Journal articles on the topic '3D-Fourier coefficients'
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Lytvyn, Oleg N., and Olesya P. Nechuiviter. "3D Fourier Coefficients on the Class of Differentiable Functions and Spline Interflatation." Journal of Automation and Information Sciences 44, no. 3 (2012): 45–56. http://dx.doi.org/10.1615/jautomatinfscien.v44.i3.40.
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Zhang, Jianfeng, and Linong Liu. "Optimum split-step Fourier 3D depth migration: Developments and practical aspects." GEOPHYSICS 72, no. 3 (May 2007): S167—S175. http://dx.doi.org/10.1190/1.2715658.
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We present an efficient scheme for depth extrapolation of wide-angle 3D wavefields in laterally heterogeneous media. The scheme improves the so-called optimum split-step Fourier method by introducing a frequency-independent cascaded operator with spatially varying coefficients. The developments improve the approximation of the optimum split-step Fourier cascaded operator to the exact phase-shift operator of a varying velocity in the presence of strong lateral velocity variations, and they naturally lead to frequency-dependent varying-step depth extrapolations that reduce computational cost significantly. The resulting scheme can be implemented alternatively in spatial and wavenumber domains using fast Fourier transforms (FFTs). The accuracy of the first-order approximate algorithm is similar to that of the second-order optimum split-step Fourier method in modeling wide-angle propagation through strong, laterally varying media. Similar to the optimum split-step Fourier method, the scheme is superior to methods such as the generalized screen and Fourier finite difference. We demonstrate the scheme’s accuracy by comparing it with 3D two-way finite-difference modeling. Comparisons with the 3D prestack Kirchhoff depth migration of a real 3D data set demonstrate the practical application of the proposed method.
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Liu, Linong, and Jianfeng Zhang. "3D wavefield extrapolation with optimum split-step Fourier method." GEOPHYSICS 71, no. 3 (May 2006): T95—T108. http://dx.doi.org/10.1190/1.2197493.
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A one-way propagator is proposed for more accurately modeling wide-angle wavefields in the presence of severe lateral variations of the velocity. The method adds a higher-order correction to improve the split-step Fourier method by directly designing a cascaded operator that matches the exact phase-shift operator of a varying velocity. Using an optimization scheme, the coefficients in the cascaded operator are determined according to the local velocity distribution and the prescribed angular range of wavefield propagation. The proposed algorithm is implemented alternately in spatial and wavenumber domains using fast Fourier transforms, as in the split-step Fourier and generalized-screen methods. This algorithm can achieve higher accuracy than the generalized-screen method for wide-angle wavefields, although the same numerical scheme is used with comparable computational cost. No extra error arises for the proposed algorithm when used for 3D wave propagation, in contrast to methods that introduce an implicit finite–difference higher-order correction to the split-step Fourier method, such as the Fourier finite difference (FFD) and wide-angle screen methods. A detailed comparison of the proposed one-way propagator with the split-step Fourier, generalized-screen, and FFD methods is presented. The 2D Marmousi and 3D SEG/EAEG overthrust data sets are used to test the prestack depth-migration schemes developed based on the proposed one-way propagators.
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Zozulya, V. V. "A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories." Journal of Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/590480.
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A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.
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Zwartjes, P., and A. Gisolf. "Fourier reconstruction of marine-streamer data in four spatial coordinates." GEOPHYSICS 71, no. 6 (November 2006): V171—V186. http://dx.doi.org/10.1190/1.2348633.
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Many methods exist for interpolation of seismic data in one and two spatial dimensions, but few can interpolate properly in three or four spatial dimensions. Marine multi-streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled. We approach the problem of interpolation of marine-streamer data in four spatial dimensions by splitting the problem into a 1D interpolation along the densely sampled streamers and a 3D Fourier reconstruction for the remaining spatial coordinates. In Fourier reconstruction, the Fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least-squares inversion. The method is computationally efficient, requires no subsurface information, and can handle uniform grids with missing data as well as nonuniform grids or random sampling. The output grid of the 1D interpolation in the first step is arbitrary. When the output grid has uniform inline midpoints spacing, the 3D Fourier reconstruction in the second step is performed in the crossline midpoint, absolute offset, and azimuth coordinates. When the first step outputs to uniform absolute offset, the 3D Fourier reconstruction handles the crossline/inline midpoint and the azimuth coordinates. In both cases, the main innovation is the inclusion of the azimuthal coordinate in the Fourier reconstruction. The azimuth multiplicity must be increased for the method to be successful, which means that overlap shooting is required. We have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored. Potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3D multiple prediction and regularization to reduce sampling-related differences in processing of time-lapse data.
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Downton, Jonathan E., and Benjamin Roure. "Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters." Interpretation 3, no. 3 (August 1, 2015): ST9—ST27. http://dx.doi.org/10.1190/int-2014-0235.1.
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Amplitude variation with offset and azimuth (AVOAz) analysis can be separated into two separate parts: amplitude variation with offset (AVO) analysis and amplitude variation with azimuth (AVAz) analysis. Useful information about fractures and anisotropy can be obtained just by examining the AVAz. The AVAz can be described as a sum of sinusoids of different periodicities, each characterized by its magnitude and phase. This sum is mathematically equivalent to a Fourier series, and hence the coefficients describing the AVAz response are azimuthal Fourier coefficients (FCs). This FC parameterization is purely descriptive. The aim of this paper is to help the interpreter understand what these coefficients mean in terms of anisotropic and fracture parameters for the case of P-wave reflectivity using a linearized approximation. The FC representation is valid for general anisotropy. However, to gain insight into the significance of FCs, more restrictive assumptions about the anisotropy or facture system must be assumed. In the case of transverse isotropic media with a horizontal axis of symmetry, the P-wave reflectivity linearized approximation may be rewritten in terms of azimuthal FCs with the magnitude and phase of the different FCs corresponding to traditional AVAz attributes. Linear slip theory is used to show that the FCs can be interpreted similarly for the cases of a single set of parallel vertical fractures in isotropic media and in transverse isotropic media with a vertical axis of symmetry (VTI). The magnitude of the FCs depends on the fracture weakness parameters and the background media. For the case of vertical fractures in a VTI background, the AVOAz inverse problem is underdetermined, so extra information must be incorporated to determine how the weights are modified due to this background anisotropy. We evaluated this on a 3D data set from northwest Louisiana for which the main target was the Haynesville shale.
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Guo, Tongqing, Di Zhou, and Zhiliang Lu. "A Double-Passage Shape Correction Method for Predictions of Unsteady Flow and Aeroelasticity in Turbomachinery." Advances in Applied Mathematics and Mechanics 9, no. 4 (January 18, 2017): 839–60. http://dx.doi.org/10.4208/aamm.2016.m1478.
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AbstractIn this paper, a double-passage shape correction (DPSC) method is presented for simulation of unsteady flows around vibrating blades and aeroelastic prediction. Based on the idea of phase-lagged boundary conditions, the shape correction method was proposed aimed at efficiently dealing with unsteady flow problems in turbomachinery. However, the original single-passage shape correction (SPSC) may show the disadvantage of slow convergence of unsteady solutions and even produce nonphysical oscillation. The reason is found to be related with the disturbances on the circumferential boundaries that can not be damped by numerical schemes. To overcome these difficulties, the DPSC method is adopted here, in which the Fourier coefficients are computed from flow variables at implicit boundaries instead of circumferential boundaries in the SPSC method. This treatment actually reduces the interaction between the calculation of Fourier coefficients and the update of flow variables. Therefore a faster convergence speed could be achieved and also the solution stability is improved. The present method is developed to be suitable for viscous and turbulent flows. And for real three-dimensional (3D) problems, the rotating effects are also considered. For validation, a 2D oscillating turbine cascade, a 3D oscillating flat plate cascade and a 3D practical transonic fan rotor are investigated. Comparisons with experimental data or other solutions and relevant discussions are presented in detail. Numerical results show that the solution accuracy of DPSC method is favorable and at least comparable to the SPSC method. However, fewer iteration cycles are needed to get a converged and stable unsteady solution, which greatly improves the computational efficiency.
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Nadeem, Qurrat-Ul-Ain, Abla Kammoun, Merouane Debbah, and Mohamed-Slim Alouini. "A Generalized Spatial Correlation Model for 3D MIMO Channels Based on the Fourier Coefficients of Power Spectrums." IEEE Transactions on Signal Processing 63, no. 14 (July 2015): 3671–86. http://dx.doi.org/10.1109/tsp.2015.2430841.
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Tsai, Yu-Chung, and Kuo-Shih Tseng. "Deep Compressed Sensing for Learning Submodular Functions." Sensors 20, no. 9 (May 2, 2020): 2591. http://dx.doi.org/10.3390/s20092591.
