Solution In Spatial Domain Research Articles

Frictional contact of one-dimensional hexagonal quasicrystal coating considering thermal effects

In this paper, the contact behavior of a one-dimensional hexagonal quasicrystal coating fully bonded to a rigid substrate under the action of a spherical indenter rotating around its own axis is investigated. The frictional heat generation and heat transfer are considered. Using the general solutions of thermoelastic fields combined with thermal–mechanical boundary conditions followed by the double Fourier transforms, the frequency response functions of the basic solutions of the thermoelastic contact problem are obtained. The basic solutions in spatial domain are calculated by the discrete convolution-fast Fourier transform (DC-FFT) algorithm and the inverse fast Fourier transform (IFFT) algorithm. The results show that the asymmetry of responses of phonon normal stress, phason normal displacement and phason normal stress are mainly caused by friction behaviors. The increase of friction coefficient does not change the phonon normal displacement, but makes the phason normal displacement and the normal stresses of phonon and phason field opposite change trends on both sides of the contact center.

Nonoverflow Representation of Electromagnetic Field From Dipole Source in Cylindrical Media With Uniaxial Anisotropy

A non-overflow representation of electromagnetic (EM) field radiated by dipoles sources in the cylindrical multilayered anisotropic media is presented. The sources include both magnetic and electric triaxial dipoles. The permeability, permittivity, and conductivity of each layer are all uniaxial anisotropic. A set of normalized reflection\transmission coefficients is defined and utilized to describe the propagation of EM wave. The recursive algorithm of EM field in each layer is with respect to the ratios of the outgoing and standing waves. In the expressions, all the Hankel or Bessel functions are in the form of their ratios, which avoid the overflow problem in numerical integral. To improve the stability and accuracy of numerical calculation, we subtract the background field from the total field in spectral domain. The background field is calculated by the algebraic solution in spatial domain rather than its integral representation. The rest of the field, namely the reflection field, has smaller convergence region compared with its total field, and is calculated using the cubic spline interpolation method. The parities of the integrand are discussed by using numerical simulations, which yield the corresponding folded expressions of the field components to accelerate the computational efficiency. This work can be widely used in the applications of geophysical exploration.

Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions

The paper presents a new solver for the numerical solution of the Boltzmann kinetic equation with the Shakhov model collision integral (S-model) for arbitrary spatial domains. The numerical method utilizes the Tucker decomposition, which reduces the required computer memory for up to 100 times, even on a moderate velocity grid. This improvement is achieved by representing the distribution function values on a structured velocity grid as a 3D tensor in the Tucker format. The resulting numerical method makes it possible to solve complex 3D problems on modern desktop computers. Our implementation may serve as a prototype code for researchers concerned with the numerical solution of kinetic equations in 3D domains using a discrete velocity method. Program summaryProgram Title: Boltzmann-TCPC Library link to program files:https://doi.org/10.17632/29wv8nmbgn.1Developer’s repository link:https://github.com/chikitkin/Boltzmann-TuckerLicensing provisions: MITProgramming language: Python 3External libraries: Solver is based on the customized version of the tucker3d library [1]Nature of problem: Numerical solution of the Boltzmann kinetic equation with the S-model collision integral in an arbitrary 3D spatial domainSolution method: Discrete velocity method utilizing tensor decomposition for memory reductionAdditional comments including restrictions and unusual features: At present, 1st order advection scheme is used, solver supports unstructured hexagonal meshes written in StarCD ASCII formatReference tucker3d (https://github.com/rakhuba/tucker3d) library contains Python implementations of several important procedures for working with tensors in the Tucker format.

