One-dimensional generalized branching annihilating random walker process with stochastic generation of offsprings

1997 ◽  
Vol 239 (4) ◽  
pp. 531-541 ◽  
Author(s):  
Ezequiel V. Albano ◽  
Miguel Hoyuelos ◽  
Héctor O. Martin
Keyword(s):  
Stochastic Generation ◽  
One Dimensional ◽  
Random Walker

scholarly journals S-shooting: a Bennett–Chandler-like method for the computation of rate constants from committor trajectories

2016 ◽  
Vol 195 ◽  
pp. 345-364 ◽  
Author(s):  
Georg Menzl ◽  
Andreas Singraber ◽  
Christoph Dellago
Keyword(s):  
Rate Constants ◽  
Simulation Method ◽  
Free Energy Calculations ◽  
Stable States ◽  
One Dimensional ◽  
Random Walker ◽  
Reaction Rate Constants ◽  
Definition Of ◽  
Double Well Potential ◽  
Condensed Systems

Mechanisms of rare transitions between long-lived stable states are often analyzed in terms of commitment probabilities, determined from swarms of short molecular dynamics trajectories. Here, we present a computer simulation method to determine rate constants from such short trajectories combined with free energy calculations. The method, akin to the Bennett–Chandler approach for the calculation of reaction rate constants, requires the definition of a valid reaction coordinate and can be applied to both under- and overdamped dynamics. We verify the correctness of the algorithm using a one-dimensional random walker in a double-well potential and demonstrate its applicability to complex transitions in condensed systems by calculating cavitation rates for water at negative pressures.

scholarly journals MULTIFRACTAL MEASURES ON SMALL-WORLD NETWORKS

Fractals ◽  
2006 ◽  
Vol 14 (02) ◽  
pp. 119-123 ◽  
Author(s):  
K. H. CHANG ◽  
B. C. CHOI ◽  
SEONG-MIN YOON ◽  
KYUNGSIK KIM
Keyword(s):  
First Passage Time ◽  
Small World ◽  
Passage Time ◽  
Small World Network ◽  
Small World Networks ◽  
First Passage ◽  
One Dimensional ◽  
Random Walker ◽  
Regular Networks ◽  
First Time

We investigate the multifractals of the first passage time on a one-dimensional small-world network with reflecting and absorbing barriers. The multifractals can be obtained from the distribution of the first passage time at which the random walker arrives for the first time at an absorbing barrier after starting from an arbitrary initial site. Our simulation is found to estimate the fractal dimension D0 = 0.920 ~ 0.930 for the different network sizes and random rewiring fractions. In particular, the multifractal structure breaks down into a small-world network, when the rewiring fraction p is larger than the critical value pc = 0.3. Our simulation results are compared with the numerical computations for regular networks.

On the Time Transition Between Short- and Long-Time Regimes of Colloidal Particles in External Periodic Potentials

2021 ◽  
Vol 9 ◽  
Author(s):  
Daniela Pérez-Guerrero ◽  
José Luis Arauz-Lara ◽  
Erick Sarmiento-Gómez ◽  
Guillermo Iván Guerrero-García
Keyword(s):  
Colloidal Particles ◽  
First Passage Time ◽  
Critical Time ◽  
Passage Time ◽  
First Passage ◽  
Escape Probability ◽  
One Dimensional ◽  
Random Walker ◽  
Dimensional Array ◽  
Long Time

The dynamics of colloidal particles at infinite dilution, under the influence of periodic external potentials, is studied here via experiments and numerical simulations for two representative potentials. From the experimental side, we analyzed the motion of a colloidal tracer in a one-dimensional array of fringes produced by the interference of two coherent laser beams, providing in this way an harmonic potential. The numerical analysis has been performed via Brownian dynamics (BD) simulations. The BD simulations correctly reproduced the experimental position- and time-dependent density of probability of the colloidal tracer in the short-times regime. The long-time diffusion coefficient has been obtained from the corresponding numerical mean square displacement (MSD). Similarly, a simulation of a random walker in a one dimensional array of adjacent cages with a probability of escaping from one cage to the next cage is one of the most simple models of a periodic potential, displaying two diffusive regimes separated by a dynamical caging period. The main result of this study is the observation that, in both potentials, it is seen that the critical time t*, defined as the specific time at which a change of curvature in the MSD is observed, remains approximately constant as a function of the height barrier U0 of the harmonic potential or the associated escape probability of the random walker. In order to understand this behavior, histograms of the first passage time of the tracer have been calculated for several height barriers U0 or escape probabilities. These histograms display a maximum at the most likely first passage time t′, which is approximately independent of the height barrier U0, or the associated escape probability, and it is located very close to the critical time t*. This behavior suggests that the critical time t*, defining the crossover between short- and long-time regimes, can be identified as the most likely first passage time t′ as a first approximation.