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The AI community has been paying attention to submodular functions due to their various applications (e.g., target search and 3D mapping). Learning submodular functions is a challenge since the number of a function’s outcomes of N sets is 2 N . The state-of-the-art approach is based on compressed sensing techniques, which are to learn submodular functions in the Fourier domain and then recover the submodular functions in the spatial domain. However, the number of Fourier bases is relevant to the number of sets’ sensing overlapping. To overcome this issue, this research proposed a submodular deep compressed sensing (SDCS) approach to learning submodular functions. The algorithm consists of learning autoencoder networks and Fourier coefficients. The learned networks can be applied to predict 2 N values of submodular functions. Experiments conducted with this approach demonstrate that the algorithm is more efficient than the benchmark approach.
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Lytvyn, Oleg, Oleg Lytvyn, and Oleksandra Lytvyn. "Analysis of the results of a computational experiment to restore the discontinuous functions of two variables using projections." Physico-mathematical modelling and informational technologies, no. 33 (September 2, 2021): 12–17. http://dx.doi.org/10.15407/fmmit2021.33.012.
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This article presents the main statements of the method of approximation of discontinuous functions of two variables, describing an image of the surface of a 2D body or an image of the internal structure of a 3D body in a certain plane, using projections that come from a computer tomograph. The method is based on the use of discontinuous splines of two variables and finite Fourier sums, in which the Fourier coefficients are found using projection data. The method is based on the following idea: an approximated discontinuous function is replaced by the sum of two functions – a discontinuous spline and a continuous or differentiable function. A method is proposed for constructing a spline function, which has on the indicated lines the same discontinuities of the first kind as the approximated discontinuous function, and a method for finding the Fourier coefficients of the indicated continuous or differentiable function. That is, the difference between the function being approximated and the specified discontinuous spline is a function that can be approximated by finite Fourier sums without the Gibbs phenomenon. In the numerical experiment, it was assumed that the approximated function has discontinuities of the first kind on a given system of circles and ellipses nested into each other. The analysis of the calculation results showed their correspondence to the theoretical statements of the work. The proposed method makes it possible to obtain a given approximation accuracy with a smaller number of projections, that is, with less irradiation.
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Zhang, Jin-Hai, Wei-Min Wang, Shu-Qin Wang, and Zhen-Xing Yao. "Optimized Chebyshev Fourier migration: A wide-angle dual-domain method for media with strong velocity contrasts." GEOPHYSICS 75, no. 2 (March 2010): S23—S34. http://dx.doi.org/10.1190/1.3350861.
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A wide-angle propagator is essential when imaging complex media with strong lateral velocity contrasts in one-way wave-equation migration. We have developed a dual-domain one-way propagator using truncated Chebyshev polynomials and a globally optimized scheme. Our method increases the accuracy of the expanded square-root operator by adding two high-order terms to the traditional split-step Fourier propagator. First, we approximate the square-root operator using Taylor expansion around the reference background velocity. Then, we apply the first-kind Chebyshev polynomials to economize the results of the Taylor expansion. Finally, we optimize the constant coefficients using the globally optimized scheme, which are fixed and feasible for arbitrary velocity models. Theoretical analysis and nu-merical experiments have demonstrated that the method has veryhigh accuracy and exceeds the unoptimized Fourier finite-difference propagator for the entire range of practical velocity contrasts. The accurate propagation angle of the method is always about 60° under the relative error of 1% for complex media with weak, moderate, and even strong lateral velocity contrasts. The method allows us to handle wide-angle propagations and strong lateral velocity contrast simultaneously by using Fourier transform alone. Only four 2D Fourier transforms are required for each step of 3D wavefield extrapolation, and the computing cost is similar to that of the Fourier finite-difference method. Compared with the finite-difference method, our method has no two-way splitting error (i.e., azimuthal-anisotropy error) for 3D cases and almost no numerical dispersion for coarse grids. In addition, it has strong potential to be accelerated when an enhanced fast Fourier transform algorithm emerges.
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Jing, Zhang, and Kang Bao Sheng. "A Novel Medical Freehand Sketch 3D Model Retrieval Method by Dimensionality Reduction and Feature Vector Transformation." Computational and Mathematical Methods in Medicine 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4738391.
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To assist physicians to quickly find the required 3D model from the mass medical model, we propose a novel retrieval method, called DRFVT, which combines the characteristics of dimensionality reduction (DR) and feature vector transformation (FVT) method. The DR method reduces the dimensionality of feature vector; only the topMlow frequency Discrete Fourier Transform coefficients are retained. The FVT method does the transformation of the original feature vector and generates a new feature vector to solve the problem of noise sensitivity. The experiment results demonstrate that the DRFVT method achieves more effective and efficient retrieval results than other proposed methods.
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Petrov, Petr V., and Gregory A. Newman. "3D finite-difference modeling of elastic wave propagation in the Laplace-Fourier domain." GEOPHYSICS 77, no. 4 (July 1, 2012): T137—T155. http://dx.doi.org/10.1190/geo2011-0238.1.
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With the recent interest in the Laplace-Fourier domain full waveform inversion, we have developed new heterogeneous 3D fourth- and second-order staggered-grid finite-difference schemes for modeling seismic wave propagation in the Laplace-Fourier domain. Our approach is based on the integro-interpolation technique for the velocity-stress formulation in the Cartesian coordinate system. Five averaging elastic coefficients and three averaging densities are necessary to describe the heterogeneous medium, with harmonic averaging of the bulk and shear moduli, and arithmetic averaging of density. In the fourth-order approximation, we improved the accuracy of the scheme using a combination of integral identities for two elementary volumes — “small” and “large” around spatial gridpoints where the wave variables are defined. Two solution approaches are provided, both of which are solved with iterative Krylov methods. In the first approach, the stress variables are eliminated and a linear system for the velocity components is solved. In the second approach, we worked directly with the first-order system of velocity and stress variables. This reduced the computer memory required to store the complex matrix, along with reducing (by 30%) the number of arithmetic operations needed for the solution compared to the fourth-order scheme for velocity only. Numerical examples show that our finite-difference formulations for elastic wavefield simulations can achieve more accurate solutions with fewer grid points than those from previously published second and fourth-order frequency-domain schemes. We applied our simulator to the investigation of wavefields from the SEG/EAGE model in the Laplace-Fourier domain. The calculation is sensitive to the heterogeneity of the medium and capable of describing the structures of complex objects. Our technique can also be extended to 3D elastic modeling within the time domain.
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Song, Pengcheng, Tiannan Yang, Yanzhou Ji, Zhuo Wang, Zhigang Yang, Longqing Chen, and Lei Chen. "A Comparison of Fourier Spectral Iterative Perturbation Method and Finite Element Method in Solving Phase-Field Equilibrium Equations." Communications in Computational Physics 21, no. 5 (March 27, 2017): 1325–49. http://dx.doi.org/10.4208/cicp.oa-2016-0114.
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AbstractThis paper systematically compares the numerical implementation and computational cost between the Fourier spectral iterative perturbation method (FSIPM) and the finite element method (FEM) in solving partial differential equilibrium equations with inhomogeneous material coefficients and eigen-fields (e.g., stress-free strain and spontaneous electric polarization) involved in phase-field models. Four benchmark numerical examples, including inhomogeneous elastic, electrostatic, and steady-state heat conduction problems demonstrate that (1) the FSIPM rigorously requires uniform hexahedral (3D) and quadrilateral (2D) mesh and periodic boundary conditions for numerical implementation while the FEM permits arbitrary mesh and boundary conditions; (2) the FSIPM solutions are comparable to their FEM counterparts, and both of them agree with the analytic solutions, (3) the FSIPM is much faster in solving equilibrium equations than the FEM to achieve the accurate solutions, thus exhibiting a greater potential for large-scale 3D computations.
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Schonewille, M. A., R. Romijn, A. J. W. Duijndam, and L. Ongkiehong. "A general reconstruction scheme for dominant azimuth 3D seismic data." GEOPHYSICS 68, no. 6 (November 2003): 2092–105. http://dx.doi.org/10.1190/1.1635063.
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Seismic data are usually irregularly and sparsely sampled along the spatial coordinates, which yields suboptimal imaging results. For time‐lapse data, differences in the spatial sampling of base and monitor surveys lead to undesired differences between the images of the surveys that are not due to differences in the subsurface. In this paper, an efficient two‐step reconstruction method is proposed for irregularly and sparsely sampled 3D seismic data recorded with a dominant azimuth for large offsets. The first step is reconstruction along the receiver lines such that the midpoints are exactly on crosslines. The second step is a 2D reconstruction in the crossline midpoint‐offset domain using a least‐squares estimation of Fourier components. Sparse sampling can be handled by optimizing the parameterization of the least‐squares estimation of the Fourier coefficients, and consequently it is possible to reconstruct data that would be aliased when considering single common‐midpoint gathers. The method can be used to do a geometry transformation of the data to any desired spatial grid. Since the method yields consistent results independent of the actual sampling, it is very well suited for 4D processing.
