微通道内电渗压力混合驱动幂律流体流动模拟

为了研究微通道内电渗压力混合驱动幂律流体的流动特性,建立了微通道内电渗压力混合驱动幂律流体的计算模型,其双电层电势、流体的流场分布分别由Poisson-Boltzmann(P-B)方程和Navier-Stokes(N-S)方程描述.讨论了无量纲Debye(德拜)参数K、壁面ζ*电势和幂律指数n对流体流动特性和Poiseuille数的影响.结果表明,当压力梯度与外加电场方向一致(Γ0)时,剪切变稀流体的速度大于剪切变稠流体;压力梯度与外加电场方向相反(Γ0)时,结果相反.Poiseuille数是无量纲Debye常数K、壁面ζ*电势和幂律指数n的增函数.     

多孔介质中的一类双扩散扰动模型的解的连续依赖性

研究了定义在有界区域上的多孔介质中一类双扩散扰动模型解的结构稳定性.假设模型在区域的边界上满足非齐次Robin边界条件,利用能量分析的方法和微分不等式技术,首先得到了解的先验估计;然后在此基础上推出了关于解的微分不等式;通过积分该微分不等式,最后建立了解对Lewis数L_e的连续依赖性结果.该结果表明,双扩散扰动模型用来描述多孔介质中流体的流动情况是精确的.     

几种电梯运行模式的比较及应用

通过对上班高峰时段的电梯运行情况进行分析,以"最后被运送的乘客的等待时间最短"的"最大最小"原则作为其评价指标,以"电梯运行周期与运行总时间之比等于电梯在一个周期内运送的乘客数与乘客总数之比"的"比例"原则为依据,对高层楼宇中人员流动高峰时段的几种电梯运行方案建立了数学模型进行描述与比较,找到了电梯停靠楼层的最佳方案,并对北京大学第三医院外科楼的运行方案做出定量的数学证明.     

基于区间数的TOPSIS方法在水驱油田开发效果评价上的应用

针对目前油田高含水期水驱开发效果评价难度大、评价方法多集中在模糊综合评价方法上,提出应用区间数的TOPSIS方法(逼近理想点排序)对油田水驱开发效果进行评价.首先对区间数多指标决策问题和区间数的相关运算进行了描述,给出了区间数TOPSIS方法的计算步骤.然后根据水驱开发效果指标评价标准及待评价区块生产数据建立评价对象区间数决策矩阵,进而确定最优方案(正理想点)和最劣方案(负理想点),并计算待评价方案与最优方案的相对贴近度,再结合[0,1]语言标度区间确定评价结果.最后,给出实例验证该方法的可行性和有效性.     

基于非对称指数型模糊数的模糊回归在害虫预报上的应用(Ⅰ)

给出了描述非对称指数型模糊数近似程度的贴近度的定义及其表达式;在此基础上建立了输入、输出为模糊数,系数为精确数的模糊多元回归模型,并应用该模型对山东南部农田鼠害夏峰期发生率进行了预测,结果与实际情况比较吻合.     

带模糊时间窗的配送问题多目标优化研究

针对配送多目标优化问题,综合考虑车辆使用数、运输总里程和客户服务水平,基于双层规划的思想,解决了车辆数函数和运输里程函数的区间伸缩指标问题,并引入客户不满意度的模糊隶属度函数来描述配送服务水平。通过去量纲将三个优化目标转化为总目标函数的功效函数,并运用模糊层次分析法对三个函数分配权重,建立以车辆使用数最少、运输总里程最小、客户不满意度最低的标量化多目标模型,并运用模拟退火算法验证了模型的合理性和普适性。     

微通道周期流动电位势及电粘性效应

求解了双电层的Poisson-Boltzmann方程和流体运动的Navier-Stokes方程,得到在周期压差作用下,二维微通道的周期流动电位势,流动诱导电场和液体流动速度的解析解．量纲分析表明,流体电粘性力与以下3个参数有关:1) 电粘性数,它表示定常流动时,通道最大电粘性力与压力梯度的比;2) 形状函数,它表示电粘性力在通道横截面的分布形态; 3) 耦合系数,它表示电粘性力的振幅衰减特征和相位差．分析结果表明,微通道周期流动诱导电场、流动速度与频率Reynolds数有关．在频率Reynolds数小于1时,流动诱导电场随频率Reynolds数变化很慢．在频率Reynolds数大于1时,流动诱导电场随频率Reynolds数的增加快速衰减．在通道宽度与双电层厚度比值较小情况下,电粘性效应对周期流动速度和流动诱导电场有重要影响．     

