Two-dimensional Fast Fourier Research Articles

Analysis of bender element test interpretation using the discrete element method

While bender element testing is now well-established as a laboratory technique to determine soil stiffness, a robust technique to interpret the data remains elusive. A discrete element method (DEM) model of a face-centred cubic packing of uniform spheres was created to simulate bender element tests to investigate this test from a fundamental perspective. During the DEM simulations transmitter and receiver signals were recorded, analogous to the data available in laboratory tests, and these macro-scale data were supplemented with particle scale measurements (forces, stresses and displacements). A range of approaches previously applied in experimental and numerical studies were used to analyse the resulting data in both the time and frequency domains. The shortcomings in these approaches are clear from the differences in the resultant shear stiffness values and the frequency-dependent nature of the values. The particle-scale data enabled visualization of the passage of the wave through the sample, and it was found not to be possible to precisely link the arrival of the shear wave at the receiver and any of the previously proposed characteristic points along the signal recorded at the receiver. The most reliable determination of the shear wave velocity was obtained by applying a two-dimensional fast Fourier transform (2D FFT) to the data describing the velocity of the particles lying between the transmitter and receiver elements. Use of the DEM model and this 2D FFT approach facilitated the sensitivity of the system response to small variations in the interparticle force–displacement law (the contact model) to be established.

Structural analysis of adventitial collagen to feature aging and aneurysm formation in human aorta

Adventitial collagen structure provides the aorta with tensile strength. Like other collagen-rich tissues, it can be affected by internal factors including aging and location. We determined whether the structural characteristics of human aortic adventitial collagen change with aging, location, and aneurysm formation. Nonatherosclerotic nonaneurysmal (NANA) human abdominal aortas were collected from 15 individuals who had died of noncardiovascular diseases (<40years old, NANA young, n= 5; >60years old, NANA old, n= 5). The architecture of adventitial collagen in the aortas was assessed by scanning electron microscopy, and fiber orientation was assessed by polarized microscopy with two-dimensional fast Fourier transform. We then analyzed retardation as an anisotropic property of adventitial collagen by polarized light microscopy. The orientation and retardation of NANA aortas were compared with those of abdominal aortic specimens from patients who were surgically treated for abdominal aortic aneurysm (AAA) (>60years old, n= 11). Adventitial collagen of the abdominal aortas on scanning electron microscopy images appeared as wavy, ropy fibers in aortas from young individuals (NANA young, n= 5) and were essentially flattened in those from older patents (NANA old, n= 5) and from those with AAA. Collagen fibers were thicker but sparser in the adventitia of aortas with AAA. Orientation maintained in the collagen fibers of NANA aortas (n= 15) on two-dimensional fast Fourier transform analysis was unrelated to either location or age and did not differ between NANA aortas and those with AAA. However, collagen fibrils in NANA aortas (n= 15) were significantly less retarded only at the level of the inferior mesenteric artery compared with other aortic locations. In addition, retardation was significantly reduced in abdominal aortas with AAA at the level of the inferior mesenteric artery. The basic structure of adventitial collagen fiber was maintained in abdominal aortas regardless of location or age. Because the molecular structure at the subfibril level changed at abdominal aorta and enhanced in aortas with AAA, alterations in the molecular structure of adventitial collagen might be associated with aneurysmal formation.

High-resolution imaging of (100) kyanite surfaces using friction force microscopy in water

In this paper, we present high-resolution friction force microscopy (FFM) images of the (100) face of kyanite (Al2SiO5) immersed in water. These images show an almost rectangular lattice presumably defined by the protruding oxygen of AlO6 polyhedra. Surface lattice parameters measured on two-dimensional fast Fourier transform (2D-FFT) plots of recorded high-resolution friction maps are in good agreement with lattice parameters calculated from the bulk mineral structure. Friction measurements performed along the [001] and [010] directions on the kyanite (100) face provide similar friction coefficients μ ≈ 0.10, even if the sequences of AlO6 polyhedra are different along the two crystallographic directions.

