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.

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

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

scholarly journals First-passage distributions for the one-dimensional Fokker-Planck equation

2018 ◽  
Vol 98 (4) ◽  
Author(s):  
Oriol Artime ◽  
Nagi Khalil ◽  
Raúl Toral ◽  
Maxi San Miguel
Keyword(s):  
Planck Equation ◽  
First Passage ◽  
One Dimensional ◽  
Fokker Planck Equation ◽  
The One ◽  
Fokker Planck

scholarly journals First-Passage Failure of Quasi-Integrable Hamiltonian Systems

2002 ◽  
Vol 69 (3) ◽  
pp. 274-282 ◽  
Author(s):  
W. Q. Zhu ◽  
M. L. Deng ◽  
Z. L. Huang
Keyword(s):  
Hamiltonian Systems ◽  
First Passage Time ◽  
Digital Simulation ◽  
Reliability Function ◽  
Passage Time ◽  
Kolmogorov Equation ◽  
Conditional Probability Density ◽  
Integrable Hamiltonian Systems ◽  
First Passage ◽  
First Passage Failure

The first-passage failure of quasi-integrable Hamiltonian systems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito^ stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamitonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

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.

On Statistics of First-Passage Failure

1994 ◽  
Vol 61 (1) ◽  
pp. 93-99 ◽  
Author(s):  
G. Q. Cai ◽  
Y. K. Lin
Keyword(s):  
Boundary Conditions ◽  
First Passage Time ◽  
Passage Time ◽  
Natural Boundary ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
First Passage Failure ◽  
First Time ◽  
Pontryagin Equation

The event in which the response of a randomly excited dynamical system passes, for the first time, a critical magnitude zc is investigated. When the response variable in question can be modeled as a one-dimensional diffusion process, defined on [zl, zc], the statistical moment of the first passage time of an arbitrary order is governed by the classical Pontryagin equation, subject to suitable boundary conditions. It is shown that, when a boundary is singular, it must be either an entrance, a regular boundary, or a repulsive natural boundary in order that a solution for the Pontryagin equation is physically meaningful. Boundary conditions are obtained for three types of singular boundaries and applied to the second-order oscillators in which the amplitude or energy process can be approximated as a Markov process. Illustrative examples are given of linear and nonlinear oscillators under additive and/or multiplicative random excitations.

An Experimental Study of First-Passage Failure of a Randomly Excited Structure

1978 ◽  
Vol 45 (4) ◽  
pp. 917-922 ◽  
Author(s):  
J. B. Roberts ◽  
S. N. Yousri
Keyword(s):  
First Passage Time ◽  
Nonlinear Effects ◽  
Theoretical Method ◽  
Passage Time ◽  
Nonlinear Damping ◽  
First Passage ◽  
Free Decay ◽  
First Passage Failure ◽  
The Mean ◽  
Decay Tests

Some experimental measurements of the mean and standard deviation of the first-passage time of randomly excited cantilevers are presented. It is shown that these results can be predicted satisfactorily by using a theoretical method based on the energy envelope of the structure, together with information on the energy loss per cycle. This information can be derived either from free decay tests or from data on specific damping factors. The prediction technique does not require the damping forces to be modeled in explicit form and enables nonlinear damping effects to be readily incorporated. Some predicted nonlinear effects are confirmed by the experimental results.

First-passage-time densities for time-non-homogeneous diffusion processes

1997 ◽  
Vol 34 (3) ◽  
pp. 623-631 ◽  
Author(s):  
R. Gutiérrez ◽  
L. M. Ricciardi ◽  
P. Román ◽  
F. Torres
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Continuous Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Natural Boundaries

In this paper we study a Volterra integral equation of the second kind, including two arbitrary continuous functions, in order to determine first-passage-time probability density functions through time-dependent boundaries for time-non-homogeneous one-dimensional diffusion processes with natural boundaries. These results generalize those which were obtained for time-homogeneous diffusion processes by Giorno et al. [3], and for some particular classes of time-non-homogeneous diffusion processes by Gutiérrez et al. [4], [5].

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