Values Of Correlation Length Research Articles

A mechano-regulation model to design and optimize the surface microgeometry of titanium textured devices for biomedical applications

In a technological context where, thanks to the additive manufacturing techniques, even sophisticated geometries as well as surfaces with specific micrometric features can be realized, we propose a mechano-regulation algorithm to determine the optimal microgeometric parameters of the surface of textured titanium devices for biomedical applications. A poroelastic finite element model was developed including a portion of bone, a portion of a textured titanium device and a layer of granulation tissue separating the bone from the device and occupying the space between them. The algorithm, implemented in the Matlab environment, determines the optimal values of the root mean square and the correlation length that the device surface must possess to maximize bone formation in the gap between the bone and the device. For low levels of compression load acting on the bone, the algorithm predicts low values of root mean square and high values of correlation length. Conversely, high levels of load require high values of root mean square and low values of correlation length. The optimal microgeometrical parameters were determined for various thickness values of the granulation tissue layer. Interestingly, the predictions of the proposed computational model are consistent with the experimental results reported in the literature. The proposed algorithm shows promise as a valuable tool for addressing the demands of precision medicine. In this approach, the device or prosthesis is no longer designed solely based on statistical averages but is tailored to each patient's unique anthropometric characteristics, as well as considerations related to their metabolism, sex, age, and more.

Probabilistic Forecast of Multiphase Transport Under Viscous and Buoyancy Forces in Heterogeneous Porous Media

AbstractWe develop a probabilistic approach to map parametric uncertainty to output state uncertainty in first‐order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two‐phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from incomplete descriptions of either porosity field, injection flux, or both. This uncertainty leads to spatiotemporal uncertainty in the saturation field. Given information about spatial/temporal statistics of spatially correlated heterogeneity, we leverage the method of distributions to derive deterministic equations that govern the evolution of pointwise cumulative distribution functions (CDFs) of saturation for a vertical reservoir, while handling the manipulation of multiple shocks arising due to buoyancy forces. Unlike the Buckley‐Leverett equation, the equation describing the fine‐grained CDF is linear in space and time. Ensemble averaging of the fine‐grained CDF results in the CDF of saturation. Thus, we give routes to circumventing the computational cost of Monte Carlo simulations (MCS), while obtaining a pointwise description of the saturation field. We conduct a set of numerical experiments for one‐dimensional transport, and compare the obtained saturation CDFs, against those obtained using MCS as our reference solution, and the statistical moment equation method. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties, that is, standard deviation and correlation length of the underlying random fields, whereas the corresponding low‐order statistical moment equations significantly deviate from the MCS results, except for very small values of standard deviation and correlation length.

Modeling tensile failure of concrete considering multivariate correlated random fields of material parameters

This paper presents a novel approach for modeling the tensile failure of quasi-brittle materials by incorporating a multivariate random field to represent material parameters in the phase field model. The aim is to characterize and propagate uncertainties in the behaviors of materials, taking into account the spatial variability and probabilistic dependence. Copula theory is employed to investigate the probability distributions and dependence configuration of the parameters. The proposed framework combines the generation approach for the multivariate random field with the phase field model, resulting in a complete numerical analysis methodology. The governing equations of the deterministic phase field model for quasi-brittle solids are outlined, followed by a description of the multivariate random field for quasi-brittle media and its uncertainty characterization procedure using copula theory. A numerical approach for generating samples of the multivariate random field is introduced. The numerical analysis procedure for the tensile fracture of concrete is presented, and the effects of material uncertainties on failure patterns and macroscopic responses are discussed. The results demonstrate that the developed methodology effectively captures the random damage and fracture processes in concrete specimens. The interaction between the correlation length of the random field and the characteristic length scale of the phase field significantly influences the probabilistic characteristics of the random responses. The research findings emphasize the importance of determining the correlation length values accurately. This study contributes to the field of structural reliability analysis by providing a comprehensive framework for modeling the stochastic behavior of quasi-brittle materials. The integration of a multivariate random field and copula theory allows for the realistic representation of material uncertainties and their probabilistic dependence. The proposed methodology, combined with the probability density evolution method (PDEM), offers a powerful tool for analyzing and predicting the probabilistic evolution of material behaviors under tensile loading conditions.

