Correlation Length Of Heterogeneity Research Articles

Effect of structural heterogeneity on work-hardening behavior of metallic glass thin film

In this study, three kinds of atomic disordered Cu50Zr50 metallic glass thin films (MGTFs) with different structural heterogeneities are prepared by controlling the substrate temperature in magnetron sputtering, i.e., controlling the thermal history. A work-hardening behavior is observed in the MGTFs by cyclic nanoindentation. The spatial distribution of structural heterogeneities, and the correlation length of the viscoelasticity of heterogeneity in three MGTFs with different thermal histories demonstrate the effect of thermal history on the viscoelasticity of three MGTFs. The activation volume of heterogeneity controlling the initiation of shear band during local deformation correlates the correlation length of viscoelastic heterogeneity, which is used to elucidate the relationship between the structural heterogeneity and the work-hardening behavior. The results show that the increase of the substrate temperature causes the viscosity of structural heterogeneity to be increased, which means the reduction of viscoelastic heterogeneity correlation length. In this case, the activation volume of heterogeneity in the MGTF is decreased, which leads the formation of shear band to be difficult.

Vortices of electro-osmotic flow in heterogeneous porous media

Traditional models of electrokinetic transport in porous media are based on homogenized material properties, which neglect any macroscopic effects of microscopic fluctuations. This perspective is taken not only for convenience, but also motivated by the expectation of irrotational electro-osmotic flow, proportional to the electric field, for uniformly charged surfaces (or constant zeta potential) in the limit of thin double layers. Here, we show that the inherent heterogeneity of porous media generally leads to macroscopic vortex patterns, which have important implications for convective transport and mixing. These vortical flows originate due to competition between pressure-driven and electro-osmotic flows, and their size are characterized by the correlation length of heterogeneity in permeability or surface charge. The appearance of vortices is controlled by a single dimensionless control parameter, defined as the ratio of a typical electro-osmotic velocity to the total mean velocity.

Molecular Weight Dependence of Methylcellulose Fibrillar Networks

Gelation of aqueous methylcellulose (MC) solutions upon heating has been shown to result from the formation of a network of semiflexible fibrils, with diameters of 15 ± 2 nm. Here, we investigate the impact of MC molecular weight on the elasticity and structure of aqueous gels at concentrations between 0.1 and 3 wt %. Small-amplitude oscillatory shear measurements conducted at a fixed concentration reveal that the gel modulus increases monotonically by a factor of 5 for weight-average molecular weights (Mw) between 22 and 550 kg/mol. Small-angle X-ray scattering data, fit to a semiflexible cylinder model, demonstrate that the fibril radius, Kuhn length, and volume fraction are approximately constant throughout this molecular weight range. Small-angle light scattering shows that the fibrillar-rich and fibrillar-depleted domains within the gel are associated with an essentially invariant heterogeneity correlation length. Direct visualization by cryo-TEM reveals that lower molecular weight MC forms fibrils o...

Using direct and coda wave envelopes to resolve the scattering and intrinsic attenuation structure of Southern California

AbstractCharacterizing scattering and absorbing properties and the power spectrum of crustal heterogeneity is a fundamental problem for informing strong ground motion estimates at high frequencies, where scattering and attenuation effects are critical. We perform a comprehensive study of local earthquake coda waves in Southern California to constrain scattering and intrinsic attenuation structure. We analyze data from 1195 spatially distributed earthquakes from 1981 to 2013 at source depths of 10 to 15 km and epicentral distances from 0 to 250 km with magnitudes larger than 1.8. We stack envelope functions from 28,127 vertical component and 27,521 transverse component seismograms, filtered from 2 to 4 Hz. We model these observations using a particle‐based Monte Carlo algorithm that includes intrinsic attenuation as well as both P and S wave scattering and both single and multiple scattering events. We find that spatially averaged coda wave behavior for Southern California can be explained only with models containing an increase in scattering strength and intrinsic attenuation within the uppermost crust, i.e., they are poorly fit with half‐space models of constant scattering strength. A reasonable fit to our data is obtained with a two‐layer model, composed of a shallow crustal layer with strong wide‐angle scattering and high P and S intrinsic attenuation and a deeper layer with weaker scattering and lower intrinsic attenuation (top 5.5 km: αQI=250, βQI=125, heterogeneity correlation length a = 50 m, fractional velocity heterogeneity ε = 0.4; lower crust: αQI=900, βQI=400, a = 2 km, ε = 0.05).