基于模糊程度层次分析法和直觉三角模糊TOPSIS的B2R绿色供应商评价研究

针对B2R供应商评价问题,以产品竞争力、服务水平、业务能力、绿色环保能力和发展前景五个方面构建B2R供应商评价指标体系.考虑到B2R供应商评价指标的不确定性和模糊性,用模糊数来描述各指标值,基于模糊程度层次分析法(FEAHP)计算指标权重,并建立直觉三角模糊TOPSIS B2R供应商评价模型.最后,通过算例证明FEAHP和直觉三角模糊TOPSIS具有稳定性和有效性.     

考虑多种形式信息的求职者与岗位双边匹配研究

针对考虑多种形式信息的求职者与岗位双边匹配问题提出了一种决策分析方法。首先,给出了求职者与岗位双边匹配的问题描述;其次．针对多评价指标下的0—1判断信息、区间数和语言评价等多种形式的信息,通过计算不同形式的评价信息与正理想点的距离定义了岗位对求职者的满意度和求职者对岗位的满意度,以岗位和求职者双方角度的满意度最大为目标建立了多目标优化模型。最后,通过BS公司的实例分析说明了该方法的实用性和有效性。     

空间分数阶非Newton流体本构及圆管流动规律研究

对非Newton流体的本构及流动规律进行研究是分析、预测和控制非Newton流体在管道中流动的关键.实验表明非Newton流体在流动过程中具有历史记忆性,基于空间分数阶微积分方法,建立了分数阶非Newton流体本构模型;并推导了该模型在圆管中的流速分布、流量、平均流速、压降、平均Reynolds数等管道流动参数;提出了分数阶非Newton流体圆管流态判别准则.研究表明非Newton流体的圆管流层间的切应力可以通过流速的轴向分布大小来描述.对于不含屈服切应力的分数阶非Newton流体,分数阶的阶数越大,断面流速分布越均匀,记忆能力越强.分数阶的阶数大小反映了流体对全域空间的记忆性强弱;而对于含有屈服切应力的分数阶非Newton流体,分数阶的阶数越大,速梯区流速分布越均匀,流核区速度越小.分数阶的阶数大小反映了局部空间记忆性强弱.该研究为非Newton流体的记忆特征提供了一种新的建模方法.     

Nowhere‐Zero Flows on Signed Complete and Complete Bipartite Graphs

Bouchet's conjecture asserts that each signed graph which admits a nowhere‐zero flow has a nowhere‐zero 6‐flow. We verify this conjecture for two basic classes of signed graphs—signed complete and signed complete bipartite graphs by proving that each such flow‐admissible graph admits a nowhere‐zero 4‐flow and we characterise those which have a nowhere‐zero 2‐flow and a nowhere‐zero 3‐flow.     

Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators

One may trace the idea that spectral flow should be given as the integral of a one form back to the 1974 Vancouver ICM address of I.M. Singer. Our main theorem gives analytic formulae for the spectral flow along a norm differentiable path of self adjoint bounded Breuer-Fredholm operators in a semifinite von Neumann algebra. These formulae have a geometric interpretation which derives from the proof. Namely we define a family of Banach submanifolds of all bounded self adjoint Breuer-Fredholm operators and on each submanifold define global one forms whose integral on a norm differentiable path contained in the submanifold calculates the spectral flow along this path. We emphasise that our methods do not give a single globally defined one form on the self adjoint Breuer-Fredholms whose integral along all paths is spectral flow rather, as the choice of the plural ‘forms’ in the title suggests, we need a family of such one forms in order to confirm Singer's idea. The original context for this result concerned paths of unbounded self adjoint Fredholm operators. We therefore prove analogous formulae for spectral flow in the unbounded case as well. The proof is a synthesis of key contributions by previous authors, whom we acknowledge in detail in the introduction, combined with an additional important recent advance in the differential calculus of functions of non-commuting operators.     

