Holographic lateral shearing interferometry with the displacement of an object under study

A new method of the holographic lateral shearing interferometry is considered. In the method, the recording of the reference holographic lateral shear interferogram is followed by the displacement of an object under study by a distance equal to the lateral shear. The method provides the simultaneous recording of several aberration-free interference patterns representing with the different sensitivity the changes in the phase of the light wave, introduced by the object under study. The method has been tested experimentally to detect optical inhomogeneities in a cylindrical crystal of the active medium of a solid-state laser.     

Nonlinear traveling wave vibration of a circular cylindrical shell subjected to a moving concentrated harmonic force

This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.     

Temperature and density extrapolations in canonical ensemble monte carlo simulations

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction potential and to compute the thermodynamic properties over a range of temperatures and densities. The calculation of the Helmholtz free energy relative to some thermodynamic reference state enables us to study phase coexistence properties. We test the method on the Lennard-Jones fluids for which many results are available.     

New developments in frequency domain optical tomography. Part I: Forward model and gradient computation

This two part study introduces new developments in frequency domain optical tomography to take into account the collimated source direction in the computation of both the forward and the adjoint models. The solution method is based on the least square finite element method associated to the discrete ordinates method where no empirical stabilization is needed. In this first part of the study, the solution method of the forward model is highlighted with an easy handling of complex boundary condition through a penalization method. Gradient computation from an adjoint method is developed rigorously in a continuous manner through a lagrangian formalism for the deduction of the adjoint equation and the gradient of the objective function. The proposed formulation can be easily generalized to stationary and time domain optical tomography by keeping the same expressions.     

Properties of One-Dimensional Highly Polarized Fermi Gases

Using both the exact Bethe ansatz method and the variational method, we study properties of the one-dimensional Fermi polaron. We focus on the binding energy, effective mass, momentum distributions, Tan contact and correlation functions. As the attraction increases, the impurity is more tightly bound and correlated with the surrounding particles, and the size of formed polaron decreases. In addition, compared with the Bethe ansatz method, the variational method is totally qualified to study the one-dimensional Fermi polaron. The intrinsic reason is that the number of particle-hole excitations in a Fermi sea, caused by a single impurity, is always rather small. The variational method can be well extended to other impurity systems.     

拉曼光谱在多组分定量分析中方法学验证的探讨

拉曼光谱在中国药典2010版第一次被收录于“附录XIX L拉曼光谱法指导原则”中,但该原则对拉曼多组分定量分析的方法学验证未作论述,对多组分复杂体系中采用拉曼数学模型定量分析时的方法学验证进行独创性的探索和研究,分别从仪器性能测试、线性、定量限、准确度等方面进行方法学验证研究;另外由于拉曼光谱定量数学模型样品为复杂成分样品,无须像传统方法提供空白样品和进行破坏实验等专属性实验验证。通过研究探讨,提出了拉曼多组分定量分析的方法学验证内容,为方法学验证的完善和标准的制定提供了基础和依据。     

Electron states at steps in semiconductor surfaces

Based on the Bethe-Peierls approximation we have developed a method to study surfaces where local deviations from periodicity are present. Since the method leaves out everything but short-range order, the effect of particular local configurations are easily studied. In particular, we apply the method to study the electronic structure of steps in Si surfaces. The results are in fair agreement with photoemission experimental data.     

Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method

In this paper, we develop an immersed boundary (IB) method to simulate the dynamics of inextensible vesicles interacting with an incompressible fluid. In order to take into account the inextensibility constraint of the vesicle, the penalty immersed boundary (pIB) method is used to virtually decouple the fluid and vesicle dynamics. As numerical tests of our current pIB method, the dynamics of single and multiple inextensible vesicles under shear flows have been extensively explored, and compared with the previous literature. The method is also validated by a series of convergence study, which confirms its consistent first-order accuracy on the velocity field, the vesicle configuration, the vesicle area and the perimeter errors. In addition, the method is also applied to study a binary-component vesicle problem.     

