球形拓扑中复杂形状生物膜泡的获得及其稳定性分析

通过在Surface Evolver软件中建立一些与目标形状相似的初始形状，经长时间演化后，得到了实验上已经观察到的具有D_2h和D_3h对称性的海星形生物膜泡.通过跟踪不同形状膜泡的Hessian矩阵的本征值，确定了双凹圆盘与海星形及哑铃形之间的相变是不连续的，其间所经历的三角扁盘及椭圆扁盘形中间相在SC模型中通常是不稳定的. 关键词： SC模型 生物膜泡 Surface Evolver     

高亏格膜泡形状的数值计算

通过对Willmore区域外,特别是中等及较小约化体积下的形状及其演化进行深入细致的研究,发现在这一区域的形状要远比原有的猜测丰富,亏格g=2的膜泡会展现出比已有结果更多迷人的形状并出现新的膜泡相变分支.同时,数值计算的结果更加期待实验验证,从而为曲率模型的正确性提供有力支持.     

单开口膜泡形状转变的研究

基于双层耦合模型,先通过求解无黏附能情况下满足给定边界条件的欧拉-拉格朗日方程组,找到了约化面积差?a稍大于1的内凹开口形状解,并发现以往Umeda和Suezaki(2005 Phys.Rev.E 71 011913)给出的杯形解是对应?a1的另一支解,该支解在?a趋于1时开口是外凸的.进而在无黏附能和有黏附能的情况下对开口膜泡的两支解进行了深入研究,发现在?a=1附近这两支解之间有一个间隙,在该间隙内不存在开口解.随着黏附半径的增大,该间隙的位置较缓慢地向右移动.在?a=1附近,在无黏附能时的闭合形状只有球形一个解,而在有黏附能的情况下,闭合形状在1附近的一个区间内都有解.在无黏附及有黏附情况下的计算结果都表明这两支开口解及闭合形状属于不同的分支,它们之间不能连续演化.在间隙右侧的这一支解随着?a的增大可以通过自交形状连续地演化到开口哑铃形.在有黏附的情况下,在?a参数空间,同一支解会发生折叠,即出现同一?a值对应多个解(形状)的情况,这在以往双层耦合模型的计算中没有出现过.讨论了?a对无黏附和有黏附开口膜泡的形状和能量的影响.     

双凹盘形解开口膜泡形状的解析法研究

随着开口膜泡在实验上的发现,对开口泡形状的数值及解析研究逐渐成为该领域的一个热点.讨论了如何由欧阳双凹盘形闭合解构造开口泡的解析解的问题.首先将开口泡要满足的三个不独立的边界条件简化为两个独立的边界条件,给出高斯测地曲率kg=-2,边界条件2可满足,然后由边界条件1得到确定膜泡边界的几何方程.进而讨论了由欧阳双凹盘解可构造的开口泡的各种可能形状,得到了三类管型拓扑解,它们是外凸管形解、类环管形解、类悬链面管形解.     

基于梯度与曲率相结合的图像平滑模型的研究

在图像处理过程中, 为了在图像去噪时更好地保留图像边缘细节信息, 首先结合扩散系数和曲率的性质建立了一个曲率平滑模型. 考虑到图像受到噪声污染时曲率会发生显著变化, 将图像的水平集曲率作为一个检测因子代入到上述模型中, 提出了一个梯度与曲率相结合的新模型. 分析与仿真结果表明, 该模型与Perona-Malik模型相比较保留了更多的图像信息, 有效地增强了图像尖锐的边缘, 同时很好地保持了图像的直线和曲线边缘、角点、斜坡和小尺度特征, 是一个理想的模型.     

