Asymptotic energy of lattices

The energy of a simple graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of eigenvalues of G. As the dimer problem and spanning trees problem in statistical physics, in this paper we propose the energy per vertex problem for lattice systems. In general for a type of lattice in statistical physics, to compute the entropy constant with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are different tasks with different hardness and may have different solutions. We show that the energy per vertex of plane lattices is independent of the toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions. In particular, the asymptotic formulae of energies of the triangular, 3³.4², and hexagonal lattices with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are obtained explicitly.     

反馈控制棘轮的定向输运效率研究

研究了反馈耦合布朗棘轮中粒子处于负载力、时变外力及噪声作用下的定向输运问题.详细讨论了外力作用时间的不对称性、外势空间的不对称性及外力周期等对反馈耦合棘轮中粒子输运效率的影响.研究发现,外力的时间不对称度能促进反馈棘轮中粒子的定向输运,随时间不对称度的增大,反馈棘轮中粒子能获得较大的效率.然而,外势空间的不对称度能有效抑制耦合棘轮中粒子的扩散,达到增强耦合粒子定向输运的效果.同时还发现,存在最优的噪声强度能使耦合粒子的输运效率达到最大.     

随机电磁高阶Bessel-Gaussian光束在海洋湍流中的传输特性

利用广义惠更斯-菲涅耳衍射积分公式得到了随机电磁高阶Bessel-Gaussian光束在海洋湍流中传输的交叉谱密度矩阵的一般表达式,通过数值计算主要研究了随机电磁高阶Bessel-Gaussian光束在海洋湍流中传输时其在远场输出面的统计特性的变化,包括归一化光谱强度、光谱偏振度、两点的光谱相干度等.数值模拟结果显示海洋湍流能够对随机电磁高阶Bessel-Gaussian光束的归一化光谱强度分布产生影响,随着传输距离的增加,零阶Bessel-Gaussian光束中心出现凹陷,高阶Bessel-Gaussian光束中心会变平坦继而又凹陷下去,不管零阶还是高阶,当传输距离增加到足够远,光强分布都会演变成最终的类高斯分布.x轴上各点的偏振度改变与相干长度δ_(xx),δ_(yy)以及海洋湍流参数有关.x轴上任意一点和原点这两点的光谱相干度也随x的增加而呈振荡变化,并且海洋的均方温度耗散率χT对光谱相干度有影响.     

Sparse MRI reconstruction using multi-contrast image guided graph representation

Accelerating the imaging speed without sacrificing image structures plays an important role in magnetic resonance imaging. Under-sampling the k-space data and reconstructing the image with sparsity constraint is one efficient way to reduce the data acquisition time. However, achieving high acceleration factor is challenging since image structures may be lost or blurred when the acquired information is not sufficient. Therefore, incorporating extra knowledge to improve image reconstruction is expected for highly accelerated imaging. Fortunately, multi-contrast images in the same region of interest are usually acquired in magnetic resonance imaging protocols. In this work, we propose a new approach to reconstruct magnetic resonance images by learning the prior knowledge from these multi-contrast images with graph-based wavelet representations. We further formulate the reconstruction as a bi-level optimization problem to allow misalignment between these images. Experiments on realistic imaging datasets demonstrate that the proposed approach improves the image reconstruction significantly and is practical for real world application since patients are unnecessarily to stay still during successive reference image scans.     

纳米结构金属表面的近场电势分布

基于均匀外电场中金属纳米半球颗粒按一定对称性从平面衬底生长出的表面结构,建立纳米半球颗粒表面附近近场电势的理论模型.采用数值计算方法得到近场电势的空间分布,并以三维曲面的形式给出.结果表明:电势分布呈现明显的几何对称性.结果为解释与纳米结构薄膜表面有关的各种异常现象提供依据,为纳米结构薄膜材料的应用研究提供参考.     

量子环上粒子体系的计算

对于量子环上带电粒子体系,组成本征函数的基矢数及哈密顿矩阵元素数都极大,数值计算量庞大.本文介绍在处理此问题时按轨道总角动量分类从基矢集中选择子基矢集的方法和技巧.应用计算机进行数值计算时,此方法比以往节省90%以上的时间.     

