Analysis of subspace migrations in limited-view inverse scattering problems

An analysis of subspace migration that occurs in the limited-view inverse scattering problem is considered herein. Based on the structure of singular vectors associated with the nonzero singular values of the multi-static response matrix, we establish a relationship between the subspace migration imaging function and Bessel functions of integer order of the first kind. The revealed structure and numerical examples show why subspace migration is applicable for imaging of small scatterers in limited-view inverse scattering problems.     

Electromagnetic MUSIC-type imaging of perfectly conducting, arc-like cracks at single frequency

We propose a non-iterative MUSIC (MUltiple SIgnal Classification)-type algorithm for the time-harmonic electromagnetic imaging of one or more perfectly conducting, arc-like cracks found within a homogeneous space R²${\mathbb{R}}^2$. The algorithm is based on a factorization of the Multi-Static Response (MSR) matrix collected in the far-field at a single, nonzero frequency in either Transverse Magnetic (TM) mode (Dirichlet boundary condition) or Transverse Electric (TE) mode (Neumann boundary condition), followed by the calculation of a MUSIC cost functional expected to exhibit peaks along the crack curves each half a wavelength. Numerical experimentation from exact, noiseless and noisy data shows that this is indeed the case and that the proposed algorithm behaves in robust manner, with better results in the TM mode than in the TE mode for which one would have to estimate the normal to the crack to get the most optimal results.     

Finite Element Error Analysis Approach for Three-Dimensional Incompressible Viscous Fluid Flow Analysis

In our previous research, the modified Galerkin method was proposed as one of the most efficient methods for the analyses of convection-diffusion problems and two-dimensional viscous fluid flow problems. In this modified Galerkin method, the inertia term is considered explicitly, so only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, we proposed a new finite element formulation for three-dimensional incompressible viscous fluid flow analysis. This formulation (‘MS’ algorithm and ‘MSR’ algorithm) is based on the modified Galerkin method coupled with the Semi-Implicit Method for Pressure-Linked Equations. The cubic cavity flow problems were investigated for the Reynolds number of 400, 1,000, 2,000 and 3,200 using non-uniform meshes. Finally, we confirmed the effectiveness of our proposed method through the comparison with other research works.     

MUSIC ALGORITHM FOR LOCATING POINT-LIKE SCATTERERS CONTAINED IN A SAMPLE ON FLAT SUBSTRATE

In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.     

Localization of small perfectly conducting cracks from far-field pattern with unknown frequency

In the inverse scattering problem, it is well-known that subspace migration yields very accurate locations of small perfectly conducting cracks when the applied frequency is known. In contrast, when the applied frequency is unknown, inaccurate locations are identified via subspace migration with wrong frequency data. This phenomenon has been examined experimentally; however, the reason for its occurrence has not been theoretically investigated. In this study, we analyze the mathematical structure of subspace migration with an unknown frequency by establishing a relationship with Bessel functions of order zero of the first kind. The identified structure of subspace migration and the corresponding results of numerical simulations provide reasons for why subspace migration with an unknown frequency yields an inaccurate crack location and ideas for improvement.     

Experimental investigation of single helium bubbles rising in FLiNaK molten salt

An experimental investigation of single helium bubbles rising in a stagnant molten fluoride salt mixture was conducted in a 25.4 mm quartz tube at 600 °C and atmospheric pressure. The fluoride salt chosen for this research was the eutectic mixture of LiF-NaF-KF (46.5–11.5–42%), also known as FLiNaK. The images obtained using a high-speed camera were processed to estimate the bubble size, rising velocity, trajectory and shape. The shape of the bubble showed typical characteristics of wobbling bubble corresponding to published classifications. The trajectory of the rising bubble showed complex path oscillations and combinations of rectilinear, zig-zag and helical motion. The projected area-equivalent diameter and experimental terminal velocity varied from 5.26 to 6.23 mm and 232.35–259.57 mm/s, respectively. Several important dimensionless numbers were calculated and reported based on the experimental results, which are closely related to the phenomena involving a gas bubble rising in liquid. The measured terminal velocity was compared with the predictions of existing correlations that include the dimensionless numbers and showed reasonable agreement. The Particle Image Velocimetry (PIV) technique was applied to complement the experimental data set with high-fidelity measurements of the velocity field of the liquid molten salt surrounding the bubble. The paper presents a unique set of PIV and two-phase experimental data capturing the behavior of rising helium bubbles in molten FLiNaK and its surrounding flow field.     

Steady state investigation on neutronics of a molten salt reactor considering the flow effect of fuel salt

The Molten Salt Reactor (MSR), one of the `Generation IV' concepts, is a liquid-fuel reactor, which is different from the conventional reactors using solid fissile materials due to the flow effect of fuel salt. The study on its neutronics considering the fuel salt flow, which is the base of the thermal-hydraulic calculation and safety analysis, must be done. In this paper, the theoretical model on neutronics under steady condition for a single-liquid-fueled MSR is conducted and calculated by numerical method. The neutronics model consists of two group neutron diffusion equations for fast and thermal neutron fluxes, and balance equations for six-group delayed neutron precursors considering the flow effect of fuel salt. The spatial discretization of the above models is based on the finite volume method, and the discretization equations are computed by the source iteration method. The distributions of neutron fluxes and the distributions of the delayed neutron precursors in the core are obtained. The numerical calculated results show that, the fuel salt flow has little effect on the distribution of fast and thermal neutron fluxes and the effective multiplication factor; however, it affects the distribution of the delayed neutron precursors significantly, especially the long-lived one. In addition, it could be found that the delayed neutron precursors influence the neutronics slightly under the steady condition.     

Analysis of a multi-frequency electromagnetic imaging functional for thin,crack-like electromagnetic inclusions

Recently, a non-iterative multi-frequency subspace migration imaging algorithm was developed based on an asymptotic expansion formula for thin, curve-like electromagnetic inclusions and the structure of singular vectors in the Multi-Static Response (MSR) matrix. The present study examines the structure of subspace migration imaging functional and proposes an improved imaging functional weighted by the frequency. We identify the relationship between the imaging functional and Bessel functions of integer order of the first kind. Numerical examples for single and multiple inclusions show that the presented algorithm not only retains the advantages of the traditional imaging functional but also improves the imaging performance.     

Music algorithm for locating point-like scatterers contained in a sample on flat substrate

In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.     

HPLC method validation for measurement of sulforaphane level in broccoli by‐products

A simple and specific analytical method was developed and tested for the determination of sulforaphane in broccoli by‐products. The method includes the optimization of the conversion of glucoraphanin to sulforaphane, followed by purification of extracts using solid‐phase extraction and high‐performance liquid chromatography (HPLC) analysis. The response surface methodology was used to find optimum conditions for the preparation and purification procedure. Chromatographic conditions for reversed‐phase HPLC with UV photodiode array detection were as follows: column, Exil ODS C₁₈, 25 × 0.46 cm, 5 μm; column temperature, 36°C; mobile phase, a 30 : 70 (v/v) mixture of acetonitrile:water; flow rate, 0.6 mL/min. The detection wavelength was UV 202 nm. Under these conditions, excellent linearity was obtained (r² = 1), and the overall recovery was 97.5 and 98.1% for fresh florets and lyophilized florets, respectively. The precision results showed that the relative standard deviation of the repeatability for florets fresh and lyophilized was 3.0 and 4.0%, respectively. Sulforaphane contents were determined in the edible portion of fresh broccoli, and broccoli crop remains. Copyright © 2009 John Wiley & Sons, Ltd.