重力输水系统

为学习微积分的读者介绍如何将基本流体力学应用于对发展中国家非常重要的简单重力输水系统的建模。首先推导出Bernoulli方程,从而了解作为沿流线运动的流体质点压力、速度和高度之间的关系。其次,应用Bernoulli方程分析一个简单的输水系统的合力和流速。然后,对层流和湍流分别考虑分压水箱、不同直径的管道及摩擦的影响。最后,讨论在密克罗尼西亚和洪都拉斯重力输水系统的设计和安装。     

应用概率方法计算室内给水管道设计秒流量

本文在深入研究现有室内给水管道设计秒流量计算方法的基础上，应用概率论，以满足使用保证率的室内给水管道设计秒流量为出发点，提出了一种新的计算方法。通过实例计算，分析了使用保证率和卫生器具放水使用概率对设计秒流量的影响，与平方根法和已有概率法作了比较，说明了该方法的合理性和通用性。     

应用全概率公式研究输水管道系统的可靠性

文中采用网络分解法,以全概率公式为依据对设置连通管的输水管道系统的可靠性进行了分析,建立了设置连通管的输水管道系统的可靠性计算模型;计算表明,三通和输水干管的管段的可靠性变化是影响系统可靠性的敏感性因素.研究成果对于输水管道系统组件的选择、施工与维护管理,具有重要的指导意义.     

一类输水线路的最佳布线问题

主要解决了如下问题 :对于从河流 L取水并输送到 L同岸的两个用水点 A,B的输水工程(图 1) ,当修建各段输水管道的耗资系数分别为 k1,k2 ,k3 时 ,如何确定抽水点 P及分水点 O才能使加权和值w =k1OA+ k2 OB+ k3OP为最小 .     

一个模型、三个问题突破第二型曲面积分概念难点

从流量问题入手，利用两种方法给出常量场流量问题模型的求解.重点阐述了三个问题，即为什么要区分有向曲面的侧，什么是有向投影，如何理解两类曲面积分的关系.以这一个模型为基础，三个问题为突破，形象地分析了第二型曲面积分概念中的难点与困惑.     

小波分频在重力异常界面反演计算过程中的应用

重力资料是研究地质结构的重要资料，通常测得的重力异常数据是地下各界面造成的异常的失加，如何把这种叠加效应剥离出来一直是一个难以解决的问题，如果能从综合信息中离出能反映各界面信息的重力异常值，我们就能将问题归结为单界面重力异常的反演问题（关于单界面重力异常的反演可参见文献[1]），小波分析提供了这类问题的新思路。     

Jeffrey流体流过有限长圆柱管时磁流体动力学的蠕动流

研究Jeffrey流体流过有限长管道时的蠕动流.在外加磁场作用时,流体呈导电性.分析是在长波长和低Reynolds数近似假设下完成.得到了压力梯度、体积流量、平均体积流量和局部壁面剪应力的表达式.研究了松弛时间、延迟时间和Hartman数,对压力、局部壁面剪应力以及蠕动泵机械效率的影响.还研究了回流现象,调查了沿管道壁波数非整倍数时的传播情况,研究有限长管道传播的内在特性.     

层流管流入口压力突然升高引起的水力瞬变的理论分析

研究了层流状态下管道入口压力突然升高引起的水力瞬变过程,建立了瞬态压力分布的偏微分方程和初边值条件,用分离变量法求得了压力的理论解．根据压力和流量间的约束关系,得到了关于流量的偏微分方程和初边值条件,用分离变量求得了瞬变过程流量分布理论解．最后,用特征线法(MOC)对该问题进行了数值求解,理论解和数值解吻合很好．     

在重力作用下的上覆无限热弹性流体对广义热弹性固体转动的影响

计及上覆无限热弹性流体的重力作用,沿界面有不同的外力作用时,研究广义热弹性固体的旋转变形问题.在Laplace和Fourier域内,通过积分变换,得到了位移、应力及温度分布的表达式.然后在物理域内,应用数值逆变换方法,得到这些分量的值,并讨论了该问题的一些特例.结果以图形方式给出,显示了介质的旋转以及重力作用的影响.     

渠道水力计算表及其原理

大家知道,各种用途的各类渠道都要进行渠道设计.在渠道的横断面设计中,必须进行渠道的水力计算.渠道水力计算的主要任务是计算渠道的断面尺寸,以保证能通过所要求的流量,或校核已建成的渠道是否具有所要求的输水能力. 梯形渠道水力计算通常采用试算法,由于试算没有定量的规律可循,所以计算往往较繁.特别是在缺乏实践经验的情况下可能会作一些不必要的试算.     

