Investigations on the power-law burst lifetime distribution characteristics of the magnetospheric system

2020 ◽  
Author(s):  
Prince Prasad ◽  
Santhosh Kumar G ◽  
Sumesh Gopinath
Keyword(s):  
Power Law ◽  
Waiting Time ◽  
Probability Distributions ◽  
Sunspot Cycle ◽  
Lifetime Distribution ◽  
Characteristic Time Scale ◽  
General Strategy ◽  
Scaling Exponent ◽  
Time Duration ◽  
Scaling Properties

<p>The waiting time distributions and associated statistical relationships can be considered as a general strategy for analyzing space weather and inner magnetospheric processes to a large extent. It measures the distribution of delay times between subsequent hopping events in such processes. In a physical system the time duration between two events is called a waiting-time, like the time between avalanches. The burst lifetime can be considered as the time duration when magnitude of fluctuations are above a given threshold intensity.  If a characteristic time scale is absent then the probability densities vary with power-law relations having a scaling exponent. The burst lifetime distribution of the substorm index called as the Wp index (Wave and planetary), which reflects Pi2 wave power at low-latitude is considered for the present analysis. Our analysis shows that the lifetime probability distributions of Wp index yield power-law exponents. Even though power-law exponents are observed in magnetospheric proxies for different solar activity periods, not many studies were made to analyze whether these features will repeat or differ depending on sunspot cycle. We compare the variations of power-law exponents of Wp index and other magnetospheric proxies, such as AE index, during solar maxima and solar minima. Thus the study classifies the activity bursts in Wp and other magnetospheric proxies that may have different dynamical critical scaling features. We also expect that the study sheds light into certain stochastic aspects of scaling properties of the magnetosphere which are not developed as global phenomena, but in turn generated due to inherent localized properties of the magnetosphere.</p>

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

scholarly journals Power Laws In Financial Markets: Scaling Exponent H And Alpha-Stable Distributions

2014 ◽  
Vol 31 (1) ◽  
pp. 305 ◽  
Author(s):  
Samet Gunay
Keyword(s):  
Crude Oil ◽  
Foreign Exchange ◽  
Power Law ◽  
Probability Distributions ◽  
Power Laws ◽  
Stable Distributions ◽  
Scaling Exponent ◽  
Parameter Estimations ◽  
Estimated Parameters ◽  
Average Index

In this study, we analyzed whether daily returns of Brent crude oil, dollar/yen foreign exchange, Dow&Jones Industrial Average Index and 12-month libor display power law features in the scaling exponent and probability distributions or not, using different methods. Due to the fact that the simulated time series with different values showed the robustness of Higuchis Fractal Dimension and Pengs Statistic, we used these two models in the analysis of the scaling features of the returns. On the other hand, in order to examine power law behaviors of probability distributions, we estimated parameters of the alpha-stable distributions for the return series using the Ecf and Percentile methods. Results showed that the Brent crude oil and 12-month libor have a high persistency in the returns, while the dollar/yen foreign exchange and Dow&Jones Industrial Average Index returns have short memory. According to the alpha-stable parameter estimations, all of the return series have thicker tails than normal distribution. Similar to the highest persistency of 12-month libor returns in the scaling exponent analysis, we have seen that this variable also has the thickest tails in the probability distributions, meaning that 12-month libor returns have the highest power law features within the series.

scholarly journals Synchronization and desynchronization in the Olami-Feder-Christensen earthquake model and potential implications for real seismicity

2011 ◽  
Vol 18 (5) ◽  
pp. 635-642 ◽  
Author(s):  
S. Hergarten ◽  
R. Krenn
Keyword(s):  
Power Law ◽  
Statistical Properties ◽  
Scaling Exponent ◽  
Power Law Distribution ◽  
Scaling Properties ◽  
Temporal Clustering ◽  
Self Organized ◽  
Earthquake Model ◽  
Self Organized Criticality ◽  
Large Earthquakes

Abstract. The Olami-Feder-Christensen model is probably the most studied model in the context of self-organized criticality and reproduces several statistical properties of real earthquakes. We investigate and explain synchronization and desynchronization of earthquakes in this model in the nonconservative regime and its relevance for the power-law distribution of the event sizes (Gutenberg-Richter law) and for temporal clustering of earthquakes. The power-law distribution emerges from synchronization, and its scaling exponent can be derived as τ = 1.775 from the scaling properties of the rupture areas' perimeter. In contrast, the occurrence of foreshocks and aftershocks according to Omori's law is closely related to desynchronization. This mechanism of foreshock and aftershock generation differs strongly from the widespread idea of spontaneous triggering and gives an idea why some even large earthquakes are not preceded by any foreshocks in nature.