温度及深度对钛中氦泡释放过程影响的分子动力学研究

利用分子动力学模拟方法对温度及He泡深度给金属Ti内He泡的体积、压强和释放过程等带来的影响进行了研究. 首先, 通过研究室温下He泡在金属Ti内不同深度处的状态, 得到He泡的形状、压强、体积等物理量随其深度的变化规律. 发现He泡压强随其深度增加逐渐变大, 体积则逐渐减小, 但当He泡深度增大到2.6 nm时, 二者均维持在某个固定值附近. 然后对包含有He泡的Ti体系在温度作用下的演化过程进行了模拟, 发现不同深度处He泡从金属Ti内释放出来所需要的临界温度有很大差别, 总体来看He泡越深, 释放所需的临界温度越高. 但不同温度下He原子的释放速率没有明显差别, 释放过程几乎均为瞬间完成. 最后通过对He泡内部压强和其上方金属Ti薄层的抗张强度进行统计对比, 阐述了金属Ti 体内He泡的释放机制: 当He泡内部压强大于其上方Ti薄层抗张强度时, He泡就会将Ti 薄层撕裂, 从而使He原子得到释放.     

连续梯度的功能层对燃料电池在初始还原过程中曲率及残余应力的影响

连续梯度的电极由于其相对于多层梯度电极能更加有效地缓解电极和电解质的热失配及改善界面黏接而受到特别的关注. 本文通过建立含连续梯度的阳极功能层的阳极支撑固体氧化物燃料电池的力学模型, 研究了连续梯度的阳极功能层对阳极支撑固体氧化物燃料电池半电池在初始还原过程中曲率及残余应力的影响. 结果表明电池的曲率在初始还原过程中随还原程度的增大而逐渐增大. 连续梯度的阳极功能层的引入不能同时改善电池的曲率和残余应力, 即连续梯度的阳极功能层在缓解应力的同时会导致曲率的增大, 反之亦然. 含有连续梯度的阳极功能层的电池在部分还原状态下, 梯度层/阳极支撑界面处具有最大的拉应力容易导致电池受损, 实际中应保证电池被完全还原.     

曲率变化对激光陀螺损耗及性能的影响研究

为了研究曲率半径变化对激光陀螺性能参数的影响,基于谐振腔理论,建立了衍射损耗理论计算模型,通过仿真计算了曲率变化引起激光陀螺束腰的变化,从而导致衍射损耗的变化。从光阑处衍射损耗对陀螺背向散射的影响出发,分析了束腰对激光陀螺性能的影响。通过分析计算得出:当反射镜曲率变化小于0.3 m时,引起衍射损耗变化3%,导致零偏最大变化约0.013;当反射镜曲率变化0.6 m时,引起衍射损耗变化约15%,导致零偏最大变化约0.021;而曲率半径变化大于1.5 m时,衍射损耗变化达30%以上,这将引起谐振腔失谐即无法产生激光振荡。通过改变不同曲率,测量陀螺腔损耗和性能,所得的试验结果和理论计算一致,曲率半径变化对衍射损耗和陀螺性能影响较为显著。     

几种典型流动条件对平板转捩过程影响的数值模拟

采用作者构造的k方程转捩湍流模型，数值模拟了较大跨度来流湍流度情况、不同来流湍流度时几种不同顺、逆压梯度存在情况、壁面存在不同热交换强度情况下平板的转捩流动过程．与实验结果对比表明，新模型具有较好地模拟转捩流动能力。     

基于电化学-热耦合模型研究隔膜孔隙结构对锂离子电池性能的影响机制

隔膜孔隙结构对锂离子电池性能具有重要的影响,本文提出了可准确描述充放电过程中锂离子电池内部复杂物理化学现象的电化学-热耦合模型,发现该模型较文献中模型的计算结果更接近实验测试数据.利用该模型探讨了隔膜孔隙率与扭曲率分别对锂离子电池性能的影响规律,发现减小孔隙率或增大扭曲率,电池输出电压、最大放电容量和平均输出功率均不断降低,电池表面温度和温升速度均不断升高;当孔隙率减小或扭曲率增大到一定程度时,放电初期电池输出电压均会出现先下降后回升的现象,且孔隙率越小或扭曲率越大,其下降的幅度越大、速度越快,回升所需时间也越长;要确保其不低于截止电压,隔膜扭曲率必须小于临界扭曲率(其下降至最低点刚好等于截止电压时的隔膜扭曲率).综合分析了放电过程中电池内部各电化学参量和产热量的动态分布规律,发现隔膜孔隙率和扭曲率主要影响放电末期电极膜片内部电化学反应以及其他放电时刻电解液中有效Li~+扩散(传导)系数.     