Numerical Analysis of the Contact Problem Considering Inhomogeneous Inclusions

Nonmetallic inclusions and cracks during the smelting generate stress concentration, which may be the fatigue source under an alternating load. The fatigue source may enable some materials to separate from the matrix material and the cracks occur.The cracks can greatly influence the fatigue life of material. Based on the semi-analytical method(SAM), the computational domain is divided into many infinitesimal cuboids, thus each inclusion can be represented by a number of infinitesimal cuboids. According to equivalent inclusion method(EIM), each cuboid has an unknown eigenstrains which are obtained by a set of simultaneous constitutive equations about stresses and strains relationship. The contact pressure is solved based on conjugate gradient method; furthermore, the subsurface stress distributions are obtained by the semi-analytical method. The two-dimensional and three-dimensional fast Fourier transform(DC-FFT) based approaches are used to speed up the computations related to deformation and eigenstress. The results show the excellent stability and convergence of the algorithm; the inclusions greatly affect the contact pressure and stress distribution; the inclusions with large size and small depth have significant effect on the contact performance.The inclusion with arbitrary shape can be modeled by this model.

Modification of a two-dimensional fast Fourier transform algorithm by the analog of the Cooley-Tukey algorithm for a rectangular signal

One-dimensional fast Fourier transform (FFT) is the most popular tool for computing the two-dimensional Fourier transform. As a rule, a standard method of combination of one-dimensional FFTs--the so-called algorithm "by rows and columns" [1]--is used in the literature. In [2, 3], the authors showed how to compute the FFT for a signal with the number of samples 2 s × 2 s with the use of an analog of the Cooley-Tukey algorithm. In the present paper, a two-dimensional analog of the Cooley-Tukey algorithm is constructed for a rectangular signal with the number of samples 2 s × 2 s + l. The number of operations in this algorithm is much less than that in the successive application of a one dimensional FFT by rows and columns. The testing of the algorithm on image-type signals shows that the speed of computation of the FFT by the algorithm proposed is about 1.7 times higher than that of the algorithm by rows and columns.

Estimation of Cross-shore Water Depth Profiles and Evaluation of Their Near-shore Fluctuation, Using X-band Radar Data

On October 16th to 26th, 2013, Japan's eastern coast was affected by three major typhoons. Having monitored the coastal area within the period, abundant data (reflected backscatters in form of consecutive series of grey-scale images) was collected and analyzed. To determine major frequencies and wave-numbers during the storms, one- and two-dimensional Fast Fourier Transform (FFT) are respectively employed for analysis of the original and filtered images. With the main wave-field characteristics in hand and using the linear dispersion relationship, water depths are calculated. Tide-adjusted cross-shore overall profiles are estimated, and analyzed near-shore water depth variation well captures the tidal oscillation within the study period.

A method for selective excitation of Ince-Gaussian modes in an end-pumped solid-state laser

A method for selective excitation of Ince-Gaussian modes is presented. The method is based on the spatial distributions of Ince-Gaussian modes as well as the transverse mode selection theory. Significant diffraction loss is introduced in a resonator by using opaque lines at zero-intensity positions, and this loss allows to excite a specific mode; we call this method “loss control.” We study the method by means of numerical simulation of a half-symmetric laser resonator. The simulated field is represented by angular spectrum of the plane waves representation, and its changes are calculated by the two-dimensional fast Fourier transform algorithm when it passes through the optical elements and propagates back and forth in the resonator. The output lasing modes of our method have an overlap of over 90 % with the target Ince-Gaussian modes. The method will be beneficial to the further study of properties and potential applications of Ince-Gaussian modes.

A two-dimensional fast Fourier transform using incremented frequency measurement for guided wave analysis

A two-dimensional fast Fourier transform using incremented frequency measurement for guided wave analysis

AN NUMERICAL METHOD BASED ITERATIVE PROCESS TO CHARACTERIZE MICROWAVE PLANAR CIRCUITS

In the present work, the modeling of microwaves planar circuits is proposed with an original method based on the Waves Concept Iterative Process (WCIP). It consists in the development of simulation software based on an iterative method. The iterative method is developed from the fast modal transform on a two-dimensional fast Fourier transform (FFT) algorithm. The method has been applied to the characterization and the modeling of patch antennas with notches in microstrip and coplanar technology and the quarter wavelength directive coupler. The obtained results are very powerful and successfully compared to others methods in term of time and reliability of convergence and particularly the accuracy of the results obtained in comparison with previous works.