Two Dimensional Incompressible Ideal Flow Around a Small Obstacle

Abstract

In this article we study the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small. Our main purpose is to identify the equation satisfied by the limit flow. We will see that the asymptotic behavior depends on γ, the circulation around the obstacle. For smooth flow around a single obstacle, γ is a conserved quantity which is determined by the initial data. We will show that if γ = 0, the limit flow satisfies the standard incompressible Euler equations in the full plane but, if γ≠ 0, the limit equation acquires an additional forcing term. We treat this problem by first constructing a sequence of approximate solutions to the incompressible 2D Euler equation in the full plane from the exact solutions obtained when solving the equation on the exterior of each obstacle and then passing to the limit on the weak formulation of the equation. We use an explicit treatment of the Green's function of the exterior domain based on conformal maps, a priori estimates obtained by carefully examining the limiting process and the Div-Curl Lemma, together with a standard weak convergence treatment of the nonlinearity for the passage to the limit.     

网络最小覆盖流问题

网络流理论中最基本的模型是最大流及最小费用流问题. 为研 究堵塞现象, 文献中出现了最小饱和流问题, 但它是NP-难的. 研究类似的最小覆盖流问题, 即求一流, 使每一条弧的流量达到一定的额定量, 而流的值为最小. 主要结果是给出多项式时间算法, 并应用于最小饱和流问题.     

FDI企业选址与东道国环境规制博弈

建立了高进入壁垒和低进入壁垒下双寡头博弈模型,应用逆向求解法,得到了引资国环境政策是否改变和FDI流出国企业是否迁址的临界条件.结果表明:在高进入壁垒的产业中,由于东道国较高的进入壁垒,外国企业可能不迁址;但如果考虑FDI产生的正外部性且溢出效应较高,引资国可能降低环境规制水平以吸引FDI企业进入,但从环境的角度考虑,此时全球环境损害更大.在低进入壁垒产业中,东道国政府选择提高环境规制水平是其占优策略,对引资国和全球都是帕累托改善的.     

Stabilization of von Kármán plate in the presence of thermal effects in a subsonic potential flow of gas

We discuss the problem of nonlinear oscillations of a clamped plate in the presence of thermal effects in a subsonic gas flow. The dynamics of the plate is described by von Kármán system in the presence of thermal effects, in which rotational inertia is accounted for. To describe influence of the gas flow we apply the linearized theory of potential flows. Our main result states that each weak solution of the problem considered tends to the set of the stationary points of the problem.     

On Gage-Hamilton's entropy formula and Harnack inequality for the curve shortening flow

By the first two derivatives of the Boltzmann entropy of the curvature, which was first studied by Gage and Hamilton for the curve shortening flow in the plane, we define a monotonicity formula which is strictly increasing unless on a shrinking circle. By calculating pointwisely we give an alternate proof of Gage-Hamilton's Harnack inequality.     

On the enrouting protocol problem under uncertainty

In this paper we present a two-stage stochastic mixed 0–1 dynamic multicommodity model and algorithm for determining the enrouting protocol in the telecommunications network under uncertainty. Given the network connectivity, node processing and buffer and arc flow capacity, the aim is to determine the outgoing arc for the information flow reaching a given node for each destination terminal node (i.e., obtaining the route to be followed by the information flow from each origin terminal node to each destination terminal node). The origin–destination (O–D) flow matrix is given by the number of information packets to be sent from the origin terminal nodes to the destination terminal nodes along a given time horizon, i.e., a call scale. The uncertainty in the O–D flow matrix is treated via a scenario tree approach. The main goal is to minimize a composite function of the expected lost information, a penalization of the deviation from the FIFO strategy on the information flow entering the network, and the expected number of nodes visited by the information packets. A mixture of an enrouting arc generation scheme and a genetic algorithm for obtaining the enrouting protocols over the scenarios is presented. The tool presented in this paper could be used for simulating the enrouting protocols to analyze the saturation of the network, but it has a time constraint for real time operation. Faster algorithms are needed to define the routing tables during the operation stage. Computational experience is reported.     

Single-source k-splittable min-cost flows

Motivated by a famous open question on the single-source unsplittable minimum cost flow problem, we present a new approximation result for the relaxation of the problem where, for a given number k, each commodity must be routed along at most k paths.     

On an extension of the H k mean curvature flow

In this note,we generalize an extension theorem in [Le-Sesum] and [Xu-Ye-Zhao] of the mean curvature flow to the Hk mean curvature flow under some extra conditions.The main difficulty in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the Hk mean curvature flow,and to do a suitable Moser iteration process.These two problems are overcome by imposing some extra conditions which may be weakened or removed in our forthcoming paper.On the other hand,we derive some estimates for the generalized mean curvature flow,which have their own interesting.