On the Pesin set of expansive geodesic flows in manifolds with no conjugate points

In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.     

Zero-sum stochastic games with unbounded costs: Discounted and average cost cases

Zero-sum stochastic games with countable state space and with finitely many moves available to each player in a given state are treated. As a function of the current state and the moves chosen, player I incurs a nonnegative cost and player II receives this as a reward. For both the discounted and average cost cases, assumptions are given for the game to have a finite value and for the existence of an optimal randomized stationary strategy pair. In the average cost case, the assumptions generalize those given in Sennott (1993) for the case of a Markov decision chain. Theorems of Hoffman and Karp (1966) and Nowak (1992) are obtained as corollaries. Sufficient conditions are given for the assumptions to hold. A flow control example illustrates the results.     

Brownian motion in a fluid in elongational flow

Brownian motion of a spherical particle in stationary elongational flow is studied. We derive the Langevin equation together with the fluctuation-dissipation theorem for the particle from nonequilibrium fluctuating hydrodynamics to linear order in the elongation-rate-dependent inverse penetration depths. We then analyze how the velocity autocorrelation function as well as the mean square displacement are modified by the elongational flow. We find that for times small compared to the inverse elongation rate the behavior is similar to that found in the absence of the elongational flow. Upon approaching times comparable to the inverse elongation rate the behavior changes and one passes into a time domain where it becomes fundamentally different. In particular, we discuss the modification of thet ^–3/2 long-time tail of the velocity autocorrelation function and comment on the resulting contribution to the mean square displacement. The possibility of defining a diffusion coefficient in both time domains is discussed.     

水翼表面粗糙带对空化抑制效果的数值研究

为研究水翼表面粗糙带对空化的抑制效果,在修改的NACA16翼型吸力面施加一粗糙带,对在不同粗糙带条件下翼型的水动力学特性和周围流场进行了数值模拟研究,得到了升阻力系数、吸力面最小压力系数和近壁面湍动能随粗糙带变化的趋势,探讨了水翼表面粗糙带对抑制表面空化的效果。结果表明,随着粗糙带宽度和高度的增大,翼型周围流场的压强显著升高并使吸力面的最低压力高于饱和蒸汽压,从而延缓了初生空化的发生。该结果为认识粗糙带对水翼抗空蚀性能的影响提供了参考。     

一种局部相含率测量方法

在局部电导探针和单丝电容探针的基础上,提出一种新型局部电容探针,用于测量两相流的局部相含率。静态研究表明,局部电容探针能够测量空气水两相流的局部相含率,测量结果不受导电相电导率变化的影响。从工业蒸馏水变化到饱和食盐水(NaCl的质量分数0～5%),局部电容探针输出结果没有明显变化。电极距离在0～30 mm的范围内变化,测量结果变化小于1%。动态实验表明,局部电容探针测量的两相流的局部相含率,能够很好反映流动过程(以弹状流为例),和实验观察结果完全一致。只需要设置简单的阈值大小,就可以得到相含率的大小。     

Properties of train traffic flow in a moving block system

The development direction of railways is toward the improvement of capacity and service quality, where the service quality includes safety, schedule, high speed, and comfort. In light of the existing cellular automaton models, in this paper, we develop a model to analyze the mixed running processes of trains with maximal speeds of 500 km/h and 350 km/h respectively in the moving block system. In the proposed model, we establish some sound rules to control the running processes of a train, where the rules include the departure rules in the intermediate stations, the overtaking rules, and the conditions of speed limitation for a train stopping at a station or passing through a station. With the consideration of the mixed ratio and the distance between two adjacent stations, the properties of the train traffic flow (including capacity and average speed) are simulated. The numerical results show that the interactions among different trains will affect the capacity, and a proper increase of the spatial distance between two adjacent stations can enhance the capacity and the average speed under the moving block.     

Thermally Radiative Rotating Magneto-Nanofluid Flow over an Exponential Sheet with Heat Generation and Viscous Dissipation:A Comparative Study

This article examines a mathematical model to analyze the rotating flow of three-dimensional water based nanofluid over a convectively heated exponentially stretching sheet in the presence of transverse magnetic field with additional effects of thermal radiation,Joule heating and viscous dissipation.Silver(Ag),copper(Cu),copper oxide(Cu O),aluminum oxide(Al_2O_3)and titanium dioxide(Ti O_2)have been taken under consideration as the nanoparticles and water(H_2O)as the base fluid.Using suitable similarity transformations,the governing partial differential equations(PDEs)of the modeled problem are transformed to the ordinary differential equations(ODEs).These ODEs are then solved numerically by applying the shooting method.For the particular situation,the results are compared with the available literature.The effects of different nanoparticles on the temperature distribution are also discussed graphically and numerically.It is witnessed that the skin friction coefficient is maximum for silver based nanofluid.Also,the velocity profile is found to diminish for the increasing values of the magnetic parameter.     

Ergodic Properties of the Quantum Geodesic Flow on Tori

We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on . We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10.     

半导体激光器的自混合散斑干涉测量流体速度

提出了一种简便的激光自混合散斑干涉测量流体速度的方法。根据散斑和法布里-珀罗腔的理论,提出了半导体激光器的自混合散斑干涉模型。研究了流体运动时在半导体激光器内产生的自混合散斑干涉效应(SMPI),给出了激光器输出增益的变化及其概率密度分布。得到了激光自混合散斑干涉平均频率与流体速度之间的关系。模拟计算和实验结果验证了这个关系。利用散斑干涉的平均频率与流体速度的关系测量了高分子材料溶液的速度,并在溶液浓度和背景光变化时,对流体速度进行了测量、比较和分析。实验表明。在溶液浓度不太低时,测量误差小于8％。