Active Contour Model Using Fast Fourier Transformation for Salient Object Detection

The active contour model is a comprehensive research technique used for salient object detection. Most active contour models of saliency detection are developed in the context of natural scenes, and their role with synthetic and medical images is not well investigated. Existing active contour models perform efficiently in many complexities but facing challenges on synthetic and medical images due to the limited time like, precise automatic fitted contour and expensive initialization computational cost. Our intention is detecting automatic boundary of the object without re-initialization which further in evolution drive to extract salient object. For this, we propose a simple novel derivative of a numerical solution scheme, using fast Fourier transformation (FFT) in active contour (Snake) differential equations that has two major enhancements, namely it completely avoids the approximation of expansive spatial derivatives finite differences, and the regularization scheme can be generally extended more. Second, FFT is significantly faster compared to the traditional solution in spatial domain. Finally, this model practiced Fourier-force function to fit curves naturally and extract salient objects from the background. Compared with the state-of-the-art methods, the proposed method achieves at least a 3% increase of accuracy on three diverse set of images. Moreover, it runs very fast, and the average running time of the proposed methods is about one twelfth of the baseline.

A time domain solution of the Modified Temperature Vegetation Dryness Index (MTVDI) for continuous soil moisture monitoring

This study presents indexes developed from remote sensing observations for continuous soil surface moisture monitoring. The Modified Temperature Vegetation Dryness Index (MTVDI) proposed in our earlier work is developed using a time domain solution method rather than the traditional spatial domain solution method, because of limitations arising from a traditional temperature-vegetation index (TVX) method. In the procedure herein proposed, the MTVDI parameterization scheme is transformed from regional scale to pixel scale, and the boundary conditions defining maximum water stress are determined pixel by pixel using the surface energy balance principle. All the parameters required for the retrieval of MTVDI are pixel specific, thereby avoiding the limitations of the traditional spatial domain solution method. Previous studies demonstrate the applicability of the TVX method with data from only a few days of clear sky conditions. In contrast, our proposed MTVDI is demonstrated using Moderate Resolution Imaging Spectroradiometer (MODIS) products over the course of a full year, and the soil moisture status over the Southern Great Plains (SGP) region is monitored continuously. Finally, the volumetric surface soil water content (θv) is estimated using a calibration procedure from the MTVDI retrievals. The results show that the accuracy of both MTVDI retrievals and θv estimates obtained in this work has reached a level comparable with those produced in previous studies. Across all sites, the correlation coefficient (r) between the MTVDI and θv measurements is 0.60. The values of r, mean absolute error (MAE) and root mean square error (RMSE) for θv estimates are 0.75, 0.019m3m−3 and 0.025m3m−3, respectively.

Semi-analytical model for rough multilayered contacts

This paper presents a new model for analysis of non-conformal rough surface contacts where one or both of the contacting bodies are coated with a multilayered coating. The model considers elastic contact of arbitrary geometry with real measured roughnesses and both normal and tangential surface loads. It predicts contact pressure distribution, surface deformations and full subsurface stress field. As such, the model offers an optimisation tool for analysis and development of multilayered coatings. Influence coefficients approach is utilised to obtain contact pressures and subsurface stresses while the contact solver is based on a standard conjugate gradient method. To improve model efficiency, a semi-analytical approach is devised, where the influence coefficients for displacements and stresses are expressed explicitly by solving the fundamental equations in the frequency domain. Fast Fourier Transforms in conjunction with discrete convolution are then utilised to provide the solution in spatial domain. Selected results are presented to first validate the model and then illustrate the potential improvements that can be achieved in the design of multilayered coatings through application of the model.

Numerical solution of nonlinear Burgers’ equation using high accuracy multi-quadric quasi-interpolation

In this paper, a numerical method is presented to approximate the solution to nonlinear Burgers’ equation which is related to many scientific research topics. A numerical scheme by using high accuracy multi-quadric quasi-interpolation is presented in which a kind of multi-quadric quasi-interpolant is used to approximate the derivatives of the solution in spatial domain and finite difference is used to approximate the derivatives of the solution in temporal domain. The advantage of the scheme is that it is mesh free and in each time step only a multi-quadric quasi-interpolant is employed so that the algorithm is easy to implement. The numerical results of this scheme are also shown and compared with other numerical schemes.

