First integrals of the axisymmetric shape equation of lipid membranes

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation(ODE) by Zheng and Liu(Phys. Rev.E 48 2856(1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor.     

基于光纤的新型矢量和微波光子移相器

针对相控阵天线中基于光纤的微波光子移相器原理进行研究,并在此基础上设计了新型方案,通过引入可调分光器和保偏光纤来精确控制相移,降低了移相器的复杂性和相干干涉损耗,增强了移相器的可控性。研究了分光系数和频率对信号相位和幅度的影响,实现了超过140的移相,并可通过功率放大器来补偿信号幅度损失