MULTIFRACTALS ON SMALL-WORLD NETWORKS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4059-4063
Author(s):  
KYUNGSIK KIM ◽  
K. H. CHANG ◽  
DEOCK-HO HA
Keyword(s):  
First Passage Time ◽  
Small World ◽  
Passage Time ◽  
Small World Network ◽  
Small World Networks ◽  
First Passage ◽  
One Dimensional ◽  
Random Walker ◽  
Regular Networks ◽  
First Time

We investigate the multifractals of the first passage time on a one-dimensional small-world network with reflecting and absorbing barriers. We analyze numerically the distribution of the first passage time at which the random walker arrives for the first time at an absorbing barrier after starting from an arbitrary initial site. Our simulation is found to estimate the fractal dimension D0 = 0.920 ∼ 0.930 for the different network sizes and random rewiring fractions. In particular, our simulation results are compared with the numerical computations for regular networks.

scholarly journals Solution and Analysis of a One-Dimensional First-Passage Problem with a Nonzero Halting Probability

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ken Yamamoto
Keyword(s):  
Moment Generating Function ◽  
Hitting Time ◽  
Gauss Hypergeometric Function ◽  
Time Behavior ◽  
First Passage ◽  
One Dimensional ◽  
Random Walker ◽  
Calculation Technique ◽  
The Right ◽  
First Passage Problem

This paper treats a kind of a one-dimensional first-passage problem, which seeks the probability that a random walker first hits the origin at a specified time. In addition to a usual random walk which hops either rightwards or leftwards, the present paper introduces the “halt” that the walker does not hop with a nonzero probability. The solution to the problem is expressed using a Gauss hypergeometric function. The moment generating function of the hitting time is also calculated, and a calculation technique of the moments is developed. The author derives the long-time behavior of the hitting-time distribution, which exhibits power-law behavior if the walker hops to the right and left with equal probability.

Searching for a one-dimensional random walker

1974 ◽  
Vol 11 (01) ◽  
pp. 86-93 ◽  
Author(s):  
Bernard J. McCabe
Keyword(s):  
Random Walk ◽  
Wiener Process ◽  
One Dimensional ◽  
Random Walker ◽  
Search Plan ◽  
Crossing Time ◽  
Definition Of ◽  
First Crossing Time ◽  
Finite Moments ◽  
Bernoulli Random Walk

Let {xk } k ≧ − r be a simple Bernoulli random walk with x –r = 0. An integer valued threshold ϕ = {ϕ k } k≧1 is called a search plan if |ϕ k+1−ϕ k |≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ 1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

Searching for a one-dimensional random walker

1974 ◽  
Vol 11 (1) ◽  
pp. 86-93 ◽  
Author(s):  
Bernard J. McCabe
Keyword(s):  
Random Walk ◽  
Wiener Process ◽  
One Dimensional ◽  
Random Walker ◽  
Search Plan ◽  
Crossing Time ◽  
Definition Of ◽  
First Crossing Time ◽  
Finite Moments ◽  
Bernoulli Random Walk

Let {xk}k ≧ − r be a simple Bernoulli random walk with x–r = 0. An integer valued threshold ϕ = {ϕk}k≧1 is called a search plan if |ϕk+1−ϕk|≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

On an exit problem in a one-dimensional random walk in the diffusion approximation

1991 ◽  
Vol 69 (10) ◽  
pp. 1284-1285
Author(s):  
Amal K. Das
Keyword(s):  
Diffusion Coefficient ◽  
Random Walk ◽  
Diffusion Approximation ◽  
Brownian Particle ◽  
Linear Chain ◽  
One Dimensional ◽  
Random Walker ◽  
Exit Problem ◽  
Traversal Time

We address a nonstandard random-walk problem in which the random walker, a Brownian particle, enters a linear chain at x = 0 and exits at x = L under the constraint that allows the particle to return to an arbitrarily close neighbourhood of the entrance point, but does not allow the entrance point to be touched back. In the diffusion approximation, the traversal time T*, calculated in an unconventional way, is found to be T/3, where T is the usual diffusion traversal time, L2/2D, D being the diffusion coefficient.

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