An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems

In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.     

An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems

In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. And the number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has a higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.     

Photon-Measurement Density Function of Fluorescence Molecular Tomography Based on Direct Method

Photon-measurement density function （PMDF）, which is the kernel of fluorescence molecular tomography （FMT）, largely determines the accuracy of reconstruction result of FMT. Based on the direct method, we propose an expression of PMDF in FMT, which is derived from the finite element method （FEM） solution of the diffusion equation. Compared with the traditional expression based on the perturbation method, the accuracy of expression based on the direct method is shown in theory. Lastly the reconstruction results of phantoms prove this accuracy in experiment.     

Voxel classification methodology for rapid Monte Carlo simulation of light propagation in complex media

Monte Carlo (MC) method is a statistical method for simulating photon propagation in media in the optical molecular imaging field.However,obtaining an accurate result using the method is quite time-consuming,especially because the boundary of the media is complex.A voxel classification method is proposed to reduce the computation cost.All the voxels generated by dividing the media are classified into three types (outside,boundary,and inside) according to the position of the voxel.The classified information is used to determine the relative position of the photon and the intersection between photon path and media boundary in the MC method.The influencing factors and effectiveness of the proposed method are analyzed and validated by simulation experiments.     

A sapphire fibre thermal probe based on fast Fourier transform and phase-lock loop

A sapphire fibre thermal probe with Cr³⁺ ion-doped end is developed by using the laser heated pedestal growth method. The fluorescence thermal probe offers advantages of compact structure, high performance and ability to withstand high temperature in a detection range from room temperature to 450℃. Based on the fast Fourier transform (FFT), the fluorescence lifetime is obtained from the tangent function of phase angle of the non-zeroth terms in the FFT result. This method has advantages such as quick calculation, high accuracy and immunity to the background noise. This FFT method is compared with other traditional fitting methods, indicating that the standard deviation of the FFT method is about half of that of the Prony method and about 1/6 of that of the log-fit method. And the FFT method is immune to the background noise involved in a signal. So, the FFT method is an excellent way of processing signals. In addition, a phase-lock amplifier can effectively suppress the noise.     

Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation

The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank–Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stable. It is shown that the method is convergent with an order of O(k2+ h2).Our scheme leads to a tri-diagonal nonlinear system. This new method has lower computational cost in comparison to the Sinc-collocation method. Finally, numerical examples demonstrate the stability and accuracy of this method.     

Sound field of thermoacoustic tomography based on a modified finite-difference time-domain method

A modified finite-difference time-domain （FDTD） method is proposed for the sound field simulation of the thermoacoustic tomography （TAT） in the acoustic speed inhomogeneous medium. First, the basic equations of the TAT are discretized to difference ones by the FDTD. Then the electromagnetic pulse, the excitation source of the TAT, is modified twice to eliminate the error introduced by high frequency electromagnetic waves. Computer simulations are carried out to validate this method. It is shown that the FDTD method has a better accuracy than the commonly used time-of-flight （TOF） method in the TAT with the inhomogeneous acoustic speed. The error of the FDTD is ten times smaller than that of the TOF in the simulation for the acoustic speed difference larger than 50%. So this FDTD method is an efficient one for the sound field simulation of the TAT and can provide the theoretical basis for the study of reconstruction algorithms of the TAT in the acoustic heterogeneous medium.     

Statistical Entropy of Horowitz—Strominger Black Hole

The partition functions of bosonic and fermionic fields in Horowitz-Strominger black hole are derived directly by quantum statistical method.Then via the improved brick-wall method (membrane model),the statistical entropy of black hole is obtained.If a proper parameter is chosen in our result,it is found out that the entropy is proportional to the area of horizon.The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist.The difficulty in solving the wave equations of scalar and Dirac fields is avoided.A new neat way of calculating the entropy of various complicated black holes is offered.     

An improved boundary element-free method （IBEFM） for two-dimensional potential problems

The interpolating moving least-squares (IMLS) method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method (BEFM), combining the boundary integral equation (BIE) method with the IMLS method, the improved boundary element-free method (IBEFM) for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker δ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker δ function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.     

Low group velocity in a photonic crystal coupled-cavity waveguide

A two-dimensional photonic crystal coupled-cavity waveguide is designed and optimized, the transmission spectrum is calculated by using the finite-difference time-domain method, and the group velocity of c/1856 is obtained. To our knowledge, this value of group velocity is the lowest group velocity in a photonic crystal waveguide calculated from its transmission spectrum so far. The result is confirmed by the photonic band structure calculated by using the plane wave expansion method, and it is found that the photonic crystal waveguide modes in a photonic band structure are in accordance with those in the transmission spectrum by using the finite-difference time-domain method. The mechanism of slow light in the coupled-cavity waveguide of photonic crystal is analysed.     

Exact Calculation of Local Density of States in Two-Dimensional Photonic Crystals

An exact calculation method of local density of states （LDOS） in two-dimensional （2D） photonic crystals （PCs） is presented. In order to calculate the LDOS, the eigen-equation of magnetic field is first solved by the plane-wave expansion method, then the eigen-modes of electric-field are obtained. There are two different ways to solve the eigen-equantion of magnetic field and three different ways to obtain the eigen-modes of the electric-field. In comparison of the numerical results from these different ways, an exact and fast method for calculating the LDOS in PCs is found. With use of this method, we investigate the LDOS of the 2D PCs consisting of a triangular lattice of cylinders. The results show the large LDOS is favorable to reside in higher dielectric-constant medium in high frequency region, rather than in lower dielectric-constant medium.     

