The response of simple nonlinear systems to a random disturbance of the earthquake type

1964 ◽  
Vol 54 (1) ◽  
pp. 263-276
Author(s):  
J. E. Goldberg ◽  
J. L. Bogdanoff ◽  
D. R. Sharpe
Keyword(s):  
Nonlinear Systems ◽  
First Passage Time ◽  
Equations Of Motion ◽  
Passage Time ◽  
Statistical Properties ◽  
Random Disturbance ◽  
Random Disturbances ◽  
Engineering Significance ◽  
Complex Linear ◽  
Velocity Spectra

abstract Stationary properties of the response of simple nonlinear systems to earthquake type (nonstationary) random disturbances are determined. The method used consists in generating member functions of the input processes, integrating the equations of motion using these as inputs to obtain output member functions, and then, from this ensemble of outputs, determining the statistical properties of interest. The method is flexible in that it is easy to apply to simple as well as complex linear and nonlinear systems; it yields a variety of statistical properties of engineering significance; it provides a method for approaching the design of aseismic structures; and more generally, shock resistant structures on a practical basis. In addition to determining and displaying input and corresponding output member functions, we determine individual as well as average velocity spectra, first passage time probabilities, and extreme value distributions of relative displacements. Comments are also offered on the utility of these results in design.

scholarly journals Passive tracer advection in the equatorial Pacific region: statistics, correlations, and a model of fractional Brownian motion

2021 ◽  
Author(s):  
Imre M. Jánosi ◽  
Amin Padash ◽  
Jason A. C. Gallas ◽  
Holger Kantz
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Southern Oscillation ◽  
First Passage Time ◽  
Time Lag ◽  
Passage Time ◽  
Equatorial Pacific ◽  
Statistical Properties ◽  
Model Parameters ◽  
Passive Tracer

Abstract. Evaluating passive tracer advection is a common tool to study flow structures, particularly Lagrangian trajectories ranging from molecular scales up to the atmosphere and oceans. Here we report on numerical experiments in the region of equatorial Pacific (20° S–20° SN), where 6600 tracer parcels are advected from a regular initial configuration during periods of one year, 25 years altogether. We demonstrate that the strength of the advection exhibits a surprisingly large year by year variability. Furthermore an analysis of cross-correlations between advection strength and El-Niño and Southern Oscillation Indices (SOI) reveal a significant anti-correlation between advection intensity and ONI (Oceanic Niño Index) and a weaker positive correlation with SOI, both with a time lag of about 3 months (the two indices are strongly anti-correlated near real-time). The statistical properties of advection (first passage time, and mean squared displacement) suggest that the westward moving tracers can be mapped into a simple 1D stochastic process, namely fractional Brownian motion. We fit the model parameters and show by numerical simulations of the fractional Brownian motion model that it is able to well reproduce the observed statistical properties of the tracers' trajectories.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap

Spectral Theory for Skip-Free Markov Chains

1989 ◽  
Vol 3 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Joseph Abate ◽  
Ward Whitt
Keyword(s):  
Markov Chains ◽  
Spectral Theory ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage Times ◽  
Simple Relationship ◽  
First Passage ◽  
Birth And Death Processes ◽  
The Laplace Transform ◽  
Passage Times

The distribution of upward first passage times in skip-free Markov chains can be expressed solely in terms of the eigenvalues in the spectral representation, without performing a separate calculation to determine the eigenvectors. We provide insight into this result and skip-free Markov chains more generally by showing that part of the spectral theory developed for birth-and-death processes extends to skip-free chains. We show that the eigenvalues and eigenvectors of skip-free chains can be characterized in terms of recursively defined polynomials. Moreover, the Laplace transform of the upward first passage time from 0 to n is the reciprocal of the nth polynomial. This simple relationship holds because the Laplace transforms of the first passage times satisfy the same recursion as the polynomials except for a normalization.

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