Influence of Stress Intensity Factor on Rail Fatigue Crack Propagation by Finite Element Method

Wheel rail rolling contact fatigue is a very common form of damage, which can lead to uneven rail treads, railhead nuclear damage, etc. Therefore, ANSYS software was used to establish a three-dimensional wheel–rail contact model and analyze the effects of several main characteristics, such as the rail crack length and crack propagation angle, on the fatigue crack intensity factor during crack propagation. The main findings were as follows: (1) With the rail crack length increasing, the position where the crack propagated by mode I moved from the inner edge of the wheel–rail contact spot to the outer edge. When the crack propagated to 0.3–0.5 mm, it propagated to the rail surface, causing the rail material to peel or fall off and other damage. (2) When the crack propagation angle was less than 30°, the cracks were mainly mode II cracks. When the angle was between 30 and 70°, the cracks were mode I–II cracks. When the angle was more than 70°, the cracks were mainly mode I cracks. When the crack propagation angle was 60°, the equivalent stress intensity factor reached the maximum, and the rail cracks propagated the fastest.

Two Dimensional Analysis of Hybrid Spectral/Finite Difference Schemes for Linearized Compressible Navier–Stokes Equations

This study seeks to compare different combinations of spatial dicretization methods under a coupled spatial temporal framework in two dimensional wavenumber space. The aim is to understand the effect of dispersion and dissipation on both the convection and diffusion terms found in the two dimensional linearized compressible Navier–Stokes Equations (LCNSE) when a hybrid finite difference/Fourier spectral scheme is used in the x and y directions. In two dimensional wavespace, the spectral resolution becomes a function of both the wavenumber and the wave propagation angle, the orientation of the wave front with respect to the grid. At sufficiently low CFL number where temporal discretization effects can be neglected, we show that a hybrid finite difference/Fourier spectral schemes is more accurate than a full finite difference method for the two dimensional advection equation, but that this is not so in the case of the LCNSE. Group velocities, phase velocities as well as numerical amplification factor were used to quantify the numerical anisotropy of the dispersion and dissipation properties. Unlike the advection equation, the dispersion relation representing the acoustic modes of the LCNSE contains an acoustic terms in addition to its advection and viscous terms. This makes the group velocity in each spatial direction a function of the wavenumber in both spatial directions. This can lead to conditions for which a hybrid Fourier spectral/finite difference method can become less or more accurate than a full finite difference method. To better understand the comparison of the dispersion properties between a hybrid and full FD scheme, the integrated sum of the error between the numerical group velocity $$V^{*}_{grp,full}$$ V g r p , f u l l ∗ and the exact solution across all wavenumbers for a range of wave propagation angle is examined. In the comparison between a hybrid and full FD discretization schemes, the fourth order central (CDS4), fourth order dispersion relation preserving (DRP4) and sixth order central compact (CCOM6) schemes share the same characteristics. At low wave propagation angle, the integrated errors of the full FD and hybrid discretization schemes remain the same. At intermediate wave propagation angle, the integrated error of the full FD schemes become smaller than that of the hybrid scheme. At large wave propagation angle, the integrated error of the full FD schemes diverges while the integrated error of the hybrid discretization schemes converge to zero. At high reduced wavenumber and sufficiently low CFL number where temporal discretization error can be neglected, it was found that the numerical dissipation of the viscous term based on the CDS4, DRP4, CCOM6 and isotropy optimized CDS4 schemes ($$\hbox {CDS4}_{{opt}}$$ CDS4 opt ) schemes was lower than the actual physical dissipation, which is only a function of the cell Reynolds number. The wave propagation angle at which the numerical dissipation of the viscous term approaches its maximum occurs at $$\pi /4$$ π / 4 for the CDS4, DRP4, CCOM6 and $$\hbox {CDS4}_{{opt}}$$ CDS4 opt schemes.

On application of the finite-difference Padé approximation of the pseudo-differential parabolic equation to the tropospheric radio wave propagation problem

Рассматривается задача численного моделирования распространения электромагнитных волн в неоднородной тропосфере на основе широкоугольных обобщений метода параболического уравнения. Используется конечно-разностная аппроксимация Паде оператора распространения. Существенно, что в предлагаемом подходе указанная аппроксимация осуществляется одновременно по продольной и поперечной координатам. При этом допускается моделирование произвольного коэффициента преломления тропосферы. Метод не накладывает ограничений на максимальный угол распространения. Для различных условий распространения радиоволн проведено сравнение с методом расщепления Фурье и методом геометрической теории дифракции. Показаны преимущества предлагаемого подхода. This paper is devoted to the numerical simulation of electromagnetic wave propagation in an inhomogeneous troposphere. The study is based on the wide-angle generalizations of the parabolic wave equation. The finite-difference Padé approximation is used to approximate the propagation operator. It is important that, within the proposed approach, the Padé approximation is carried out simultaneously along with the longitudinal and transverse coordinates. At the same time, the proposed approach gives an opportunity to model an arbitrary tropospheric refractive index. The method does not impose restrictions on the maximum propagation angle. The comparison with the split-step Fourier method and the geometric theory of diffraction is discussed. The advantages of the proposed approach are shown.

