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1.
该文主要研究平面上Wulff流情形下的等周不等式.利用凸域的某些量在Wulff流情形下的变化规律(单调性、不变性),得到了Wulff-Gage等周不等式与曲率的Wulff-熵不等式的新的简单证明;进一步地,得到了一个新的Wulff流情形下的不等式.  相似文献   

2.
考虑紧的、一致凸的n维无边曲而光滑地进入到具有常曲率的黎曼流形中,得到了平均曲率流下拉普拉斯算子特征值的发展方程,并且构造了一些沿着平均曲率流单调的几何量.  相似文献   

3.
本文对Euclid空间中的有界区域引进一类新的完全非线性曲率流并证明其存在及指数收敛性.沿该曲率流,本文将证明所有的均质积分(quermassintegral)都随时间单调变化,由此得以证明关于均质积分的一类Alexandrov-Fenchel不等式.  相似文献   

4.
本文提出了一类带有边界条件的新的曲率流问题,说明了它们的理论来源和实际背景.对Gauss曲率情形,建立了这种曲率流古典解的存在唯一性,并用一种适用于更一般曲率情形的方法,研究了这种曲率流的渐近性。  相似文献   

5.
由曲率函数和外力场之差支配的凸超曲面的发展   总被引:1,自引:0,他引:1  
考虑由曲率函数和外力场之差支配的凸超曲面的发展.证明了外力场为常向量场时,初始超曲面的凸性是保持的,且曲率流在有限时间内爆破.对于线性外力场,初始超曲面的凸性保持.而且,若线性常数为负数,则曲率流在有限时间内收敛到一点;若线性常数为正数且初始曲率小于某一与外力场有关的常数,则曲率流光滑地存在于任意有限时间区间,并发散到无穷;若线性常数为正数且初始曲率大于某一与外力场有关的常数,则曲率流在有限时间内爆破.  相似文献   

6.
C.Guenther利用中心流形以及极大正规性原理,讨论了常曲率空间中DeTurck流的稳定性问题.将常曲率空间推广为拟常曲率空间并讨论"拟"DeTurck流的稳定性问题,得到类似于C.Guenther所得的结果.  相似文献   

7.
 本文在星形多边形网格上, 构造了扩散方程新的单调有限体积格式.该格式与现有的基于非线性两点流的单调格式的主要区别是, 在网格边的法向流离散模板中包含当前边上的点, 在推导离散法向流的表达式时采用了定义于当前边上的辅助未知量, 这样既可适应网格几何大变形, 同时又兼顾了当前网格边上物理量的变化. 在光滑解情形证明了离散法向流的相容性.对于具有强各向异性、非均匀张量扩散系数的扩散方程, 证明了新格式是单调的, 即格式可以保持解析解的正性. 数值结果表明在扭曲网格上, 所构造的格式是局部守恒和保正的, 对光滑解有高于一阶的精度, 并且, 针对非平衡辐射限流扩散问题, 数值结果验证了新格式在计算效率和守恒精度上优于九点格式.  相似文献   

8.
本文提出了一类带有边界条件的新的曲率流问题,说明了它们的理论来源和实际背景对Gauss曲 率情形,建立了这种曲率流古典解的存在唯一性,并用一种适用于更一般曲率情形的方法,研究了这 种曲率流的渐近性。  相似文献   

9.
标准球面上的预定纯量曲率问题已经得到很好的研究,为此,几种不同的方法发展起来了.它的高维对应的问题即预定Q-曲率问题也吸引了众多人的注意.负梯度流的方法在处理此类问题上似乎十分有效,至少在曲率备选函数是正的情形下是如此的.本文的目的在于指出,对于指数非线性增长的预定Q-曲率问题,Q-曲率备选函数的正性假设是不必要的.  相似文献   

10.
本文研究了广义L_p-混合投影体及广义L_p-混合质心体的单调性问题.利用解析不等式,获得了广义L_p-混合投影体与广义L_p-混合质心体的均质积分与对偶均质积分形式的单调不等式,推广了L_p-投影体及L_p-质心体的体积形式的单调性.  相似文献   

11.
The basic equations for fluids with microstructure are applied to the steady flow between two parallel plates under the action of a constant pressure gradient. The flow is governed by a microstructure parameter α*. The classical flow is recovered when α* → ∞, while maximum effects of microstructure correspond to α* → 0. For a Poiseuille flow, the microstructure fluid exhibits resistance to motion greater than or equal to that of the classical flow. For a Couette flow it is shown that for a given applied velocity to the moving plate, the shearing stress at the plate is greater than or equal to that corresponding to the classical flow situation. For a Generalised Couette flow, it is shown that for a given pressure gradient in the direction of flow, the flow is retarded; while for an adverse pressure gradient the back flow is controlled.  相似文献   