scholarly journals Crackling noise and avalanches in minerals

2021 ◽  
Vol 48 (5) ◽  
Author(s):  
Ekhard K. H. Salje ◽  
Xiang Jiang
Keyword(s):  
Electric Fields ◽  
Power Law ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fractal Dimensions ◽  
Similar Time ◽  
Scaling Properties ◽  
Pattern Formations ◽  
Observation Method ◽  
Great Complexity

AbstractThe non-smooth, jerky movements of microstructures under external forcing in minerals are explained by avalanche theory in this review. External stress or internal deformations by impurities and electric fields modify microstructures by typical pattern formations. Very common are the collapse of holes, the movement of twin boundaries and the crushing of biominerals. These three cases are used to demonstrate that they follow very similar time dependences, as predicted by avalanche theories. The experimental observation method described in this review is the acoustic emission spectroscopy (AE) although other methods are referenced. The overarching properties in these studies is that the probability to observe an avalanche jerk J is a power law distributed P(J) ~ J−ε where ε is the energy exponent (in simple mean field theory: ε = 1.33 or ε = 1.66). This power law implies that the dynamic pattern formation covers a large range (several decades) of energies, lengths and times. Other scaling properties are briefly discussed. The generated patterns have high fractal dimensions and display great complexity.

scholarly journals A Brief Review of Generalized Entropies

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 813 ◽  
Author(s):  
José Amigó ◽  
Sámuel Balogh ◽  
Sergio Hernández
Keyword(s):  
Diffusion Processes ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Point Of View ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Physical Systems ◽  
New Phenomena ◽  
Generalized Entropies

Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon–Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.

scholarly journals Estimating The Sea Ice Floe Size Distribution Using Satellite Altimetry: Theory, Climatology, and Model Comparison

2019 ◽  
Author(s):  
Christopher Horvat ◽  
Lettie Roach ◽  
Rachel Tilling ◽  
Cecilia Bitz ◽  
Baylor Fox-Kemper ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Model Comparison ◽  
Climate Model ◽  
Thickness Distribution ◽  
Wave Model ◽  
Polar Regions ◽  
Scaling Exponent ◽  
Ocean Surface Waves

Abstract. In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are spare – traditionally taken via a pain-staking analysis of ice surface photography – and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this power-law hypothesis. Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radio altimetric record, covering the period from 2010–2018, and incorporating 11 million individual floe samples, we produce the first climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture.

On Higher-Order Crack-Tip Fields in Creeping Solids

1999 ◽  
Vol 67 (2) ◽  
pp. 372-382 ◽  
Author(s):  
B. N. Nguyen ◽  
P. R. Onck ◽  
E. van der Giessen
Keyword(s):  
Power Law ◽  
Crack Tip ◽  
Small Strain ◽  
Higher Order ◽  
Single Edge ◽  
Constraint Effect ◽  
Scaling Properties ◽  
Crack Tip Fields ◽  
Asymptotic Development ◽  
Loading Parameter

In view of the near-tip constraint effect imposed by the geometry and loading configuration, a creep fracture analysis based on C* only is generally not sufficient. This paper presents a formulation of higher-order crack-tip fields in steady power-law creeping solids which can be derived from an asymptotic development of near-tip fields analogous to that of Sharma and Aravas and Yang et al. for elastoplastic bodies. The higher-order fields are controlled by a parameter named A2*, similar as in elastoplasticity, and a second loading parameter, σ∞. By means of the scaling properties for power-law materials, it is shown that A2* for a flat test specimen is independent of the loading level. Finally, we carry out small-strain finite element analyses of creep in single-edge notched tension, centered crack panel under tension, and single-edge notched bending specimens in order to determine the corresponding values of A2* for mode I cracks under plane-strain conditions. [S0021-8936(00)01202-2]

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

2018 ◽  
Vol 20 (32) ◽  
pp. 20827-20848 ◽  
Author(s):  
Ru Hou ◽  
Andrey G. Cherstvy ◽  
Ralf Metzler ◽  
Takuma Akimoto
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Power Law ◽  
Waiting Time ◽  
Continuous Time ◽  
Zero Drift ◽  
Renewal Processes ◽  
Waiting Time Distributions ◽  
Continuous Time Random Walks ◽  
Ergodicity Breaking

We examine renewal processes with power-law waiting time distributions and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics.

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