Topography Optimization for Sustainable Dropwise Condensation: The Critical Role of Correlation Length

AbstractAn effective pathway to enhance the heat transfer process is to induce the formation of highly mobile condensate droplets, employing micro‐nanoengineered superhydrophobic surfaces. However, the design of the topography of these surfaces for sustained high performance constitutes a significant scientific and technological challenge. Herein, the critical role of the correlation length of topography is demonstrated as an important factor when designing superhydrophobic surfaces for heat transfer applications. Specifically, it is shown that a) a high correlation length value corresponds to increased space between surface structures and higher lateral distances between nucleating droplets, which results in lower droplet departure diameter and significantly delayed flooding of the surface and b) correlation length has to surpass a critical value for dropwise condensation (DWC) to be sustained in hierarchical structured surfaces, when the droplets are growing in a partial Cassie state. Following this rationale, droplets are categorized in three different energy and wetting states (Wenzel droplets, Cassie droplets of low kinetic energy and high energy jumping droplets), depending on the correlation length of the topography. Heat transfer experiments demonstrate an increase of 126% in the heat transfer coefficient (HTC) of surfaces exhibiting the maximum correlation length when compared to the flat hydrophobic surface.

Statistical Roughness Properties of the Bed Surface in Braided Rivers

Braided rivers are widespread in nature, and their bed morphology is complex and variable. This paper aims to investigate and quantitatively analyze the bed surface roughness of braided rivers utilizing statistical theory. In this paper, a physical model of braided rivers is developed, and four constant discharge experiments are carried out. Based on Structure-from-Motion photogrammetry and direct measurement of bedload transport using a load cell, data on bedload transport rate, bed morphology, and bed elevation are obtained, facilitating the in-depth investigation of the correlations between these parameters. The results show that the morphological active width increases with increasing discharge. There was a significant positive correlation between the morphological active width and the bedload transport rate, although there is considerable scatter due to the inherent variability in braided river morphodynamics. The elevation probability distribution of bed surfaces shows negative skewness and leptokurtic distribution. There is a relatively significant correlation between skewness and the dimensionless bedload transport rate. The two-dimensional variogram values of bed elevation are variable, and the bed is anisotropic. Additionally, both the longitudinal sill and correlation length values exhibit an increase with the rise in stream power. Remarkably, the correlation between the dimensionless sill and correlation length, as well as the dimensionless bedload transport rate, proves to be highly significant. Consequently, this correlation can serve as a reliable general factor for predicting bedload transport rate in the reach.

Spatial variation of permeability and consolidation behaviors of soil using ordinary kriging method

The present study is aimed at finding out spatial distribution of permeability characteristic of soil using ordinary kriging method at any location using the data from a few boreholes at NIT (National Institute of Technology) Patna Bihta campus. Kriging is also popularly known as BLUE (i. e. Best Linear Unbiased Estimator) which can be used to interpolate the data obtained from a few locations to get an estimate of any parameter at other locations throughout the study area. In the present work, soil samples collected from eight boreholes have been tested to obtain various geotechnical properties including liquid limit (LL), plastic limit (PL), plasticity index (IP), coefficient of volume compressibility (mv) etc. These values have been used as inputs in an Ordinary Kriging model to calculate coefficient of consolidation (Cv) and coefficient of permeability (k) throughout the NIT Patna, Bihta campus and build contour plots of (Cv) and (k) over the NIT Patna campus to show their spatial variation. The novelty of the current work lies in the first time proposed method for developing the spatial distribution of(Cv) and(k). Markov correlation matrix has been used to develop the correlation behavior of the parameters considering different values of correlation length. In the present study, it is found that the coefficient of consolidation Cv of soil ranges 10−8 (m2/sec). The Kriged values of k are in the range of 10−11 to 10−10 (m/s). Finally, semi-variogram have been shown to display the auto-correlation of the measured data points and cross-validation of data set which establish that the Kriged data are reasonably correlated. Also, various error estimators such as Mean Error, Root Mean Square Error, Average Standard Error, Root Mean Square Standard Error, Mean Standard Error have been calculated using the Kriged data points over the entire area and, it is found that the error level in the predicted Kriged data are reasonably small.

