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Offshore torpedo piles are increasingly being utilised in deepwater oil and gas development as part of a taut-leg mooring system. As these piles commonly experience inclined loading in service, accurately determining their lateral holding capacity is crucial. Despite the fact that natural soil characteristics exhibit significant spatial variability, existing studies are mostly deterministic in nature. This paper presents probabilistic analyses of the lateral holding capacity of torpedo piles, explicitly considering the spatial variability of soil shear strength. Large deformation finite element calculations are combined with three-dimensional random field generation in a Monte Carlo framework. The results show that while spatial variability does not apparently alter the failure mechanism of laterally loaded torpedo piles, it significantly influences their holding capacity. The routine deterministic calculation, neglecting spatial variability, would probably yield unconservative estimates. To address this challenge, a probabilistic Broms method is developed, which enables engineers to produce lateral holding capacity estimates with varying confidence levels, using local strength data rather than central tendency. Furthermore, endeavours are also made to calibrate the safety factor, extensively employed in deterministic design practices, from a probabilistic perspective, providing practicing engineers with a viable alternative in scenarios where a local strength profile is unavailable. [ABSTRACT FROM AUTHOR]

Neutron dark-field imaging is a powerful tool for the spatially resolved characterization of microstructural features of materials and components. Recently, a novel achromatic technique based on a single absorption grating for the concurrent measurement of attenuation, dark-field and differential phase contrast was introduced. However, the range of measurable length scales of the technique in quantitative dark-field measurements appeared limited to some 10–100 nanometers, due to the relatively high spatial resolution requirement to detect the projected beam modulation. Here, we show how using grating–detector distances beyond the resolution limit for a given collimation produces a sequence of inverse and regular projection patterns and, thus, leads to a significant extension of the range of accessible length scales probed by dark-field imaging. In addition, we show that this concept can also be applied to 2D grating structures, which will enable concurrent three-fold directional dark-field measurements at a wide range of length scales. The approach is demonstrated with measurements on an electrical steel sheet sample, which confirm the validity of combining the results from the regular and inverse grating patterns. [ABSTRACT FROM AUTHOR]

At present, in the suspension system of maglev train, the self-diagnosis of most of the components can be realized employing direct sensor measurement, however, there are still some components that cannot be directly measured by sensors or model-based methods, such as the power components in the suspension control box, electromagnetics and related connectors. And although the detection method based on Stable Kernel Representation (SKR) can detect the fault, the length of the data used for SKR affects the speed and results of the detection. To obtain better detection results with the shortest possible data, this paper studies a component-level fault detection method based on autocorrelation length and SKR. This method uses the autocorrelation length to determine the length of the data used to identify the SKR, and then applies the SKR to build a residual generator and set the residual threshold. The experimental results show that the studied method can detect faults of the suspension control box in real-time and effectively, and the simulation results show that the studied method can detect faults of the electromagnet in real-time and effectively. In addition, compared with the traditional method, the method in this paper can obtain better results with less data. [ABSTRACT FROM AUTHOR]

Neutron dark-field imaging is a powerful tool for the spatially resolved characterization of microstructural features of materials and components. Recently, a novel achromatic technique based on a single absorption grating for the concurrent measurement of attenuation, dark-field and differential phase contrast was introduced. However, the range of measurable length scales of the technique in quantitative dark-field measurements appeared limited to some 10–100 nanometers, due to the relatively high spatial resolution requirement to detect the projected beam modulation. Here, we show how using grating–detector distances beyond the resolution limit for a given collimation produces a sequence of inverse and regular projection patterns and, thus, leads to a significant extension of the range of accessible length scales probed by dark-field imaging. In addition, we show that this concept can also be applied to 2D grating structures, which will enable concurrent three-fold directional dark-field measurements at a wide range of length scales. The approach is demonstrated with measurements on an electrical steel sheet sample, which confirm the validity of combining the results from the regular and inverse grating patterns.