Computation of Green’s Function of 3-D Radiative Transport Equations for Non-isotropic Scattering of P and Unpolarized S Waves

In this work, I propose to model the propagation of high-frequency seismic waves in the heterogeneous Earth by means of a coupled system of radiative transfer equations for P and S waves. The model describes the propagation of both coherent and diffuse waves in a statistically isotropic heterogeneous medium and takes into account key phenomena such as scattering conversions between propagation modes, scattering anisotropy and absorption. The main limitation of the approach lies in the neglect of the shear wave polarization information. The canonical case of a medium with uniform scattering and absorption properties is studied in details. Using an adjoint formalism, Green’s functions (isotropic point source solutions) of the transport equation are shown to obey a reciprocity relation relating the P energy density radiated by an S source to the S energy density radiated by a P source. A spectral method of calculation of the Green’s function is presented. Application of Fourier, Hankel and Legendre transforms to time, space and angular variables, respectively, turns the equation of transport into a numerically tractable penta-diagonal linear system of equations. The implementation of the spectral method is discussed in details and validated through one-to-one comparisons with Monte Carlo simulations. Numerical experiments in different propagation regimes illustrate that the ratio between the correlation length of heterogeneities and the incident wavelength plays a key role in the rate of stabilization of the P-to-S energy ratio in the coda. The results suggest that the rapid stabilization of energy ratios observed in the seismic coda is a signature of the broadband nature of crustal heterogeneities. The impact of the texture of the medium on both pulse broadening and generation of converted S wave arrivals by explosion sources is illustrated. The numerical study indicates that smooth media enhance the visibility of ballistic-like S arrivals from P sources.

Variation in P-wave modulus with frequency and water saturation: Extension of dynamic-equivalent-medium approach

We have developed a new modeling approach for the complex-valued P-wave modulus of a rock saturated with two-phase fluid accounting for the variation with frequency and water saturation. Our method is based on the dynamic-equivalent-medium approach theory, which predicts P-wave modulus dispersion due to mesoscopic-scale wave-induced fluid flow (WIFF). Although the application of the original theory was limited to small fluctuation media, we have extended it to also be applicable for high-fluctuation media such as partially saturated rock. Our modification and extension consists of two components. The first is introducing a scaling by the rigorous bounds for P-wave velocity dispersion by mesoscopic-scale WIFF. The second is to develop a model representing the effective patch size of stiffer fluid that controls the location of the dispersion curve. We have found that the spatial correlation length of heterogeneity of saturated rock used in the original theory does not appropriately capture the effective heterogeneity scale responsible for mesoscale pressure diffusion. Its variation with saturation can be properly accounted for by the proposed patch-sized variation model. The comparison of the theoretical prediction with the published laboratory velocity and attenuation measurements suggests that our approach predicts the wave properties for high-fluctuation media with reasonable accuracy. The effect of mesoscopic-scale pressure diffusion is significant and the amount of velocity dispersion and attenuation is large in high-fluctuation media; therefore, our extension will improve quantitative characterization of, for example, a [Formula: see text]-sequestrated reservoir either by P-wave velocity or attenuation.

Analysis of the permeability tensor and the correlation length of heterogeneities in paper using X-ray microtomography

ABSTRACTA technique to determine the permeability from X-ray microtomographic images was developed and applied to paper structures. The images are thresholded and a skeleton of the pore space is obtained from the images. The skeleton is represented by means of a network of resistances. The total resistance of the network along the principal directions is now determined both in the in-plane (X, Y) as well as through the plane (Z) directions. The network resistance for structures at each section is determined. From this data, a correlation length for the network resistance is obtained. Correlation length data are used for determining the effect of heterogeneities on transport properties of paper structures. From this analysis, it is possible to analyze and simulate the moisture transport processes such as wicking and drying in paper, reproducing smaller-scale variations. Permeabilities in the thickness direction were calculated from the X-ray microtomographic reconstructions of the pore space. A set of paper samples prepared with different amounts of fines but with similar porosity and density was analyzed. The permeabilities of the X-ray reconstructions were reduced significantly in papers with fines in agreement with macroscopic measurements of flow through the same sheets. This demonstrated the higher tortuosities of the papers and their increased flow resistance, although the macroscopic porosity and density were relatively unchanged. The same analysis was repeated for a set of pilot machine sample papers to demonstrate variations in permeability predicted by X-ray microtomographic analyses in agreement with expected increases due to refining of pulps.

