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Correlation Length (correlation + length)
Selected AbstractsHeterogeneity effects on possible salinity-driven free convection in low-permeability strataGEOFLUIDS (ELECTRONIC), Issue 4 2009J. M. SHARP JR Abstract Although studies of free convection commonly focus on highly permeable strata, but numerical analyses indicate that density-driven free convection may also occur in heterogeneous low-permeability strata. Traditional Rayleigh number criteria are overly conservative in predicting thermohaline convection in these systems; so, numerical models are used to make inferences on the process. Simulations with stochastic realizations of permeability fields show that dense plumes can take preferential pathways to sink through generally low-permeability strata; patch analysis using percolation theory shows that the threshold permeability for the onset of free convection can be as low as 10,16 m2 even with a mean permeability of 10,18 m2. Threshold permeability for the percolation pathways decreases with increasing concentration gradient, vertical correlation length and the mean and variance of the permeability. The connectedness of relatively high-permeability zones is important in initiating and controlling plume fingers of free convection in both single-layer and sand-shale sequence models. Permeable units above and below are conducive to free convection through intervening low-permeability strata if buoyancy gradients exist. This heterogeneity is on scales that are difficult to sample by drilling and too localized to be simulated in regional models but may be significant in solute transport in these systems. [source] Search for direct empirical spatial correlation signatures of the critical triggering earthquake modelGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2004G. Ouillon SUMMARY We propose a new test of the critical earthquake model based on the hypothesis that precursory earthquakes are ,actors' that create fluctuations in the stress field which exhibit an increasing correlation length as the critical large event becomes imminent. Our approach constitutes an attempt to build a more physically based time-dependent indicator (cumulative scalar stress function), in the spirit of, but improving on, the cumulative Benioff strain used in previous works documenting the phenomenon of accelerating seismicity. Using a simplified scalar space and time-dependent viscoelastic Green's function in a two-layer model of the Earth's lithosphere, we compute spatiotemporal pseudo-stress fluctuations induced by a series of events before four of the largest recent shocks in southern California. Through an appropriate spatial wavelet transform, we then estimate the contribution of each event in the series to the correlation properties of the simplified pseudo-stress field around the location of the mainshock at different scales. This allows us to define a cumulative scalar pseudo-stress function which reveals neither an acceleration of stress storage at the epicentre of the mainshock nor an increase of the spatial stress,stress correlation length similar to those observed previously for the cumulative Benioff strain. The earthquakes we studied are thus either simple ,witnesses' of a large-scale tectonic organization, or are simply unrelated, and/or the Green's function describing interactions between earthquakes has a significantly longer range than predicted for standard viscoelastic media used here. [source] Synthesis and properties of crosslinked polyvinylformamide and polyvinylamine hydrogels in conjunction with silica particlesJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 18 2002Torsten Meyer Abstract Polyvinylamine hydrogels with silica particles encapsulated (PVAm/silica) were produced by a two-step synthesis. In the first step, polyvinylformamide/silica (PVFA/silica) hybrids were synthesized from vinylformamide (VFA) and 1,3-divinylimidazolidin-2-one (1,3-bisvinylethyleneurea, BVU), as the crosslinker, by radical copolymerization in silica/water suspensions using different compositions of VFA/BVU. The target product PVAm/silica was obtained by acidic hydrolysis of the PVFA/silica hydrogels in a second step. The chemical structures of both hydrogels, PVFA/silica and PVAm/silica, respectively, were revealed by solid-state 13C(1H) cross-polarity/magic-angle spinning NMR spectroscopy. Both hydrogels swelled significantly in water. The swelling capacity of the two systems was characterized by the correlation length , (or hydrodynamic blob size) of the network meshes with small-angle neutron scattering experiments. , is significantly larger for PVAm/silica than for PVFA/silica, which corresponds to the observed higher swelling capacity of this polyelectrolyte material. Furthermore, the swelling behavior of the hybrid hydrogels was quantitatively described in terms of free swell capacity, centrifuge-retention capacity, adsorption against pressure, and free swell rate as compared with values of the corresponding copolymer hydrogels. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3144,3152, 2002 [source] Calcium induced volume transition in polyelectrolyte gelsMACROMOLECULAR SYMPOSIA, Issue 1 2003Ferenc Horkay Abstract The osmotic properties and the small angle neutron scattering (SANS) behaviour of fully neutralized sodium polyacrylate gels are investigated in the presence of calcium ions. Analysis of the SANS response displays three characteristic length scales, two of which are of thermodynamic origin, while the third, associated with the frozen-in structural inhomogeneities, is static. The SANS results are consistent with direct osmotic observations which indicate that the thermodynamic properties cannot be adequately described by a single correlation length. The concentration dependence of the osmotic pressure displays a power law behaviour with an exponent that decreases with increasing calcium concentration. [source] The angular correlation function of the ROSAT All-Sky Survey Bright Source CatalogueMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2000A. Akylas We have derived the angular correlation function of a sample of 2096 sources detected in the ROSAT All-Sky Survey (RASS) Bright Source Catalogue, in order to investigate the clustering properties of active galactic nuclei (AGN) in the local Universe. Our sample is constructed by rejecting all known stars, as well as extended X-ray sources. Areas with |b|<30° and declination ,<,30° are also rejected owing to the high or uncertain neutral hydrogen absorption. Cross-correlation of our sample with the Hamburg/RASS optical identification catalogue suggests that the vast majority of our sources are indeed AGN. A 4.1, correlation signal between 0° and 8° was detected with w(,<8°)=2.5±0.6×10,2. Assuming a two-point correlation function of the form w(,)=(,,0),0.8, we find ,0=0062. Deprojection on three dimensions, using Limber's equation, yields a spatial correlation length of r0,6.0±1.6 h,1 Mpc. This is consistent with the AGN clustering results derived at higher redshifts in optical surveys and suggests a comoving model for the clustering evolution. [source] Short-range order diffuse scattering in quasicrystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010Akiji Yamamoto A theory for the diffuse scattering intensity owing to short-range order (SRO) in quasicrystals is given. The diffuse scattering intensity can be calculated based on higher-dimensional cluster models of quasicrystals. It is determined by the overlapped area (or volume) of occupation domains separated from each other by distances up to the correlation length and the SRO correlation functions. It is applied to a random atom distribution in phason flip sites in the Penrose pattern. To confirm the validity of the derived formula, analytical and numerical results for this case have been compared. Both results give similar diffuse scattering intensity, suggesting the validity of the theory. [source] Magnetic short-range order diffuse scattering in quasicrystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010Akiji Yamamoto An analytical expression is derived for the short-range order (SRO) magnetic neutron diffuse scattering intensity in quasicrystals, and it is applied to a fictitious model of spin-orientation disorder in the Penrose pattern. The SRO diffuse scattering intensity depends on the overlapped volume of the occupation domains which are separated from each other by distances less than the correlation length and the SRO correlation functions. Analytical results for four different spin arrangements in the Penrose pattern are compared with numerical ones. The corresponding analytical and numerical results for all the cases are quite similar, suggesting the validity of the analytical expression. [source] Functional renormalization group approach to the BCS-BEC crossoverANNALEN DER PHYSIK, Issue 9 2010S. Diehl Abstract The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization group equation, describe the scale dependence of the flowing or average action. They interpolate continuously from the microphysics at atomic or molecular distance scales to the macroscopic physics at much larger length scales, as given by the interparticle distance, the correlation length, or the size of the experimental probe. We discuss the phase diagram as a function of the scattering length and the temperature and compute the gap, the correlation length and the scattering length for molecules. Close to the critical temperature, we find the expected universal behavior. Our approach allows for a description of the few-body physics (scattering and molecular binding) and the many-body physics within the same formalism. [source] Light transport and correlation length in a random laserANNALEN DER PHYSIK, Issue 12 2009R. Frank Abstract A random laser is a strongly disordered, laser-active optical medium. The coherent laser feedback, which has been demonstrated experimentally to be present in these systems beyond doubt, requires the existence of spatially localized photonic quasimodes. However, the origin of these quasimodes has remained controversial. We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission. From the causality of wave propagation in an amplifying, diffusive medium we derive a novel length scale which we identify with the average mode radius of the lasing quasi-modes. We show that truly localized modes do not exist in the system without photon number conservation. However, we find that causality in the amplifying medium implies the existence of a novel, finite intensity correlation length which we identify with the average mode volume of the lasing quasimodes. We show further that the surface of the laser-active medium is crucial in order to stabilize a stationary lasing state. We solve the laser transport theory with appropriate surface boundary conditions to obtain the spatial distributions of the light intensity and of the occupation inversion. The dependence of the intensity correlation length on the pump rate agrees with experimental findings. [source] A one-way wave equation for modelling seismic waveform variations due to elastic heterogeneityGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2005D. A. Angus SUMMARY The application of a new one-way narrow-angle elastic wave equation to isotropic heterogeneous media is described. This narrow-angle finite-difference propagator should provide an efficient and accurate method of simulating primary body wave(s) passing through smoothly varying heterogeneous media. Although computationally slower than ray theory, the narrow-angle propagator can model frequency-dependent forward