scholarly journals First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Aljaž Godec ◽  
Ralf Metzler
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean

Some mean first-passage time approximations for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (3) ◽  
pp. 600-604 ◽  
Author(s):  
Marlin U. Thomas
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Accurate Method ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Numerical Comparisons ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.

scholarly journals Polymer Translocation Across a Corrugated Channel: Fick–Jacobs Approximation Extended Beyond the Mean First-Passage Time

Polymers ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 251 ◽  
Author(s):  
Paolo Malgaretti ◽  
Gleb Oshanin
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
Characteristic Time Scale ◽  
Mean First Passage Time ◽  
First Passage ◽  
Systematic Analysis ◽  
Corrugated Channel ◽  
The Mean ◽  
Polymer Translocation

Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time-scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocation dynamics of a Gaussian polymer in a periodically-corrugated channel using an appropriately generalized Fick–Jacobs approach. Our main aim is to probe an effective broadness of the first-passage time distribution (FPTD), by determining the so-called coefficient of variation γ of the FPTD, defined as the ratio of the standard deviation versus the mean first-passage time (MFPT). We present a systematic analysis of γ as a function of a variety of system’s parameters. We show that γ never significantly drops below 1 and, in fact, can attain very large values, implying that the MFPT alone cannot characterize the first-passage statistics of the translocation process exhaustively well.

Some mean first-passage time approximations for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (03) ◽  
pp. 600-604 ◽  
Author(s):  
Marlin U. Thomas
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Accurate Method ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Numerical Comparisons ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.

scholarly journals Mean first-passage time of a tumor cell growth system with time delay and colored cross-correlated noises excitation

2017 ◽  
Vol 37 (2) ◽  
pp. 191-198 ◽  
Author(s):  
Shenghong Li ◽  
Yong Huang
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Tumor Cell Growth ◽  
First Passage ◽  
Growth System ◽  
The Mean ◽  
Correlated Noises

In this paper, the mean first-passage time of a delayed tumor cell growth system driven by colored cross-correlated noises is investigated. Based on the Novikov theorem and the method of probability density approximation, the stationary probability density function is obtained. Then applying the fastest descent method, the analytical expression of the mean first-passage time is derived. Finally, effects of different kinds of delays and noise parameters on the mean first-passage time are discussed thoroughly. The results show that the time delay included in the random force, additive noise intensity and multiplicative noise intensity play a positive role in the disappearance of tumor cells. However, the time delay included in the determined force and the correlation time lead to the increase of tumor cells.

Scaling of average receiving time on double-weighted polygon networks

2021 ◽  
Author(s):  
Xiaoyan Li ◽  
Yu Sun
Keyword(s):  
Iterative Method ◽  
Path Length ◽  
First Passage Time ◽  
Passage Time ◽  
Traffic Networks ◽  
Mean First Passage Time ◽  
First Passage ◽  
Specific Calculation ◽  
Calculation Process ◽  
The Mean

In this paper, we introduce a class of double-weighted polygon networks with two different meanings of weighted factors [Formula: see text] and [Formula: see text], which represent path-difficulty and path-length, respectively, based on actual traffic networks. Picking an arbitrary node from the hub nodes set as the trap node, and the double-weighted polygon networks are divided into [Formula: see text] blocks by combining with the iterative method. According to biased random walks, the calculation expression of average receiving time (ART) of any polygon networks is given by using the intermediate quantity the mean first-passage time (MFPT), which is applicable to any [Formula: see text] ([Formula: see text]) polygon networks. What is more, we display the specific calculation process and results of ART of the double-weighted quadrilateral networks, indicating that ART grows exponentially with respect to the networks order and the exponent is [Formula: see text] which grows with the product of [Formula: see text]. When [Formula: see text] increases, ART increases linearly ([Formula: see text]) or sublinearly ([Formula: see text]) with the size of networks, and the smaller value of [Formula: see text], the higher transportation efficiency.

Calculations of first passage time of delayed tree-like networks

2015 ◽  
Vol 29 (28) ◽  
pp. 1550200
Author(s):  
Shuai Wang ◽  
Weigang Sun ◽  
Song Zheng
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
The Novel ◽  
Mean First Passage Time ◽  
First Passage ◽  
Initial Node ◽  
Network Parameters ◽  
Self Similar ◽  
The Mean

In this paper, we study random walks in a family of delayed tree-like networks controlled by two network parameters, where an immobile trap is located at the initial node. The novel feature of this family of networks is that the existing nodes have a time delay to give birth to new nodes. By the self-similar network structure, we obtain exact solutions of three types of first passage time (FPT) measuring the efficiency of random walks, which includes the mean receiving time (MRT), mean sending time (MST) and mean first passage time (MFPT). The obtained results show that the MRT, MST and MFPT increase with the network parameters. We further show that the values of MRT, MST and MFPT are much shorter than the nondelayed counterpart, implying that the efficiency of random walks in delayed trees is much higher.

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