Parametric resonance,stability and heteroclinic bifurcation in a nonlinear oscillator with time-delay: Application to a quarter-car model

This work examines dynamical behavior of a nonlinear oscillator with symmetric potential that models a quarter-car forced by the road profile under parametric excitation. The parametric resonance of a harmonically excited nonlinear quarter-car model with position and velocity time-delayed active control are investigated. We focus on the influence of delay and parametric excitation in the system. The influence of parametric excitation, time-delay and feedback gain parameters on the stability of the steady state response are investigated. By means of Melnikov's method, conditions for onset of chaos resulting from heteroclinic bifurcation is derived analytically and numerically.     

The Motion Behavior of a Group of Charged Droplets in Liquid-Liquid Electrostatic Spray

The droplet sizes and electrical charges under different applied electrical voltages are experimentally measured for a liquid-liquid electrostatic spray system. Considering droplet size and charge distributions, the two-dimensional motion for a group of charged droplets in a liquid-liquid electrostatic atomization system is simulated. From measured droplet size and charge distributions, the simulation can obtain the velocities and positions in a two-dimensional domain for all simulated droplets at different times. The various forces acting on droplet as well as their effects on droplet velocity and trajectory are analyzed and the liquid-liquid electrostatic atomization characteristics are revealed. In addition, for one-dimensional motion trajectory of larger droplet, the comparison between simulation and experiment is also conducted and a general agreement can be obtained.     

马来酸在多孔铅锌电极上电还原特性

在甲磺酸镀液中电沉积Pb-Zn镀层,然后用体积分数为10%的H2SO4腐蚀镀层,使镀层中的Zn脱溶,成功得到多孔Pb-Zn电极,该镀层由铅(Fm3m)和锌（P63/mmc）的混合物组成。 采用循环伏安、阴极极化、计时电量及电化学阻抗等方法,研究了马来酸在多孔Pb-Zn电极和Pb电极上的电化学还原特性。 结果表明,马来酸在电极上先发生吸附,然后进行不可逆电子传递反应;马来酸在Pb电极和多孔Pb-Zn电极上还原的扩散系数分别为1.2×10-7和1.7×10-7 cm2/s;随着温度升高,马来酸在Pb电极上表观交换电流密度稳定性不如多孔Pb-Zn电极,多孔Pb-Zn电极上马来酸在低温处i0与温度呈线性关系,从50 ℃开始,i0急剧增加,至65 ℃,i0迅速下降,其在多孔Pb-Zn电极上电还原在50～60 ℃最好。 马来酸在多孔Pb-Zn电极比相应的Pb电极上具有更高的电催化活性。     

美人蕉和绿萝在修复富营养化水体过程中对Cr(Ⅵ)胁迫的生理生化响应

研究了陆生植物美人蕉（Canna indica）和绿萝（Scindapsus aureum）在修复富营养化水体过程中对不同质量浓度Cr（Ⅵ）胁迫的生理生化响应.结果表明,Cr（Ⅵ）胁迫影响植物生长,Cr（Ⅵ）质量浓度为10 mg·L-1时两种植物生长明显受到抑制.Cr（Ⅵ）质量浓度为2 mg·L-1时促进美人蕉及绿萝可溶性蛋白质的合成,提高了美人蕉及绿萝SOD、CAT、POD活性,对两种植物MDA积累无明显影响;当Cr（Ⅵ）质量浓度5 mg·L-1时抑制美人蕉和绿萝可溶性蛋白质合成及绿萝CAT活性,提高美人蕉SOD、CAT、POD及绿萝SOD、POD活性,对美人蕉MDA积累影响不大,增加绿萝MDA积累;当Cr（Ⅵ）质量浓度达到10 mg·L-1时,明显抑制两种植物可溶性蛋白质的合成,且抑制美人蕉CAT、POD活性和绿萝CAT活性,提高美人蕉和绿萝SOD活性及绿萝POD活性,显著增加两种植物MDA积累.本试验条件下,美人蕉生长速度大于绿萝,对铬胁迫的耐受能力更强.