diffraction and scattering as well as the averaging effects due to smooth variations in medium parameters that vary on the sub-Fresnel zone level. Example waveforms are presented for the propagation of body waves in deterministic as well as stochastic heterogeneous 3-D Earth models. Extrapolation within deterministic media will highlight various familiar wave-diffraction and pulse-distortion effects associated with large-scale inhomogeneities, such as geometrical spreading, wavefront folding and creeping-wave diffraction by a compact object. Simulation within stochastic media will examine the effects of varying the correlation lengths of random heterogeneities on wave propagation. In particular, wave phenomena such as frequency-dependent forward scattering, the appearance of random caustics and the generation of seismic coda will be shown. [source] On the investigation of shell buckling due to random geometrical imperfections implemented using Karhunen,Loève expansionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2008K. J. Craig Abstract For the accurate prediction of the collapse behaviour of thin cylindrical shells, it is accepted that geometrical and other imperfections in material properties and loading have to be accounted for in the simulation. There are different methods of incorporating imperfections, depending on the availability of accurate imperfection data. The current paper uses a spectral decomposition of geometrical uncertainty (Karhunen,Loève expansions). To specify the covariance of the required random field, two methods are used. First, available experimentally measured imperfection fields are used as input for a principal component analysis based on pattern recognition literature, thereby reducing the cost of the eigenanalysis. Second, the covariance function is specified analytically and the resulting Friedholm integral equation of the second kind is solved using a wavelet-Galerkin approach. Experimentally determined correlation lengths are used as input for the analytical covariance functions. The above procedure enables the generation of imperfection fields for applications where the geometry is slightly modified from the original measured geometry. For example, 100 shells are perturbed with the resulting random fields obtained from both methods, and the results in the form of temporal normal forces during buckling, as simulated using LS-DYNA®, as well as the statistics of a Monte Carlo analysis of the 100 shells in each case are presented. Although numerically determined mean values of the limit load of the current and another numerical study differ from the experimental results due to the omission of imperfections other than geometrical, the coefficients of variation are shown to be in close agreement. Copyright © 2007 John Wiley & Sons, Ltd. [source] HTSC cuprate phase diagram using a modified Boson,Fermion,Gossamer model describing competing orders, a quantum critical point and possible resonance complexINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009Richard H. Squire Abstract There has been considerable effort expended toward understanding high temperature superconductors (HTSC), and more specifically the cuprate phase diagram as a function of doping level. Yet, the only agreement seems to be that HTSC is an example of a strongly correlated material where Coulomb repulsion plays a major role. This manuscript proposes a model based on a Feshbach resonance pairing mechanism and competing orders. An initial BCS-type superconductivity at high doping is suppressed in the two particle channel by a localized preformed pair (PP) (Nozieres and Schmitt-Rink, J Low Temp Phys, 1985, 59, 980) (circular density wave) creating a quantum critical point. As doping continues to diminish, the PP then participates in a Feshbach resonance complex that creates a new electron (hole) pair that delocalizes and constitutes HTSC and the characteristic dome (Squire and March, Int J Quantum Chem, 2007, 107, 3013; 2008, 108, 2819). The resonant nature of the new pair contributes to its short coherence length. The model we propose also suggests an explanation (and necessity) for an experimentally observed correlated lattice that could restrict energy dissipation to enable the resonant Cooper pair to move over several correlation lengths, or essentially free. The PP density wave is responsible for the pseudogap as it appears as a "localized superconductor" since its density of states and quasiparticle spectrum are similar to those of a superconductor (Peierls,Fröhlich theory), but with no phase coherence between the PP. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Spatial variability of O layer thickness and humus forms under different pine beech,forest transformation stages in NE GermanyJOURNAL OF PLANT NUTRITION AND SOIL SCIENCE, Issue 1 2006Oliver Bens Abstract Spatial variability of humus layer (O layer) thicknesses can have important impacts upon soil water dynamics, nutrient storage and availability, as well as plant growth. The purpose of the present study was to elucidate the impact of forest-transformation practices on the spatial variability of O layer thicknesses. The study focused on the Kahlenberg forest area (NE Germany) with stands of Scots pine (Pinus sylvestris) and European beech (Fagus sylvatica) of different age structures that form a transformation chronosequence from pure Scots pine stands towards pure European beech stands. Topsoil profiles including both, the O layer and the uppermost humic mineral soil horizon were excavated at intervals of 0.4 m along 15,20 m long transects, and spatial variability of O layer thicknesses was quantified by variogram analysis. The correlation lengths of total O layer thickness increased in the sequence consisting of pure pine stand (3.1 m) , older mixed stand (3.7 m) , pure beech stand (4.5 