Mean curvature flow with a forcing term in minkowski space

We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending on the boundary conditions at infinity. It is a pleasure to thank my PhD advisors Klaus Ecker and Gerhard Huisken for their assistance and encouragement. I also thank Maria Athanassenas, Oliver Schnürrer and Marty Ross for their interest and useful comments, and the Max Planck Gesellschaft for financial support.     

Homogeneous hypersurfaces in complex hyperbolic spaces

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.      

On the K-stability of complete intersections in polarized manifolds

We consider the problem of existence of constant scalar curvature Kähler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai–Umemura–Tian like example of Fano 5-fold admitting no Kähler–Einstein metric, and a strong evidence of K-stability of complete intersections in Grassmannians.     

The investigation of the (p,ρ,T) and (ps,ρs,Ts) properties of {(1−x)CH3OH + xLiBr} for the application in absorption refrigeration machines and heat pumps

The (p,ρ,T) and (p_s,ρ_s,T_s) properties of {(1−x)CH₃OH + xLiBr} over a wide range of state parameters are reported for the first time. The experiments were carried out in a constant volume piezometer over a temperature range from 298.15 K to 398.15 K, at 0.08421, 0.13617, 0.19692, 0.23133 and 0.26891 mole fractions and from atmospheric pressure up to 60 MPa. The experimental uncertainties are ΔT=±3 mK for temperature, Δp=±5·10⁻² MPa for high pressure and Δp=±5·10⁻⁴ MPa for atmospheric pressure, Δρ=±3·10⁻² kg · m⁻³ for density. An equation of state was derived for correlation of the experimental data of the solutions.     

Accuracy and CPU time of JE-TLM,PLRC-TLM and CRC-TLM methods for plasma medium

The current density (JE), the piecewise linear recursive convolution (PLRC) and the constant convolution recursive (CRC) techniques are developed and integrated into the transmission line matrix (TLM) algorithm. A comparison of these three schemes according to the criteria of accuracy and CPU time is presented. Numerical experiments show that JE provides the most accurate solution and requires the least CPU time; PLRC is nearly as accurate but consumes more CPU time than CRC.     

非线性电路振荡周期分岔及费根鲍姆常数的测量

设计一种实验装置 ,能显示非线性电路中振荡周期分岔与混沌现象 ;同时 ,测出了该实验装置非线性电阻的伏安特性 ;利用该装置介绍一种测量费根鲍姆常数 (Feigen baumConstant)的方法     

Snap-through under unilateral displacement control with constant velocity

When the side of a beverage can or the domed lid of a jar is pushed inward, all or part of the structure may suddenly snap into an inverted configuration. The velocity of the pushing motion affects this instability. Most previous analyses of snap-through have considered force control (increasing the pushing force, e.g., a weight). Snap-through under dynamic, unilateral displacement control is investigated here, with the indentor moving at constant velocity (as in a universal testing machine) until snap-through occurs. Shallow elastic arches with immovable pinned ends are analyzed. Attention is focused on the critical height of the indentor at which snap-through is initiated. The effects of the indentor velocity, indentor location along the span, initial arch height, and damping magnitude are investigated. In addition, experiments are conducted on shallow buckled beams, which behave similarly to arches. Usually, the higher the indentor velocity, the further the indentor must move before snap-through occurs.     

修正D形线圈轮廓线的解析解

聚变堆的纵场线圈通常采用无弯矩的恒张力线圈,即D形线圈,这是种尺寸巨大且场强高的纵场线圈,其受电磁力的作用机械支撑问題甚突出。 恒张力线圈的概念最初由File等人提出。最初的D形轮廓线(通常称为PrincetonD)是根据纵场场强与半径成反比(即B_θ∝1/R)的简化条件求解的,也就是假定整个环形纵场线圈沿环向连续均匀地分布。但实际上,纵场线圈总是做成分立的。因为诸如各种注入、加热和抽真空等通道需在线圈之间插入,目前的趋势是在满足等离子体外缘磁场纹波要