Research on Multi-Core PC Parallel Computation Based on OpenMP

Along with quad-core PC coming into the market and invention of 80-core processor in the laboratory, Software development will go through a foundational innovation due to multicore technology. The technique of parallel programming on multi-core computers is explored in this thesis. First, the OpenMP standard which is an application programming interface (API) on parallel programming model of shared-memory is introduced and an overview of a set of compiler directives and a library of support functions are given. The OpenMP programs requires an OpenMP-compatible compiler and thread-safe libraries，therefore, both Intel C++ compiler 9.1 and Microsoft Visual Studio 2005 are perfect choices. Then, two-dimensional discrete fast Fourier transform (FFT) is studied by focusing on parallel program design，realization and optimization technology. Finally，the thesis predicts that high performance parallel computing software component library must be a perfect exploitation field in the further future.

Validation of Dispersion Curve Reconstruction Techniques for the A0 and S0 Modes of Lamb Waves

The properties of ultrasonic Lamb waves, such as relatively small attenuation and high sensitivity to structural changes of the object being investigated, allow performing of non-destructive testing of various elongated structures like pipes, cables, etc. Due to the dispersion effect of Lamb waves, a waveform of the received informative signal is usually distorted, elongated and overlapping in the time domain. Therefore, in order to investigate objects using the ultrasonic Lamb waves and to reconstruct the dispersion curves, it is necessary to know the relationship between frequency, phase and group velocities and thickness of the plate. The zero-crossing technique for measurement of phase velocity of Lamb waves (the A0 and S0 modes) has been investigated using modelled dispersed signals and experimental signals obtained for an aluminium plate having thickness of 2 mm. A comparison between two reconstruction methods of Lamb wave phase velocity dispersion curves, namely, the two-dimensional fast Fourier transform (2D-FFT) and zero-crossing technique, along with the theoretical (analytical) dispersion curves is presented. The results indicate that the proposed zero-crossing method is suitable for use in reconstruction of dispersion curves in the regions affected by strong dispersion, especially for the A0 mode.

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.

Ultrasonic leaky guided waves in fluid-coupled generic waveguides: hybrid finite-boundary element dispersion analysis and experimental validation

A numerical procedure is presented for the computation of dispersive parameters in elastic mechanical waveguides of generic cross-section immersed in non-viscous fluids. The method uses a semi-analytical finite element formulation to describe the solid waveguide, while a two-and-a-half dimensional boundary element method is used to represent the unbounded surrounding fluid. Leaky and trapped guided wave modes are found on the appropriate Riemann sheets by enforcing the generalized Snell–Descartes law along the fluid-structure interface and solving a nonlinear eigenvalue problem. The method is validated experimentally by extracting the frequency-real wavenumber dispersion curves of a rectangular bar and a thin angle aluminum bar via a two-dimensional Fast Fourier Transform. In both cases, a very good agreement is observed between the numerical and the experimental solutions.

Mechanical properties of electrospun bilayer fibrous membranes as potential scaffolds for tissue engineering

Bilayer fibrous membranes of poly(l-lactic acid) (PLLA) were fabricated by electrospinning, using a parallel-disk mandrel configuration that resulted in the sequential deposition of a layer with fibers aligned across the two parallel disks and a layer with randomly oriented fibers, both layers deposited in a single process step. Membrane structure and fiber alignment were characterized by scanning electron microscopy and two-dimensional fast Fourier transform. Because of the intricacies of the generated electric field, bilayer membranes exhibited higher porosity than single-layer membranes consisting of randomly oriented fibers fabricated with a solid-drum collector. However, despite their higher porosity, bilayer membranes demonstrated generally higher elastic modulus, yield strength and toughness than single-layer membranes with random fibers. Bilayer membrane deformation at relatively high strain rates comprised multiple abrupt microfracture events characterized by discontinuous fiber breakage. Bilayer membrane elongation yielded excessive necking of the layer with random fibers and remarkable fiber stretching (on the order of 400%) in the layer with fibers aligned in the stress direction. In addition, fibers in both layers exhibited multiple localized necking, attributed to the nonuniform distribution of crystalline phases in the fibrillar structure. The high membrane porosity, good mechanical properties, and good biocompatibility and biodegradability of PLLA (demonstrated in previous studies) make the present bilayer membranes good scaffold candidates for a wide range of tissue engineering applications.

Analysis of Computed Diffraction Pattern Diagram for Measuring Yarn Twist Angle

In this article a method measuring the twist angle of textile yarn is described in which the intensity diagram of a yarn diffraction pattern is utilized that can be achieved by projecting a parallel beam of monochromatic coherent light onto a yarn surface or computed through a two-dimensional discrete fast Fourier transform of a source digital yarn image. The orientation of this diagram provides the measurement of the twist angle of yarn. Examples of calculating twist angles for different yarns that confirm this method are available in this paper.