m), with the exception of the younger mixed stand, for which no correlation lengths of total O layer thickness could be determined. The degree of spatial correlation, i.e., the percentage of the total variance which can be described by variograms, was highest for the two monospecies stands, whereas this percentage was distinctly lower for the two mixed stands. A similar minimum for the two mixed stands was observed for the correlation lengths of the Oh horizon. These results suggest that the spatial structures of forest-transformation stands may be interpreted in terms of a disturbance (in the form of the underplanting of beech trees). After this disturbance, the forest ecosystem requires at least 100 y to again reach relative equilibrium. These findings are in line with the results of other soil-related investigations at these sites. Räumliche Variabilität der Humuslagenmächtigkeit und Humusformen in verschiedenen Stadien des Waldumbaus von Kiefer zu Buche in NO-Deutschland Die räumliche Variabilität der Humusauflagenmächtigkeit kann einen bedeutenden Einfluss auf die Bodenwasserdynamik, Nährstoffspeicherung und -verfügbarkeit sowie das Pflanzenwachstum haben. Ziel dieser Studie war es, die Auswirkungen von Waldumbaumaßnahmen auf die räumliche Verteilung der Auflagehumusmächtigkeiten zu untersuchen. Im Forstrevier Kahlenberg, mit Beständen von Kiefer (Pinus sylvestris) und Buche (Fagus sylvatica) unterschiedlichen Alters, welche eine Transformations-Chronosequenz von einem Kiefern-Reinbestand hin zu einem reinen Buchenbestand darstellen, wurden Humusprofile entlang von 15,20 m langen Transekten in Abständen von 0,4 m aufgenommen. Die räumliche Variabilität der Mächtigkeiten der Auflagehumushorizonte wurde durch Variogramm-Analysen quantifiziert. Die Korrelationslängen der Mächtigkeiten des gesamten Auflagehumus stiegen in der Reihenfolge reiner Kiefernbestand (3,1 m) , älterer Mischbestand (3,7 m) , reiner Buchenbestand (4,5 m) an. Aus dieser Reihe fällt der jüngere Mischbestand heraus; für ihn konnten keine Korrelationslängen ermittelt werden. Der Grad der räumlichen Korrelation, d. h. der Anteil der gesamten Varianz, der durch Variogramme beschrieben wird, ist für die beiden Reinbestände am höchsten, während er für die beiden Mischbestände deutlich geringer ist. Ein ähnliches Minimum für die beiden Mischbestände ergibt sich, wenn nur die Korrelationslängen der Oh-Mächtigkeiten betrachtet werden. Diese Ergebnisse deuten darauf hin, dass die räumlichen Strukturen von Waldumbaubeständen im Sinne einer Störung gedeutet werden können (wobei die Umbaumaßnahme und der Unterbau mit Buchen die Störung darstellt). Diese Störung dauert offenbar mindestens 100 a an. Dieser Befund stimmt mit den Ergebnissen aus Studien zu weiteren relevanten Bodeneigenschaften an Forststandorten im nordostdeutschen Tiefland überein. [source] Dislocation density assessment via X-ray GaN rocking curve scansPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 7-8 2010I. Booker Abstract The line shape of X-ray diffraction (XRD) rocking curves of GaN layers grown epitaxially on (0001) oriented sapphire substrates is analyzed. Measurements performed with double- and triple-crystal setup show a q -3 and q -4 intensity decay, respectively, as expected for peak broadening dominated by randomly distributed dislocations. A model developed in [2], based on a restricted random dislocation distribution is fitted to the entire peak shape and used to extract dislocation densities and correlation lengths for edge and screw type threading dislocations. Parameters extracted by double- and triple-crystal x-ray diffraction measurements agree well with each other but still must be verified by systematic cross-sectional TEM measurements. (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Diagnosis and formulation of heterogeneous background-error covariances at the mesoscaleTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 651 2010Thibaut Montmerle Abstract This study focuses on diagnosing variations of background-error covariances between precipitating and non-precipitating areas, and on presenting a heterogeneous covariance formulation to represent these variations in a variational framework. The context of this work is the assimilation of observations linked to precipitation (radar data especially) in the AROME model, which has been running operationally at Météo-France since December 2008 over French territory with a 2.5 km horizontal resolution. This system uses multivariate background-error covariances deduced from an ensemble-based method. At first, such statistics have been computed for 17 precipitating cases using an ensemble of AROME forecasts coupled with an ALADIN ensemble assimilation. Results, obtained from 3 h forecast differences performed separately for non-precipitating and precipitating columns, display large discrepancies in error variances, correlation lengths and the correlations between humidity, temperature and divergence errors. These results argue in favour of including heterogeneous background-error covariances in AROME incremental 3D-Var, allowing different covariances to be used in regions with different meteorological patterns. Such a method enables us to get increments more adequately structured in those regions, and thus potentially to make better use of observations in a data assimilation system. The implementation consists of expressing the analysis increment as the sum of two terms, one for precipitating areas and the other for non-precipitating areas, making use of a mask that defines rainy regions. This implies a doubling in the size of the control variable and of the gradient of the cost function. The feasibility of this method is shown through experiments with four isolated observations. Copyright © 2010 Royal Meteorological Society [source] | |||||||||||||||||||