behavior of the density depends only on the mean first-passage time of the corresponding normal diffusive process. In addition, we give explicit evaluations of the first-passage time distribution for general three-dimensional bounded domains. These results are relevant to systems involving anomalous diffusion in confinements.     

First-passage time statistics of stochastic transcription process for time-dependent reaction rates

The European Physical Journal E - To theoretically understand force generation properties of actin filaments, many models consider growing filaments pushing against a movable obstacle or barrier....     

First-passage time distributions for linear chain segments with general site-dependent waiting-time distributions

First-passage time distributions (FPTD) of the arrival of a walk at a terminal site of a finite linear chain are considered, where the individual transition processes between the sites are specified by rather general waiting-time distributions. An exact expression for the first-passage time distribution can be given in Laplace space in terms of finite continued fractions. The circumstances under which the calculation of FPTD by this technique offers advantages over conventional calculations via master equations are discussed and possible applications to systems of biophysical interest are indicated. Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic, 26–30 May 1997.     

First-passage times in a critical stochastic model

Average first-passage times for a single-variable stochastic model with a critical fixed point at the origin are computed by exact enumeration. The numerical measurements show excellent agreement with analytical results. The scaling function approaches the predicted asymptotic dependence.     

First-passage times for random walks in bounded domains

We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical simulations. Their range of validity is discussed. We also consider the case of a starting site and two targets. In addition, we present the extension to continuous Brownian motion. These results are of great relevance to any system involving diffusion in confined media.     

On using the dynamic snap-through motion of MEMS initially curved microbeams for filtering applications

Numerical and experimental investigations of the dynamics of micromachined shallow arches (initially curved microbeams) and the possibility of using their dynamic snap-through motion for filtering purposes are presented. The considered MEMS arches are actuated by a DC electrostatic load along with an AC harmonic load. Their dynamics is examined numerically using a Galerkin-based reduced-order model when excited near both their first and third natural frequencies. Several simulation results are presented demonstrating interesting jumps and dynamic snap-through behavior of the MEMS arches and their attractive features for uses as band-pass filters, such as their sharp roll-off from pass-bands to stop-bands and their flat response. Experimental work is conducted to test arches realized of curved polysilicon microbeams when excited by DC and AC loads. Experimental data of the micromachined curved beams are shown for the softening and hardening behavior near the first and third natural frequencies, respectively, as well as dynamic snap-through motion.     

First-passage Monte Carlo algorithm: diffusion without all the hops

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.     

First passage time on a multifurcating hierarchical structure

Asymptotic behaviour of the moments of the first passage time (FPT) on a one-dimensional lattice holding a multifurcating hierarchy of teeth is studied. There is a transition from ordinary to anomalous diffusion when the parameter controlling the relative sizes of the teeth, is varied with respect to the furcating number of the hierarchy. The scaling behaviour of the moments of FPT with the linear dimensions of the lattice segment indicates that in the anomalcus phase the probability density of the FPT is multifractal.     

Networks with time structure from time series

We propose a method of constructing a network, in which its time structure is directly incorporated, based on a deterministic model from a time series. To construct such a network, we transform a linear model containing terms with different time delays into network topology. The terms in the model are translated into temporal nodes of the network. On each link connecting these nodes, we assign a positive real number representing the strength of relationship, or the “distance,” between nodes specified by the parameters of the model. The method is demonstrated by a known system and applied to two actual time series.     

Probability Evolution and Mean First-passage Time for Non-Markovian Processes Driven by Nonlinear Noise

We investigate a stochastic differential equation with general noxilinearity in the noise.With the help of the projection operator techniques, we derive an integro-differential equation for the probability density and an approximate equation for the mean firstpassage time (MFPT). The concrete calculations are made for two important examples.     

First-passage behavior of periodic potential system driven by correlated noise

In this paper, the first-passage time (FPT) of periodic potential system driven by correlated noise is discussed. One-dimensional non-Markovian process in the system is stochastically equivalent to two-dimensional Markovian process according to the statistical characteristics of noise. The 5 × 10⁴ response tracks of the system is simulated by the fourth-order Runge-Kutta algorithm, and the FPT of the Brownian particle is recorded, then the mean first-passage time (MFPT) is calculated by averaging these values and the probability density function (PDF) of the FPT is simulated. Finally, the influence of the relevant parameters in the system on MFPT and the PDF of the FPT are discussed. Besides, it is found that resonance activation (RA) phenomenon appears in the system.     

Measurement of the time structure of a coherent synchrotron radiation burst in NewSUBARU

The time structure of a burst of coherent synchrotron radiation (CSR) emitted from a high-peak-current beam in the electron storage ring NewSUBARU has been investigated. The source of this CSR burst is fine time structure in a bunch produced by longitudinal beam instability. This burst is unstable but very easy to obtain, so it can be used for some experimental applications with appropriate averaging of data. With an averaging period of 10 ms, the fluctuation of the integrated power was about 10%.     

First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation

First-passage failure of a classical business cycle model subject to time-delayed feedback control and wide-band random excitation is investigated in this paper. First, we get the averaged equation by using a stochastic averaging method, and then a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations analytically and numerically with suitable initial and boundary conditions. The results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first-passage time of the controlled economics system.     

Asymmetry of the time dynamics of breathers in the electroconvection twist structure of a nematic

Dynamics of breather defects in the periodic structures of rolls arising at electroconvection in nematic liquid crystals twisted by π/2 has been studied experimentally and theoretically. The axial components of the velocity of a hydrodynamic flow in the twist structures of nematics are opposite in the neighboring rolls. Dynamics of the breather defect is the periodic creation and annihilation of a pair of classical dislocations with the topological indices “+1” and “-1.” The annihilation occurs faster than the creation. It has been shown that the asymmetric time dynamics of the breather defect is described well by the solution of the perturbed sine-Gordon equation in the form of an interacting soliton and antisoliton.