Measuring the Angle of Twist of a Fiber on the Basis of its Computer Image

A method is proposed for determining the angle of twist of a fiber from the distribution of the intensity of the pixels of a computer image of the fiber’s diffraction pattern. The two-dimensional fast Fourier transform is used to calculate the distribution based on the computer image. The value of the angle of twist is determined from an intensity distribution diagram constructed in polar coordinates. A computer program has been written in the language C++ (with use of the platform Net 3.5) to realize the new method. It is known that diffraction-based laser methods make it possible to use the mutual position of maxima on a diffraction pattern to perform a continuous quantitative check of the main parameters of textiles that are related to the periodic repetition of their geometric structure. These parameters are independent of the color and the material of textile. The same purpose can be served through the use of calculated diffraction patterns instead of patterns obtained on a screen by directly illuminating a specimen by a laser beam [2]. Such patterns can be calculated from an original computer image of the specimen with the use of the Frenkel– Kirchhoff integral [3] corrected with allowance for the possible dependence of the amplitude of the illumination u(ζ, η) on the coordinates of the points of the image that are being examined [1]:

Vacancy and Substitution Defects of β-Li2TiO3 Prepared by Hydrothermal Method

Abstract Fine β-Li2TiO3 particles were synthesized by hydrothermal reaction. Lithium vacancies and titanium substitution existed in the (002) lattice plane (pure lithium layer) via hydrothermal reaction, while after calcination, the titanium ions diffuse away from the (002) lattice plane into the LiTi2 layer, confirmed by two-dimensional fast Fourier transformation spectrum of the high-resolution transmission images and the Raman spectra.

Combining triangle Gaussian integration and modified NUFFT for evaluating two-dimensional Fourier transform integrals

The regular fast Fourier transform (FFT) requires a uniform Cartesian orthogonal grid which has considerable stair-casing errors when dealing with the function having an arbitrary shape boundary. The recently proposed two-dimensional discontinuous fast Fourier transform (2D-DFFT) can overcome this problem by using triangle mesh discretization and Gaussian numerical integration. However, the interpolation is used for the function data in the original 2D-DFFT, which reduces the accuracy performance especially for the case of oscillating functions. This work presents a useful modification of the original 2D-DFFT by removing the requirement of function interpolation to obtain significant accuracy improvement. In addition, the modified 2D nonuniform fast Fourier transform (NUFFT) with real-valued least-square interpolation coefficients are developed to speed up the computation of numerical Fourier transform over the triangle mesh. Numerical experiments are conducted to demonstrate the effectiveness and advantages of the proposed algorithms.

Double Two-Dimensional Discrete Fast Fourier Transform for Determining of Geometrical Parameters of Fibers and Textiles

We have developed a computing method to determine the geometrical parameters of fibers and the textile periodical structure. This method combines two two-dimensional discrete fast Fourier transforms to calculate a diffraction pattern from a diffraction pattern image of material under consideration. The result is the same as that of observation of a diffraction pattern which is achieved by illuminating the diffraction pattern image of material by a beam of coherent monochromatic light. After the first transform we obtain the Fraunhofer diffraction picture with clearly visible elements of the periodical structure of material, but distances in this picture are reciprocally proportional to distances in the periodical structure of the source object so additional calculations are required. After the second transform we have a clear periodical structure of diffraction maximums where distances between them are equal to distances between repeating elements in the source material (fibers, knots, yarns, etc.).

Experimental and numerical studies for nondestructive evaluation of human enamel using laser ultrasonic technique

In this paper, a nondestructive laser ultrasonic technique is used to generate and detect broadband surface acoustic waves (SAWs) on human teeth with different demineralization treatment. A scanning laser line-source technique is used to generate a series of SAW signals for obtaining the dispersion spectrum through a two-dimensional fast Fourier translation method. The experimental dispersion curves of SAWs are studied for evaluating the elastic properties of the sound tooth and carious tooth. The propagation and dispersion of SAWs in human teeth are also been studied using the finite element method. Results from numerical simulation and experiment are compared and discussed, and the elastic properties of teeth with different conditions are evaluated by combining the simulation and experimental results.