scholarly journals Dynamic correlation length scales under isochronal conditions

2015 ◽  
Vol 142 (6) ◽  
pp. 064504 ◽  
Author(s):  
R. Casalini ◽  
D. Fragiadakis ◽  
C. M. Roland
Keyword(s):  
Correlation Length ◽  
Length Scales ◽  
Dynamic Correlation

scholarly journals Statistical characterization of gas-patch distributions in partially saturated rocks

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA51-WA64 ◽  
Author(s):  
Julianna Toms-Stewart ◽  
Tobias M. Müller ◽  
Boris Gurevich ◽  
Lincoln Paterson
Keyword(s):  
Correlation Function ◽  
Autocorrelation Function ◽  
Correlation Length ◽  
Wave Attenuation ◽  
Length Scales ◽  
Gas Saturation ◽  
Partially Saturated ◽  
Statistical Measures ◽  
Fluid Saturation ◽  
Limestone Sample

Reservoir rocks are often saturated by two or more fluid phases forming complex patterns on all length scales. The objective of this work is to quantify the geometry of fluid phase distribution in partially saturated porous rocks using statistical methods and to model the associated acoustic signatures. Based on X-ray tomographic images at submillimeter resolution obtained during a gas-injection experiment, the spatial distribution of the gas phase in initially water-saturated limestone samples are constructed. Maps of the continuous variation of the percentage of gas saturation are computed and associated binary maps obtained through a global thresholding technique. The autocorrelation function is derived via the two-point probability function computed from the binary gas-distribution maps using Monte Carlo simulations.The autocorrelation function can be approximated well by a single Debye correlation function or a superposition of two such functions. The characteristic length scales and show sensitivity (and hence significance) with respect to the percentage of gas saturation. An almost linear decrease of the Debye correlation length occurs with increasing gas saturation. It is concluded that correlation function and correlation length provide useful statistical information to quantify fluid-saturation patterns and changes in these patterns at the mesoscale. These spatial statistical measures are linked to a model that predicts compressional wave attenuation and dispersion from local, wave-induced fluid flow in randomly heterogeneous poroelastic solids. In particular, for a limestone sample, with flow permeability of 5 darcies and an average gas saturation of [Formula: see text], significant [Formula: see text]-wave attenuation is predicted at ultrasonic frequencies.

FRACTALS AND THE UNIVERSE

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 567-579
Author(s):  
PAUL H. COLEMAN
Keyword(s):  
Correlation Length ◽  
Galaxy Formation ◽  
Power Law ◽  
Fractal Geometry ◽  
Fractal Structure ◽  
Length Scales ◽  
Small Scales ◽  
Walker Metric ◽  
Galaxy Masses ◽  
The Universe

Many examples of fractal geometry are seen in the field of Astronomy, from nearby objects such as our Sun, to phenomena at intermediate length scales in our Galaxy such as the distribution of masers. This paper will give many examples of various length scales and finally concentrates on the largest scales which can be probed in our universe, with analyses of locations of galaxies. It has been known for some twenty years that the distribution of galaxies on small scales is fractal. This is seen in analyses which indicate that both galaxies and their clusters are power law correlated (a signature of fractal behavior). At larger length scales the distribution is supposed to exhibit a so-called correlation length and was thought to then become homogeneous—except for occasional fluctuations. More data and subsequent analysis have shown that these fluctuations are anything but occasional, as structures are seen to exist on length scales up to the maximum scales which can be probed with the new data. By reanalyzing the data, with methods that are particularly suited to fractal distributions, one finds no correlation length at all—indicating that the fractal structure may extend up to perhaps the largest length scales possible. Analysis also indicates that when galaxy masses are considered, the distribution may be multifractal. These conclusions have serious implications for many subfields in astrophysics today, from galaxy formation to the Robertson-Walker metric of spacetime.

scholarly journals Spatial Correlation Length Scales of Sea-Ice Concentration Errors for High-Concentration Pack Ice

2021 ◽  
Vol 13 (21) ◽  
pp. 4421
Author(s):  
Stefan Kern
Keyword(s):  
Time Series ◽  
Sea Ice ◽  
Correlation Length ◽  
Large Scale ◽  
Total Error ◽  
Grid Cell ◽  
High Concentration ◽  
Sea Ice Concentration ◽  
Length Scales ◽  
Ice Concentration

