Reflection Matrix Method Research Articles

Analytical solution for seepage pressure of multilayered sand seabed considering interaction between wave-current action and shield tunnel

Existing theoretical studies of the seepage field around subsea shield tunnels under wave action take less account of the tunnel lining permeability, especially the effect of wave and current action on tunnel. Moreover, the solutions generally treat the sand as homogeneous and isotropic, ignoring the influence of multilayered seabed. In this paper, the analytical solutions are presented for the seepage pressure and liquefaction evaluation of sand around tunnel in multilayered seabed under wave and current action. The pore pressure response of pure seabed is obtained by the transmission and reflection matrix method. The mirror image method is introduced to establish governing equation of excess pore pressure reflected by tunnel, and the analytical solution of equation is obtained by Fourier series expansion under the condition of continuous seepage between sand and lining. Based on the superposition principle, the seepage pressure and liquefaction evaluation of sand around tunnel in multilayered seabed are obtained. Then the analytical solutions are compared with numerical and experimental results, and good agreement is obtained. In addition, the influencing factors of wave parameters (wavelength, period, current), seabed parameters (permeability, shear modulus, saturation) and tunnel parameters (lining thickness, lining permeability) are analyzed.

Modelling of critical speed of railway tracks on a multi-layered transversely isotropic saturated ground

The responses of railway tracks are significantly amplified when the high-speed train travels around the speed of waves propagating in underlying soils. The dynamic amplification phenomenon corresponding to the issue of the critical speed may compromise the stability and safety of operation and increase track damage. This paper proposes an analytical model to analyze the effect of the transverse isotropy of ground on the critical speed of railway tracks on stratified saturated soils. By using the Biot's theory, the general solutions of the transversely isotropic saturated porous medium are derived by employing the potential decomposition and Fourier transform. The transmission and reflection matrix method is extended to derive the three-dimensional fundamental solution for moving point loads acting on a multi-layered transversely isotropic saturated half-space. The models for railway tracks and wheel-axle loads are subsequently coupled to the ground. The proposed model is validated through a comparison with two existing models. Numerical studies demonstrate that the material anisotropy changes the critical speed and the corresponding dynamic amplification coefficient by up to 20%. The anisotropy in the shear modulus has the most significant influence on the critical speed, followed by Young's modulus and the permeability coefficient. The material anisotropy and soil layering cannot be ignored for the assessment of the critical speed of a track-ground system.

On beam shaping of the field radiated by a line source coupled to finite or infinite photonic crystals.

Comparison of the beam-shaping effect of a field radiated by a line source, when an ideal infinite structure constituted by two photonic crystals and an actual finite one are considered, has been carried out by means of two different methods. The lattice sums technique combined with the generalized reflection matrix method is used to rigorously investigate the radiation from the infinite photonic crystals, whereas radiation from crystals composed of a finite number of rods along the layers is analyzed using the cylindrical-wave approach. A directive radiation is observed with the line source embedded in the structure. With an increased separation distance between the crystals, a significant edge diffraction appears that provides the main radiation mechanism in the finite layout. Suitable absorbers are implemented to reduce the above-mentioned diffraction and the reflections at the boundaries, thus obtaining good agreement between radiation patterns of a localized line source coupled to finite and infinite photonic crystals, when the number of periods of the finite structure is properly chosen.

Quantum Dynamics Study on the Effects of Vibration, Translational Energy and Incident Angle on H2 Adsorption on a Defective Pt(111) Surface

Quantum dynamics calculations via the local reflection matrix method are performed to investigate the effects of the vibration and initial translational energy on the dissociative adsorption of H2 approaching a defective Pt(111) surface at different incident angles and adsorption sites. The sticking probability plot for H2 incident on the top site at 15° shows that as the translational energy is increased, the probability rapidly rises to unity which suggests that H2 is easily adsorbed on the Pt surface. The plot also shows that even though the adsorption process is non-activated, there is a probability that H2 will not be adsorbed on the Pt surface at low translational energies due to quantum mechanical effects. For the rest of the configurations, an S-shaped region is observed in the plots suggesting an activated adsorption process. The plots show that when the initial translational energy (Et) is less that the barrier, H2 sticks to the Pt surface by tunneling through the barrier and when Et is greater ...

RHEED wave functions and the effect of reconstruction on secondary electron emission from the Si(1 0 0) surface

The effect of surface reconstruction on contrast in scanning electron microscopy of the Si(1 0 0)-2 × 1 surface is investigated. A theory of the initial secondary production rate is developed and an upper bound on the rate is shown to depend on the product of the integrated intensities of the initial and final RHEED states. These states are calculated with a reflection matrix method and their depth dependence is investigated. The results are used to analyse scanning electron microscopy contrast in images of 1 × 2- and 2 × 1-regions of the Si(1 0 0)-2 × 1 surface reported by Watanabe et al. The calculated integrated intensities are consistent with the experimental images and with the experimentally observed dependence of the contrast on the azimuth of the incident electron beam. This supports the idea that the observed contrast is caused by the effect of surface reconstruction on the RHEED states.

A robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies.

This paper presents a robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies. The formulation is an alternative to that based on the transfer matrix method, which suffers from numerical instabilities when the frequency and/or thickness parameters become large. This numerical difficulty can be attributed to the mixture of exponentially growing and decaying terms during the transfer matrix calculations. To be more instructive, the numerical instability is delineated in terms of upward-bounded and downward-bounded waves within each layer. In accordance with such boundedness association, a recursive scheme not involving any growing terms is developed based on the scattering matrices to eliminate the instability. The resulting reflection matrix method is extremely concise and preserves the simplicity and convenience of the transfer matrix method. Using the reflection matrices, the generalized Green's functions that relate the particle velocity and the rate of electric potential change to the surface stress and charge are formulated succinctly. These Green's functions are useful for having incorporated the electrical properties of the vacuum above the surface. Numerical computations are exemplified to demonstrate the instabilities of the transfer matrix method and to justify the robustness of the reflection matrix formula.

Recurrence relations for computing complete P and SV seismograms

Summary. A set of recurrence relations which are computationally more efficient than those of the reflection matrix method of Kennett & Kerry is presented for P- and SV-wave generation in a (n+ 1) layered medium. The recurrence relations contain no growing terms and thus provide a stable algorithm for computing complete P and SV synthetic seismograms. Our algorithm requires a fewer algebraic operations for computing the reflectivity and transmissivity coefficients, ranging from 15 per cent less for a source in the half-space to 30 per cent less for a source in the top layer, than the reflection matrix method.