Critical Behavior of the Two-Dimensional First Passage Time
نویسنده
چکیده
We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probability p and 1 p, respectively. We prove that as the zero-time bonds approach the percolation threshold p~, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys ~(p) ~ ]p-p, . I ~', then the first passage time constant satisfies /x(p)~ Ip-p , . [ ' . At p,, where it has been asserted that the first passage time from 0 to x scales as Ixl to a power ~b with 0 < ~ < 1, we show that the passage times grow like log IxJ, i.e., the fluid spreads exponentially rapidly.
منابع مشابه
Analysis of Structural Vibrations due to Passage of Underground Trains
During the last decades, the railway traffic in densely populated areas has increased. At the same time, passenger trains have become faster and freight trains have become heavier. Consequently, trains are an increasing source of ground vibration, which may be a nuisance to people, buildings and sensitive equipment. In this research, a two-dimensional dynamic system, including underground train...
متن کاملAn Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation
Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...
متن کاملPost-critical Behavior of Three- dimensional Composite Beams Near the Autoparametric Resonance under Flapwise Excitation
The bifurcation analysis of a composite beam subjected to harmonic flapwise base excitation is studied when the ratio of flapwise and chordwise internal resonances is 1:2. Results are obtained by the numerical solution of modulation equations. Chracteristics of the response are investigated in terms of time history, phase portraits diagrams and bifurcation diagram of poincare maps. It is observ...
متن کاملHealth Information-Seeking Behavior of Iranian first-time Mothers and First-Time Pregnant Women in Northwest Health Centers of Tehran
Introduction: Pregnancy, especially the first pregnancy and childbirth, affects the women’s quality of life. Improving information-seeking behavior facilitates the decision-making process of women during pregnancy and postpartum. The aim of this study was to investigate the health information-seeking behavior of Iranian first-time mothers and first-time pregnant women. Methods: This research...
متن کاملMultifractal Measures Characterized by the Iterative Map with Two Control Parameters
A one dimensional iterative map with two control parameters, i.e. the Kim Kong map, is proposed. Our purpose is to investigate the characteristic properties of this map, and to discuss numerically the multifractal behavior of the normalized first passage time. Especially, based on the Monte Carlo simulation, the normalized first passage time to arrive at the absorbing barrier after starting fro...
متن کامل