Probabilistic assessment of seismic response of toe-excavated hillslopes retained using anchored sheet-pile-wall

This paper reports the probabilistic seismic stability analyses conducted for toe-excavated hillslopes, both for unsupported slopes and that retained by anchored sheet pile wall system. Both pseudo-static and nonlinear dynamic analyses are carried out to decipher the seismic response of toe-excavated hillslope. It is found that due to incorporation of uncertainty in the soil parameters or seismic coefficients, slope sections otherwise rendered safe from deterministic analyses can exhibit significant probability of failure. Further study highlights that pseudo-static analysis overestimates the slope failure probability as compared to the nonlinear dynamic analysis. In this study, the probability of failure of the cut slope obtained from the nonlinear analysis (ranges between 21.4% and 70.1%, with a mean Pf value hovering at approximately 45%) is highly overestimated in a pseudostatic analysis, approximately in the tune of 68%. A significant effect of the correlation length characterizing the spatial variation of soil shear strength parameters on the seismic response of toe-excavated slopes is also manifested and reported. The present study shows that a cut slope retained with SPAR system exhibits a very low probability of failure for dimensionless correlation length value up to 0.1 under the cases of dynamic excitation.

Arctic Sea-Ice Surface Elevation Distribution from NASA’s Operation IceBridge ATM Data

In this paper, we characterize the sea-ice elevation distribution by using NASA’s Operation IceBridge (OIB) Airborne Topographic Mapper (ATM) L1B data over the Arctic Ocean during 94 Spring campaigns between 2009 and 2019. The ultimate objective of this analysis is to better understand sea-ice topography to improve the estimation of the sea-ice freeboard for nadir-looking altimeters. We first introduce the use of an exponentially modified Gaussian (EMG) distribution to fit the surface elevation probability density function (PDF). The characteristic function of the EMG distribution can be integrated in the modeling of radar altimeter waveforms. Our results indicate that the Arctic sea-ice elevation PDF is dominantly positively skewed and the EMG distribution is better suited to fit the PDFs than the classical Gaussian or lognormal PDFs. We characterize the elevation correlation characteristics by computing the autocorrelation function (ACF) and correlation length (CL) of the ATM measurements. To support the radar altimeter waveform retracking over sea ice, we perform this study typically on 1.5 km ATM along-track segments that reflect the footprint diameter size of radar altimeters. During the studied period, the mean CL values range from 20 to 30 m, which is about 2% of the radar altimeter footprint diameter (1.5 km).

The influence of cylinders in tandem arrangement on unsteady aerodynamic loads

This paper presents an experimental study on the unsteady pressure loading for two circular cylinders in tandem arrangement for the Reynolds number in the subcritical regime. Experiments were conducted on two heavily instrumented cylinders, each with multiple static and dynamic pressure sensor devices positioned at various peripheral and spanwise locations, enabling extensive dynamic surface pressure, coherence, and turbulence length-scale analysis. Results show that the root-mean-squared pressure magnitude of the pressure distribution results is much larger for the rear cylinder than for the front cylinder. In the case of small spacing ratios, the surface pressure density findings show a decreased shedding frequency on both cylinders, however the critical spacing ratio shows a quick jump in shedding frequency. The lateral coherence results also revealed that beyond the critical spacing, a prominent peak at the fundamental vortex shedding frequency exists, with weaker peaks at shedding harmonics on the front and rear cylinders, resulting in smaller correlation length values than those for smaller spacing ratios. The discovery of tonal peaks and their associated flow mechanics on cylinders in tandem were reinforced by the lift and drag power spectral density as well as the higher-order spectral analysis, such as wavelet analysis and persistence spectrum.

