Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

2011 ◽  
Vol 52 (8) ◽  
pp. 083301 ◽  
Author(s):  
A. T. Silva ◽  
E. K. Lenzi ◽  
L. R. Evangelista ◽  
M. K. Lenzi ◽  
H. V. Ribeiro ◽  
...  
Keyword(s):  
Anomalous Diffusion ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Fokker Planck Equation ◽  
Fokker Planck

Non-Markovian Fokker-Planck equation: Solutions and first passage time distribution

2006 ◽  
Vol 73 (3) ◽  
Author(s):  
P. C. Assis ◽  
R. P. de Souza ◽  
P. C. da Silva ◽  
L. R. da Silva ◽  
L. S. Lucena ◽  
...  
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Fokker Planck Equation ◽  
Fokker Planck

First-Passage Time for Oscillators With Nonlinear Damping

1978 ◽  
Vol 45 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
First Passage Time ◽  
Digital Simulation ◽  
Planck Equation ◽  
Passage Time ◽  
Nonlinear Damping ◽  
First Passage ◽  
One Dimensional ◽  
Fokker Planck Equation ◽  
First Passage Failure ◽  
Fokker Planck

A simple numerical scheme is proposed for computing the probability of first passage failure, P(T), in an interval O-T, for oscillators with nonlinear damping. The method depends on the fact that, when the damping is light, the amplitude envelope, A(t), can be accurately approximated as a one-dimensional Markov process. Hence, estimates of P(T) are found, for both single and double-sided barriers, by solving the Fokker-Planck equation for A(t) with an appropriate absorbing barrier. The numerical solution of the Fokker-Planck equation is greatly simplified by using a discrete time random walk analog of A(t), with appropriate statistical properties. Results obtained by this method are compared with corresponding digital simulation estimates, in typical cases.

scholarly journals First passage time distribution for anomalous diffusion

2000 ◽  
Vol 273 (5-6) ◽  
pp. 322-330 ◽  
Author(s):  
Govindan Rangarajan ◽  
Mingzhou Ding
Keyword(s):  
Anomalous Diffusion ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage

First passage time distribution of a Wiener process with drift concerning two elastic barriers

1996 ◽  
Vol 33 (01) ◽  
pp. 164-175 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Explicit Expression ◽  
Wiener Process ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Special Choice ◽  
First Passage ◽  
Special Cases ◽  
Reflecting Barriers

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of elastic boundaries and a fixed start point. An explicit expression is obtained for the first passage density. The cases with pure absorbing and/or reflecting barriers arise for a special choice of a parameter constellation. These special cases are compared with results in Darling and Siegert [5] and Sweet and Hardin [15].

scholarly journals The flight of the hornbill: drift and diffusion in arboreal avian movement

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ankit Vikrant ◽  
Janaki Balakrishnan ◽  
Rohit Naniwadekar ◽  
Aparajita Datta
Keyword(s):  
Diffusion Coefficients ◽  
Animal Movement ◽  
Anthropogenic Activities ◽  
First Passage Time ◽  
Mechanistic Model ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Human Settlements ◽  
Fokker Planck

AbstractCapturing movement of animals in mathematical models has long been a keenly pursued direction of research1. Any good model of animal movement is built upon information about the animal’s environment and the available resources including whether prey is in abundance or scarce, densely distributed or sparse2. Such an approach could enable the identification of certain quantities or measures from the model that are species-specific characteristics. We propose here a mechanistic model to describe the movement of two species of Asian hornbills in a resource-abundant heterogenous landscape which includes degraded forests and human settlements. Hornbill telemetry data was used to this end. The birds show a bias both towards features of attraction such as nesting and roosting sites as well as possible bias away from points of repulsion such as human presence. These biases are accounted for with suitable potentials. The spatial patterns of movement are analyzed using the Fokker–Planck equation, which helps explain the variation in movement of different individuals. Search times to target locations were calculated using first passage time equations dual to the Fokker–Planck equations. We also find that the diffusion coefficients are larger for breeding birds than for non-breeding ones—a manifestation of repeated switching of directions to move back to the nest from foraging sites. The degree of directedness towards nests and roosts is captured by the drift coefficients. Non-breeding hornbills show similar values of the ratio of the two coefficients irrespective of the fact that their movement data is available from different seasons. Therefore, the ratio of drift to diffusion coefficients is indicative of an individual’s breeding status, as seen from available data. It could possibly also characterize different species. For all individuals, first passage times increase with proximity to human settlements, in agreement with the premise that anthropogenic activities close to nesting/roosting sites are not desirable.

First passage time distribution of a Wiener process with drift concerning two elastic barriers

1996 ◽  
Vol 33 (1) ◽  
pp. 164-175 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Explicit Expression ◽  
Wiener Process ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Special Choice ◽  
First Passage ◽  
Special Cases ◽  
Reflecting Barriers

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of elastic boundaries and a fixed start point. An explicit expression is obtained for the first passage density. The cases with pure absorbing and/or reflecting barriers arise for a special choice of a parameter constellation. These special cases are compared with results in Darling and Siegert [5] and Sweet and Hardin [15].

Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

1987 ◽  
Vol 1 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Mark Brown ◽  
Yi-Shi Shao
Keyword(s):  
Markov Processes ◽  
Time Distribution ◽  
Infinitesimal Generator ◽  
Spectral Representation ◽  
First Passage Time ◽  
Passage Time ◽  
Spectral Approach ◽  
Generator Matrix ◽  
Eigenvalues And Eigenvectors ◽  
First Passage

The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.

Anomalous diffusion: Fractional Fokker–Planck equation and its solutions

2003 ◽  
Vol 44 (5) ◽  
pp. 2179-2185 ◽  
Author(s):  
E. K. Lenzi ◽  
R. S. Mendes ◽  
Kwok Sau Fa ◽  
L. C. Malacarne ◽  
L. R. da Silva
Keyword(s):  
Anomalous Diffusion ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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