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Halász, Marianna, Péter Tamás, József Gräff, and Lajos Szabó. "Computer Aided Measuring of Textile-Mechanical Parameters." Materials Science Forum 589 (June 2008): 311–16. http://dx.doi.org/10.4028/www.scientific.net/msf.589.311.
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A new equipment for measuring the draping characteristics of static cloth is presented in the paper. In contrast with Kawabata Evaluation System 3D geometrical data of the sample are captured from photo images. Based on a mathematical reconstruction of geometry, and drape coefficients and mechanical parameters are evaluated upon the geometrical model. The computer controlled equipment moves a round table positioned in the centre providing the natural pleating of fabric for the measuring. The core part of the equipment is a computer moved frame. The sample is scanned by laser-beams. Lasers light the cross section curves of the sample on different levels. There are four cameras on the frame taking the pictures of cross section curves in different levels. 3D geometry is reconstructed upon the pictures. A mass, spring and damping element system is the basis of the cloth simulator. Springs are assumed to be linear, while damps are proportional to the velocity. The physics engine running the simulator calculates vertex positions at a time based on interaction forces with neighbouring vertices, including stretch, bend and shear forces. Collision of the cloth model with the model of the underlying object is performed and handled in each time step. To evaluate the influence of the individual parameters, a series of simulations was performed. For the real cloth samples, a range of cross-section curves is captured, digitalized and interpolated by Fourier series. The same Fourier coefficients are determined for the cloth model as a function of simulation parameters. The actual simulation parameters are defined by the minimum of the difference between the modelled and the measured geometry.
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Kountchev, Roumen K., Rumen P. Mironov, and Roumiana A. Kountcheva. "Hierarchical Cubical Tensor Decomposition through Low Complexity Orthogonal Transforms." Symmetry 12, no. 5 (May 25, 2020): 864. http://dx.doi.org/10.3390/sym12050864.
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In this work, new approaches are proposed for the 3D decomposition of a cubical tensor of size N × N × N for N = 2n through hierarchical deterministic orthogonal transforms with low computational complexity, whose kernels are based on the Walsh-Hadamard Transform (WHT) and the Complex Hadamard Transform (CHT). On the basis of the symmetrical properties of the real and complex Walsh-Hadamard matrices are developed fast computational algorithms whose computational complexity is compared with that of the famous deterministic transforms: the 3D Fast Fourier Transform, the 3D Discrete Wavelet Transform and the statistical Hierarchical Tucker decomposition. The comparison results show the lower computational complexity of the offered algorithms. Additionally, they ensure the high energy concentration of the original tensor into a small number of coefficients of the so calculated transformed spectrum tensor. The main advantage of the proposed algorithms is the reduction of the needed calculations due to the low number of hierarchical levels compared to the significant number of iterations needed to achieve the required decomposition accuracy based on the statistical methods. The choice of the 3D hierarchical decomposition is defined by the requirements and limitations related to the corresponding application area.
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Wu, Z., and J. Lu. "Study of Surface Residual Stress by Three-Dimensional Displacement Data at a Single Point in Hole Drilling Method." Journal of Engineering Materials and Technology 122, no. 2 (October 14, 1999): 215–20. http://dx.doi.org/10.1115/1.482790.
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A method combining moire´ interferometry, Twyman–Green interferometry, and blind hole drilling method is proposed for simple and accurate determination of residual stress. The relationship between the three-dimensional surface displacements produced by introducing a blind hole and the corresponding residual stress is established by employing the Fourier expansion solution containing a set of undetermined coefficients. The coefficients are calibrated by 3D finite element method. The surface in-plane displacements Ux,Uy, and the out-of-plane displacement Uz produced by the relaxation of residual stress are measured by moire´ interferometry and Twyman–Green interferometry, respectively, after the hole-drilling procedure. The complete three-dimensional displacement data at any single point around the hole can be used for residual stress determination. The accuracy of the method is analyzed and the experimental procedure is described to determine the sign of residual stresses. As an implementation of the method, a shot peening residual stress problem is studied. [S0094-4289(00)00802-1]
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Berdnyk, Mykhailo. "MATHEMATIC MODEL OF AND METHOD FOR SOLVING THE DIRICHLET HEAT-EXCHANGE PROBLEM FOR ONE-SHEET ROTARY HYPERBOLOID." System technologies 1, no. 126 (March 27, 2020): 23–36. http://dx.doi.org/10.34185/1562-9945-1-126-2020-03.
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It is the first generalized 3D mathematical model developed for calculating temperature fields in the thin-wall one-sheet rotary hyperboloid, which rotates with constant angular velocity around the axis OZ, ; the model was created with the help of known equations of generating lines in cylindrical coordinate system with taking into account finite velocity of heat conductivity and in the form of the Dirichlet boundary problem for the hyperbolic equation of heat conduction under condition that heat-conduction properties of the body were constant, and no internal sources of the heat were available. At initial moment of time, the body temperature was constant; values of temperature on outside surfaces of the body were known and presented continuous function of coordinate.The hyperbolic heat-conductivity equation was derived from the generalized energy transfer equation for the moving element of continuous medium with taking into account finiteness of the heat conductivity velocity.In order to solve the boundary problem, the desired temperature field was represented as a complex Fourier series. The obtained boundary problems for the Fourier coefficients were found with the help of Laplace integral transformations and the new integral transformation for two-dimensional finite space. Intrinsic values and intrinsic functions for the integral transformation kernel were found by method of finite element and the Galerkin methods. Besides, the domain was divided into simplex element.As a result, the temperature field in the thin-wall one-sheet rotary hyperboloid was found in the form of convergent series in Fourier functions.
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Mohammed, Dhrgham Hani, and Laith Ali Abdul-Rahaim. "A Proposed of Multimedia Compression System Using Three - Dimensional Transformation." Webology 18, SI05 (October 30, 2021): 816–31. http://dx.doi.org/10.14704/web/v18si05/web18264.
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Video compression has become especially important nowadays with the increase of data transmitted over transmission channels, the reducing the size of the videos must be done without affecting the quality of the video. This process is done by cutting the video thread into frames of specific lengths and converting them into a three-dimensional matrix. The proposed compression scheme uses the traditional red-green-blue color space representation and applies a three-dimensional discrete Fourier transform (3D-DFT) or three-dimensional discrete wavelet transform (3D-DWT) to the signal matrix after converted the video stream to three-dimensional matrices. The resulting coefficients from the transformation are encoded using the EZW encoder algorithm. Three main criteria by which the performance of the proposed video compression system will be tested; Compression ratio (CR), peak signal-to-noise ratio (PSNR) and processing time (PT). Experiments showed high compression efficiency for videos using the proposed technique with the required bit rate, the best bit rate for traditional video compression. 3D discrete wavelet conversion has a high frame rate with natural spatial resolution and scalability through visual and spatial resolution Beside the quality and other advantages when compared to current conventional systems in complexity, low power, high throughput, low latency and minimum the storage requirements. All proposed systems implement using MATLAB R2020b.
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Li, Chengxi, and Jijian Lian. "Development and Application of a Pre-Corrected Fast Fourier Transform Accelerated Multi-Layer Boundary Element Method for the Simulation of Shallow Water Acoustic Propagation." Applied Sciences 10, no. 7 (April 1, 2020): 2393. http://dx.doi.org/10.3390/app10072393.
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Because of the complexities associated with the domain geometry and environments, accurate prediction of acoustics propagation and scattering in realistic shallow water environments by direct numerical simulation is challenging. Based on the pre-corrected Fast Fourier Transform (PFFT) method, we accelerated the classical boundary element method (BEM) to predict the acoustic propagation in a multi-layer shallow water environment. The classical boundary element method formulate the acoustics propagation problem as a linear equation system in the form of [A]{x}={b}, where [A] is an N×N dense matrix composed of influence coefficients. Solving such linear equation system requires O(N2/N3) computational cost for iterative/direct methods. The developed method, PFFT-BEM, can effectively reduce the computational efforts for direct numerical simulations from O(N2~3) to O(Nlog N), where N is the total number of boundary unknowns. To numerically simulate the sound propagation in a shallow water environment, we applied the first-order non-reflecting boundary condition in the truncated numerical domain boundary to eliminate the errors due to reflected waves. Multi-layer coupled formulation was used to include the environment inhomogeneity in PFFT-BEM. Through multiple convergence tests on the number of layers and elements, we validated and quantified the accuracy of PFFT-BEM. To demonstrate the usefulness and capability of the developed PFFT-BEM, we simulated three-dimensional (3D) underwater sound propagation through 3D geometries to check the efficacy of the established classical method: the 3D Parabolic equation model. Finally, PFFT-BEM was employed to simulate sound propagation through a complex multi-layer shallow water environment with internal waves. The “3D+T” results obtained by PFFT-BEM compared well with the physical test, thereby proving the capability and correctness of this method.