Evaluation Method of Soil Surface Roughness after Ditching Operation Based on Wavelet Transform

Soil surface roughness (SSR) is an important parameter affecting surface hydrology, erosion, gas exchange and other processes. The surface roughness of the farmland environment is directly related to the tillage process. In order to accurately characterize the random roughness (RR) parameters of the surface after ditching, a three-dimensional (3D) digital model of the surface was obtained by laser scanning under the conditions of an indoor ditching test, and the influence of oriented roughness components formed by removing ridge characteristics on the RR of the surface was analyzed by introducing the wavelet processing method. For this reason, four groups of ditching depths and two types of surface conditions (whether the surface was agglomerated or not) were designed in this paper. By comparing the root mean squared height (RMSH) and correlation length (CL) data calculated before and after wavelet processing under each group of tests, it was concluded that the RMSH values of the four groups before and after wavelet processing all change more than 200%, the change amplitude reached 271.02% under the treatment of 12 cm ditching depth, meanwhile, the average CL value of five cross-sections under each group of ditching depths decreased by 1.43–2.28 times, which proves that the oriented roughness component formed by furrows and ridges has a significant influence on the calculation of RR. By further analyzing the roughness value differences of clods and pits in different directions and local areas before and after wavelet transform, it was shown that the wavelet transform can effectively remove the surface anisotropy characteristics formed in the tillage direction and provide a uniform treatment method for the evaluation of surface RR at different ditching depths.

Statistical properties of double-slit interference of partially coherent polarization singular vector beams

The Young’s double-slit interference of partially coherent polarization singular vector beams (PC-PSVBs) is investigated both theoretically and experimentally. Unlike the case of scalar or linearly polarized light beams, the far-field interference pattern of PC-PSVB’s have spatial dependence both in horizontal and vertical directions. The visibility of these patterns is governed by the input spatial correlation length. The number of minima along the vertical direction (y-axis) depicts the magnitude of Poincaré-Hopf index (PHI) of the incident beam. Our results reveal that the far-field statistical properties namely, intensity pattern, degree of polarization (DOP) distribution and Stokes-parameters distributions of the PC-PSVBs diffracted through a double-slit are strongly influenced by the spatial correlation length of the incident beam. It is observed that the DOP distribution of the diffracted PC-PSVB does not follow the azimuthally symmetric DOP profile of the input PC-PSVB. Interestingly, the DOP distributions contain the information of the magnitude of PHI of the incident PC-PSVB even for a low value of spatial correlation length. However, the maximum value of DOP deteriorates with the decrease in the input spatial correlation length. Furthermore, the Stokes field (S12(ρ,z)) of the diffracted PC-PSVB contains the information of both the magnitude and polarity of the PHI of the input beam. The experimental results are in good agreement with the theoretical predictions, and may find applications in the areas where the statistical properties of a light field are important.

Microstructural and Energy-Dispersive X-ray Analyses on Argon Ion Implantations in Tantalum Thin Films for Microelectronic Substrates

In the present study, the microstructural and statistical properties of unimplanted in comparison to argon ion-implanted tantalum-based thin film surface structures are investigated for potential application in microelectronic thin film substrates. In the study, the argon ions were implanted at the energy of 30 keV and the doses of 1 × 1017, 3 × 1017, and 7 × 1017 (ion/cm2) at an ambient temperature. Two primary goals have been pursued in this study. First, by using atomic force microscopy (AFM) analysis, the roughness of samples, before and after implantation, has been studied. The corrosion apparatus wear has been used to compare resistance against tantalum corrosion for all samples. The results show an increase in resistance against tantalum corrosion after the argon ion implantation process. After the corrosion test, scanning electron microscopy (SEM) analysis was applied to study the sample morphology. The elemental composition of the samples was characterized by using energy-dispersive X-ray (EDX) analysis. Second, the statisticalcharacteristics of both unimplanted and implanted samples, using the monofractal analysis with correlation function and correlation length of samples, were studied. The results show, however, that all samples are correlated and that the variation of ion doses has a negligible impact on the values of correlation lengths. Moreover, the study of height distribution and higher-order moments show the deviation from Gaussian distribution. The calculations of the roughness exponent and fractal dimension indicates that the implanted samples are the self-affine fractal surfaces.

