scholarly journals Power-law patterns in sequences of statistically related events preceding to the main event

2020 ◽  
pp. 102-109
Author(s):  
О.В. Шереметьева
Keyword(s):  
Statistical Analysis ◽  
Power Law ◽  
Power Laws ◽  
Energy Class ◽  
Large Sample Size ◽  
Temporal Region ◽  
Relaxation Model ◽  
Spatio Temporal ◽  
The One ◽  
Seismic Catalog

Используя статистическую модель связанных событий и данные сейсмического каталога КФ ФИЦ ГС РАН за период 01.01.1962-31.12.2002 (n = 79283 события) для зоны субдукции Курило-Камчатской островной дуги (50°-60° с.ш., 156°-166° в.д., классы 4.1-16.1, глубины 0-600 км) построены последовательности событий, предшествующих главному событию заданной магнитуды и связанных с ним в пространственно-временной области. Проведён статистический анализ наличия степенных закономерностей в этих последовательностях на основании релаксационной модели деформационной активности. Степенные закономерности были выделены только в последовательностях связанных событий, предшествующих главному событию с энергетическим классом меньше 12 (показатель степени 0.5-0.7). Это объясняется большим объёмом выборки для главных событий такого класса и небольшой пространственно-временной областью их подготовки, что уменьшает вероятность попадания афтершоков от более крупных событий, предшествующих главному удару, в рассматриваемые последовательности. Using a statistical model of related events and data from the seismic catalog of the FRC GS RAS for the period 01.01.1962-31.12.2002 (n = 79283 events) for the subduction zone of the Kuril-Кamchatka island arc (50°-60° N, 156°-166° E, classes 4.1-16.1, depths 0-600 km) the sequences of events preceding the main event of a given magnitude and associated with it in the spatio-temporal region are constructed. A statistical analysis of the power laws presence in these sequences was carried out on the basis of the relaxation model of deformation activity. It was possible to obtain power-law patterns in sequences of related events for main events thet energy class is less than 12. The exponent takes the values of 0.5-0.7. The possibility of detecting of power-law patterns for the main events of such an energy class is explained by a large sample size for them and by a by a small spatio-temporal region of event preparation that reduces the probability to got the aftershocks from events with larger energy preceding the one under consideration into the sequence of related events.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals Blocks Size Frequency Distribution in the Enceladus Tiger Stripes Area: Implications on Their Formative Processes

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 82
Author(s):  
Maurizio Pajola ◽  
Alice Lucchetti ◽  
Lara Senter ◽  
Gabriele Cremonese
Keyword(s):  
Frequency Distribution ◽  
Power Law ◽  
Size Frequency Distribution ◽  
Surface Stresses ◽  
Size Frequency ◽  
The One ◽  
Power Law Index ◽  
Comet 67P ◽  
South Polar ◽  
Degree Of Fragmentation

We study the size frequency distribution of the blocks located in the deeply fractured, geologically active Enceladus South Polar Terrain with the aim to suggest their formative mechanisms. Through the Cassini ISS images, we identify ~17,000 blocks with sizes ranging from ~25 m to 366 m, and located at different distances from the Damascus, Baghdad and Cairo Sulci. On all counts and for both Damascus and Baghdad cases, the power-law fitting curve has an index that is similar to the one obtained on the deeply fractured, actively sublimating Hathor cliff on comet 67P/Churyumov-Gerasimenko, where several non-dislodged blocks are observed. This suggests that as for 67P, sublimation and surface stresses favor similar fractures development in the Enceladus icy matrix, hence resulting in comparable block disaggregation. A steeper power-law index for Cairo counts may suggest a higher degree of fragmentation, which could be the result of localized, stronger tectonic disruption of lithospheric ice. Eventually, we show that the smallest blocks identified are located from tens of m to 20–25 km from the Sulci fissures, while the largest blocks are found closer to the tiger stripes. This result supports the ejection hypothesis mechanism as the possible source of blocks.

