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

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 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

Correlations versus causality in Stochastic Long-range Forecasting as a Past Value Problem

2021 ◽  
Author(s):  
Lenin Del Rio Amador ◽  
Shaun Lovejoy
Keyword(s):  
Granger Causality ◽  
Long Range ◽  
Power Law ◽  
Weather Prediction ◽  
Emergent Properties ◽  
Relaxation Processes ◽  
Initial Value ◽  
Relaxation Equation ◽  
Cross Correlations

<p>Over time scales between 10 days and 10-20 years – the macroweather regime – atmospheric fields, including the temperature, respect statistical scale symmetries, such as power-law correlations, that imply the existence of a huge memory in the system that can be exploited for long-term forecasts. The Stochastic Seasonal to Interannual Prediction System (StocSIPS) is a stochastic model that exploits these symmetries to perform long-term forecasts. It models the temperature as the high-frequency limit of the (fractional) energy balance equation (fractional Gaussian noise) which governs radiative equilibrium processes when the relevant equilibrium relaxation processes are power law, rather than exponential. They are obtained when the order of the relaxation equation is fractional rather than integer and they are solved as past value problems rather than initial value problems.</p><p>Long-range weather prediction is conventionally an initial value problem that uses the current state of the atmosphere to produce ensemble forecasts. In contrast, StocSIPS predictions for long-memory processes are “past value” problems that use historical data to provide conditional forecasts. Cross-correlations can be used to define teleconnection patterns, and for identifying possible dynamical interactions, but they do not necessarily imply any causation. Using the precise notion of Granger causality, we show that for long-range stochastic temperature forecasts, the cross-correlations are only relevant at the level of the innovations – not temperatures. Extended here to the multivariate case, (m-StocSIPS) produces realistic space-time temperature simulations. Although it has no Granger causality, we are able to reproduce emergent properties including realistic teleconnection networks and El Niño events and indices.</p>

Using regional scaling for temperature forecasts with the Stochastic Seasonal to Interannual Prediction System (StocSIPS).

2021 ◽  
Author(s):  
Lenin Del Rio Amador ◽  
Shaun Lovejoy
Keyword(s):  
Stochastic Model ◽  
Power Law ◽  
Grid Point ◽  
Relaxation Processes ◽  
Prediction System ◽  
Relaxation Equation ◽  
Deterministic Models ◽  
Global Circulation Models ◽  
Skill Scores

Abstract Over time scales between 10 days and 10–20 years – the macroweather regime – atmospheric fields, including the temperature, respect statistical scale symmetries, such as power-law correlations, that imply the existence of a huge memory in the system that can be exploited for long-term forecasts. The Stochastic Seasonal to Interannual Prediction System (StocSIPS) is a stochastic model that exploits these symmetries to perform long-term forecasts. It models the temperature as the high-frequency limit of the (fractional) energy balance equation (fractional Gaussian noise) which governs radiative equilibrium processes when the relevant equilibrium relaxation processes are power law, rather than exponential. They are obtained when the order of the relaxation equation is fractional rather than integer and they are solved as past value problems rather than initial value problems. StocSIPS was first developed for monthly and seasonal forecast of globally averaged temperature. In this paper, we extend it to the prediction of the spatially resolved temperature field by treating each grid point as an independent time series. Compared to traditional global circulation models (GCMs), StocSIPS has the advantage of forcing predictions to converge to the real-world climate. It extracts the internal variability (weather noise) directly from past data and does not suffer from model drift. Here we apply StocSIPS to obtain monthly and seasonal predictions of the surface temperature and show some preliminary comparison with multi-model ensemble (MME) GCM results. For one month lead time, our simple stochastic model shows similar values of the skill scores than the much more complex deterministic models.

scholarly journals Transient Deformation and Stress Patterns Induced by the 2010 Maule Earthquake in the Illapel Segment

2021 ◽  
Vol 9 ◽  
Author(s):  
Carlos Peña ◽  
Oliver Heidbach ◽  
Marcos Moreno ◽  
Daniel Melnick ◽  
Onno Oncken
Keyword(s):  
Power Law ◽  
Postseismic Deformation ◽  
Relaxation Processes ◽  
Megathrust Earthquakes ◽  
Transient Deformation ◽  
Maule Earthquake ◽  
2010 Maule Earthquake ◽  
Illapel Earthquake ◽  
The Impact ◽  
Rheology Model

Evaluating the transfer of stresses from megathrust earthquakes to adjacent segments is fundamental to assess seismic hazard. Here, we use a 3D forward model as well as GPS and seismic data to investigate the transient deformation and Coulomb Failure Stresses (CFS) changes induced by the 2010 Maule earthquake in its northern segment, where the Mw 8.3 Illapel earthquake occurred in 2015. The 3D model incorporates the coseismically instantaneous, elastic response, and time-dependent afterslip and viscoelastic relaxation processes in the postseismic period. We particularly examine the impact of linear and power-law rheology on the resulting postseismic deformation and CFS changes that may have triggered the Illapel earthquake. At the Illapel hypocenter, our model results in CFS changes of ∼0.06 bar due to the coseismic and postseismic deformation, where the coseismic deformation accounts for ∼85% of the total CFS changes. This is below the assumed triggering threshold of 0.1 bar and, compared to the annual loading rate of the plate interface, represents a clock advance of approximately only 2 months. However, we find that sixteen events with Mw ≥ 5 in the southern region occurred in regions of CFS changes > 0.1 bar, indicating a potential triggering by the Maule event. Interestingly, while the power-law rheology model increases the positive coseismic CFS changes, the linear rheology reduces them. This is due to the opposite polarity of the postseismic displacements resulting from the rheology model choice. The power-law rheology model generates surface displacements that fit better to the GPS-observed landward displacement pattern.

scholarly journals Insight into Electrical and Dielectric Relaxation of Doped Tellurite Lithium-Silicate Glasses with Regard to Ionic Charge Carrier Number Density Estimation

Materials ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5232
Author(s):  
Young Hoon Rim ◽  
Chang Gyu Baek ◽  
Yong Suk Yang
Keyword(s):  
Power Law ◽  
Direct Current ◽  
Lithium Ion ◽  
Lithium Silicate ◽  
Relaxation Processes ◽  
Ionic Charge ◽  
Potential Wells ◽  
Disordered Solids ◽  
Direct Current Conductivity ◽  
Current Activation

We investigate the role of tellurite on a lithium-silicate glass 0.1 TeO2 − 0.9 (Li2O-2SiO2) (LSTO) system proposed for the use in solid electrolyte for lithium ion batteries. The measurements of electrical impedance are performed in the frequency 100 Hz–30 MHz and temperature from 50 to 150 °C. The electrical conductivity of LSTO glass increases compared with that of Li2O-2SiO2 (LSO) glass due to an increase in the number of Li+ ions. The ionic hopping and relaxation processes in disordered solids are generally explained using Cole–Cole, power law and modulus representations. The power law conductivity analysis, which is driven by the modified Rayleigh equation, presents the estimation of the number of ionic charge carriers explicitly. The estimation counts for direct contribution of about a 14% increase in direct current conductivity in the case of TeO2 doping. The relaxation process by modulus analysis confirms that the cations are trapped strongly in the potential wells. Both the direct current and alternating current activation energies (0.62–0.67 eV) for conduction in the LSO glass are the same as those in the LSTO glass.

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