Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

Spatially modulated polarimetry based on a vortex retarder and Fourier analysis

We report a spatially modulated polarimetry scheme by using a zero-order vortex half-wave retarder(ZVHR)and a spatial Fourier analysis method.A ZVHR is employed to analyze the input polarized light and convert it into a vectorial optical field,and an analyzer is set after the ZVHR to form an hourglass intensity pattern due to the spatial polarization modulation.Then,the input light’s Stokes parameters can be calculated by spatial Fourier analysis of the hourglass pattern with a single shot.The working principle of the polarimeter has been analyzed by the Stokes-Mueller formalism,and some quantitative measuring experiments of different polarization states have been demonstrated.The experimental results indicate that the proposed polarimeter is accurate,robust,and simple to use.

Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening

We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation.Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsening.We also present numerical tests supporting the theoretical results and the heuristic ideas.The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.

Fourier analysis of elastic light scattering spectrum of epithelial cell nuclei

A new method for simultaneously determining the size and refractive index of epithelial cell nuclei is presented. The function of the modified elastic light scattering spectrum is regarded as a function of wave number factor, Q=2λ-1sin（θ/2）. The modified spectrum has a constant oscillation period with its frequency proportional to the average diameter of cell nuclei. To the same average diameter, the different relative refractive indexes of epithelial cell nuclei only induce the horizontal shift of the spectra. Both the oscillation frequency and the horizontal shift are quantified by the fast Fourier transform on the modified spectra. The average diameter can be figured out through the peak frequency divided by the value of the refractive index of the surrounding medium. The phase angle of the peak frequency has an approximate linear relationship with the relative refractive index of epithelial cell nuclei.

Local Fourier Analysis for Edge-Based Discretizations on Triangular Grids

In this paper,we present a local Fourier analysis framework for analyzing the different components within multigrid solvers for edge-based discretizations on triangular grids.The different stencils associated with edges of different orientation in a triangular mesh make this analysis special.The resulting tool is demonstrated for the vector Laplace problem discretized by mimetic finite difference schemes.Results from the local Fourier analysis,as well as experimentally obtained results,are presented to validate the proposed analysis.

Fourier and Wavelet Spectral Analysis of EMG Signals in 1-km Cycling Time-Trial

Frequency domain analyses in electromyographic (EMG) signals are frequently applied to assess muscle fatigue and similar variables. Moreover, Fourier-based approaches are typically used for investigating these procedures. Nonetheless, Fourier analysis assumes the signal as stationary which is unlikely during dynamic contractions. As an alternative method, wavelet-based treatments do not assume this pattern and may be considered as more appropriate for joint time-frequency domain analysis. Based on the previous statements, the purpose of the present study was to compare the application of Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) to assess muscle fatigue in dynamic exercise of a 1-km of cycling (time-trial condition). The results of this study indicated that CWT and STFT analyses have provided similar fatigue estimates (slope) (p> 0.05). However, CWT application represents lesser dispersion (p< 0.05) for vastus medialis (189.9 ± 82.1 for STFT vs 148.6 ± 60.2 for CWT) and vastus lateralis (151.6 ± 49.6 for STFT vs 103.5 ± 27.9 for CWT). In conclusion, despite the EMG signal did not change (p> 0.05) according to different methods, it is important to note that these responses seem to show greater values for CWT compared to STFT for 2 superficial muscles. Thereby, we are capable of considering CWT as a reliable and useful method to take into consideration when non-stationary or oscillating exercise models are evaluated.

Adaptive Fourier Decomposition Based Time-Frequency Analysis

The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.

Analysis of Wood Anatomy Characteristics by Fast Fourier Transfer Image Analysis

Fast Fourier Transfer Image Processing was widely applied to the analysis of wood anatomy structure in re-cent years. The cells in the wood transverse section have obviously periodicity and regularity. FFT power spectral patternscan extract the periodic characteristics so that they can be compared. identified and classified quaytitatively. This paperSummarizes the application of FFT image analysis in wood science and the general way to study wood anatomy by FFT.

On the global smooth solutions of 3D incompressible Hall-MHD equations

The present paper is devoted to the well-posedness issue for the 3D incompressible Hall-MHD system obtained from kinetic models. Our analysis strongly relies on the use of the Fourier analysis. We establish the global existence of smooth solutions for a class of large initial data, this result implies the initial velocity and magnetic field can be arbitrarily large.