The effects of molecular fine structure on rice starch granule gelatinization dynamics as investigated by in situ small-angle X-ray scattering

Dynamic changes of rice starch granules selected for different amylose contents were analyzed in excess water while heated in-situ in a small-angle X-ray scattering (SAXS) instrument. Normal rice starch (NS) and rice starch with high amylopectin (HAP) and high amylose (HAM) were used as models. A 1D linear correlation function and a combination power-law and Gaussian function were used to extract the starch lamellar structure parameters and the fractal dimension, ordering and distribution of starch lamellae from SAXS data. For the resulting starch paste/gels, a model of two-correlation length was fitted to afford the correlation length (ξ) for the paste/gel system. The results showed that HAM exhibited higher long period (LP) and thickness of the crystalline layers (dc) values than HAP and NS. However, HAP showed the highest ordering lamellar structure. HAP granules were more thermostable than the amylose containing starches. For the gelatinized starches, HAM showed the highest correlation length values but these notably decreased with increasing temperature indicating strong chain segment interaction. This research reveals essential structural changes in lamellae of rice starch granules and rice starch gel structure, which provides potentially useful in the working of starch-based foods and materials.

Probabilistic Settlement Analysis of Strip Footing on Spatially Random Soil

The prediction of settlement in a traditional design approach usually uses a deterministic value of modulus of elasticity (E), which is estimated as an average value by testing the soil at selected locations. However, these deterministic properties of soil may not represent the actual properties of soil and site condition. Due to numerous sources of uncertainty, the properties of soil mass are spatially varying and anisotropic in the natural field condition. In this study, a random finite element method (RFEM) is used to evaluate the reliability of settlement of the strip footing on spatially random soil. Modulus of elasticity is the only considered random parameter. For this purpose, 2000 spatially random realizations of E-field are generated using Monte Carlo Simulation. Each of these realizations of heterogeneous soil profile is passed to FEM to analyze the settlement of footing. The final settlement results measured in all these realizations are then statistically evaluated and compared. The results of analysis show that the mean and standard deviation of the footing settlement are increased with increasing spatial correlation length. The large value of isotropic correlation length led to an increase in the mean settlement value by more than 25% as compared with the deterministic settlement calculations. Also, it is concluded that the rate of increase of settlements for anisotropic correlation length is lower than the one under isotropic condition.

Imprecise random field analysis for non-linear concrete damage analysis

Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a damage model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding random field is discretized by Karhunen-Loève expansion. In a first study, the effect of the series truncation is discussed as well as the resulting variance error on the probability box (p-box) that represents uncertainty on the damage in a concrete beam as a result of the imprecise random field. It is shown that a certain awareness for the influence of the truncation order on the local field variance is needed when the series is truncated according to a fixed mean variance error. In the following case study, the main investigation is on the propagation of imprecise random fields in the context of non-linear finite element problems, i.e. quasi-brittle damage of a four-point bended concrete beam. The global and local damage as the quantities of interest are described by a p-box. The influence of several imprecise random field input parameters to the resulting p-boxes is studied. Furthermore, it is examined whether correlation length values located within the interval, so-called intermediate values, affect the p-box bounds. It is shown that, from the engineering point of view, a pure vertex analysis of the correlation length intervals is sufficient to determine the p-box in this context.

Testing the Validity of Greenwood and Tripp’s Sum Surface Assumption for Elastic-Plastic Contact

Abstract The complexity of modeling friction between rough surfaces has prompted many researchers to use Greenwood and Tripp’s sum surface assumption to simplify the analysis. This assumption approximates the contact between two rough surfaces as contact between their equivalent sum surface and a rigid plane. In this work, we develop detailed finite element models to test the sum surface assumption for surfaces with Gaussian and exponential autocorrelation functions. We consider surfaces with differing surface roughness and correlation length values. For each case, we conduct simulations of two rough surfaces interacting in compression followed by shear, and a corresponding equivalent surface model based on the sum surface assumption. Multiple realizations of each parameter combination are simulated to obtain a statistical picture of the responses. We find that (a) the sum surface assumption consistently under-predicts the static coefficient of friction and (b) the equivalent surface model is less accurate for surfaces with differing correlation length-to-surface roughness ratios.