Formation Mechanisms of Exit-Chippings in Rotary Ultrasonic Drilling and Conventional Drilling of Glass BK7

This paper presented a fundamental investigation on the exit-chipping formation mechanisms involved in rotary ultrasonic drilling (RUD) and conventional drilling (CD) of glass BK7. It was found that the mutual tool-material extrusion initially activated the subsurface crack with the maximum depth (incipient crack) at the margin of the machined surface, and its penetration of the undrilled thickness brought about the emergence of the exit-chipping at Region I. Subsequently, the opposite propagations of two ring-cracks along the circumferential direction of the drilled hole were conducive to the collapse of the machined cylinder, thus leading to the appearance of the exit-chipping at Region II. Ultrasonic superposition significantly decreased the actual undrilled thickness of the machined surface, while slightly increased the exit-chipping width. All the exit-chippings, generated with and without ultrasonic, exhibited the elliptic and symmetrical morphologies accompanied by the corrugated stripes winding the entire chipping surfaces. The quantitative relationship between the instantaneous extrusion pressure and the propagation direction of the incipient crack was proposed, revealing that the propagation angle was inversely proportional to the extrusion pressure. Ultrasonic superimposition augmented the extrusion pressure exerted the machined surface, which reduced the propagation angle of the incipient crack. The elliptic morphology characteristics of the exit-chipping were attributed to the parabolic variation of the additional bending moment with the circumferential spreading of the ring-crack. Ultrasonic superposition increased the propagation angle of the ring-crack, thus deteriorating the exit quality of the drilled hole.

Improving the least-squares image by using angle information to avoid cycle skipping

In the past few decades, the least-squares reverse time migration (LSRTM) algorithm has been widely used to enhance images of complex subsurface structures by minimizing the data misfit function between the predicted and observed seismic data. However, this algorithm is sensitive to the accuracy of the migration velocity model, which, in the case of real data applications (generally obtained via tomography), always deviates from the true velocity model. Therefore, conventional LSRTM faces a cycle-skipping problem caused by a smeared image when using an inaccurate migration velocity model. To address the cycle-skipping problem, we have introduced an angle-domain LSRTM algorithm. Unlike the conventional LSRTM algorithm, our method updates the common source-propagation angle image gathers rather than the stacked image. An extended Born modeling operator in the common source-propagation angle domain is was derived, which reproduced kinematically accurate data in the presence of velocity errors. Our method can provide more focused images with high resolution as well as angle-domain common-image gathers (ADCIGs) with enhanced resolution and balanced amplitudes. However, because the velocity model is not updated, the provided image can have errors in depth. Synthetic and field examples are used to verify that our method can robustly improve the quality of the ADCIGs and the finally stacked images with affordable computational costs in the presence of velocity errors.

Fluorescence imaging with tailored light

Fluorescence microscopy has long been a valuable tool for biological and medical imaging. Control of optical parameters such as the amplitude, phase, polarization, and propagation angle of light gives fluorescence imaging great capabilities ranging from super-resolution imaging to long-term real-time observation of living organisms. In this review, we discuss current fluorescence imaging techniques in terms of the use of tailored or structured light for the sample illumination and fluorescence detection, providing a clear overview of their working principles and capabilities.

On the Influence of Swell Propagation Angle on Surface Drag

A combination of turbulence-resolving large-eddy simulations and observations are used to examine the influence of swell amplitude and swell propagation angle on surface drag. Based on the analysis a new surface roughness parameterization with nonequilibrium wave effects is proposed. The surface roughness accounts for swell amplitude and wavelength and its relative motion with respect to the mean wind direction. The proposed parameterization is tested in uncoupled three-dimensional Weather and Research Forecasting (WRF) simulations at grid sizes near 1 km where we explore potential implications of our modifications for two-way coupled atmosphere–wave models. Wind–wave misalignment likely explains the large scatter in observed nondimensional surface roughness under swell-dominated conditions. Andreas et al.’s relationship between friction velocity and the 10-m wind speed under predicts the increased drag produced by misaligned winds and waves. Incorporating wave-state (speed and direction) influences in parameterizations improves predictive skill. In a broad sense, these results suggest that one needs information on winds and wave state to upscale buoy measurements.