3D-Scalar Fourier Eigenvector Expansion Method (Fourier-EEM) for analyzing optical waveguide discontinuities

In this paper we propose a Fourier Eigenvector Expansion Method (Fourier-EEM) with coordinate-stretching type PML absorbing boundary conditions. This technique has been used to analyze, under the scalar assumption, 3D optical devices with abrupt discontinuities in the longitudinal direction (i.e. Multimode Interference devices (MMI)). The obtained results clearly confirm the accuracy and efficiency of the proposed approach to calculate the transmission and reflection characteristics of photonic devices.     

An Accurate and Fast Simulated Model of CPW Discontinuities

A space-domain integral equation (SDIE) which is solved using the method of moments is used to study the CPW discontinuities. And this paper attempts for the first time to use a fast, efficient computational method and leads to reasonable computation times. Good agreement has been found. The driving closed-form expressions and available models are useful in the design of coplanar circuits such as filters.     

A Unified Approach to the Analysis of a Category of H-Plane Discontinuities

Based on the mode matching method, the generalized scattering parameters including the fundamental and higher order modes (multi-modes) are obtained for the discontinuity interface of a category of waveguide H-plane discontinuities. Then by using a general port-connection order-decrease method raised by the author, the whole discontinuity including the two interfaces and the intermediate part of finite length or zero length (as is the case for very thin inductive windows or irises) can be combined into one network, and the generalized scattering parameters of this network can be obtained from which the scattering parameters of the fundamental mode can be extracted. If needed, the equivalent circuit parameters can be calculated directly from the scattering parameters. Examples are given to show the validity and versatility of this new method for dielectric filled waveguide, inductive iris and/or window, E-plane metal and/or finline insert, and even the offset E-plane finline insert, etc.. Multiple inserts, windows and irises can also be analysed.     

Measurements of sound velocity of laser-irradiated iron foils relevant to Earth core condition

We present a novel scheme to measure sound velocity of shock-compressed iron of geophysical interest. The sound velocity of laser-irradiated iron foils was obtained with side-on X-ray radiograph technique from measured rarefaction wave velocity of shocked iron. Iron foils were irradiated with a two-stepped square laser pulse to reach Earth's core condition by double compression. The experimental parameters of temperature and pressure were very close to the Earth's core condition.     

Detecting derivative discontinuity locations in piecewise continuous functions from Fourier spectral data

We present a method that uses Fourier spectral data to locate jump discontinuities in the first derivatives of functions that are continuous with piecewise smooth derivatives. Since Fourier spectral methods yield strong oscillations near jump discontinuities, it is often difficult to distinguish true discontinuities from artificial oscillations. In this paper we show that by incorporating a local difference method into the global derivative jump function approximation, we can reduce oscillations near the derivative jump discontinuities without losing the ability to locate them. We also present an algorithm that successfully locates both simple and derivative jump discontinuities. This work was partially supported by NSF grants CNS 0324957 and DMS 0510813, and NIH grant EB 02553301 (AG).     

Analysis of periodic 3D viscous flows using a quadratic discrete Galerkin boundary element method

A discrete Galerkin boundary element technique with a quadratic approximatión of the variables was developed to simulate the three-dimensional (3D) viscous flow established in periodic assemblages of particles in suspensions and within a periodic porous medium. The Batchelor's unit-cell approach is used. The Galerkin formulation effectively handles the discontinuity in the traction arising in flow boundaries with edges or corners, such as the unit cell in this case. For an ellipsoidal dilute suspension over the range of aspect ratio studied (1 to 54), the numerical solutions of the rotational velocity of the particles and the viscosity correction were found to agree with the analytic values within 0.2% and 2% respectively, even with coarse meshes. In a suspension of cylindrical particles the calculated period of rotation agreed with the experimental data. However, Burgers' predictions for the correction to the suspension viscosity were found to be 30% too low and therefore the concept of the equivalent ellipsoidal ratio is judged to be inadequate. For pressure-driven flow through a fixed bed of fibres, the prediction on the permeability was shown to deviate by as much as 10% from the value calculated based on approximate permeability additivity rules using the corresponding values for planar flow past a periodic array of parallel cylinders. These applications show the versatility of the technique for studying viscous flows in complicated 3D geometries.     

Inverse problems for Sturm–Liouville operators with interior discontinuities and boundary conditions dependent on the spectral parameter

In this paper, we discuss the inverse problem for Sturm–Liouville operators with arbitrary number of interior discontinuities and boundary conditions having fractional linear function of spectral parameter on the finite interval [0,1]. Using Weyl function techniques, we establish some uniqueness theorems for the Sturm–Liouville operator. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiphase free discontinuity problems: Monotonicity formula and regularity results

The purpose of this paper is to analyze regularity properties of local solutions to free discontinuity problems characterized by the presence of multiple phases. The key feature of the problem is related to the way in which two neighboring phases interact: the contact is penalized at jump points, while no cost is assigned to no-jump interfaces which may occur at the zero level of the corresponding state functions. Our main results state that the phases are open and the jump set (globally considered for all the phases) is essentially closed and Ahlfors regular. The proof relies on a multiphase monotonicity formula and on a sharp collective Sobolev extension result for functions with disjoint supports on a sphere, which may be of independent interest.     

Weighted Compact Scheme for Shock Capturing

In this paper a new class of finite difference schemes - the Weighted Compact Schemes are proposed. According to the idea of the WENO schemes, the Weighted Compact Scheme is constructed by a combination of the approximations of derivatives on candidate stencils with properly assigned weights so that the non-oscillatory property is achieve when discontinuities appear. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the Weighted Compact Scheme. This new scheme not only preserves the characteristic of standard compact schemes and achieves high order accuracy and high resolution using a compact stencil, but also can accurately capture shock waves and discontinuities without oscillation. Numerical examples show the new scheme is very promising and successful.