Analysis of the Characteristics of Inertia-Gravity Waves during an Orographic Precipitation Event

A numerical experiment was performed using the Weather Research and Forecasting（WRF） model to analyze the generation and propagation of inertia-gravity waves during an orographic rainstorm that occurred in the Sichuan area on 17 August 2014. To examine the spatial and temporal structures of the inertia-gravity waves and identify the wave types, three wavenumber-frequency spectral analysis methods（Fourier analysis, cross-spectral analysis, and wavelet cross-spectrum analysis）were applied. During the storm, inertia-gravity waves appeared at heights of 10-14 km, with periods of 80-100 min and wavelengths of 40-50 km. These waves were generated over a mountain and propagated eastward at an average speed of 15-20 m s^（-1）. Meanwhile, comparison between the reconstructed inertia-gravity waves and accumulated precipitation showed there was a mutual promotion process between them. The Richardson number and Scorer parameter were used to demonstrate that the eastward-moving inertia-gravity waves were trapped in an effective atmospheric ducting zone with favorable reflector and critical level conditions, which were the primary causes of the long lives of the waves. Finally, numerical experiments to test the sensitivity to terrain and diabatic heating were conducted, and the results suggested a cooperative effect of terrain and diabatic heating contributed to the propagation and enhancement of the waves.

Experimental analysis of infragravity waves in two eroded microtidal beaches

This work aims to contribute to the characterization and understanding ofinfragravity waves on two beaches with erosion problems. For this reason, we have used an array of ADCP and a pressure sensor to measure wave parameters and pressure inside and outside of the surf zone during the dry and rainy period in the beaches of Galerazamba and Manzanillo del Mar （both dissipative and eroded beaches） located in the Colombian Caribbean coast. Based on these measurements, we have carried out a spectral analysis in order to identify the frequency components that characterize the wave and its energy; thus, we identified the characteristic frequencies of iufragravity waves to finally filter the infragravity signal on each beach in different seasonal periods. Among the results of the Welch spectrum applied to surface elevation time series, we found that, the frequencies＇ energy of the sea-swell band decreases due to bottom friction and wave breaking as the wave approaches the shore, while the frequencies＇ energy of the infragravity band increases significantly. In addition, for the wavelet analysis, we could observe how the energy of the infragravity band, especially the lowest frequencies gain energy as the waves approaches the coast. Furthermore, based on the infragravity wave obtained from the extreme wave event registered during the field campaign we can conclude that the contribution of this signal is important in the erosion problems presented in the beaches of Galerazamba and Manzanillo del Mar. Finally, these results show the need to realize other studies that allow us to understand deeply, the role of infragravity waves on the morphological changes that occurs in these beaches.

Identification of five Pampus species from the coast of China based on sagittal otolith morphology analysis

Sagittal otoliths morphology were compared to identify five Pampus species of the Chinese coast（Chinese pomfret Pampus chinensis, grey pomfret P. cinereus, southern lesser pomfret P. minor, plumage pomfret P.punctatissmus, and Pampus sp.）. Otoliths demonstrated species-specific characteristics with noticeable differences in overall shape, margin and anterior region among species. With species divergence, otoliths get thinner following further developed rostrum and anti-rostrum. Interspecies variation in otolith could associate with experienced different temperature and water column. The discriminant analysis presented a high classification accuracy of 96.6%, which confirms the inter-specific distinction of otolith shape and enable the species identification.

Coconut Fiber Pyrolysis: Bio-Oil Characterization for Potential Application as an Alternative Energy Source and Production of Bio-Degradable Plastics

The current energy crisis could be alleviated by enhancing energy generation using the abundant biomass waste resources. Agricultural and forest wastes are the leading organic waste streams that can be transformed into useful alternative energy resources. Pyrolysis is one of the technologies for converting biomass into more valuable products, such as bio-oil, bio-char, and syngas. This work investigated the production of bio-oil through batch pyrolysis technology. A fixed bed pyrolyzer was designed and fabricated for bio-oil production. The major components of the system include a fixed bed reactor, a condenser, and a bio-oil collector. The reactor was heated using a cylindrical biomass external heater. The pyrolysis process was carried out in a reactor at a pressure of 1atm and a varying operating temperature of 150˚C, 250˚C, 350˚C to 450˚C for 120 minutes. The mass of 1kg of coconut fiber was used with particle sizes between 2.36 mm - 4.75 mm. The results show that the higher the temperature, the more volume of bio-oil produced, with the highest yield being 39.2%, at 450˚C with a heating rate of 10˚C/min. The Fourier transformation Infrared (FTIR) Spectroscopy analysis was used to analyze the bio-oil components. The obtained bio-oil has a pH of 2.4, a density of 1019.385 kg/m3, and a calorific value of 17.5 MJ/kg. The analysis also showed the presence of high-oxygenated compounds;carboxylic acids, phenols, alcohols, and branched oxygenated hydrocarbons as the main compounds present in the bio-oil. The results inferred that the liquid product could be bestowed as an alternative resource for polycarbonate material production.