Influence of soil spatial variability on the response of strip footing on geocell-reinforced slope

Abstract The present study investigates the influences of spatial variability and randomness of the soil strength parameters on the load-settlement response of a strip footing placed on a geocell-reinforced soil slope by combining finite difference method with random field model. Both isotropic and anisotropic random fields of lognormally distributed soil friction angle are generated with the utilization of Cholesky-Decomposition technique. In some representative cases, cross-correlation between soil friction angle and soil cohesion, and spatial variability of soil dilation angle are considered. The mean and variation in the load carrying capacity of the footing corresponding to a particular settlement value are obtained after running several numbers of Monte-Carlo simulations. Mean load carrying capacity of the footing reduces with increasing randomness and spatial variation in soil properties, which are defined by the higher values of coefficient of variation and lower values of correlation lengths in both the horizontal and vertical directions. Influence of soil dilatancy is found significant for higher values of soil friction angle. Apart from the above-mentioned parameters, effects of footing setback distance, position of water table, and flexural rigidity of the geocell mattress on the load-settlement response of the footing are examined. Finally, the importance of performing probabilistic analysis is explained from the point of view of failure probability of the footing, calculated with respect to few design factors of safety.

Probabilistic bearing capacity of strip footing on reinforced anisotropic soil slope

The probabilistic bearing capacity of a strip footing placed on the edge of a purely cohesive reinforced soil slope is computed by combining lower bound finite element limit analysis technique with random field method and Monte Carlo simulation technique. To simulate actual field condition, anisotropic random field model of undrained soil shear strength is generated by using the Cholesky-Decomposition method. With the inclusion of a single layer of reinforcement, dimensionless bearing capacity factor, N always increases in both deterministic and probabilistic analysis. As the coefficient of variation of the undrained soil shear strength increases, the mean N value in both unreinforced and reinforced slopes reduces for particular values of correlation length in horizontal and vertical directions. For smaller correlation lengths, the mean N value of unreinforced and reinforced slopes is always lower than the deterministic solutions. However, with the increment in the correlation lengths, this difference reduces and at a higher correlation length, both the deterministic and probabilistic mean values become almost equal. Providing reinforcement under footing subjected to eccentric load is found to be an efficient solution. However, both the deterministic and probabilistic bearing capacity for unreinforced and reinforced slopes reduces with the consideration of loading eccentricity.

Hardness correlation length in a self-compacting concrete

ABSTRACT: This paper presents an experimental study of spatial variation of hardness or indentation strength of a self-compacting concrete. With the pourpose of validation, the comparison between the used methodologies with the values obtained by numerical simulation is presented. The correlation length (Lcor) obtained on the semivariogram using a Gaussian model is similar to the numerically simulated value, especially when the distance between the measurements is less than the sought Lcor. Using sclerometry, it was possible to infer that to find the value of concrete correlation length it is necessary to measure nearby points, at ca. 2cm apart. With this scheme, the value of Lcor found is close to the obtained using macro-indentation, a more complex and time-consuming procedure. Finally, for the studied self-compacting concrete, the correlation length is equivalent to a value between 5 to 6 times the maximum aggregate size.

Conformational transition of polyelectrolytes in mixed solvent by dielectric spectroscopy: Electrostatic and hydrophobic interactions

ABSTRACTWe studied conformational transition of poly(acrylic acid)‐graft‐dodecyl (PAA‐g‐dodecyl), and PAA‐graft‐poly(ethylene oxide)‐graft‐dodecyl (PAA‐g‐PEO‐g‐dodecyl) molecules in DMF/H2O solvent by dielectric analysis method utilizing a double‐layer polarization theory. In addition to the hydrophobic interaction which has been demonstrated to be vital for their conformational transition with water content, it is confirmed that the electrostatic interaction is crucial. For PAA‐g‐dodecyl molecules, at a critical value of water content, a peak value of correlation length is reached originating from the delicate balance between electrostatic and hydrophobic interactions. For PAA‐g‐PEO‐g‐dodecyl molecules, chains conformation is mainly determined by electrostatic interaction over the entire range of water content due to the low content of dodecyl groups. Meanwhile, H‐bond associative interaction prevents the dissociation of free carboxyl groups over the range of lower water content, thus their stretched transition moves to higher water content. Our results provide the underlying insights needed to understand solvent effect on the conformational transition for polyelectrolytes with hydrophobic groups. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1716–1724