Spatiotemporal heterogeneity of local free volumes in highly supercooled liquid

We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions. To trace voids heterogeneously existing with lower local densities, which move along with the structural relaxation, we employ the minimum local density for each particle in a time window whose width is set along with the structural relaxation time. Particles subject to free volumes correspond well to the configuration rearranging region of dynamical heterogeneity. While the correlation length for dynamical heterogeneity grows with temperature decrease, no growth in the correlation length of heterogeneity in the minimum local density distribution takes place. A comparison of these results with those of normal mode analysis reveals that superpositions of lower-frequency soft modes extending over the free volumes exhibit spatial correlation with the broken bonds. This observation suggests a possibility that long-ranged vibration modes facilitate the interactions between fragile regions represented by free volumes, to induce dynamical correlations at a large scale.

Influence of weak-layer heterogeneity on snow slab avalanche release: application to the evaluation of avalanche release depths

AbstractThe evaluation of avalanche release depths constitutes a great challenge for risk assessment in mountainous areas. This study focuses on slab avalanches, which generally result from the rupture of a weak layer underlying a cohesive slab. We use the finite-element code Cast3M to build a mechanical model of the slab/weak-layer system, taking into account two key ingredients for the description of avalanche release: weak-layer heterogeneity and stress redistribution via slab elasticity. The system is loaded by increasing the slope angle until rupture. We first examine the cases of one single and two interacting weak spots in the weak layer, in order to validate the model. We then study the case of heterogeneous weak layers represented through Gaussian distributions of the cohesion with a spherical spatial covariance. Several simulations for different realizations of weak-layer heterogeneity are carried out and the influence of slab depth and heterogeneity correlation length on avalanche release angle distributions is analyzed. We show, in particular, a heterogeneity smoothing effect caused by slab elasticity. Finally, this mechanically based probabilistic model is coupled with extreme snowfall distributions. A sensitivity analysis of the predicted distributions enables us to determine the values of mechanical parameters that provide the best fit to field data.

Longitudinal Dispersion in River Flows Characterized by Random Large-Scale Bed Irregularities: First-Order Analytical Solution

AbstractA stochastic Lagrangian approach is proposed for the analytical derivation of a longitudinal dispersion coefficient that accounts for both transverse and longitudinal flow field variability in straight-axis open channels characterized by longitudinal large-scale bed heterogeneity, that is, by longitudinal bed irregularities over a wide range of representative lengths, from the simple grain roughness to large undulations (up to order of kilometers), possibly related to topographical discontinuities or to extended and inhomogeneous depositional processes carried out by natural or anthropogenic agents. The resulting dimensionless expression, involving the average Chezy coefficient and the ratios of river width and longitudinal heterogeneity correlation length to the average flow depth, is obtained at the first order in the depth fluctuations as a time-dependent function given by the sum of three distinct components. The first main component is related to the transverse velocity distribution and would...

High‐frequency wave propagation in the uppermost mantle

Short‐period, three‐component recordings of the seismic wave field of peaceful nuclear explosions recorded on deep seismic sounding profiles (Quartz and Ruby‐I, collected in 1984 and 1988, respectively) in northern Russia are used to constrain the nature of the high‐frequency teleseismic Pn phase, which can be observed for receiver distances of >3000 km. We suggest that this phase is caused by velocity fluctuations in the upper mantle acting as scatterers. To test this hypothesis and to determine the properties of the upper mantle scatterers, the elastic reflectivity method (one‐dimensional isotropic models) was used to model the coda of the high‐frequency teleseismic Pn phase. Both the observed data and the synthetic record sections were analyzed by examining the coda decay rates of the teleseismic Pn phase at 5 Hz. Synthetic seismograms are computed for different models based on the global model IASP91 with an added zone of randomly distributed velocity fluctuations (lamellae) just below the crust‐mantle boundary. These models may be characterized by the thickness of the scattering layer L, the vertical heterogeneity correlation length a, and the heterogeneity standard deviation σ. The numerical simulation of the wave propagation in these models generated a high‐frequency teleseismic Pn phase with a well‐pronounced, long coda. A comparison of the modeling results with the observations shows clearly that a velocity model containing fluctuations in the upper mantle can easily explain the presence of a high‐frequency teleseismic Pn. Comparing the coda decay rates of synthetic seismograms with the observation, we tried to constrain the properties of the velocity fluctuations in the upper mantle, L, a, and σ. In the distance range of the uninterfered high‐frequency teleseismic Pn phase beyond 1300 km, the coda decay rates for our best fitting model are similar to the observed ones. This model has a 75 km thick zone of scatterers below the Moho, containing lamellae with an average thickness of 2 km and a RMS velocity perturbation of 5%. The modeling results show also that two other possible models, the whispering gallery phase along the crust‐mantle boundary and scattering in the lower crust, taken alone are not able to explain the coda properties of the high‐frequency teleseismic Pn phase.