WAVELET ANALYSIS IN TESTING SIGNALS

In this paper, Wavelet Analysis Method (WAM) is introduced to analyse the non-stationary, shock signals. The theory and construction method of wavelet, the fast algorithms of wavelet analysis are presented. As an example, the gear testing signal has been analysed by WAM, and the results of WAM are compared with that of Fourier spectrum. The advantages of WAM are clearly shown.

Low-frequency laboratory measurements of the elastic properties of solids using a distributed acoustic sensing system

In recent decades,low-frequency(LF)experiments based on the forced-oscillation(FO)method have become common practice in many rock physics laboratories for measuring the elastic and anelastic properties of rocks.However,the use of the electronic displacement sensors in traditional acquisition systems of FO devices such as conventional capacitive transducers or strain gauges seriously limits both the efficiency and productivity of LF measurements,and,due to the limited contact area of the displacement sensors with a sample under test,increases the requirements for sample homogeneity.In this paper,we present the first results obtained in the development of a new laboratory method elaborated to measure the elastic properties of solids.The method is a further development of the FO method where traditional data acquisition is replaced by acquisition based on fiber-optic distributed acoustic sensing(DAS)technology.The new method was tested in a laboratory study using two FO setups designed for measurements under uniaxial and confining pressures.The study was carried out on a sample made from polymethyl methacrylate(PMMA)and an aluminium standard,first under uniaxial pressure at FO frequencies of 1,10,30,60 and 100 Hz,and then under confining pressure at an FO frequency of 1 Hz.Both uniaxial and confining pressures were equal to 10 MPa,and the strain in the PMMA sample in all measurements did not exceed 4×10^(-8).The performance of DAS acquisition was compared with the measurements conducted at a strain of 1×10^(-6) using the traditional FO method based on the use of semiconductor strain gauges and the ultrasonic method.The results of the DAS measurements are in good agreement with the FO measurements carried out using semiconductor strain gauges and with the literature data.

傅里叶变换用于地下电缆故障检测(英文)

An analysis of underground power cables is performed using Fourier analysis with the objective of detecting fault and average life of the cables.Three types of cables are used in this experiment:a normal cable,a shorted cable, and a cable with holes.The impedance in each case is computed and Fourier transformation is applied so that the resulting impedance magnitude and impedance phase can be examined in the frequency domain.Various windowing techniques are applied to the experimental data to eliminate any interference.Fourier analysis is then applied to the impedance data calculated from both the sending end voltage and differential voltage.This analysis reveals differences in the frequency response of the three different types of a cable and can eventually be used as a measure for fault detection. Preliminary results reveal the differences in the frequency response.Accordingly,Fourier type methods can be effectively used as low cost and viable solutions to identify and detect faults in underground cables.

CFD Based Determination of Dynamic Stability Derivatives in Yaw for a Bird

Dynamic yaw stability derivatives of a gull bird are determined using Computational Fluid Dynamics（CFD） method. Two kinds of motions are applied for calculating the dynamic yaw stability derivatives CNr and CNβ. The first one relates to a lateral translation and, separately, to a yaw rotation. The second one consists of a combined translational and rotational motion. To determine dynamic yaw stability derivatives, the simulation of an unsteady flow with a bird model showing a harmonic motion is performed. The flow solution for each time step is obtained by solving unsteady Euler equations based on a finite volume approach for a small reduced frequency. Then, an evaluation of unsteady forces and moments for one cycle is conducted using harmonic Fourier analysis. The results of the dynamic yaw stability derivatives for both simulations of the model show a good agreement.

Description of shape characteristics through Fourier and wavelet analysis

In this paper, Fourier and Wavelet transformation were adopted to analyze shape char- acteristics, with twelve simple shapes and two types of second phases from real microstructure mor- phology. According to the results of Fast Fourier transformation （FFT）, the Fourier descriptors can be used to characterize the shape from the aspects of the first eight Normalization amplitudes, the number of the largest amplitudes to inverse reconstruction, similarity of shapes and profile roughness. And the Diepenbroek Roughness was rewritten by Normalization amplitudes of FFT results. Moreover, Sum Square of Relative Errors （SSRE） of Wavelet transformation （WT） signal sequence, including approximation signals and detail signals, was introduced to evaluate the simi- larity and relative orientation among shapes. As a complement to FFT results, the WT results can retain more detailed information of shapes including their orientations. Besides, the geometric sig- natures of the second phases were extracted by image processing and then were analyzed by means of FFT and WT.

Determination of the free lunar libration modes from ephemeris DE430

The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013,and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory（GRAIL）. Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies,the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as 1.471′′in longitude, 0.025′′in latitude and 8.19′′× 3.31′′for the wobble, with the respective periods of1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.