Mixed-integer models for topology optimization in sheet metal design

Topology optimization lies at the heart of many design tasks in mechanical engineering. For those sheet metal products that consist of a bundle of separate channels (such as conduits) we formulate the design task as a linear mixed-integer optimization problem. The design goal is to find a topology where each channel has a given cross section area, using a minimum amount of sheet met al. In addition to a light-weight design, stiffness should also be taken into account. The entire approach is demonstrated in the design of a conduit with five separate channels. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design of a distributed fiber transport network with hubbing topology

This paper deals with the comprehensive design of a distributed network, whose structure includes a large-scale fiber transport network where switching centers are interconnected via optical fiber cable. For real-world applicability, this design study covers in an integrated framework all three major decision sets: locating hub facilities, placing conduits and installing cables therein. The complex problem is formulated as a simple variant of the classical network design model by judiciously redefining commodity-Rows. Exploiting the special structure of the problem, a dual-based heuristic is then developed which yields near-optimal design plans. Computational experiments show that the performance of the proposed heuristic is satisfactory in both speed and the quality of the design solutions generated.     

Fórmulas para el cálculo del factor de impacto de estructuras semienterradas en líneas de ferrocarril de alta velocidad

Underpasses are common in modern railway lines. Wildlife corridors and drainage conduits often fall into this category of partially buried structures. Their dynamic behavior has received far less attention than that of other structures such as bridges, but their large number makes their study an interesting challenge from the viewpoint of safety and cost savings. The bridge design rules in accordance with the Eurocode involve checks on stresses according to dynamic loading. In the case of underpasses, those checks may be as much as those for bridges. Therefore, simplified design rules may align the design effort with their cost. Such a set of rules may provide estimations of response parameters based on the key parameters influencing the result. This paper contains a proposal based on a parametric study.     

Integer linear programming models for topology optimization in sheet metal design

The process of designing new industrial products is in many cases solely based on the intuition and experience of the responsible design engineer. The aid of computers is restricted to visualization and manual manipulation tools. We demonstrate that the design process for conduits, which are made out of sheet metal plates, can be supported by mathematical optimization models and solution techniques, leading to challenging optimization problems. The design goal is to find a topology that consists of several channels with a given cross section area using a minimum amount of sheet metal and, at the same time, maximizing its stiffness. We consider a mixed integer linear programming model to describe the topology of two dimensional slices of a three dimensional sheet metal product. We give different model formulations, based on cuts and on multicommodity flows. Numerical results for various test instances are presented.     

Geometry Optimization of Branched Sheet Metal Products

Geometry Optimization plays an important role concerning to design tasks in mechanical engineering. For those we are studying sheet metal products like cable conduits. We formulate a nonlinear, continuous optimization problem to find an optimal geometry for such a sheet metal product. The goal is to find from a given topology the optimal geometry parameters concerning to the minimal bending of a cable conduit, spanning a huge distance. Hereby a lot of constraints, like given sizes of cross-section areas of the chambers, given quantity of sheet metal, and so on have to be fullfilled. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller

This paper examines chaos control of two four-dimensional chaotic systems, namely: the Lorenz–Stenflo (LS) system that models low-frequency short-wavelength gravity waves and a new four-dimensional chaotic system (Qi systems), containing three cross products. The control analysis is based on recursive backstepping design technique and it is shown to be effective for the 4D systems considered. Numerical simulations are also presented.     

Unified description of cosmological and static solutions in affine generalized theories of gravity: Vecton-scalaron duality and its applications

We briefly describe the simplest class of affine theories of gravity in multidimensional space-times with symmetric connections and their reductions to two-dimensional dilaton-vecton gravity field theories. The distinctive feature of these theories is the presence of an absolutely neutral massive (or tachyonic) vector field (vecton) with an essentially nonlinear coupling to the dilaton gravity. We emphasize that the vecton field in dilaton-vecton gravity can be consistently replaced by a new effectively massive scalar field (scalaron) with an unusual coupling to the dilaton gravity. With this vecton-scalaron duality, we can use the methods and results of the standard dilaton gravity coupled to usual scalars in more complex dilaton-scalaron gravity theories equivalent to dilaton-vecton gravity. We present the dilaton-vecton gravity models derived by reductions of multidimensional affine theories and obtain one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully applicable to studying static and cosmological solutions in multidimensional theories and also in general one-dimensional dilaton-scalaron gravity models. We focus on general and global properties of the models, seeking integrals and analyzing the structure of the solution space. In integrable cases, it can be usefully visualized by drawing a “topological portrait” resembling the phase portraits of dynamical systems and simply exposing the global properties of static and cosmological solutions, including horizons, singularities, etc. For analytic approximations, we also propose an integral equation well suited for iterations.     

The study and applications of photochemical-dynamical gravity wave model Ⅱ-- The effects of stable gravity wave on chemical species distribution in mesosphere

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Euclidean and Lorentzian quantum gravity—lessons from two dimensions

No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum gravity. It represents one of the rare settings in a quantum-gravitational context where one can calculate quantities truly independent of any background geometry.We review recent progress in our understanding of 2d quantum gravity, and in particular the relation between the Euclidean and Lorentzian sectors of the quantum theory. We show that conventional 2d Euclidean quantum gravity can be obtained from Lorentzian quantum gravity by an analytic continuation only if we allow for spatial topology changes in the latter. Once this is done, one obtains a theory of quantum gravity where space-time is fractal: the intrinsic Hausdorff dimension of usual 2d Euclidean quantum gravity is four, and not two. However, certain aspects of quantum space-time remain two-dimensional, exemplified by the fact that its so-called spectral dimension is equal to two.