TESTING POWER-LAW RELAXATION SCENARIOS IN A METASTABLE LIQUID

2012 ◽  
Vol 26 (29) ◽  
pp. 1250146 ◽  
Author(s):  
BHASKAR SEN GUPTA ◽  
SHANKAR P. DAS
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Hard Sphere ◽  
Numerical Solutions ◽  
Packing Fraction ◽  
Equilibrium Density ◽  
Density Correlation ◽  
Density Correlation Function ◽  
Basic Model ◽  
The One

The renormalized dynamics described by the equations of nonlinear fluctuating hydrodynamics (NFH) treated at one loop order gives rise to the basic model of the mode coupling theory (MCT). We investigate here by analyzing the density correlation function, a crucial prediction of ideal MCT, namely the validity of the multi step relaxation scenario. The equilibrium density correlation function is calculated here from the direct solutions of NFH equations for a hard sphere system. We make first detailed investigation for the robustness of the correlation functions obtained from the numerical solutions by varying the size of the grid. For an optimum choice of grid size we analyze the decay of the density correlation function to identify the multi-step relaxation process. Weak signatures of two step power law relaxation is seen with exponents which do not match predictions from the one loop MCT. For the final relaxation stretched exponential (KWW) behavior is seen and the relaxation time grows with increase of density. But apparent power law divergences indicate a critical packing fraction much higher than the corresponding MCT predictions for a hard sphere fluid.

scholarly journals Power Laws in Economics: An Introduction

2016 ◽  
Vol 30 (1) ◽  
pp. 185-206 ◽  
Author(s):  
Xavier Gabaix
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Power Laws ◽  
Economic Fluctuations ◽  
Formal Definition ◽  
Empirical Power

Many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. However a series of power laws in economics do count as true and nontrivial quantitative laws—and they are not only established empirically, but also understood theoretically. I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock market. I summarize some of the theoretical explanations that have been proposed. I suggest that power laws help us explain many economic phenomena, including aggregate economic fluctuations. I hope to clarify why power laws are so special, and to demonstrate their utility. In conclusion, I list some power-law-related economic enigmas that demand further exploration. A formal definition may be useful.

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

scholarly journals POWER LAWS IN REAL ESTATE PRICES DURING BUBBLE PERIODS

2012 ◽  
Vol 16 ◽  
pp. 61-81 ◽  
Author(s):  
TAKAAKI OHNISHI ◽  
TAKAYUKI MIZUNO ◽  
CHIHIRO SHIMIZU ◽  
TSUTOMU WATANABE
Keyword(s):  
Real Estate ◽  
Power Law ◽  
House Price ◽  
Power Laws ◽  
Cross Sectional ◽  
Price Distribution ◽  
Before And After ◽  
Real Estate Prices ◽  
Using Data ◽  
The U.S

How can we detect real estate bubbles? In this paper, we propose making use of information on the cross-sectional dispersion of real estate prices. During bubble periods, prices tend to go up considerably for some properties, but less so for others, so that price inequality across properties increases. In other words, a key characteristic of real estate bubbles is not the rapid price hike itself but a rise in price dispersion. Given this, the purpose of this paper is to examine whether developments in the dispersion in real estate prices can be used to detect bubbles in property markets as they arise, using data from Japan and the U.S. First, we show that the land price distribution in Tokyo had a power-law tail during the bubble period in the late 1980s, while it was very close to a lognormal before and after the bubble period. Second, in the U.S. data we find that the tail of the house price distribution tends to be heavier in those states which experienced a housing bubble. We also provide evidence suggesting that the power-law tail observed during bubble periods arises due to the lack of price arbitrage across regions.