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Jin, Guoyong, Tiangui Ye, and Shuangxia Shi. "Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions." Shock and Vibration 2015 (2015): 1–29. http://dx.doi.org/10.1155/2015/896204.
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This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.
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Feng, Chun-Rong, Jun Jian, Xiao-Hong Chen, Quan Du, and Ling Wang. "Investigations on the Local Structures and the Spin Hamiltonian Parameters for Cu2+ in (90–x)TeO2–10GeO2–xWO3 Glasses." Zeitschrift für Naturforschung A 73, no. 1 (December 20, 2017): 5–11. http://dx.doi.org/10.1515/zna-2017-0308.
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AbstractThe local structures and the spin Hamiltonian parameters (SHPs) for Cu2+ in (90–x)TeO2–10GeO2–xWO3 glasses are theoretically investigated at various WO3 concentrations (x=7.5, 15, 22.5 and 30 mol%). Subject to the Jahn-Teller effect, the [CuO6]10− groups are found to experience the small or moderate tetragonal elongation distortions (characterised by the relative tetragonal elongation ratios ρ≈0.35–3.09%) in C4 axis. With only three adjusted coefficients a, b and ω, the relevant model parameters (Dq, k and ρ) are described by the Fourier type and linear functions, respectively, and the measured concentration dependences of the d–d transition bands and SHPs are reproduced. The maximum of g∥ and the minimum of |A∥| at x=15 mol% are illustrated from the abrupt decrease of the copper–oxygen electron cloud admixtures or covalency and the obvious decline of the copper 3d–3s (4s) orbital admixtures due to the decreasing electron cloud density around oxygen ligands spontaneously bonding with Cu2+ and Te4+ (W6+), respectively.
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Zhang, Ying, Dongyan Shi, Dongze He, and Dong Shao. "Free Vibration Analysis of Laminated Composite Double-Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method." Shock and Vibration 2021 (March 3, 2021): 1–25. http://dx.doi.org/10.1155/2021/8811747.
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An analytical model of laminated composite double-plate system (LCDPS) is established, which efficiently analyzes the common 3D plate structure in engineering applications. The proposed model combines the first-order shear deformation theory (FSDT) and the classical delamination theory, and then the LCDPS’s vibration characteristics are investigated. In the process of analysis, the improved Fourier series method (IFSM) is used to describe the displacement admissible function of the LCDPS, which can remove the potential discontinuities at the boundaries. Five sets of artificial springs are introduced to simulate the elastic boundary constraints, and the restraints of the Winkler elastic layer can be adjustable. The improved Fourier series is substituted into the governing equations and boundary conditions; then, applying the Rayleigh–Ritz method, we take all the series expansion coefficients as the generalized coordinates. After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the free vibration with complex boundary conditions are carried out, including the influence of boundary conditions, lamination scheme, plate geometric parameters, and elastic coefficient between two plates.
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Spinu, Sergiu. "FFT-ASSISTED ALGORITHMS FOR 3D LINE-CONTACT PROBLEMS." International Journal of Modern Manufacturing Technologies 13, no. 2 (December 20, 2021): 124–29. http://dx.doi.org/10.54684/ijmmt.2021.13.2.124.
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The line-contact is a particular type of contact with a contact length much greater than its width. Such contact scenarios can be treated in the frame of a two-dimensional plane-strain problem if the contacting surfaces can be considered nominally smooth. However, surface irregularities inherent to any manufacturing technique lead to a discontinuous contact area that differs from the one derived on the basis of the smooth profile assumption. It is therefore tantalizing to pursue the solution of a line-contact problem using an intrinsically three-dimensional (3D) model, which can only be numerical due to lack of general analytical solutions in contact mechanics. Considering the geometry of the line-contact, a major challenge in its numerical modelling is that the expected contact area is orders of magnitude larger in one direction compared to the other. This may lead to an unreasonably large number of grids in the contact length direction, which translates to a prohibitive computational burden. An alternative approach, employed in this paper, is to treat the line-contact as non-periodic in the contact width direction, but periodic in the contact length direction, with a period equal to the window required to capture and replicate the surface specific texture. This periodicity encourages the contact problem solution by spectral methods based on the fast Fourier transform (FFT) algorithm. Based on this idea, two methods are derived in this paper from the existing Discrete Convolution Fast Fourier Transform (DCFFT) technique, which was previously developed for purely non-periodic contact problems. A first algorithm variant employs a special padding technique for pressure, whereas a second one mimics the contribution of multiple pressure periods by summation of the influence coefficients over a domain a few times larger than the target domain. Both techniques are validated against the existing analytical Hertz solution for the line-contact and a good agreement is found. The advanced methods seem well adapted to the simulation of contact problems that can be approximated as periodic in one direction and non-periodic in the other.
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Zhang, Jin-Hai, and Zhen-Xing Yao. "Reducing two-way splitting error of FFD method in dual domains." GEOPHYSICS 76, no. 4 (July 2011): S165—S175. http://dx.doi.org/10.1190/1.3590214.
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The Fourier finite-difference (FFD) method is very popular in seismic depth migration. But its straightforward 3D extension creates two-way splitting error due to ignoring the cross terms of spatial partial derivatives. Traditional correction schemes, either in the spatial domain by the implicit finite-difference method or in the wavenumber domain by phase compensation, lead to substantially increased computational costs or numerical difficulties for strong velocity contrasts. We propose compensating the two-way splitting error in dual domains, alternately in the spatial and wavenumber domains via Fourier transform. First, we organize the expanded square-root operator in terms of two-way splitting FFD plus the usually ignored cross terms. Second, we select a group of optimized coefficients to maximize the accuracy of propagation in both inline and crossline directions without yet considering the diagonal directions. Finally, we further optimize the constant coefficient of the compensation part to further improve the overall accuracy of the operator. In implementation, the compensation terms are similar to the high-order corrections of the generalized-screen method, but their functions are to compensate the two-way splitting error rather than the expansion error. Numerical experiments show that optimized one-term compensation can achieve nearly perfect circular impulse responses and the propagation angle with less than 1% error for all azimuths is improved up to 60° from 35°. Compared with traditional single-domain methods, our scheme can handle lateral velocity variations (even for strong velocity contrasts) much more easily with only one additional Fourier transform based on the two-way splitting FFD method, which helps retain the computational efficiency.
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Cao, Anzhou, Haibo Chen, Jicai Zhang, and Xianqing Lv. "Optimization of Open Boundary Conditions in a 3D Internal Tidal Model with the Adjoint Method around Hawaii." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/950926.
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Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs) in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients ofM2internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs). In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP) strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, theM2internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.
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Klar, Assaf, Michael Roed, Irene Rocchi, and Ieva Paegle. "Evaluation of Horizontal Stresses in Soil during Direct Simple Shear by High-Resolution Distributed Fiber Optic Sensing." Sensors 19, no. 17 (August 24, 2019): 3684. http://dx.doi.org/10.3390/s19173684.
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This paper presents an approach for evaluating the horizontal stresses that develop in geotechnical Direct Simple Shear (DSS) tests through the use of high-resolution distributed fiber optic sensing. For this aim, fiber optics were embedded in 3D printed rings used for confining the soil in the test procedure. An analytical approach linking the measured spatially-distributed strain profile and the internal soil-ring contact stresses is developed in the paper. The method is based on representation of the contact stresses by a Fourier series expansion, and determining the coefficients of the series by minimizing the difference between the measured strain and the analytical strain within the linear elastic ring. The minimization problem results in a linear set of equations that can easily be solved for a given measurement. The approach is demonstrated on a set of drained DSS tests on clean sand specimens. Stress paths using the evaluated horizontal stresses are plotted together with Mohr circles at failure. These illustrate how, in these specific tests, the horizontal stress increases and principal stress direction rotates, until failure occurs along horizontal planes.
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Mousa, Wail A., Mirko van der Baan, Said Boussakta, and Desmond C. McLernon. "Designing stable extrapolators for explicit depth extrapolation of 2D and 3D wavefields using projections onto convex sets." GEOPHYSICS 74, no. 2 (March 2009): S33—S45. http://dx.doi.org/10.1190/1.3077621.