容器内角处流体界面特性与Surface Evolver程序适用性的研究

微重力条件下内角处液体行为的研究对于认识表面张力主导的液体行为, 预测和控制空间微重力条件下的液体位置、瞬时状态, 以及对空间流体进行有效的管理等方面都非常重要. 通过分析接触角与流体界面在容器内角处的接触线方向之间的关系, 并与Concus-Finn理论进行比较, 提出了内角处接触线、接触角和几何形状之间相互关联的机理, 并探讨了Concus和Finn等 的相关理论结果的物理内涵. 在此基础上, 进一步将内角处的相关理论结果与Surface Evolver程序得出的数值结果进行了比较, 指出当容器中的内角小于180°时, Surface Evolver程序通过自动划分网格即可比较准确地预言内角处的接触线和液面行为, 但是当内角大于180°时, 自动划分网格得到的数值结果有较大的误差, 需要通过手动划分网格减少网格奇异才能减小误差. 因此, 对于具有复杂几何形状的容器, 需注意网格的奇异性, 并对内角处的液面进行定量的验证, 才能有效判断Surface Evolver程序结果的正确性. 本工作对于深入认识内角处的液面特性和机理, 理解Surface Evolver程序的适用条件, 以及分析微重力条件下容器内角处的液体行为等方面都具有明显意义.     

Some new results on the two-dimensional kinetic Ising model in the phase coexistence region

We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL with open boundary conditions, in the absence of an external field and at large inverse temperature . We prove that the gap in the spectrum of the generator restricted to the invariant subspace of functions which are even under global spin flip is much larger than the true gap. As a consequence we are able to show that there exists a new time scalet _even, much smaller than the global relaxation timet _rel, such that, with large probability, any initial configuration first relaxes to one of the two phases in a time scale of ordert _even and only after a time scale of the order oft _rel does it reach the final equilibrium by jumping, via a large deviation, to the opposite phase. It also follows that, with large probability, the time spent by the system during the first jump from one phase to the opposite one is much shorter than the relaxation time.     

Spheres and prolate and oblate ellipsoids from an analytical solution of the spontaneous-curvature fluid-membrane model

An analytic solution for the Helfrich spontaneous curvature membrane model [H. Naito, M.Okuda, and Ou-Yang Zhong-Can, Phys. Rev. E 48, 2304 (1993); 54, 2816 (1996)], which has the conspicuous feature of representing a circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as (i) a flat plane (trivial case), (ii) a sphere, (iii) a prolate ellipsoid, (iv) a capped cylinder, (v) an oblate ellipsoid, (vi) a circular biconcave shape, (vii) a self-intersecting inverted circular biconcave shape, and (viii) a self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with a minimum of local curvature energy.     

Double phase-image encryption using gyrator transforms,and structured phase mask in the frequency plane

Fully-phase image encryption is considered more secure as compared to an amplitude image encryption. In the present paper, an encryption scheme is proposed for double phase-images. The phase-images are bonded with random phase masks and then gyrator transformed. The two resulting images are then added and subtracted to give intermediate images which are bonded with a structured phase mask (SPM) based on devil’s vortex Fresnel lens (DVFL) in the frequency plane. Thereafter, the images are once again transformed using a gyrator transform (GT) to give the corresponding encrypted images. The use of a structured phase mask enhances the key space for encryption and also overcomes the problem of axis alignment associated with an optical set-up. The decryption process is the reverse of encryption. The validity of the proposed scheme is established from the computer simulation results using MATLAB 7.1 platform. The performance of the scheme is evaluated in terms of mean-squared-error (MSE) between the input-, and the decrypted images. In addition, the sensitivity to encryption keys such as SPM parameters, and transform angles of GT is investigated. The technique is likely to provide enhanced security in view of the increased number of encryption parameters. Robustness of the system against occlusion and noise attacks has also been investigated.     