The long-term safety of radioactive waste disposal facilities is ensured by developing performance assessment models. The general requirement of these models is to assess the risk caused by failure of disposal systems that leads to radionuclide release into the geosphere and their migration toward the near-field biosphere. The radiation dose and risk due to disposal practice are the endpoints of assessment of the model. A two-dimensional radionuclide transport model with a decaying source is modeled numerically to compute the radiological impact caused by radionuclide, iodine-129 (I-129) in the biosphere. The intrinsic part of the performance assessment model requires consideration of uncertainties and variabilities in the system that are indicated by the inherent variability (heterogeneity in the geological medium), measurement, and modeling uncertainties (the geohydrological, geochemical properties of the radionuclides being released and transported). In this study, the spatial variability in the geological medium is addressed by treating the hydraulic conductivity of the medium as a random field. The probability of the radiation dose exceeding the design threshold (i.e., the probability of failure) is computed using subset simulation method. The influence of autocorrelation length and coefficient of variation of hydraulic conductivity on the probability of failure and the transport behavior of radionuclide are also studied. Thus, the results showed that a probabilistic framework that accounts for spatial variability in the geological medium is necessary for performance assessment of radioactive waste disposal facilities. [ABSTRACT FROM AUTHOR]

Percolation threshold is a very important parameter to estimate the sealing performance. Thus, it is crucial to determine the correct value of the percolation threshold for contact sealing surfaces. In this paper, we applied a numerical generation method, in which the autocorrelation length can be easily controlled, to obtain different Gaussian isotropic rough surfaces. Then, the contact status between a rigid flat half-space and numerically generated rough surfaces were calculated using the conjugate gradient-fast Fourier transform method. Based on the contact status, the percolation threshold was obtained using a search method. The calculated results established that the percolation threshold of A / A 0 ≈ 0. 48 is determined for Gaussian isotropic contacting rough surfaces. To obtain an exact value of the percolation threshold, the finite size of the generated rough surfaces should be six times greater than the autocorrelation length, and the autocorrelation length should not be smaller than 20 times the sampling interval. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the effect of wear on the ice adhesion of elastomeric coatings. Approaches in designing surfaces with lower ice adhesion include imparting hydrophobicity, lubrication, crosslink density reduction or induction of interfacial slippage. For icephobic surfaces to find widespread use, it is imperative that they are durable. In the current work, a suitable plasticizer is used to modify the cross-link density and stiffness of a polyurethane elastomeric coating. The wear behavior of the modified elastomer under two body abrasion is studied in terms of its weight loss and topography evolution. The wear loss varies with the coating stiffness, wherein the elastomer with lower stiffness exhibits higher weight loss. The evolution of surface topography as a function of wear is analyzed in terms of roughness parameters and autocorrelation length, and its effect on the ice adhesion behavior of the coating. The results show that wear initially increases ice adhesion, but adhesion reduces as wear propagates due to the evolution of surface topography. The study shows that, among the samples tested, a 20%–30% plasticizer content produces a good combination of icephobicity and wear resistance. • The wear and ice adhesion behavior of elastomeric icephobic surfaces are analyzed. • The spatial evolution of wear surface and its effect on ice adhesion are reported. • Ice adhesion with roughness and autocorrelation length evolution are reported. • The impact of the onset and progression of wear on ice adhesion is elucidated. [ABSTRACT FROM AUTHOR]

This paper investigates the evolution of amplitude and spatial roughness parameters during rolling contact fatigue experiments on carburized samples with around 0%, 15% and 70% retained austenite (RA) under boundary lubrication condition. The 0% RA samples failed due to early crack initiation and rapid crack propagation. The 15% and 70% RA samples showed initiation and propagation of micropitting. Four amplitude surface parameters (R a , R RMS , R sk and R ku ) and one spatial parameter (2D auto-correlation length) were analyzed for correlations between micropitting initiation and propagation during RCF cycles. It was observed that during run-in, a significant decrease in R a and R RMS were observed, while the correlation length increased and stabilized for all samples. The evolution of the 2D autocorrelation length correlated well with the evolution of crack propagation. It was observed that, while R a and R RMS values follow the same trend as propagation of micropitting, skewness and kurtosis can be used to better predict initiation and propagation of micropitting on the surface. Significant propagation of micropitting was accompanied by a decreasing trend of skewness and increasing trend of kurtosis. Transverse directional correlation length also showed good correlation with propagation of micropitting, with the correlation length decreasing during increase of micropitting on sample surfaces. [ABSTRACT FROM AUTHOR]