The European Organisation for the Exploitation of Meteorological Satellites-Ocean and Sea Ice Satellite Application Facility–European Space Agency-Climate Change Initiative (EUMETSAT-OSISAF–ESA-CCI) Level-4 sea-ice concentration (SIC) climate data records (CDRs), named SICCI-25km, SICCI-50km and OSI-450, provide gridded SIC error estimates in addition to SIC. These error estimates, called total error henceforth, comprise a random, uncorrelated error contribution from retrieval and sensor noise, aka the algorithm standard error, and a locally-to-regionally correlated contribution from gridding and averaging Level-2 SIC into the Level-4 SIC CDRs, aka the representativity error. However, these CDRs do not yet provide an error covariance matrix. Therefore, correlation scales of these error contributions and the total error in particular are unknown. In addition, larger-scale SIC errors due to, e.g., unaccounted weather influence or mismatch between the actual ice type and the algorithm setup are neither well represented by the total error, nor are their correlation scales known for these CDRs. In this study, I attempt to contribute to filling this knowledge gap by deriving spatial correlation length scales for the total error and the large-scale SIC error for high-concentration pack ice. For every grid cell with >90% SIC, I derive circular one-point correlation maps of 1000 km radius by computing the cross-correlation between the central 31-day time series of the errors and all other 31-day error time series within that circular area (disc) with 1000 km radius. I approximate the observed decrease in the correlation away from the disc’s center with an exponential function that best fits this decrease and thereby obtain the correlation length scale L sought. With this approach, I derive L separately for the total error and the large-scale SIC error for every high-concentration grid cell, and map, present and discuss these for the Arctic and the Southern Ocean for the year 2010 for the above-mentioned products. I find correlation length scales are substantially smaller for the total error, mostly below ~200 km, than the SIC error, ~200 km to ~700 km, in both hemispheres. I observe considerable spatiotemporal variability of the SIC error correlation length scales in both hemispheres and provide first directions to explain these. For SICCI-50km, I present the first evidence of the method’s robustness for other years and time series of L for 2003–2010.

Evaluating the Antarctic Observational Network with the Antarctic Mesoscale Prediction System (AMPS)

2014 ◽  
Vol 142 (10) ◽  
pp. 3847-3859 ◽  
Author(s):  
Karin A. Bumbaco ◽  
Gregory J. Hakim ◽  
Guillaume S. Mauger ◽  
Natalia Hryniw ◽  
Eric J. Steig
Keyword(s):  
Network Design ◽  
Correlation Length ◽  
East Antarctica ◽  
Prediction System ◽  
West Antarctica ◽  
Length Scales ◽  
Temperature Correlation ◽  
Optimal Network Design ◽  
Optimal Network ◽  
The Antarctic

Abstract Station siting for environmental observing networks is usually made subjectively, which suggests that the monitoring goals for the network may not be met optimally or cost effectively. In Antarctica, where harsh weather conditions make it difficult to install and maintain stations, practical considerations have largely guided the development of the staffed and automated weather station network. The current network coverage in Antarctica is evaluated as a precursor to optimal network design. The Antarctic Mesoscale Prediction System (AMPS) 0000 UTC analysis is used for 4 years (2008–12) with 15-km horizontal grid spacing, and results show that AMPS reproduces the daily correlations in surface temperature and pressure observed between weather stations across the continent. Temperature correlation length scales are greater in East Antarctica than in West Antarctica (including the Antarctic Peninsula), implying that more stations per unit area are needed to sample weather in West Antarctica compared to East Antarctica. There is variability in the temperature correlation length scales within these regions, emphasizing the need for objective studies such as this one for determining the impact of current and new stations. Further analysis shows that large regions are not well sampled by the current network, particularly on daily time scales. Observations are particularly limited in West Antarctica. Combined with the shorter temperature correlation length scales, this implies that West Antarctica is a compelling location for implementing an objective, optimal network design approach.