Optical security system using jigsaw transforms of the second random phase mask and the encrypted image in a double random phase encoding system

In this paper, we have described a simple and secure double random phase encoding and decoding system to encrypt and decrypt a two-dimensional gray scale image. We have used jigsaw transforms of the second random phase mask and the encrypted image. The random phase mask placed in the Fourier plane is broken into independent non-overlapping segments by applying the jigsaw transform. To make the system more secure, a jigsaw transform on the encrypted image is also carried out. The encrypted image is also broken into independent non-overlapping segments. The jigsaw transform indices of random phase code and the encrypted image form the keys for the successful retrieval of the data. Encrypting with this technique makes it almost impossible to retrieve the image without using both the right keys. Results of computer simulation have been presented in support of the proposed idea. Mean square error (MSE) between the decrypted and the original image has also been calculated in support of the technique.     

Cornu's spiral in the Fresnel regime studied using ultrasound: a phase study

A simple experimental technique for measuring the phase and amplitude of diffracting ultrasound wave [A. Hitachi and M. Takata, Am. J. Phys. 78, 678 (2010)] has been applied to diffracting objects with straight edges as a demonstration of the Cornu spiral. Babinet's principle is studied observing the ultrasound field behind a slit and a complementary strip obstacle and is verified directly by comparing vectors (phasors) in the complex plane. The phase of the diffracted wave observed in the geometrical shadow of the straight screen has the form of a cylindrical wave originating at the edge of the straight screen as the boundary diffraction wave proposed by Young. In addition, the incident wave has a phase delay of π/4 behind the wave passing through on the center line of the slit, the plane of symmetry, has been observed as predicted by Huygens-Fresnel diffraction theory.     

Some rare processes in a model of composite quarks and leptons

The branching ratios of some rare processes, i.e. meson →μe, meson →meson μe, baryon → baryon μe, are calculated in a composite quark and lepton model. Use is made of an effective Hamiltonian which originates from hypercolor singlet 0^? and 1^? bound state exchange mechanism, acting at a mass scaleM _P andM _V respectively. Under the reasonable assumptionM _P =M _V onlyK _L →μe puts a significant limit on the composite scale.     

Some new optical measurement techniques for the study of crystal growth and electrode processes

This paper discusses some new optical measurement techniques for the study of crystal growth and electrode processes, namely, holographic phase-contrast interferometric microphotography (HPCIM), phase conjugation interferometry (PCI) and laser diffractometry. Using these techniques, real-time crystal growth and electrode processes can be observed; solid-liquid interface boundary layers and the crystal surface morphology can be studied quantitatively and solution saturation and crystal growth rates can be measured precisely. These techniques are also compared with other methods.     

用弛豫法探寻新的双开口膜泡

基于面积差弹性模型, 用弛豫法探寻满足开口膜泡边界条件的欧拉-拉格朗日方程组的新解, 得到了双开口的哑铃形分支解, 并结合以前得到的单开口哑铃形及闭合哑铃形, 对它们之间的相变进行了深入的研究. 为了探究实验上是否可能发现这些形状, 与以往实验上观察到的较小约化弛豫面积差的杯形、管形、烟囱形开口形状的能量进行了比较, 发现这些新形状在较大的约化弛豫面积差值时, 在某些线张力区间比以往发现的形状能量更低. 另外为了对比, 本文对于实验上已知的杯形、管形、烟囱形及球形之间的相变行进行了探讨, 并对两者之间的不同特点进行了对比.