Abstract
Finite time processes within the limits of the Newton equation and zero inertia motion (i.e., road to chaos) are studied by numerically solving the ordinary, stochastic Langevin equation in 1D for a free particle with inertial moving in a medium with viscosity {gamma}. In this simulations, the scaling behaviour of particle trajectories {chi}(t) and velocities v(t) with time are derived and the inclusion of non-zero particle masses is shown to define the asymptotic time limit {tau}{sub c} at which - independently of {gamma} - the system evolves into the well-known statistically stationary state characterized by < {chi}{sup 2}(t) > is proportional to t and flicker noise. The time {tau}{sub c} is further analysed from the correlation length given by the 2-point autocorrelation function of the particle velocity at each value of {gamma}. It is found that the noise power spectrum of v(t) is characterized by flicker noise for frequencies f {<=} f{sub c} {approx} 1/{tau}{sub c}, whereas for f > f{sub c}, the noise power spectra behave as 1/f{sup {upsilon}}, where {upsilon} varies between the limits of Newton`s equation (i.e., {upsilon} = 3) and road to chaos (i.e., {upsilon} = 1). Furthermore, at times {tau} < {tau}{sub c} and 0
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Citation Formats
Canessa, E, and Nguyen, V L.
Stochastic dynamics: Crossover from 1/f{sup 3} to flicker noise.
IAEA: N. p.,
1993.
Web.
Canessa, E, & Nguyen, V L.
Stochastic dynamics: Crossover from 1/f{sup 3} to flicker noise.
IAEA.
Canessa, E, and Nguyen, V L.
1993.
"Stochastic dynamics: Crossover from 1/f{sup 3} to flicker noise."
IAEA.
@misc{etde_10144756,
title = {Stochastic dynamics: Crossover from 1/f{sup 3} to flicker noise}
author = {Canessa, E, and Nguyen, V L}
abstractNote = {Finite time processes within the limits of the Newton equation and zero inertia motion (i.e., road to chaos) are studied by numerically solving the ordinary, stochastic Langevin equation in 1D for a free particle with inertial moving in a medium with viscosity {gamma}. In this simulations, the scaling behaviour of particle trajectories {chi}(t) and velocities v(t) with time are derived and the inclusion of non-zero particle masses is shown to define the asymptotic time limit {tau}{sub c} at which - independently of {gamma} - the system evolves into the well-known statistically stationary state characterized by < {chi}{sup 2}(t) > is proportional to t and flicker noise. The time {tau}{sub c} is further analysed from the correlation length given by the 2-point autocorrelation function of the particle velocity at each value of {gamma}. It is found that the noise power spectrum of v(t) is characterized by flicker noise for frequencies f {<=} f{sub c} {approx} 1/{tau}{sub c}, whereas for f > f{sub c}, the noise power spectra behave as 1/f{sup {upsilon}}, where {upsilon} varies between the limits of Newton`s equation (i.e., {upsilon} = 3) and road to chaos (i.e., {upsilon} = 1). Furthermore, at times {tau} < {tau}{sub c} and 0 < {gamma} < {infinity}, and ad-hoc exponent for the scaling of the variance of particle velocities with time is shown to characterize a subset of multifractal dimensions d{sub f}({gamma}) while the single particle trajectories are shown to display a rather different subset of exponents on increasing {gamma}. Generic features of this transition are nicely given by Poincare maps in the velocity space. (author). 23 refs, 8 figs.}
place = {IAEA}
year = {1993}
month = {Jan}
}
title = {Stochastic dynamics: Crossover from 1/f{sup 3} to flicker noise}
author = {Canessa, E, and Nguyen, V L}
abstractNote = {Finite time processes within the limits of the Newton equation and zero inertia motion (i.e., road to chaos) are studied by numerically solving the ordinary, stochastic Langevin equation in 1D for a free particle with inertial moving in a medium with viscosity {gamma}. In this simulations, the scaling behaviour of particle trajectories {chi}(t) and velocities v(t) with time are derived and the inclusion of non-zero particle masses is shown to define the asymptotic time limit {tau}{sub c} at which - independently of {gamma} - the system evolves into the well-known statistically stationary state characterized by < {chi}{sup 2}(t) > is proportional to t and flicker noise. The time {tau}{sub c} is further analysed from the correlation length given by the 2-point autocorrelation function of the particle velocity at each value of {gamma}. It is found that the noise power spectrum of v(t) is characterized by flicker noise for frequencies f {<=} f{sub c} {approx} 1/{tau}{sub c}, whereas for f > f{sub c}, the noise power spectra behave as 1/f{sup {upsilon}}, where {upsilon} varies between the limits of Newton`s equation (i.e., {upsilon} = 3) and road to chaos (i.e., {upsilon} = 1). Furthermore, at times {tau} < {tau}{sub c} and 0 < {gamma} < {infinity}, and ad-hoc exponent for the scaling of the variance of particle velocities with time is shown to characterize a subset of multifractal dimensions d{sub f}({gamma}) while the single particle trajectories are shown to display a rather different subset of exponents on increasing {gamma}. Generic features of this transition are nicely given by Poincare maps in the velocity space. (author). 23 refs, 8 figs.}
place = {IAEA}
year = {1993}
month = {Jan}
}