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We have developed a robust algorithm for designing explicit depth extrapolation operators using the projections-onto-convex-sets (POCS) method. The operators are optimal in the sense that they satisfy all required extrapolation design characteristics. In addition, we propose a simple modification of the POCS algorithm (modified POCS, or MPOCS) that further enhances the stability of extrapolated wavefields and reduces the number of iterations required to design such operators to approximately 2% of that required for the basic POCS design algorithm. Various synthetic tests show that 25-coefficient 1D extrapolation operators, which have 13 unique coefficients, can accommodate dip angles up to 70°. We migrated the SEG/EAGE salt model data with the operators and compare our results with images obtained via extrapolators based on modified Taylor series and with wavefield extrapolation techniques such as phase shift plus interpolation (PSPI) and split-step Fourier. The MPOCS algorithm provides practically stable depth extrapolators. The resulting migrated section is comparable in quality to an expensive PSPI result and visibly outperforms the other two techniques. Strong dips and subsalt structures are imaged clearly. Finally, we extended the 1D extrapolator design algorithm, using MPOCS for 2D extrapolation, to the 2D case to perform 3D extrapolation; the result is a perfect circularly symmetric migration impulse response.
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García-Gutiérrez, Nerea, Jorge Mellado-Carretero, Christophe Bengoa, Ana Salvador, Teresa Sanz, Junjing Wang, Montse Ferrando, Carme Güell, and Sílvia de Lamo-Castellví. "ATR-FTIR Spectroscopy Combined with Multivariate Analysis Successfully Discriminates Raw Doughs and Baked 3D-Printed Snacks Enriched with Edible Insect Powder." Foods 10, no. 8 (August 5, 2021): 1806. http://dx.doi.org/10.3390/foods10081806.
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In a preliminary study, commercial insect powders were successfully identified using infrared spectroscopy combined with multivariate analysis. Nonetheless, it is necessary to check if this technology is capable of discriminating, predicting, and quantifying insect species once they are used as an ingredient in food products. The objective of this research was to study the potential of using attenuated total reflection Fourier transform mid-infrared spectroscopy (ATR-FTMIR) combined with multivariate analysis to discriminate doughs and 3D-printed baked snacks, enriched with Alphitobius diaperinus and Locusta migratoria powders. Several doughs were made with a variable amount of insect powder (0–13.9%) replacing the same amount of chickpea flour (46–32%). The spectral data were analyzed using soft independent modeling of class analogy (SIMCA) and partial least squares regression (PLSR) algorithms. SIMCA models successfully discriminated the insect species used to prepare the doughs and snacks. Discrimination was mainly associated with lipids, proteins, and chitin. PLSR models predicted the percentage of insect powder added to the dough and the snacks, with determination coefficients of 0.972, 0.979, and 0.994 and a standard error of prediction of 1.24, 1.08, and 1.90%, respectively. ATR-FTMIR combined with multivariate analysis has a high potential as a new tool in insect product authentication.
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Prpić-Oršić, Jasna, Marko Valčić, and Zoran Čarija. "A Hybrid Wind Load Estimation Method for Container Ship Based on Computational Fluid Dynamics and Neural Networks." Journal of Marine Science and Engineering 8, no. 7 (July 20, 2020): 539. http://dx.doi.org/10.3390/jmse8070539.
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The estimation of wind loads on ships and other marine objects represents a continuous challenge because of its implication for various aspects of exposed structure exploitation. An extended method for estimating the wind loads on container ships is presented. The method uses the Generalized Regression Neural Network (GRNN), which is trained with Elliptic Fourier Descriptors (EFD) of sets of frontal and lateral closed contours as inputs. Wind load coefficients (Cx, Cy, CN), used as outputs for network training, are derived from 3D steady RANS CFD analysis. This approach is very suitable for assessing wind loads on container ships wherever there is a wind load database for a various container configuration. In this way, the cheaper and faster calculation can bridge the gap for the container configurations for which calculations or experiments have not already been made. The results obtained by trained GRNN are in line with available experimental measurements of the wind loads on various container configuration on the deck of a 9000+ TEU container ship obtained through a series of wind tunnel tests, as well as with performed CFD simulation for the same conditions.
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Čapek, Martin, Michaela Blažíková, Ivan Novotný, Helena Chmelová, David Svoboda, Barbora Radochová, Jiří Janáček, and Ondrej Horváth. "The Wavelet-Based Denoising Of Images in Fiji, With Example Applications in Structured Illumination Microscopy." Image Analysis & Stereology 40, no. 1 (April 9, 2021): 3–16. http://dx.doi.org/10.5566/ias.2432.
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Filtration of super-resolved microscopic images brings often troubles with removing undesired image parts like, e.g., noise, inhomogenous background and reconstruction artifacts. Standard filtration techniques, e.g., convolution- or Fourier transform-based methods are not always appropriate, since they may lower image resolution that was acquired by hi-tech and expensive microscopy systems. Thus, in this article it is proposed to filter such images using discrete wavelet transform (DWT). Newly developed Wavelet_Denoise plugin for free available Fiji software package demonstrates important possibilities of applying DWT to images: Decomposition of a filtered picture using various wavelet filters and levels of details with showing decomposed images and visualization of effects of back transformation of the picture with chosen level of suppression or denoising of wavelet coefficients. The Fiji framework allows, for example, using a plethora of various microscopic image formats for data opening, users can easily install the plugin through a menu command and the plugin supports processing 3D images in Z-stacks. The application of the plugin for removal of reconstruction artifacts and undesirable background in images acquired by super-resolved structured illumination microscopy is demonstrated as well.
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Zhiqiang, Lu, Hou Yuanbing, Chai Xiuli, and Meng Yun. "A grid gradient approximation method of energy-efficient gait planning for biped robots." International Journal of Advanced Robotic Systems 18, no. 2 (March 1, 2021): 172988142110043. http://dx.doi.org/10.1177/17298814211004327.
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In this article, an energy-efficient gait planning algorithm that utilizes both 3D body motion and an allowable zero moment point region (AZR) is presented for biped robots based on a five-mass inverted pendulum model. The product of the load torque and angular velocity of all joint motors is used as an energy index function (EIF) to evaluate the energy consumption during walking. The algorithm takes the coefficients of the finite-order Fourier series to represent the motion space of the robot body centroid, and the motion space is gridded by discretizing these coefficients. Based on the geometric structure of the leg joints, an inverse kinematics method for calculating grid intersection points is designed. Of the points that satisfy the AZR constraints, the point with the lowest EIF value in each network line is selected as the seed. In the neighborhood of the seed, the point with the minimum EIF value in the motion space is successively approximated by the gradient descent method, and the corresponding joint angle sequence is stored in the database. Given a distance to be traveled, our algorithm plans a complete walking trajectory, including two starting steps, multiple cyclic steps, and two stopping steps, while minimizing the energy consumption. According to the preset AZR, the joint angle sequences of the robot are read from the database, and these sequences are adjusted for each step according to the zero-moment-point feedback during walking. To determine the effectiveness of the proposed algorithm, both dynamic simulation and walking experiment in the real environment were carried out. The experimental results show that compared with algorithms based on the fixed body height or vertical body motion, our gait algorithm has a significant energy-saving effect.
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Ji, Yuanjin, Junwei Zeng, and Wenjing Sun. "Research on Wheel-Rail Local Impact Identification Based on Axle Box Acceleration." Shock and Vibration 2022 (February 25, 2022): 1–17. http://dx.doi.org/10.1155/2022/3226253.
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Abnormal vibration signals of tramcar are mostly nonstationary and nonlinear signals. This study applied the Hilbert–Huang transform (HHT) to analyze abnormal vibration of the tramcar, aiming to overcome the limitations of some traditional time-frequency analysis methods, such as Fourier transform, in dealing with nonstationary and nonlinear signals. Additionally, to address mode aliasing produced during empirical mode decomposition (EMD) used in classical HHT, this study proposed to first use complete EMD with adaptive noise for the decomposition of original vibration data, then eliminate the trend-term components with the calculated correlation coefficients, and finally perform denoising on high-frequency noisy components using the wavelet threshold method. After weighted reconstruction using denoised high-frequency components and low-frequency information components, data processing was finally optimized via HHT. Taking a tramcar as an example, the Hilbert spectra of the vertical acceleration of axle box were plotted via HHT, and the time-instantaneous, frequency-instantaneous energy 3D relations were obtained for the location of impact points. Further, the vibration characteristics were analyzed and quality indexes were calculated in combination with the marginal spectra so as to judge the reasons for abnormal vibration and failure modes of the tramcar. The results revealed that the proposed method was feasible and effective in vibration feature extraction and vibration impact analysis for tramcars.
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Sukhoterin, Mikhail, Sergey Baryshnikov, Tatiana Knysh, and Elena Rasputina. "Stability of rectangular cantilever plates with high elasticity." E3S Web of Conferences 244 (2021): 04004. http://dx.doi.org/10.1051/e3sconf/202124404004.
