A stochastic approach to the freezing of supercooled liquids

1983 ◽  
Vol 61 (7) ◽  
pp. 1046-1049 ◽  
Author(s):  
Amal K. Das
Keyword(s):  
Multiplicative Noise ◽  
First Passage Time ◽  
Planck Equation ◽  
Supercooled Liquid ◽  
Stochastic Approach ◽  
Passage Time ◽  
Supercooled Liquids ◽  
Mean First Passage Time ◽  
Deterministic Equation ◽  
The Mean

We have considered the freezing of a supercooled liquid, in particular water, experimentally found to be describable by the phenomenological deterministic equation dn/dt = κn(1–n), n(t) being the fraction of ice. In order to start the process of nucleation, a white noise fluctuation is invoked. This fluctuation is considered both additively and multiplicatively with respect to the deterministic equation. The mean first passage time, a quantity of direct physical interest, is calculated in both cases. With the multiplicative noise, the Itô–Stratonovich route is avoided through a suitable transformation of the Langevin equation and through the study of the resulting Fokker–Planck equation thereof.

The mean first passage time and stochastic resonance in gene transcriptional system with time delay

2016 ◽  
Vol 30 (11) ◽  
pp. 1650067 ◽  
Author(s):  
Y. L. Feng ◽  
J. Zhu ◽  
M. Zhang ◽  
L. L. Gao ◽  
Y. F. Liu ◽  
...  
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Noise Correlation ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Correlation Strength

In this paper, the gene transcriptional dynamics driven by correlated noises are investigated, where the time delay for the synthesis of transcriptional factor is introduced. The effects of the noise correlation strength and time delay on the stationary probability distribution (SPD), the mean first passage time and the stochastic resonance (SR) are analyzed in detail based on the delay Fokker–Planck equation. It is found that both the time delay and noise correlation strength play important roles in the bistable transcriptional system. The effect of the correlation strength reduces but the time delay enhances the mean first passage time (MFPT). Finally, the SR for this gene transcriptional system is found to be enhanced by the time delay.

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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