12.
The behavior of the flow between two coaxial conical cylinders with the inner one rotating and the outer one stationary is studied numerically. Special attention is paid to the occurrence of Taylor vortices in basic flow and unsteady helical vortices. It is found that, in basic flow, the vortices occur in the direction toward smaller radius, while toward bigger radius in unsteady helical vortices; moreover, the unsteady helical vortices can coexist with unstable steady Taylor vortices. The results suggest that the behavior of conical flow is dominated by a competition between the meridional flow and radial flow. The effect of meridional flow is most significant at small apex angle or in basic flow and helical vortices, while the radial flow dominates the structure at larger apex angle or in steady vortical flow. In order to get better understanding the competition and the transition of Taylor–Couette flow to conical flow, a velocity angle related to velocity components is defined, and the pattern evolution of velocity, streamlines and the velocity angle are examined with respect to apex angle, as well as Reynolds number. Finally, the statistical properties of turbulent conical flow are investigated.  相似文献   

13.
The Bingham fluid model represents viscoplastic materials that display yielding, that is, behave as a solid body at low stresses, but flow as a Newtonian fluid at high stresses. In any Bingham flow, there may be regions of solid material separated from regions of Newtonian flow by so-called yield boundaries. Such materials arise in a range of industrial applications. Here, we consider the helical flow of a Bingham fluid between infinitely long coaxial cylinders, where the flow arises from the imposition of a steady rotation of the inner cylinder (annular Coutte flow) on a steady axial pressure driven flow (Poiseuille flow), where the ratio of the rotational flow compared to the axial flow is small. We apply a perturbation procedure to obtain approximate analytic expressions for the fluid velocity field and such related quantities as the stress and viscosity profiles in the flow. In particular, we examine the location of yield boundaries in the flow and how these vary with the rotation speed of the inner cylinder and other flow parameters. These analytic results are shown to agree very well with the results of numerical computations.  相似文献   

14.
非牛顿流体偏心环空螺旋流的解析解   总被引:2,自引:0,他引:2  
石油和化工中许多问题需要求解非牛顿流体偏心环空螺旋流。本文全面地研究了幂律流体和宾汉流体在偏心环空中层流螺旋流的流动规律与流动状态的判别。在理论上,根据流体力学原理,运用数学方法,在作者同心环空螺旋流的理论基础上,通过对偏心环空螺旋流流场的无限细分法,给出了该流场的视粘度分布、速度分布、流量和压降方程,进而建立了判别流态的稳定性参数。  相似文献   

15.
在全面关系流管理理论的基础上,研究人体血液自然分布单位组织全面血液关系流的实现与维护.实现关系流应该从关系流的性质、时间约束、血液自然分布单位的状态与行为,以及可行性等方面综合考虑.当全面关系流建立起来后,人体组织就基于血液关系流建立起自然法则,当血液关系流不再适用时,相关的血液自然分布单位需进行关系流的再设计,以适应新的组织行为.  相似文献   

16.
This paper deals with the numerical solution of a pulsatile laminar flow through a locally constricted channel. A finite difference technique has been employed to solve the governing equations. The effects of the flow parameters such as Reynolds number, flow pulsation in terms of Strouhal number, constriction height and length on the flow behaviour have been studied. It is found that the peak value of the wall shear stress has significantly changed with the variation of Reynolds numbers and constriction heights. It is also noted that the Strouhal number and constriction length have little effect on the peak value of the wall shear stress. The flow computation reveals that the peak value of the wall shear stress at maximum flow rate time in pulsatile flow situation is much larger than that due to steady flow. The constriction and the flow pulsation produce flow disturbances at the vicinity of the constriction of the channel in the downstream direction.  相似文献   

17.
林浩  林澜 《运筹学学报》2014,18(4):96-104
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.  相似文献   

18.
The proportional network flow problem is a generalization of the equal flow problem on a generalized network in which the flow on arcs in given sets must all be proportional. This problem appears in several natural contexts, including processing networks and manufacturing networks. This paper describes a transformation on the underlying network that reduces the problem to the equal flow problem; this transformation is used to show that algorithms that solve the equal flow problem can be directly applied to the proportional network flow problem as well, with no increase in asymptotic running time. Additionally, computational results are presented for the proportional network flow problem demonstrating equivalent performance to the same algorithm for the equal flow problem.  相似文献   

19.
In this paper, we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space. We show that under suitable assumptions on the initial data $g$ one has a weak approximate discrete Morse flow for the Yamabe type heat flow on any time interval. This phenomenon is very different from the smooth Yamabe flow, where the finite time blow up may exist.  相似文献   

20.
Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Minkowski spaces, a special case of Finsler manifolds, we prove the short time existence and uniqueness for solutions of the mean curvature flow and prove that the flow preserves the convexity and mean convexity. We also derive some comparison principles for the mean curvature flow.  相似文献   

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