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The problem of cantilever plate stability has been little studied due to the difficulty of solving the corresponding boundary problem. The known approximate solutions mainly concern only the first critical load. In this paper, stability of an elastic rectangular cantilever plate under the action of uniform pressure applied to its edge opposite to the clamped edge is investigated. Under such conditions, thin canopies of buildings made of new materials can be found at sharp gusts of wind in longitudinal direction. At present, cantilever nanoplates are widely used as key components of sensors to create nanoscale transistors where they are exposed to magnetic fields in the plate plane. The aim of the study is to obtain the critical force spectrum and corresponding forms of supercritical equilibrium. The deflection function is selected as a sum of two hyperbolic trigonometric series with adding special compensating summands to the main symmetric solution for the free terms of the decomposition of the functions in the Fourier series by cosines. The fulfillment of all conditions of the boundary problem leads to an infinite homogeneous system of linear algebraic equations with regard to unknown series coefficients. The task of the study is to create a numerical algorithm that allows finding eigenvalues of the resolving system with high accuracy. The search for critical loads (eigenvalues) giving a nontrivial solution of this system is carried out by brute force search of compressive load value in combination with the method of sequential approximations. For the plates with different side ratios, the spectrum of the first three critical loads is obtained, at which new forms of equilibrium emerge. An antisymmetric solution is obtained and studied. 3D images of the corresponding forms are presented.
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Liang, Z. R., P. C. Philippi, C. P. Fernandes, and F. S. Magnani. "Prediction of Permeability from the Skeleton of Three-Dimensional Pore Structure." SPE Reservoir Evaluation & Engineering 2, no. 02 (April 1, 1999): 161–68. http://dx.doi.org/10.2118/56006-pa.
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Summary The main purpose of the present work is to predict the permeability of a porous medium from its three-dimensional (3D) porous structure network. In this work, 3D porous structure is reconstructed by the truncated Gaussian method using Fourier transform and starting from a 2D binary image obtained from a thin section of a porous sample. The skeleton of the 3D porous structure provides a way of visualizing the graph of the pore network. It is determined using a thinning algorithm, which is conceived to preserve topology. It gives both visual and quantitative information about the connectivity of the pore space, the coordination number for every node and local hydraulic radius. Once the network of the pore structure is obtained, the macroscopic transport properties, such as the permeability, can be predicted. The method is applied to a 500 mD Berea sandstone and the predicted permeability is in good agreement with the experimental value and empirical correlations. Introduction The prediction of equilibrium and transport properties of porous media is a long-standing problem of great theoretical and practical interest, particularly in petroleum reservoir engineering.1 Past theoretical attempts to derive macroscopic transport coefficients from the microstructure of porous media entailed a simplified representation of the pore space, often as a bundle of capillary tubes.1–3 These models have been widely applied because of their convenience and familiarity to the engineers. But they do have some limitations. For example, they are not well suited for describing the effect of the pore space interconnectivity and long range correlation in the system. Network models have been advanced to describe phenomena at the microscopic level and have been extended in the last few years to describe various phenomena at the macroscopic level. These models are mostly based on a network representation of the porous media in which larger pores (pore bodies) are connected by narrower pores (pore throats). Network models represent the most important and widely used class of geometric models for porous media.2 A network is a graph consisting of a set of nodes or sites connected by a set of links or bonds. The nodes can be chosen deterministically or randomly as in the realization of a Poisson or other stochastic point process. Similarly the links connecting different nodes may be chosen according to some deterministic or random procedure. Finally, the nodes are dressed with convex sets such as spheres representing pore bodies, and the bonds are dressed with tubes providing a connecting path between the pore bodies. The original idea of representing a porous structure by a network is rather old, but it was only in the early 1980s that systematic and rigorous procedures were developed to map, in principle, any disordered rock onto an equivalent random network of bonds and sites. Once this mapping is complete one can study a given phenomenon in porous media in great detail.3 Dullien1 reviewed the details of various pore-scale processes, including detailed descriptions of many aspects of network models. The most important features of pore network geometry and topology that affect fluid distribution and flow in reservoir rocks are the pore throat and pore body size distributions, the pore body-to-pore throat size aspect ratio and the pore body coordination number.4 These data have been tentatively assumed in the previous works. The extension of these techniques to real porous media has been complicated by the difficulty in describing the complex three-dimensional (3D) pore structure of real porous rocks. Information about the pore structure of reservoir rocks is often obtained from mercury intrusion and sorption isotherm. Mercury intrusion and sorption isotherm data provide statistical information about the pore throat size distribution, or, more correctly, the distribution of the volumes that may be invaded within specified pore throat sizes. Advanced techniques such as microcomputed tomography5 and serial sectioning6,7 do provide a detailed description of the 3D pore structures of rocks. Recently, image analysis methods used over pictures of highly polished surfaces of porous materials (e.g., Refs. 8-10), taken with an electron scanning microscope have been used to describe the porous structure. Image analysis techniques such as opening (2D and 3D)11,13 and median line graphs (2D)13 were developed. Information on porous structure is obtained from the analysis of 2D binary images. For isotropic media, a 3D microstructure may be reconstructed from any statistically homogeneous 2D section. The general objective of a reconstructed porous structure is to mimic more closely the geometry of real media. This method has been previously applied to the prediction of important petrophysical and reservoir engineering properties, such as permeability8 and formation factor14 with reasonable success. Thovert et al.15 used the reconstructed porous structure and developed thinning algorithms to obtain the graph of the 3D pore structure. Some topological characteristics such as the number of loops were derived. Bakke and O/ren16 generated 3D pore networks based on numerical modeling of the main sandstone forming geological processes. Absolute and relative permeability were computed for a Bentheimer sandstone. However, although their algorithms worked well on their models, the problem of connectivity preservation for a 3D thinning algorithm appears to be only correctly taken into account by Ma,17 who proposed sufficient conditions for providing a 3D thinning algorithm to preserve connectivity.
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Chu, Chunlei, and Paul L. Stoffa. "Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method." GEOPHYSICS 77, no. 4 (July 1, 2012): T117—T123. http://dx.doi.org/10.1190/geo2011-0415.1.
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Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency.
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Rakesh Y and Sri Rama Krishna K. "Short time fourier transform with coefficient optimization for detecting salient regions in stereoscopic 3D images: GSDU." Multimedia Tools and Applications 79, no. 13-14 (October 4, 2018): 8801–24. http://dx.doi.org/10.1007/s11042-018-6686-x.
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Blankenburg, Christoph, Christian Daul, and Joachim Ohser. "ESTIMATING TORSION OF DIGITAL CURVES USING 3D IMAGE ANALYSIS." Image Analysis & Stereology 35, no. 2 (April 14, 2016): 81. http://dx.doi.org/10.5566/ias.1420.
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Curvature and torsion of three-dimensional curves are important quantities in fields like material science or biomedical engineering. Torsion has an exact definition in the continuous domain. However, in the discrete case most of the existing torsion evaluation methods lead to inaccurate values, especially for low resolution data. In this contribution we use the discrete points of space curves to determine the Fourier series coefficients which allow for representing the underlying continuous curve with Cesàro’s mean. This representation of the curve suits for the estimation of curvature and torsion values with their classical continuous definition. In comparison with the literature, one major advantage of this approach is that no a priori knowledge about the shape of the cyclic curve parts approximating the discrete curves is required. Synthetic data, i.e. curves with known curvature and torsion, are used to quantify the inherent algorithm accuracy for torsion and curvature estimation. The algorithm is also tested on tomographic data of fiber structures and open foams, where discrete curves are extracted from the pore spaces.
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Havrysh, V. I., O. S. Korol, R. R. Shkrab, and B. O. Kviatkovskyi. "Thermal 3D model for non-homogeneous elements in mobile devices." Scientific Bulletin of UNFU 29, no. 8 (October 31, 2019): 130–33. http://dx.doi.org/10.36930/40290824.
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A mathematical model for the analysis of heat exchange between the environment and an isotropic space layer with an alien inclusions is developed, which is heated by a heat flux centered on one of the boundary surfaces. For this purpose, using the theory of generalized functions, the coefficient of thermal conductivity of this structure is depicted as one unit for the whole system. In view of this, instead of two equations of thermal conductivity for the layer and the inclusion and conditions of perfect thermal contact on the surfaces of the junction between them, one equation of thermal conductivity was obtained in the generalized derivatives with breaking coefficients. We consider the case when the inclusion sizes are small compared to the distances from the inclusion surfaces to the boundary surfaces of the layer. In this connection, the combined thermophysical parameters were introduced and the thermal coefficients of the thermal conductivity equation were transformed into singular ones. For the solution of the boundary value problem of thermal conductivity containing this equation and boundary conditions on the boundary surfaces of the layer, an integral Fourier transform was used and, as a result, an analytical solution of the problem in the images was obtained. The inverse integral Fourier transform was applied to this solution, which made it possible to obtain the final analytical solution of the original problem. The analytical solution obtained is presented as a non-native double convergent integral. To determine the numerical values of the temperature in the above design, as well as to analyze the heat exchange between the layer and the environment caused by different temperature regimes due to the heating of the inhomogeneous layer by a heat source concentrated in the area of inclusion, computational programs have been developed. Using these programs, graphs are displayed showing the behavior of curves constructed using numerical values of the temperature distribution depending on the spatial coordinates for different inclusion materials. The obtained numerical values of temperature indicate a significant influence of the inclusion on its distribution in the design "layer-inclusion". The software also makes it possible to analyze these inhomogeneous media with respect to their heat resistance during heating. As a consequence, it becomes possible to raise and protect it from overheating, which can cause destruction not only of individual elements, but also of the whole structure.