Design of a very high frame rate camera based on an asynchronous CCD driving method

A very high frame rate camera is designed based on an innovative CCD driving method. The CCD driving method is mainly implemented on frame transfer CCDs. Asynchronous drive timing sequences are applied in the image and storage section of the CCDs. Several rows of the charge in the image section are binned onto the same row in the storage section, and there are the same number of images to be stored in the storage section before they are read out. Based on the new driving method, the frame transfer CCDs can work at a very high frame rate in acquiring burst images though the reading speed remains at a lower level. A very high frame rate camera is designed in this paper. The innovative CCD driving method is mainly of concern. An e2v's CCD60 is adopted in the camera system, whose full size resolution is 128 × 128, and the up most frame rate is 1000 Hz in the conventional CCD driving method. By using the presented method, the CCD60 based imager is capable of operating at up to 40000 frames per second (fps) at a recognizable resolution of 128 × 32. Comparing cameras using traditional binning and region of interest technologies, the frame rate is normally less than 5000 fps while the resolution is only 32 × 32 left.     

Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

The spin-weighted spheroidal equation in the case of s=1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics.The first-five terms of the superpotential in the series of parameter β are given.The general form for the n-th term of the superpotential is also obtained,which could also be derived from the previous terms W k,k < n.From these results,it is easy to obtain the ground eigenfunction of the equation.Furthermore,the shape-invariance property in the series of parameter β is investigated and is proven to be kept.This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics.We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.     

Self-Assembling of Colloidal Particles Dispersed in Mixture of Ethanol and Water at the Air-Liquid Interface of Colloidal Suspension at Room Temperature

Self-assembling of colloidal particles dispersed in a mixture of ethanol and water at the air-liquid interface of the colloidal suspension at room temperature is investigated, and a method of rapidly assembling colloidal particles is proposed. By this method, a uniform colloidal crystal thin film over ten square centimeters in area can be fabricated in lOmin without special facilities and heating the suspension. SEM images and a normal incidence transmission spectrum of the sample show that the colloidal crystal film fabricated by this method is of high quality. In addition, this method is very suitable for fabricating colloidal crystal heterostructures.     

A reliable acoustic path： Physical properties and a source localization method

<正>The physical properties of a reliable acoustic path(RAP) are analysed and subsequently a weighted-subspacefitting matched field(WSF-MF) method for passive localization is presented by exploiting the properties of the RAP environment.The RAP is an important acoustic duct in the deep ocean,which occurs when the receiver is placed near the bottom where the sound velocity exceeds the maximum sound velocity in the vicinity of the surface.It is found that in the RAP environment the transmission loss is rather low and no blind zone of surveillance exists in a medium range. The ray theory is used to explain these phenomena.Furthermore,the analysis of the arrival structures shows that the source localization method based on arrival angle is feasible in this environment.However,the conventional methods suffer from the complicated and inaccurate estimation of the arrival angle.In this paper,a straightforward WSF-MF method is derived to exploit the information about the arrival angles indirectly.The method is to minimize the distance between the signal subspace and the spanned space by the array manifold in a finite range-depth space rather than the arrival-angle space.Simulations are performed to demonstrate the features of the method,and the results are explained by the arrival structures in the RAP environment.     

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

On the basis of the reproducing kernel particle method (RKPM), a new meshless method, which is called the complex variable reproducing kernel particle method (CVRKPM), for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.     

A Novel Method for Enhancing Goos-Hänchen Shift in Total Internal Reflection

Due to the tiny shift in order of optical wavelength for Goos-Hǎnchen （GH） shift, it is very difficult to directly measure and apply the GH shift. We develop a new method for enhancing GH shift of both TE and TM polarized waves. The method is based on a total reflection prism made of BK9 glass combined with a precise measurement of the resulting spatial displacement with a one-dimensional charge coupled device （CCD）. Measurements are performed to examine the validity of the method. Experimental and theoretical results indicate the feasibility of the method with an enhancement in optical wavelenghth shift at millimetre scale. The method is advantageous to application the GH shift in the optical domain, and is also meaningful for measuring even smaller changes in the refractive index of a liquid.     

In-situ measurement of magnetic field gradient in a magnetic shield by a spin-exchange relaxation-free magnetometer

A method of measuring in-situ magnetic field gradient is proposed in this paper.The magnetic shield is widely used in the atomic magnetometer.However,there is magnetic field gradient in the magnetic shield,which would lead to additional gradient broadening.It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell,whose length of side is several centimeters.The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell,which is significant for the spin relaxation study.The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free(SERF) magnetometer by adding a magnetic field modulation in the probe beam's direction.The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction,and the method proposed in this paper is independent of the intensity of the probe beam,which means that the method is independent of the cell's transmissivity.This feature makes the method more practical experimentally.Moreover,the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement.The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium's D1 line.Furthermore,the residual magnetic fields are measured with +-σ-and σ-polarized pump beams,which can further suppress the effect of the AC-Stark shift.The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 p T/mm.     

THE COMPUTATION OF PARTIAL COHERENCE FUNCTION APPLIED FOR SOUND SOURCE IDENTIFICATION

In this paper,a new method is applied to get the computation formula of partial coherence function.The main attention is paid to the computation formula of the partial coherence function with three andfour signals.The advantages of the method discussed in the paper are clear in physical meaning and easyto compute at the end of the paper,the application of the method to the identification of an aircompressor noise source is presented and the results are satisfactory.     

An interpolating boundary element-free method (IBEFM) for elasticity problems

The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.