Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.     

A study of type I intermittency of a circular differential equation under a discontinuous right-hand side

In this paper we study a circular differential equation under a discontinuous periodic input, developing a quadratic differential equations system on S¹ and a linear differential equations system in the Minkowski space M³. The symmetry groups of these two systems are, respectively, PSOo(2,1) and SOo(2,1). The Poincaré circle map is constructed exactly, and a critical value αc of the parameter is identified. Depending on α of the input amplitude the equation may exhibit periodic, subharmonic or quasiperiodic motions. When α varies from α>αc to α<αc, there undergoes an inverse tangent bifurcation; consequently, the resultant Poincaré circle map offers one route to the quasiperiodicity via a type I intermittency. In the parameter range of α<αc the orbit generated by the Poincaré circle map is either m-periodic or quasiperiodic when n/m is a rational or an irrational number.     

工件带到达时间的两阶段柔性流水作业的近似算法

研究了工件带到时间的两阶段柔性流水作业的排序问题,基于求解流水作业和平行机问题的算法思想,提出两个相应的近似算法H(R)和H(MR(?)),证明了这两个算法的最坏情况性能比分别为3-1/m和2/5-1/m,讨论了界的紧性,并利用数值模拟以分析算法与最优值的近似性能比.     

钯作基体改进剂FIA－HG－GFAAS法测定锗及其机理研究

采用钯，钯－镁作基体改进剂，ＦＩＡ－ＨＧ－ＧＦＡＡＳ法成功地测定了锗。灵敏度、精密度和分析速度都得到很大的提高。峰值吸收的特征质量８．０ｐｇ，检出限１０．９ｐｇ，相对标准偏差０．３４％，同时探讨了基体改进剂钯的稳定作用机理及锗在石墨管中的原子化机理。     

Vehicle density and velocity estimation on highways for on-ramp metering control

A scheme for vehicle density and velocity estimation in a stretch of highway based on a modified cell transmission model [C. F. Daganzo, Transportation Research, Part B, 28B(4),269–287, 1994. Elsevier is presented. The scheme is intended for use with on-ramp metering control algorithms, providing local knowledge of densities and velocities that is helpful to improve on-ramp metering control performance. Estimation of density is obtained by nonlinear estimators, while velocity estimation is obtained by gradient algorithms. There is one density–velocity estimator for free traffic flow and other for congested traffic flow. Both estimator schemes work in parallel. The final estimation of density and velocity results from a convex combination of the predictions of the two estimators. This combination depends on occupancy or density measurements at the boundaries of the stretch and is produced by a fuzzy inference system. Stability and convergence of the density and velocity estimation scheme is proved by Lyapunov based techniques. Simulation results comparing measured and estimated traffic data are presented. They confirm good performance of the estimators. Research sponsored by grants UNAM PAPIIT IN110403 and CONACYT 47583.     

Design and operation characteristics of a high power transverse flow pulser sustained cw CO2 laser

A transverse flow, transverse discharge cw CO₂ laser in which de discharge is sustained by employing high repetition rate high voltage pulses has been developed. Pulser sustained discharge through electrodes of innovative design provided uniform excitation at electrical input power densities more than 10 W/cc. Laser output power more than 2.5 kW was obtained in a laser gas mixture consisting of 0.5 mbar of CO₂, 16 mbar of N₂ and 38.5 mbar of He. Design details and operational characteristics of this laser are presented.     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

Lower bounds for the blow-up time in a temperature dependent Navier-Stokes flow

In this paper we consider two different initial-boundary value problems in temperature dependent viscous flow when the temperature equation has a nonlinear heat source term. When blow-up occurs we derive lower bounds for the blow-up time in each case.     

Spatial decay in a double diffusive convection problem in Darcy flow

This paper deals with a model of time-dependent double diffusive convection in Darcy flow. In particular it is concerned with the spatial decay of solutions when the flow is confined to a semi-infinite cylinder. Decay bounds for an energy expression are derived.     

小长径比垂直管气液两相流动特性分析

实验观察了小长径比垂直上流管内流型及特点,并对管入口处的压力波动特性和系统的压差波动特性进行了试验研究.结果表明:小长径比(L/D)垂直管内流型表现为泡状流、塞状流、乳沫状流、环状流和液束环状流;分别增加管线中的气量、液量,或者同时增加气液流量,均会造成垂直管入口处压力波动的均值和最大压力的增加;压力信号的概率密度(PDF)大部分呈双峰分布,也存在单峰和多峰分布;差压信号的概率密度符合正态分布,其功率谱密度同压力信号相比具有频率波动范围宽、幅值小的特点.