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Seright, R. S., J. Liang, W. Brent Lindquist, and John H. Dunsmuir. "Characterizing Disproportionate Permeability Reduction Using Synchrotron X-Ray Computed Microtomography." SPE Reservoir Evaluation & Engineering 5, no. 05 (October 1, 2002): 355–64. http://dx.doi.org/10.2118/79717-pa.
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Summary X-ray computed microtomography was used to investigate why gels reduce permeability to water more than that to oil in strongly water-wet Berea sandstone and in an oil-wet porous polyethylene core. Although the two porous media had very different porosities (22% vs. 40%), the distributions of pore sizes and aspect ratios were similar. A Cr(III)-acetate-HPAM gel caused comparable oil and water permeability reductions in both porous media. In both cores, the gel reduced permeability to water by a factor 80 to 90 times more than that to oil. However, the distributions of water and oil saturations (vs. pore size) were substantially different before, during, and after gel placement. This paper examines the mechanism for the disproportionate permeability reduction in the two porous media. Introduction Many polymers and gels can reduce the permeability to water more than that to oil or gas.1–15 This property is critical to the success of water-shutoff treatments in production wells if hydrocarbon- productive zones cannot be protected during polymer or gelant placement.2,3 However, the magnitude of the effect has been unpredictable from one application to the next. Presumably, the effect would be more predictable and controllable if we understood why the phenomenon occurs. Although many mechanisms have been considered (see Table 1), the underlying cause of the disproportionate permeability reduction remains elusive. Previously, we used NMR imaging to observe disproportionate permeability reduction on a microscopic scale.16 Results from these experiments revealed that the imaging technique had many limitations that prevented us from obtaining reliable pore-level images. Most importantly, the spatial resolution was on the order of hundreds of micrometers, which was too low to clearly distinguish fluid pathways on the pore level. In this paper, we describe imaging experiments using high-resolution computed X-ray microtomography (XMT) to compare the oil and water pathways and fluid distributions before and after gel treatment. The current generation of synchrotron-based XMT scanners provides the ability to obtain 3D pore-level images of rock samples with a spatial resolution on the order of micrometers. 17–23 For this study, we used the ExxonMobil beamline X2-B at the Natl. Synchrotron Light Source.18 X2-B is a dedicated XMT imaging facility capable of producing continuous registered stacks of 2,048×2,048×1,024 14-bit 3D images of X-ray linear attenuation coefficients at energies tunable from 8 to 40 keV. The highly collimated synchrotron X-rays permit the reconstruction of a 3D image from 2D projections taken at uniformly spaced angles between 0 and 180°. X2-B converts the pattern X-rays transmitted by the specimen (projections) to a visible light image with a thin single crystal of CsI(Na). This image was magnified by an optical microscope objective onto a 1,024×1,024 charge coupled device (CCD). Using Fourier methods, the set of angular projections at each row of pixels in the CCD was used to reconstruct the crosssectional slice at that row. These slices were stacked to form the 3D image. In this work, a 5×microscope objective was used to provide a pixel size of 4.1 µm and a 4.1-mm field of view. Because part of the core was outside the imaged area, a profile extension method was used to supress edge artifacts. Several authors used XMT to characterize the microscopic structure of porous media.17,19,23 For a 15-darcy sandstone, Coles et al.19 found a mean tortuosity of 2.7, with a range from 1.5 to 4.5. Along a 2.2-mm-long section of this core, porosity varied only a few percent around the average value (26.4%). After oilflooding, this core was waterflooded to a water saturation of 25.1%. Interestingly, large variations in water saturation were observed along the 2.2-mm-long section, ranging from 12 to 39%. A 3D view showed the nonwetting phase (water, in this case) to exist as large ganglia (blobs of nonwetting phase that extend over multiple pores, often exhibiting a branched structure).19 Chatzis et al.24,25 suggested that rock heterogeneity can be responsible for saturation variations within a porous medium. Nonwetting phase saturations that are lower than expected can occur when clusters of small pores are dispersed in a matrix dominated by large pores. In contrast, nonwetting phase saturations that are higher than expected can occur when clusters of large pores are dispersed in a matrix dominated by small pores.24 However, significant saturation variations can occur even in homogeneous porous media, depending on the pore-body/pore-throat aspect ratio. For homogeneous 2D micromodels, Chatzis et al.24 reported piston-like displacements with very little trapping of the nonwetting phase when the aspect ratio was 2 or less. However, for aspect ratios around 3, large nonwetting phase clusters formed as the wetting phase formed fingers while displacing the nonwetting phase. At higher aspect ratios, the nonwetting phase tended to be trapped in individual pores rather than in large clusters of pores. The pore coordination number had a minor effect on nonwetting phase residual saturations.24 Using XMT data, Lindquist et al.23 extensively characterized pore- and throat-size distributions for Fontainebleau sandstones. As core porosity increased from 7.5 to 22%, they found that the average pore coordination number increased from 3.4 to 3.8; the average channel length decreased from 200 to 130 µm; the average throat area increased from 1,600 to 2,200 mum2; and the average pore volume remained fairly constant at approximately 0.0004 mm3. The aspect ratio (effective average pore radius/effective average throat radius) was greater than 2 in 65% of pores and greater than 3 in 40%. The aspect ratios tended to increase slightly as porosity decreased.
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Eswaramoorthi, S., K. Loganathan, Reema Jain, and Sonam Gyeltshen. "Darcy-Forchheimer 3D Flow of Glycerin-Based Carbon Nanotubes on a Riga Plate with Nonlinear Thermal Radiation and Cattaneo-Christov Heat Flux." Journal of Nanomaterials 2022 (May 5, 2022): 1–20. http://dx.doi.org/10.1155/2022/5286921.
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The current investigation deliberates the consequence of the glycerin-based carbon nanotubes with velocity slip in Darcy-Forchheimer porous medium on a convectively heated Riga plate. The Fourier heat flux theory was replaced by the Cattaneo-Christov theory. Moreover, nonlinear facets of radiation are also included in the energy expression, and this creates the energy expression which becomes highly nonlinear. The governing flow problems are altered into an ODE model with the help of suitable variables. The reduced models are solved numerically by applying MATLAB bvp4c theory and analytically by HAM idea. The impact of diverse physical parameters on velocity, temperature, skin friction coefficients, local Nusselt number, entropy generation, and Bejan number are scrutinized through tables and graphs. It is seen that both directions of fluid motion elevate when raising the modified Hartmann number, and it diminishes when escalating the quantity of the Forchheimer number and porosity parameter. The fluid warmth grows when the higher magnitude of the Biot number and heat generation/consumption parameter, and it downturns when enriching the thermal relaxation time parameter. The entropy generation slumps when heightening the slip parameter, whereas it improves when rising the radiation parameter. The Bejan number upturns when upgrading the Biot number and heat generation/consumption parameter.
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Chen, Xiaoyi, Hui-Hui Dai, and Erick Pruchnicki. "On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method." Mathematics and Mechanics of Solids, August 27, 2020, 108128652094960. http://dx.doi.org/10.1177/1081286520949602.
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An asymptotic reduction method is introduced to construct a rod theory for a linearized general anisotropic elastic material for space deformation. The starting point is Taylor expansions about the central line in rectangular coordinates, and the goal is to eliminate the two cross-section spatial variables in order to obtain a closed system for displacement coefficients. This is first achieved, in an ‘asymptotically inconsistent’ way, by deducing the relations between stress coefficients from a Fourier series for the lateral traction condition and the three-dimensional (3D) field equation in a pointwise manner. The closed system consists of 10 vector unknowns, and further refinements through elaborated calculations are performed to extract bending and torsion terms and to obtain recursive relations for the first- and second-order displacement coefficients. Eventually, a system of four asymptotically consistent rod equations for four unknowns (the three components of the central-line displacement and the twist angle) are obtained. Six physically meaningful boundary conditions at each edge are obtained from the edge term in the 3D virtual work principle, and a one-dimensional rod virtual work principle is also deduced from the weak forms of the rod equations.
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Heryanto, Yusri Dwi, Chin-Yi Cheng, Yutaka Uchida, Kazushi Mimura, Masaru Ishii, and Ryo Yamada. "Integrated analysis of cell shape and movement in moving frame." Biology Open 10, no. 3 (March 15, 2021). http://dx.doi.org/10.1242/bio.058512.