The use of self-penetrating torpedo anchors is gaining increasing popularity in practice. Whilst many research works have been undertaken concerning its dynamic installation, the vast bulk of them are deterministic in nature. This article presents three-dimensional large deformation random finite element analyses with proper consideration of strain rate and strain softening effects to probe into the anchor penetration mechanism and embedment depth in spatially variable seabed. The random heterogeneity of undrained shear strength is approximated as a non-stationary random field. Numerous realizations of the random field are passed to Coupled Eulerian-Lagrangian finite element program within the Monte-Carlo framework to analyze the stochastic behavior. The influence of spatial variability is found to be most significant when the torpedo anchor enters the deceleration stage. The ultimate embedment depth reflects the accumulated strength of soil lying in the penetration trajectory. The dispersion of stochastic results is much affected by the coefficient of variation the of random strength field. A reliability-based design approach is eventually developed, where a factor of safety is introduced to provide a safety margin against spatial variability. This is likely helpful for engineers to select appropriate safety factors based on the guaranteed rate required for specific projects. • The continuous penetration of torpedo anchor in spatially variable clay is explicitly modelled where the influence of spatial variability on the penetration mechanism and ultimate anchor embedment depths is investigated. • Simultaneous consideration of random heterogeneity, large deformation, and strain softening and strain rate effects distinguishes the present work from most of the others. • The influence of spatial variability is most manifest when the torpedo anchor enters the deceleration stage. The ultimate anchor embedment depth reflects the accumulated strength condition of soil lying in the entire penetration trajectory. • The relationship between safety factor and failure probability is established, with which a reliability-based approach is developed to help engineers do probability-based design practices. [ABSTRACT FROM AUTHOR]

The effect of fluctuating local tensile strength on a coupled energetic–statistical size effect in plain concrete beams under bending was numerically investigated. First, the influence of varying autocorrelation length of the random field describing a spatial variation of local tensile strength was studied. Next, the influence of the coefficient of variation of local tensile strength was analyzed. The numerical FE investigations were performed for unnotched concrete beams of similar geometry under quasi-static three point bending within elasto-plastic model assumptions, accounting for non-local softening. The FE analyses were carried out for four different beam sizes. In the calculations, the tensile strength took the form of spatially correlated random field described by a Gaussian distribution. [ABSTRACT FROM AUTHOR]

We present electron microscope (FEI NanoSEM) and atomic force microscopy measurements of surface roughness in nanochannels in photonic crystal fibers (PCF). A method was invented to cleave the PCF along the axis without damaging the surface structure in the nanochannels allowing us to characterize the morphology of the nanochannels in the PCF. A multi-wall carbon nanotube mounted onto commercial AFM probes and super sharp silicon non-contact mode AFM probes were used to characterize the wall roughness in the nanochannels. The roughness is shown to have a Gaussian distribution, and has an amplitude smaller than 0.5 nm. The height–height correlation function is an exponential correlation function with an autocorrelation length of 13 nm, and 27 nm corresponding with scan sizes of 200×100 nm 2 , and 1600×200 nm 2 , respectively. [ABSTRACT FROM AUTHOR]

Landscapes' theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of an especial kind of landscape called elementary landscape. The elementary landscape decomposition of a combinatorial optimization problem is a useful tool for understanding the problem. Such decomposition provides an additional knowledge on the problem that can be exploited to explain the behavior of some existing algorithms when they are applied to the problem or to create new search methods for the problem. In this paper we analyze the 0-1 Unconstrained Quadratic Optimization from the point of view of landscapes' theory. We prove that the problem can be written as the sum of two elementary components and we give the exact expressions for these components. We use the landscape decomposition to compute autocorrelation measures of the problem, and show some practical applications of the decomposition. [ABSTRACT FROM AUTHOR]

Most studies addressing the use of recycled asphalt materials in asphalt paving mixtures are based on experimental tests and performance evaluation. Investigating the effect of adding recycled materials to the microstructure of asphalt mixtures has received little consideration. For example, higher-order microstructural information can be used in place of simple volumetric information as input in micromechanical models that can more accurately predict the effective properties of asphalt mixtures. In this paper, the influence of adding three different recycled materials, reclaimed asphalt pavement (RAP), manufacturer waste scrap shingles (MWSS), and tear-off scrap shingles (TOSS), on the microstructural distribution of the aggregate phase is investigated using digitally processed images of asphalt mixtures and numerical evaluations of two- and three-point correlation functions. No significant variations are found among the gradation curves, and minimal differences were observed for two- and three-point correlation functions. This indicates that the addition of the recycled materials does not significantly affect the aggregate spatial distribution of asphalt mixtures. However, an increase in autocorrelation length was found for some of the mixtures containing recycled shingles. [ABSTRACT FROM AUTHOR]