Statistical analyses of the physiochemical properties of derived savanna, rainforest landscapes of Delta State Nigeria

2021 ◽  
Vol 1 (2) ◽  
pp. 053-067
Author(s):  
Apezi Okiemute EDEWOR ◽  
Augustus Orowhigo ATUBI
Keyword(s):  
Statistical Analysis ◽  
Soil Fertility ◽  
Physiochemical Properties ◽  
Significance Level ◽  
Fertility Index ◽  
Physiochemical Parameters ◽  
Soil Constituent ◽  
Derived Savanna ◽  
Soil Fertility Index ◽  
The One

The derived savanna landscape of Delta state situated within the rainforest region are always considered with apathy as they are viewed as idle, marginalized or abandoned landscapes. The study therefore focused on statistical analysis of the physiochemical properties of the derived savanna, rainforest and fallow landscapes of Delta state. The statistical analysis gave impetus for the derivation of Soil Fertility Index (SFI). The hypothesis formulated to guide the study was tested using the one-way Analysis of Variance (ANOVA). This was used to test the variation between soil physiochemical parameters of the various landscapes at 0.05 significance level. Specifically, the study found out that the physiochemical parameters of the landscapes studied are significantly correlated. Thus, implying basic similarities in soil fertility and soil constituent tendencies between the landscapes.

Evaluation of changes in mechanical properties of O-ring in one-piece and two-piece ball retained implant-supported overdentures: A three-year retrospective study.

2021 ◽  
Author(s):  
Fathima Banu Raza ◽  
Anand Kumar
Keyword(s):  
Mechanical Properties ◽  
Wear Resistance ◽  
Retrospective Study ◽  
Statistical Analysis ◽  
Wear Rate ◽  
Digital Camera ◽  
Maximum Displacement ◽  
Pin On Disc ◽  
The One ◽  
Insight Into

The o-rings in ball retained overdentures deteriorate with time and need replacement to restore the retentive quality. We evaluated retrospectively the mechanical properties of o-rings after 3 years in function in one and two-piece implant-supported overdentures. The o-rings were retrieved from one-piece (Myriad snap, Equinox-Straumann, 3.3 x 13mm) and two-piece (Neo Biotech, 3.3 x 13mm) implant-supported overdenture patients. A total of 16 pairs of matrices were tested for wear, type of damage and elasticity using Pin on Disc method, USB Digital Camera in 30x zoom and Universal Tensile Machine respectively. The statistical analysis for independent groups were done with the Mann-Whitney U test. Assessment of used O-rings showed 84% more wear in the two-piece system with an abrasive type of damage while 46% wear in the one-piece system with a compressive type of damage. The o-rings in one-piece system showed increase in elongation and maximum displacement to 2% and 7% respectively, while two-piece system showed decrease in elongation and maximum displacement by 13% and 6% respectively. In one-piece system, the loss of retention was more with slow wear rate and in two-piece system, the wear resistance of O-rings decreased due to increased stiffness. Further studies to evaluate the changes in O-ring with increased sample size and at interval 1 year will pave way for insight into the progressive changes in the mechanical properties of an O-ring.

AC Loss Modeling in Ba0.5Sr0.5TiO3 Using Dielectric Relaxation

2004 ◽  
Vol 833 ◽  
Author(s):  
Nadia K. Pervez ◽  
Jiwei Lu ◽  
Susanne Stemmer ◽  
Robert A. York
Keyword(s):  
Dielectric Loss ◽  
Dielectric Relaxation ◽  
Power Law ◽  
Fractional Power ◽  
Ac Loss ◽  
Dielectric Susceptibility ◽  
Network Analyzer ◽  
Q Factor ◽  
Relaxation Model ◽  
Q Factors

ABSTRACTIn universal relaxation, a material's complex dielectric susceptibility follows a fractional power law f1-n where 0 < n < 1 over multiple decades of frequency. In a variety of materials, including Ba0.5Sr0.5Ti03, dielectric relaxation has been observed to follow this universal relaxation model with values of n close to 1. In this work we have shown that the universal relaxation model can be used to calculate dielectric loss even when n is very close to 1. Our calculated Q-factors agree with measured values at 1 MHz; this agreement suggests that this technique may be used for higher frequencies where network analyzer measurements and electrode parasitics complicate Q-factor determination.

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