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ABSTRACT The cell's movement and morphological change are two interrelated cellular processes. An integrated analysis is needed to explore the relationship between them. However, it has been challenging to investigate them as a whole. The cell's trajectory can be described by its speed, curvature, and torsion. On the other hand, the three-dimensional (3D) cell shape can be studied by using a shape descriptor such as spherical harmonic (SH) descriptor, which is an extension of a Fourier transform in 3D space. We propose a novel method using parallel-transport (PT) to integrate these shape-movement data by using moving frames as the 3D-shape coordinate system. This moving frame is purely determined by the velocity vector. On this moving frame, the movement change will influence the coordinate system for shape analysis. By analyzing the change of the SH coefficients over time in the moving frame, we can observe the relationship between shape and movement. We illustrate the application of our approach using simulated and real datasets in this paper.
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Zhang, P. Y., D. F. Diao, and Z. J. Wang. "Three-Dimensional Local Yield Maps of Hard Coating Under Sliding Contact." Journal of Tribology 134, no. 2 (March 6, 2012). http://dx.doi.org/10.1115/1.4005265.
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The local yield maps for the identification of the yield initiation positions of hard coating on three-dimensional (3D) elastic half space under sliding contact were developed. In this study, the semi-analytical method (SAM), which is based on the conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) technique, was employed to analyze the contact problem. By using this method, the von Mises stress distributions for various combinations of coating thicknesses, friction coefficients, and elastic moduli of the coating and substrate were calculated. Then, the positions of yield initiation were found with the calculated results by comparing the critical maximum contact pressure Pmax,c for von Mises yielding at or in the different positions (surface, coating, interface, and substrate), and the 3D-local yield maps were introduced in relation to the yield strength ratio of the coating to the substrate (Yf/Yb) and the ratio of the coating thickness to the Hertzian contact radius (t/a0). Finally, the effect of critical friction coefficient on the transition of yielding positions was discussed.
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Moaven, Mahyar, Abbishek Gururaj, Zu Puayen Tan, Sarah Morris, Brian Thurow, and Vrishank Raghav. "Development and Uncertainty Characterization of Rotating 3D Velocimetry using a Single Plenoptic Camera." 14th International Symposium on Particle Image Velocimetry 1, no. 1 (August 1, 2021). http://dx.doi.org/10.18409/ispiv.v1i1.104.
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Rotating 3D velocimetry (R3DV) is a single-camera PIV technique designed to track the evolution of flow over a rotor in the rotating reference frame. A high-speed (stationary) plenoptic camera capable of 3D imaging captures the motion of particles within the volume of interest through a revolving mirror from the central hub of a hydrodynamic rotor facility, a by-product being an undesired image rotation. R3DV employs a calibration method adapted for rotation such that during MART reconstruction, voxels are mapped to pixel coordinates based on the mirror’s instantaneous azimuthal position. Interpolation of calibration polynomial coefficients using a fitted Fourier series is performed to bypass the need to physically calibrate volumes corresponding to each fine azimuth angle. Reprojection error associated with calibration is calculated on average to be less than 0.6 of a pixel. Experimental uncertainty of cross-correlated 3D/3C vector fields is quantified by comparing vectors obtained from imaging quiescent flow via a rotating mirror to an idealized model based purely on rotational kinematics. The uncertainty shows no dependency on azimuth angle while amounting to approximately less than 0.21 voxels per timestep in the in-plane directions and correspondingly 1.7 voxels in the radial direction, both comparable to previously established uncertainty estimations for single-camera plenoptic PIV.
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Wilde, Maria V., Maria Yu Surova, and Nadezhda V. Sergeeva. "Asymptotically correct boundary conditions for the higher-order theory of plate bending." Mathematics and Mechanics of Solids, April 29, 2022, 108128652210885. http://dx.doi.org/10.1177/10812865221088528.
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The construction of refined boundary conditions for the case of edge loading, corresponding to the theory with modified inertia in respect to the order of asymptotic approximation, is considered. The methods of investigation are based on the works of A. L. Goldenveizer and A. V. Kolos. The solution of three-dimensional (3D) problem is constructed as a superposition of the long-wave approximation and boundary layers. The traction on the edge is presented as generalized Fourier expansions, using the Legendre polynomials. This approach allows to obtain explicit expressions for the coefficients of boundary layers via an iteration procedure, in course of which the boundary conditions are satisfied with a pure asymptotic error. As a result, the refined boundary conditions (RBCs) are constructed. Effective stress resultants and couples are introduced, the coefficients of which (the Goldenveizer–Kolos constants) are the simple polynomial functions of Poisson’s ratio. In addition, the contribution of boundary layers to edge displacements is determined. The comparison of the dispersion curve for the edge wave, calculated on the basis of the theory with modified inertia and RBC, with the 3D solution show good agreement in the 10 times wider frequency range than that of the Kirchhoff’s theory. The same result is obtained for the amplitude of a transient edge wave, excited by edge loading. It is also shown that with making use of RBC one can consider the action of a self-equilibrated edge load in the framework of two-dimensional (2D) theory.
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Philcox, Oliver H. E., Zachary Slepian, Jiamin Hou, Craig Warner, Robert N. Cahn, and Daniel J. Eisenstein. "encore: An $\mathcal {O}(N_g^2)$ Estimator for Galaxy N-Point Correlation Functions." Monthly Notices of the Royal Astronomical Society, October 20, 2021. http://dx.doi.org/10.1093/mnras/stab3025.
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Abstract We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}\left(N_\mathrm{FFT}\log N_\mathrm{FFT}\right)$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ∼ 100 CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogs. Our approach can be straightforwardly applied to current and future datasets to unlock the potential of constraining cosmology from the higher-point functions.
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Houriez--Gombaud-Saintonge, Sophia, Elie Mousseaux, Ioannis Bargiotas, Alain De Cesare, Thomas Dietenbeck, Kevin Bouaou, Alban Redheuil, et al. "Comparison of different methods for the estimation of aortic pulse wave velocity from 4D flow cardiovascular magnetic resonance." Journal of Cardiovascular Magnetic Resonance 21, no. 1 (December 2019). http://dx.doi.org/10.1186/s12968-019-0584-x.
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Abstract Background Arterial pulse wave velocity (PWV) is associated with increased mortality in aging and disease. Several studies have shown the accuracy of applanation tonometry carotid-femoral PWV (Cf-PWV) and the relevance of evaluating central aorta stiffness using 2D cardiovascular magnetic resonance (CMR) to estimate PWV, and aortic distensibility-derived PWV through the theoretical Bramwell-Hill model (BH-PWV). Our aim was to compare various methods of aortic PWV (aoPWV) estimation from 4D flow CMR, in terms of associations with age, Cf-PWV, BH-PWV and left ventricular (LV) mass-to-volume ratio while evaluating inter-observer reproducibility and robustness to temporal resolution. Methods We studied 47 healthy subjects (49.5 ± 18 years) who underwent Cf-PWV and CMR including aortic 4D flow CMR as well as 2D cine SSFP for BH-PWV and LV mass-to-volume ratio estimation. The aorta was semi-automatically segmented from 4D flow data, and mean velocity waveforms were estimated in 25 planes perpendicular to the aortic centerline. 4D flow CMR aoPWV was calculated: using velocity curves at two locations, namely ascending aorta (AAo) and distal descending aorta (DAo) aorta (S1, 2D-like strategy), or using all velocity curves along the entire aortic centreline (3D-like strategies) with iterative transit time (TT) estimates (S2) or a plane fitting of velocity curves systolic upslope (S3). For S1 and S2, TT was calculated using three approaches: cross-correlation (TTc), wavelets (TTw) and Fourier transforms (TTf). Intra-class correlation coefficients (ICC) and Bland-Altman biases (BA) were used to evaluate inter-observer reproducibility and effect of lower temporal resolution. Results 4D flow CMR aoPWV estimates were significantly (p < 0.05) correlated to the CMR-independent Cf-PWV, BH-PWV, age and LV mass-to-volume ratio, with the strongest correlations for the 3D-like strategy using wavelets TT (S2-TTw) (R = 0.62, 0.65, 0.77 and 0.52, respectively, all p < 0.001). S2-TTw was also highly reproducible (ICC = 0.99, BA = 0.09 m/s) and robust to lower temporal resolution (ICC = 0.97, BA = 0.15 m/s). Conclusions Reproducible 4D flow CMR aoPWV estimates can be obtained using full 3D aortic coverage. Such 4D flow CMR stiffness measures were significantly associated with Cf-PWV, BH-PWV, age and LV mass-to-volume ratio, with a slight superiority of the 3D strategy using wavelets transit time (S2-TTw).