A detailed study of Mathieu-Gauss beams propagation through an apertured ABCD optical system

Using Collins formula and the expansion of Mathieu beams in terms of Bessel beams we derive the exact propagation equations of Mathieu-Gauss beams through an apertured paraxial ABCD optical system. A comparison between the exact propagation equations and the approximated ones, which are derived by expanding the circ function into a finite sum of Gaussian functions, is presented. The propagation characteristics of zeroth-order Mathieu-Gauss beams in (y-z) and (x-z) planes are analyzed with detailed numerical calculations. It is found that the profile of the propagated Mathieu-Gauss beam is similar to that of Bessel-Gauss beam. Furthermore, the focalization of the Mathieu-Gauss beams through a thin lens is illustrated and analyzed with numerical results.     

Interaction function of coupled bursting neurons

The interaction functions of electrically coupled Hindmarsh–Rose(HR) neurons for different firing patterns are investigated in this paper.By applying the phase reduction technique,the phase response curve(PRC) of the spiking neuron and burst phase response curve(BPRC) of the bursting neuron are derived.Then the interaction function of two coupled neurons can be calculated numerically according to the PRC(or BPRC) and the voltage time course of the neurons.Results show that the BPRC is more and more complicated with the increase of the spike number within a burst,and the curve of the interaction function oscillates more and more frequently with it.However,two certain things are unchanged:Φ = 0,which corresponds to the in-phase synchronization state,is always the stable equilibrium,while the anti-phase synchronization state with Φ = 0.5 is an unstable equilibrium.     

Spatial Chaos of Bose-Einstein Condensates in a Cigar-Shaped Trap

The spatial chaos of Bose-Einstein condensates in a cigar-shaped trap is studied. For a system with a steady current, we construct the general solution of the 1st-order equation. From the boundedness condition of the general solution, we obtain the Melnikov function predicting the onset of chaos. The unpredictability of the system's distribution of atom density is also theoretically analyzed. For a 23Na system meeting the perturbation condition, numerical simulations show the existence of chaos, which is in accordance with our analytical results. Numerical simulations of a 87 Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system. The case without a current is also investigated.     

薄油层SAGD开发蒸汽腔发育和生产指标预测

通过分析现场生产数据和数值模拟结果,将薄层稠油油藏蒸汽辅助重力驱油(SAGD)生产中蒸汽腔发育分为横向扩展和向下运移两个过程,并进行简化处理预测SAGD生产指标.联合质量守恒方程、能量守恒方程和周围地层散热模型得到一个描述蒸汽腔发育的综合表达式,该方程属于典型的第二类Volterra积分函数.通过拉普拉斯变换对Volterra积分函数进行半解析求解,最终得到不同时刻蒸汽腔发育状态.为验证模型的正确性,将模型的计算结果与CMG Stars的计算结果对比,整体误差小于5%.新模型可以方便简单地预测SAGD生产中蒸汽腔发育过程和生产动态指标,从而确定SAGD生产的极限油藏参数和合理的注采参数.     

Study on the imaging characteristics of far-field superlens

The optical transfer function of the far-field superlens imaging system is established in this thesis to make it easy to describe the corresponding relation between the far-field angular spectrum and the near-field object superresolution information. We utilized the established optical transfer function to make detailed research on the imaging characteristics of the far-field superresolution, also reconstruct the near-field nano-information through the far-field angular spectrum, which proves that the resolution of the far-field superlens with structure coupled with metal grating can reach 50 nm, and provides a helpful reference for the study of the new optical microscope imaging of superresolution.     

Contact position and width effect of graphene electrode on the electronic transport properties of dehydrobenzoannulenne molecule under bias

By applying nonequilibrium Green?s function formalism in combination with density functional theory, we have investigated the electronic transport properties of dehydrobenzoannulenne molecule attached to different positions of the zigzag graphene nanoribbons (ZGNRs) electrode. The different contact positions are found to drastically turn the transport properties of these systems. The negative differential resistance (NDR) effect can be found when the ZGNRs electrodes are mirror symmetry under the xz midplane, and the mechanism of NDR has been explained. Moreover, parity limitation tunneling effect can be found in a certain symmetry two-probe system and it can completely destroy electron tunneling process. The present findings might be useful for the application of ZGNRs-based molecular devices.     

Rapidly convergent series for high-accuracy calculation of the Voigt function

A rapidly convergent series, based on Fourier expansion of the exponential multiplier, is presented for highly accurate approximation of the Voigt function (VF). The corresponding algorithm enables the rapid calculation, required for its implementation as a subprogram in an interpolation approach. The numerical analysis of this VF approximation suggests that it may be more accurate than 10⁻⁹ in the Humlí?ek regions 3 and 4.     

红外热不对称分析用于面神经功能损伤的客观评估

健康人体的温度分布存在一种双侧对称性,当面神经功能受损时,将改变这种热分布的对称性。人体热量大多通过红外辐射的形式散发,因此利用红外热成像技术可以有效捕捉这种红外热辐射分布的改变。本文提出一种新的热不对称分析的方法——有效热面积比,即计算面部特定区域与对侧区域的温差乘以温度异常区面积与总面积之比。利用这种方法对面神经功能损伤的患者和健康人群作对照性试验,结果显示:此方法的特异性和敏感性平均为0.90和0.87,比常规方法提高了7%和26%,有效热面积比与面神经功能的损伤程度正相关,平均为0.664。因此,关于诊断和评估面神经功能,红外热成像是一种有力的工具,有效热面积比是一项高效的临床指标。     

基于RBF神经网络的较低浓度下同步荧光光谱的溢油鉴别

针对海面溢油样品的含量难以确定,同时考虑到海水掺杂及风化等问题的影响,提出了在较低非线性浓度范围内采集溢油嫌疑样品的同步荧光光谱,获取其训练样本集,利用主成分分析法(Principal com-ponent analysis,PCA)提取其特征光谱,结合径向基函数(Radial basis function,RBF)神经网络对肇事样本和嫌疑样本进行模式识别的方法。通过对相近油源原油样品分类识别研究表明:该方法仅需单次对肇事样本同步光谱测量,再借助数据分析,就可以很好区分相近油源溢油样品,外扰对识别率影响也不大。RBF神经网络算法识别率在92%左右。该结论对海洋环境中溢油的实时检测及油指纹数据信息库的建立有重要意义。