Long Distance Fracture Surface Roughness on a Dendritic Aluminum Alloy

1999 ◽  
Vol 578 ◽  
Author(s):  
J. Aldaco ◽  
F.J. Garza ◽  
M. Hinojosa
Keyword(s):  
Aluminum Alloy ◽  
Fracture Surface ◽  
Correlation Length ◽  
Wide Spectrum ◽  
Charpy Impact ◽  
Long Distance ◽  
Length Scales ◽  
Microstructural Parameters ◽  
Roughness Exponent ◽  
Wide Range

AbstractThe long distance roughness of the fracture surface of a dendritic aluminum alloy is studied over a wide range of length scales. Self-affinity analysis was performed over samples broken in Charpy impact tests. Simultaneous use of Atomic Force Microscopy, SEM and stylus profilometry allowed us to cover a wide spectrum of length scales, spanning over seven decades, from a few nanometers up to one centimeter. The roughness exponent and correlation length were obtained using the variable bandwidth method. For the roughness exponent, a value of 0.8 was obtained, corresponding to the reported universal exponent. Correlation length was found to correspond well to the characteristic length of the largest heterogeneities in the complex microstructure. Our results provide information that can help to improve our understanding of the role of microstructural parameters on crack propagation mechanisms.

scholarly journals The Impact of Altimeter Sampling Patterns on Estimates of Background Errors in a Global Wave Model

2005 ◽  
Vol 22 (12) ◽  
pp. 1895-1917 ◽  
Author(s):  
Diana J. M. Greenslade ◽  
Ian R. Young
Keyword(s):  
Correlation Length ◽  
Irregular Sampling ◽  
Altimeter Data ◽  
Length Scale ◽  
Observational Method ◽  
Model Errors ◽  
Length Scales ◽  
Wave Fields ◽  
Anomaly Correlation ◽  
The Impact

Abstract One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the observational method of Hollingsworth and Lönnberg. The observational method considers correlations of the differences between observations and the background. For the case of significant wave height (SWH), potential observations come from satellite altimeters. In this work, the effect of the irregular sampling pattern of the satellite on estimates of background errors is examined. This is achieved by using anomalies from a 3-month mean as a proxy for model errors. A set of anomaly correlations is constructed from modeled wave fields. The isotropic length scales of the anomaly correlations are found to vary considerably over the globe. In addition, the anomaly correlations are found to be significantly anisotropic. The modeled wave fields are then sampled at simulated altimeter observation locations, and the anomaly correlations are recalculated from the simulated altimeter data. The results are compared to the original anomaly correlations. It is found that, in general, the simulated altimeter data can capture most of the geographic and seasonal variability in the isotropic anomaly correlation length scale. The best estimates of the isotropic length scales come from a method in which correlations are calculated between pairs of observations from prior and subsequent ground tracks, in addition to along-track pairs of observations. This method was found to underestimate the isotropic anomaly correlation length scale by approximately 10%. The simulated altimeter data were not so successful in producing realistic anisotropic correlation functions. This is because of the lack of information in the zonal direction in the simulated altimeter data. However, examination of correlations along ascending and descending ground tracks separately can provide some indication of the areas on the globe for which the anomaly correlations are more anisotropic than others.

scholarly journals Length scales and scale-free dynamics of dislocations in dense solid solutions

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Gábor Péterffy ◽  
Péter D. Ispánovity ◽  
Michael E. Foster ◽  
Xiaowang Zhou ◽  
Ryan B. Sills
Keyword(s):  
Solid Solution ◽  
Correlation Length ◽  
Critical Stress ◽  
Random Noise ◽  
Dislocation Line ◽  
Length Scales ◽  
Scale Free ◽  
Solid Solution Strengthening ◽  
Depinning Transition ◽  
Dynamics Simulations

Abstract The fundamental interactions between an edge dislocation and a random solid solution are studied by analyzing dislocation line roughness profiles obtained from molecular dynamics simulations of Fe0.70Ni0.11Cr0.19 over a range of stresses and temperatures. These roughness profiles reveal the hallmark features of a depinning transition. Namely, below a temperature-dependent critical stress, the dislocation line exhibits roughness in two different length scale regimes which are divided by a so-called correlation length. This correlation length increases with applied stress and at the critical stress (depinning transition or yield stress) formally goes to infinity. Above the critical stress, the line roughness profile converges to that of a random noise field. Motivated by these results, a physical model is developed based on the notion of coherent line bowing over all length scales below the correlation length. Above the correlation length, the solute field prohibits such coherent line bow outs. Using this model, we identify potential gaps in existing theories of solid solution strengthening and show that recent observations of length-dependent dislocation mobilities can be rationalized.

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