Magnetic-anomaly Fourier spectrum of a 3D Gaussian source

I obtain a closed-form expression for the total-field magnetic anomaly generated by a 3D Gaussian magnetization distribution. The solution is evaluated by a novel contour integration in the complex-wavenumber domain. The spatial-domain solution is then computed by a numerical inverse Fourier transform. This calculated field can be used to interpret magnetic data because a 3D Gaussian function can represent a compact and smooth source. The method, moreover, allows for calculation of the Fourier components as a function of the distance between the depth of the source and the height of the observation level. The solution is thus useful for the inverse problem, spectral analysis, or data continuation.

Modeling Impacts of Thaw Lakes to Ground Thermal Regime in Northern Alaska

In northern Alaska, the ground is largely underlain by permafrost. Many engineering problems in this region can be attributed to the variations of ground thermal regime. Engineering projects such as construction of gas pipelines must be based on a good understanding of ground thermal regime and its interaction with seasonal climate changes. Numerical modeling is used to simulate a multimedia system with transient heat transfer in this research. The system includes a snow cover on the top, a shallow lake in the middle, and soils beneath the lake. The finite-element method is used for the spatial domain solution, and the finite-difference method is used for the temporal domain solution. The model is applied to three sites in northern Alaska for a nine-month period during the winter of 1995–1996. The result reveals the impacts of thaw lake on the ground thermal regime, the formation of the talik, as well as the formation of ice in the lake. The model is verified against field observations. The difference bet...

Scattering of sound by a fluid-loaded plate with a distributed mass inhomogeneity

The scattering of a plane acoustic wave by a fluid-loaded, thin, elastic plate, of infinite extent, with a distributed mass inhomogeneity is investigated. Two approaches are presented, an iterative approach valid when a measure of the distributed impedance is much lower than that of the uniform fluid-loaded plate, and a full numerical solution which while having no restricting assumptions is somewhat demanding computationally. For the iterative solution a set of correction terms is evaluated and applied to the response of the uniform plate with no inhomogeneities. The number of correction terms required is dependent on the relative magnitude of the inhomogeneity. In the full numerical solution, the presence of the distributed inhomogeneity in the equation of motion, when expressed in the wave-number domain, results in a Fredholm integral equation of the third kind. By substituting for the product of the response and the plate characteristic equation (impedance), the Fredholm integral of the third kind is reduced to a Fredholm integral of the second kind. The plate response in the spectral wave-number domain is obtained from the solution of the Fredholm integral. Inverse Fourier transforming the wave-number domain response function gives the spatial domain solution for the response. The hybrid numerical analytical approach [J. Acoust. Soc. Am. 95, 1998–2005 (1994)] is used to perform the inverse Fourier transform. The far-field scattered pressure is obtained from the spectral domain solution of the response. Response and scattered pressure results for distributed mass inhomogeneities, with different distribution functions, are presented and compared to the results for a line inhomogeneity.

Acoustic scattering from a fluid-loaded elastic plate with a distributed mass inhomogeneity

The scattering of a plane acoustic wave by a fluid-loaded, thin, elastic plate, of infinite extent, with a distributed inhomogeneity is investigated by solving the equation of motion in the wave-number domain using the hybrid numerical analytical approach [J. Acoust. Soc. Am. 95, 1998–2005 (1994)]. The presence of the distributed inhomogeneity in the equation of motion, when expressed in the wave-number domain, results in a Fredholm integral equation of the third kind. By substituting for the product of the response and the plate characteristic equation, the Fredholm integral of the third kind is reduced to a Fredholm integral of the second kind. The plate response in the wave-number domain is obtained from the solution of the Fredholm integral. Inverse Fourier transforming the wave-number domain response function gives the spatial domain solution for the response. The hybrid approach is used to perform the inverse Fourier transform. The scattered pressure is obtained in a similar manner. Response and scattered pressure results for distributed mass inhomogeneities, with different distribution functions, are presented and compared to the results for a line inhomogeneity. [Work sponsored by ONR.]