Poincaré recurrences and Ulam method for the Chirikov standard map

We study numerically the statistics of Poincaré recurrences for the Chirikov standard map and the separatrix map at parameters with a critical golden invariant curve. The properties of recurrences are analyzed with the help of a generalized Ulam method. This method allows us to construct the corresponding Ulam matrix whose spectrum and eigenstates are analyzed by the powerful Arnoldi method. We also develop a new survival Monte Carlo method which allows us to study recurrences on times changing by ten orders of magnitude. We show that the recurrences at long times are determined by trajectory sticking in a vicinity of the critical golden curve and secondary resonance structures. The values of Poincaré exponents of recurrences are determined for the two maps studied. We also discuss the localization properties of eigenstates of the Ulam matrix and their relation with the Poincaré recurrences.     

Comparison of the solutions from a novel variational method with numerical results for the study of beam propagation in a Kerr medium with nonlinear absorption

We present results from a novel variational method for the study of beam propagation in a Kerr medium with nonlinear absorption. This new method combines the variational method and a nonlinear absorption equation and gives a concise expression for the combination. The results obtained with this method show good quantitative agreement with numerical solutions obtained with the finite-difference method. It is shown that the variational method takes much less time than a numerical simulation with the finite-difference method for analysis of beam propagation in a thick medium with nonlinear absorption and nonlinear refraction. The new method makes detailed analysis of beam propagation in a Kerr medium with nonlinear absorption very simple and fast.     

近红外光谱技术鉴别海面溢油

为快速了解和掌握海面溢油的种类,以便采取应急措施,提出了近红外光谱技术结合模式识别鉴别海面溢油的方法。自行配制了56个汽油、柴油、润滑油的模拟海水样品,用有机溶剂萃取出海水中的溢油后记录其近红外光谱,将原始光谱进行多元散射校正(MSC)和Norris一阶导数平滑预处理后,在主成分分析(PCA)提取不同种类溢油样品特征的基础上引入马氏距离建立溢油样品的识别模型。研究了光谱预处理对溢油鉴别的影响;探讨了马氏距离阈值的确定。结果表明,主成分分析可将原始数据压缩而马氏距离判别可给出离群点的阈值,本文建立的校正模型能正确判别浓度在0.4 μL·mL-1以上的溢油类别,为近红外光谱结合化学计量学方法建立校正模型进行海面实际溢油样品的分类提供了思路。     

一类各项异性半线性椭圆方程自然边界元与有限元耦合法

将冯康和余德浩提出的自然边界归化方法用于研究一类半线性椭圆方程外区域问题，提出一种自然边界元与有限元的耦合算法、针对某一类半线性椭圆方程，应用变分原理，研究其弱解性及Galerkin逼近，得到有限元解的误差估计及收敛阶O(h^n)，最后给出相应数值例子。     

Ray tracing method with Fresnel’s transmission to calculate polarized radiation power distribution focused by a terahertz Silicon lens antenna

We study a method for simulating a power-flow density distribution of terahertz-wave focused by a hemispherical Silicon lens antenna. A regular ray-tracing method is not enough to evaluate a correct radiation power-flow because it does not take into account transmittances dependent on angles of incidence at different positions on the spherical boundary of the Si-lens. In this study, we propose a ray-tracing method including Fresnel’s transmission coefficients on the surface of a Si-lens for incoming polarized rays. The power-flow-density distribution calculated by the proposed method has a good agreement except for interference and diffraction with the result obtained by an electromagnetic wave simulator. Our method is so simple and reliable that it is useful for designing and evaluating THz optical systems using dielectric lens antennas.     

A finite element scheme to study the nonlinear optical response of a finite grating without and with defect

We present a simple numerical scheme based on the finite element method (FEM) using transparent-influx boundary conditions to study the nonlinear optical response of a finite one-dimensional grating with Kerr medium. Restricting first to the linear case, we improve the standard FEM to get a fourth order accurate scheme maintaining a symmetric-tridiagonal structure of the finite element matrix. For the full nonlinear equation, we implement the improved FEM for the linear part and a standard FEM for the nonlinear part. The resulting nonlinear system of equations is solved using a weighted-averaged fixed-point iterative method combined with a continuation method. To illustrate the method, we study a periodic structure without and with defect and show that the method has no problem with large nonlinear effect. The method is also found to be able to show the optical bistability behavior of the ideal and the defect structure as a function of either the frequency or the intensity of the input light. The bistability of the ideal periodic structure can be obtained by tuning the frequency to a value close to the bottom or top linear band-edge while that of the defect structure can be produced using a frequency near the defect mode or near the bottom of the linear band-edge. The threshold value can be reduced by increasing the number of layer periods. We found that the threshold needed for the defect structure is much lower then that for a strictly periodic structure of the same length.     

