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.     

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.     

生物膜泡形状问题的理论研究

生命活动中的物质代谢、能量转化、信息传递等过程都与生物膜的形态及功能密切相关.本文综述了基于Helfrich自发曲率模型的闭合膜泡、开口膜泡的控制方程及其解析解,并提出了经由开口膜泡边界条件证明分裂膜泡颈端条件的可能方案.     

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.     

条形耦合波导对光子晶体耦合缺陷模的影响

光子晶体的耦合缺陷模可以通过透射谱形状来表征,而透射谱形状则与连接缺陷的条形耦合波导相关.不同于直接耦合时信号相移只依赖于缺陷模的共振频率,当存在耦合波导时信号相移也决定于波导的长度和色散关系.随着波导长度的增加,透射谱形状发生从三峰到两峰,再到平项,最后又回到三峰的周期性变化.时间耦合模的分析表明,在缺陷模频率附近理论结果与时域有限差分法的计算结果完全一致,表明在此复杂情况下理论模型依然有效.     

多结超导环在外磁场中的行为

分析和计算了双结超导环在无偏置电流时的磁通、环流、自由能与外磁场的关系.发现双结环与单结环在磁场中的行为有所不同.当两个结的Ic相等时，双结环在1＜β=2πLIcΦ0＜2时，若无偏置电流，总磁通Φ、环流I与外磁通Φe的关系仍然是非回滞的曲线.仅当β≥2时，曲线才出现回滞.另外双结环有两支解，并且每支解的周期为2Φ0. 关键词： 双结环 双支解 2Φ0周期 回滞     

垂直电偶极子在球外侧电磁场的闭合解及验证

给出了理想导体球外侧垂直电偶极子激励电场的闭合解，解决了直接场的级数表达式的不连续性问题.同球外电磁场直接级数求和表达式的计算结果进行了比较.在相同的电磁模型下，利用闭合解对一种近似方法进行了验证：当垂直电偶极子以及场点在球体表面附近并且频率较低时，这两种方法的计算结果非常一致；当垂直电偶极子以及场点不在球体表面附近并且频率较高时，闭合解的计算结果逐渐出现了近似方法未出现的干涉现象.     

电制备巨囊泡的方法和机理探索

利用倒置显微镜研究电制备巨囊泡, 并分析其形成和成长的动力学机理. 由于磷脂头部的电特性, 电场对水化的磷脂双层的静电力促使磷脂膜内双层之间分离. 在动力学的作用下, 双层两叶的不对称受力引发其弯曲、出芽、膨胀、封闭以及相互融合. 结果表明, 电场参数、干磷脂膜的均匀性、缓冲液以及温度等因素影响巨囊泡的粒径、形状和稳定性.     

电制备巨囊泡的方法和机理探索

利用倒置显微镜研究电制备巨囊泡,并分析其形成和成长的动力学机理.由于磷脂头部的电特性,电场对水化的磷脂双层的静电力促使磷脂膜内双层之间分离.在动力学的作用下,双层两叶的不对称受力引发其弯曲、出芽、膨胀、封闭以及相互融合.结果表明,电场参数、干磷脂膜的均匀性、缓冲液以及温度等因素影响巨囊泡的粒径、形状和稳定性.     

模拟囊泡形变动力学的新方法离散空间变分法

提出了全新的离散空间变分法研究二维囊泡形变动力学过程，克服了原先解析或数值解囊泡形状方程遇到的困难，结果表明动力学终态与已有理论方法的计算结果完全一致；说明这一方法正确而且解法稳定有效，这一方法可进一步推广至研究三维无对称性的囊泡形状以及膜与膜之间有长程相互作用的情形，这为囊泡形状的研究提供了新的理论手段. 关键词： 离散空间变分法 囊泡 动力学 Helfrich方程     

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.     

Critical dynamics of vesicle stretching transition in elongational flow

We present results on the stretching of single tubular vesicles in an elongation flow toward dumbbell shapes, and on their relaxation. A critical strain rate epsilonc exists; for strain rates epsilon相似文献   

A COMPLETE CLASSIFICATION OF CLOSED SHAPES FOR CYLINDRICAL VESICLES

We study the one-dimensional solution of the shape equation of bilayer membranes within the Helfrich spontaneous curvature model.The general integral of the cylindrical shape equation is obtained which gives a complete classification of the cylindrical surfaces corresponding to the shape equation.For closed vesicles,they are inward noduloids,outward noduloids,alternatively inward and outward noduloids and polygonal shapes.The curvature of the contours of the cross sections of these surfaces can be expressed in terms of elliptic functions of their arc lengths.     

Influence of polarization on the hole formation with picosecond laser

Linear polarization effects on laser drilling were investigated by the use of a picosecond laser system. It was observed that the exit shapes of stainless steel were placed perpendicular to the direction of polarization. According to theoretical analysis, the main factor that determines the exit hole shape is the difference between R _s and R _p. When this gap is large enough, the bulges on the exit hole will be easily observed. Inversely, when the gap is small, bulges can be barely spotted on the exit hole. This is further confirmed by comparative experiment and calculation conducted on a copper sheet.     

Formation of three kinds of hard domains by low-bias-field method

The formation of three kinds of hard domains (HDs) at low bias field was studied experimentally. Low-bias-field method provides a simple way to produce the three kinds of HDs in different proportions. Also, the relationship between the shape of the multi-branched domains (MBDs) and the different kinds of domains was studied. Most branches of the MBDs correspond to the first kind of dumbbell domains or the second kind of dumbbell domains; in contrast, few branches of the MBDs correspond to the hard bubbles or soft bubbles.     

Quadrupolar ordering of phospholipid molecules in narrow necks of phospholipid vesicles

Shapes of phospholipid vesicles that involve narrow neck(s) were studied theoretically. It is taken into account that phospholipid molecules are intrinsically anisotropic with respect to the membrane normal and that they exhibit quadrupolar orientational ordering according to the difference between the local principal membrane curvatures. Direct interactions between oriented molecules were considered within a linear approximation of the energy coupling with the deviatoric field. The equilibrium shapes of axisymmetric closed vesicles were studied by minimization of the free energy of the phospholipid bilayer membrane under relevant geometrical constraints. The variational problem was stated by a system of Euler-Lagrange differential equations that revealed a singularity in the derivative of the meridian curvature at points where the effect of the orientational ordering exactly counterbalances the effect of the isotropic bending. The system of Euler-Lagrange differential equations was solved numerically to yield consistently related equilibrium orientational distribution of the phospholipid molecules and vesicle shape. According to our estimation of the model constants the formation of the neck is promoted if direct interactions between the oriented molecules are taken into account. It was shown that the energy of the equilibrium shapes is considerably affected by the quadrupolar ordering of phospholipid molecules.     

On the surface tension of fluctuating quasi-spherical vesicles

We calculate the stress tensor for a quasi-spherical vesicle and we thermally average it in order to obtain the actual, mechanical, surface tension t \tau of the vesicle. Both closed and poked vesicles are considered. We recover our results for t \tau by differentiating the free energy with respect to the proper projected area. We show that t \tau may become negative well before the transition to oblate shapes and that it may reach quite large negative values in the case of small vesicles. This implies that spherical vesicles may have an inner pressure lower than the outer one.     

Fermi hole near a metal surface

The canonical density matrix for a non-interacting electron gas bounded by a planar infinite barrier is calculated exactly by solving the Bloch equation for free particles. A closed expression describing the shape and size of the Fermi hole is thereby obtained.