scholarly journals Power-law decay in first-order relaxation processes

2005 ◽  
Vol 72 (2) ◽  
Author(s):  
A. Fondado ◽  
J. Mira ◽  
J. Rivas
Keyword(s):  
Power Law ◽  
Relaxation Processes ◽  
First Order ◽  
Power Law Decay

scholarly journals When an oscillating center in an open system undergoes power law decay

2018 ◽  
Vol 57 (3) ◽  
pp. 750-768 ◽  
Author(s):  
Sandip Saha ◽  
Gautam Gangopadhyay
Keyword(s):  
Power Law ◽  
Open System ◽  
Power Law Decay

scholarly journals Examination of Particle Tails

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Tim Blackwell ◽  
Dan Bratton
Keyword(s):  
Power Law ◽  
Difference Equations ◽  
Particle Swarm ◽  
Second Order ◽  
Particle Swarm Optimisation ◽  
Position Distribution ◽  
Length Scales ◽  
Stochastic Difference Equations ◽  
First Order ◽  
Second Order Equations

The tail of the particle swarm optimisation (PSO) position distribution at stagnation is shown to be describable by a power law. This tail fattening is attributed to particle bursting on all length scales. The origin of the power law is concluded to lie in multiplicative randomness, previously encountered in the study of first-order stochastic difference equations, and generalised here to second-order equations. It is argued that recombinant PSO, a competitive PSO variant without multiplicative randomness, does not experience tail fattening at stagnation.

scholarly journals Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Nils O. Abeling ◽  
Lorenzo Cevolani ◽  
Stefan Kehrein
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Light Cone ◽  
Relativistic Quantum ◽  
Initial State ◽  
Quantum Theories ◽  
Luttinger Model ◽  
Power Law Decay ◽  
Exactly Solvable ◽  
Exponentially Small

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

LONG RANGE CORRELATION PROPERTIES OF AFTERSHOCK RELAXATION SIGNALS

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 839-847 ◽  
Author(s):  
A. VESPIGNANI ◽  
A. PETRI ◽  
A. ALIPPI ◽  
G. PAPARO ◽  
M. COSTANTINI
Keyword(s):  
Time Series ◽  
Acoustic Emission ◽  
Statistical Analysis ◽  
Power Spectrum ◽  
Power Law ◽  
Amplitude Distribution ◽  
Relaxation Processes ◽  
Critical Dynamics ◽  
Range Correlation ◽  
Correlation Properties

Relaxation processes taking place after microfracturing of laboratory samples give rise to ultrasonic acoustic emission signals. Statistical analysis of the resulting time series has revealed many features which are characteristic of critical phenomena. In particular, the autocorrelation functions obey a power-law behavior, implying a power spectrum of the kind 1/f. Also the amplitude distribution N(V) of such signals follows a power law, and the obtained exponents are consistent with those found in other experiments: N(V) dV≃V–γ dV, with γ=1.7±0.2. We also analyzed the distribution N(τ) of the delay time τ between two consecutive acoustic emission events. We found that a N(τ) distribution rather close to a power law constitutes a common feature of all the recorded signals. These experimental results can be considered as a striking evidence for a critical dynamics underlying the microfracturing processes.

scholarly journals Scale properties as a basis of power law relaxation processes

2007 ◽  
Vol 228 (2) ◽  
pp. 107-111 ◽  
Author(s):  
A. Fondado ◽  
J. Mira ◽  
J. Rivas
Keyword(s):  
Power Law ◽  
Relaxation Processes ◽  
Scale Properties

scholarly journals A formula for hidden regular variation behavior for symmetric stable distributions

Extremes ◽  
2020 ◽  
Vol 23 (4) ◽  
pp. 667-691
Author(s):  
Malin Palö Forsström ◽  
Jeffrey E. Steif
Keyword(s):  
Power Law ◽  
Spectral Measure ◽  
Regular Variation ◽  
Stable Distributions ◽  
Decay Rates ◽  
Random Vectors ◽  
Power Law Decay ◽  
Exact Power ◽  
Hidden Regular Variation ◽  
Stable Random Vectors

Abstract We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the set. One sees different decay rates in “different directions”, illustrating the phenomenon of hidden regular variation. We give several examples and obtain quite varied behavior, including sets which do not have exact power-law decay.

scholarly journals On The Critical Phenomena in The Dynamics of Asteroids

1999 ◽  
Vol 172 ◽  
pp. 383-386
Author(s):  
Ivan I. Shevchenko
Keyword(s):  
Phase Space ◽  
Critical Phenomena ◽  
Power Law ◽  
Anomalous Transport ◽  
Selection Effects ◽  
Recurrence Times ◽  
Statistical Selection ◽  
Power Law Decay ◽  
Statistical Effects

AbstractTwo statistical effects in the long-term chaotic asteroidal dynamics are considered, namely the power-law character of the dependence of recurrence times on local Lyapunov times and the power-law decay in the tails of the recurrence distributions. The dependences in both cases are shaped by effects of anomalous transport, due to the presence of the chaos border in phase space, and by statistical selection effects.

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