用Recursion方法计算晶格声子谱

用Recursion方法计算了体心、面心、金刚石结构晶体的声子谱。计算结果表明了这种方法计算复杂晶格结构谱密度的有效性。这一工作也为用Recursion方法处理复杂结构无序体系问题提供了准备。 关键词：     

KBM method based on the homotopy analysis

The KBM method is effective in solving nonlinear problems.Unfortunately,the traditional KBM method strongly depends on a small parameter,which does not exist in most of the practice physical systems.Therefore this method is limited to dealing with the system with strong nonlinearity.In this paper we present a procedure to study the resonance solutions of the system with strong nonlinearities by employing the homotopy analysis technique to extend the KBM method to the strong nonlinear systems,and we also ana...     

Multiquadric Finite Difference (MQ-FD) Method and Its Application

The conventional finite difference (FD) schemes are based on the low order polynomial approximation in a local region. This paper shows that when the polynomial approximation is replaced by the multiquadric (MQ) function approximation in the same region, a new FD method, which is termed as MQ-FD method in this work, can be developed. The paper gives analytical formulas of the MQ-FD method and carries out a performance study for its derivative approximation and solution of Poisson equation and the incompressible Navier-Stokes equations. In addition, the effect of the shape parameter $c$ in MQ on the formulas of the MQ-FD method is analyzed. Derivative approximation in one-dimensional space and Poisson equation in two-dimensional space are taken as model problems to study the accuracy of the MQ-FD method. Furthermore, a lid-driven flow problem in a square cavity is simulated by the MQ-FD method. The obtained results indicate that this method may solve the engineering problem very accurately with a proper choice of the shape parameter $c$.     

改变溶液折射率方法研究Fermi共振

Fermi共振现象在光谱分析中的谱线认证、归属有重要应用,然而,它蕴含的丰富物理规律、内容及研究方法亟待开发和研究.本文提出了一种改变溶液折射率研究Fermi共振的方法,该方法以Onsager电介质极化理论为依据,利用分子在溶液中的Raman散射强度(散射系数)随溶液折射率的变化来研究Fermi共振规律.该方法不仅能给出Fermi共振各参数间及与溶液折射率之间的关系,而且发现了Fermi共振双峰的非对称移动、倍频的基频也受Fermi共振调谐等现象.为全面认识Fermi共振规律提供了一种研究方法.     

A simple temperature-insensitive fiber Bragg grating displacement sensor

The study on fiber Bragg grating (FBG) displacement sensor based on monitoring the back-reflected power from an array of novelly embedded FBG sensors is presented. The sensor is a uniform FBG with three sections that are embedded in different layer in a composite lamina. Its bandwidth is displacement dependent and hence its reflected power varies almost linearly with displacement and it is insensitive to temperature variation. Thus, only low-cost photodetector (PD) is required to monitor displacement. This study demonstrates a novel fiber sensor, a method of fabricated the same, and a method to achieve simultaneous multi-sensor measurement.     

Prediction method for sound from passing vehicle transmitted through building façade

This study proposes a prediction method for assessing the sound of a passing vehicle that is transmitted through a glass plate, which employs the vibro-acoustic finite-difference time-domain (FDTD) method. The noise that is transmitted through the glass in a building façade, which is affected by the sound-insulation characteristics of its glass plates, can have a psychological influence such as a sleep disorder on the residents. In this study, a prediction method for the spectral characteristics of the transmitting sound through glass plates is proposed. The sound-insulation characteristics of glass plates are obtained using a vibro-acoustic FDTD method, and are then synthesized with the sound of passing vehicles obtained by in situ measurement. Firstly, the sound transmitted through several kinds of glass plates is simulated using the proposed method. Then, in order to confirm the validity of this method, the simulated results are compared to measured sounds transmitted by passing vehicles into a room near the street.