Abstract: In this article we provide an exact expression for computing the autocorrelation coefficient and the autocorrelation length of any arbitrary instance of the Quadratic Assignment Problem (QAP) in polynomial time using its elementary landscape decomposition. We also provide empirical evidence of the autocorrelation length conjecture in QAP and compute the parameters and for the 137 instances of the QAPLIB. Our goal is to better characterize the difficulty of this important class of problems to ease the future definition of new optimization methods. Also, the advance that this represents helps to consolidate QAP as an interesting and now better understood problem. [Copyright &y& Elsevier]

In order to study the scale characteristics of heterogeneities in complex media, a random medium is constructed using a statistical method and by changing model parameters (autocorrelation lengths a and b), the scales of heterogeneous geologic bodies in the horizontal and the vertical Cartesian directions may be varied in the medium. The autocorrelation lengths a and b represent the mean scale of heterogeneous geologic bodies in the horizontal and vertical Cartesian directions in the random medium, respectively. Based on this model, the relationship between model autocorrelation lengths and heterogeneous geologic body scales is studied by horizontal velocity variation and standard deviation. The horizontal velocity variation research shows that velocities are in random perturbation. The heterogeneous geologic body scale increases with increasing autocorrelation length. The recursion equation for the relationship between autocorrelation lengths and heterogeneous geologic body scales is determined from the velocity standard deviation research and the actual heterogeneous geologic body scale magnitude can be estimated by the equation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper an extension of Weibull theory by the introduction of a statistical length scale is presented. The classical Weibull strength theory is self-similar; a feature that can be illustrated by the fact that the strength dependence on structural size is a power law (a straight line on a double logarithmic graph). Therefore, the theory predicts unlimited strength for extremely small structures. In the paper, it is shown that such a behavior is a direct implication of the assumption that structural elements have independent random strengths. By the introduction of statistical dependence in the form of spatial autocorrelation, the size dependent strength becomes bounded at the small size extreme. The local random strength is phenomenologically modeled as a random field with a certain autocorrelation function. In such a model, the autocorrelation length plays the role of a statistical length scale. The focus is on small failure probabilities and the related probabilistic distributions of the strength of composites. The theoretical part is followed by applications in fiber bundle models, chains of fiber bundle models and the stochastic finite element method in the context of quasibrittle failure. [Copyright &y& Elsevier]

Abstract: Forged duplex steels possess a highly anisotropic two-phase microstructure. Due to the mismatch of the coefficients of thermal expansion thermal stresses evolve during cyclic thermal loading which can lead to plastification of one or both phases. While the macroscopic deformation of specimens is well understood, open questions related to the effect of traction free surfaces still remain. Experimental evidence is found for a characteristic evolution of the surface roughness depending on the microstructure of the material. In this work micromechanical models based on a continuum mechanical description of the phase domains are evaluated with respect to surface roughness. Parameters for the description of the amplitude and the anisotropy of surface deformations are proposed and the model predictions are compared with experimental results. [Copyright &y& Elsevier]

Sidewall roughness (SWR) of fluorinated polyether waveguides fabricated using reactive ion etching in pure oxygen gas was directly measured using atomic force microscopy (AFM). We confirm that SWR is not the replicate of line edge roughness (LER) of the waveguides. Statistical information such as standard deviation of roughness, autocovariance function (ACF), and autocorrelation length (ACL) have been obtained from AFM measurements. The ACL varies in the similar manner as SWR along the depth of the waveguide, and both are dependent on the etch depth. The depth dependence can be explained by the change in the arrival dynamics of etchant ions in a mechanism involving both shadowing and first-order reemission effects. [Copyright &y& Elsevier]

In this paper we provide a probabilistic characterization of the random Max r -Sat problem. We study the variance of the number of clauses satisfied by a random assignment, and the covariance of the numbers of clauses satisfied by a random pair of assignments of an arbitrary distance. Closed-form formulas for the expected value and the variance of these quantities are provided. We asymptotically and probabilistically analyze these formulas and use them to gain insights on the similarity of instances. Based on the above probabilistic characterization, we show that the correlation between the numbers of clauses satisfied by a random pair of assignments of distance d = c n , 0 ≤ c ≤ 1 , converges in probability to ( (1 − c) r − 1 ∕ 2 r) ∕ (1 − 1 ∕ 2 r). Our main result is that the so-called normalized autocorrelation length of Max r -Sat converges in probability to (1 − 1 ∕ 2 r) ∕ r. The latter quantity is of interest in the area of landscape analysis as a way to better understand problems and assess their hardness for local search heuristics. A former result regarding the same quantity only expressed it in terms of Walsh coefficients. All our results apply to random r -Sat as well. [ABSTRACT FROM AUTHOR]