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121.
A study of the stabifity of plane Poiseuille flow at higher Reynolds number is made. Within a "triple-deck" structural framework, the qualitative behaviour of the eigenvalue of Orr-Sommerfeld equation is analytically obtained. The corresponding eigenfunction is formulated approximately. 相似文献
122.
The aim of this paper is to study numerical realization of the conditions of Max Nther's residual intersection theorem. The numerical realization relies on obtaining the intersection of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determining the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic,even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time. 相似文献
123.
本文应用同伦技术和摄动技术,提出了一种新的摄动思想。这种方法有别于传统的摄动理论,它不依赖于小参数,而且是应用同伦技术,构造一个含嵌入参数p∈「0,1」的方程,然后把嵌入参数为“小参数”,因此这种新方法可以克服传统摄动理论的不足,而又充中种摄动方法。 相似文献
124.
In this paper the well-known non-linear equation f‴+½ff″=0 with boundary conditions f(0)=0, f′(0)=0 and f (∞)=1 is used as an example to describe the basic ideas of a kind of general boundary element method for non-linear problems whose governing equations and boundary conditions may not contain any linear terms at all. 相似文献
125.
The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and Al2O3, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions are derived by the homotopy analysis method (HAM). The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically. 相似文献
126.
127.
Saeed Dinarvand Mohammad Mehdi Rashidi Ahmad Doosthoseini 《Central European Journal of Physics》2009,7(4):791-799
In this paper, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two
moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved analytically
by using the homotopy analysis method (HAM). Graphical results are presented to investigate the influence of the nondimensional
wall dilation rate α and permeation Reynolds number Re on the velocity, normal pressure distribution and wall shear stress.
The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. The present problem for
slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through
contracting or expanding vessels.
相似文献
128.
Zhang Kaipeng Wu Daihua 《Acta Mechanica Solida Sinica》2005,18(3):278-282
I. INTRODUCTIONStructural damages due to the loss of sti?ness such as crack, localization bulking have remarkablein?uences on the physical properties of structure such as deformation, stress, frequency and modelshape. So the change of these properties can be used to identify the damage location and degree ofstructures. The damage identification techniques based on these properties’ changes have attractedmuch attention in recent years, and many approaches have been developed[1??5].Nowaday… 相似文献
129.
林金坤 《数学物理学报(B辑英文版)》2009,29(5):1395-1404
This study proves a general result on convergence of α2x ∈ ExtA^s+2.tq+2q+1 (Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q-4S which is represented in the Adams spectral sequence by α2fn,α2fn,α2huhmhn ∈ ExtA^5,tq+2q+1(Zp,Zp) with tq=p^n+1q+2p^nq,2p^n+1q_P^nq,p^uq+p^mq+p^nq,respectively, where α2∈Extα^2,2q+1(Zp,Zp),fn∈ExtA^3,p^n+1q+2p^nq(Zp,Zp),fn∈ExtA^3,2p^n+2q+p^nq(Zp,Zp),hn∈ExtA^1,p^nq(Zp,Zp)and p≥5 is a prime,q=2(p=-1),n≥2. 相似文献
130.
Jun Cheng Jie Cang Shi-Jun Liao 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):450-478
A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated
by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies exponentially with
the magnitude of the stream function, while remaining constant on a particular streamline. The so-called Dubreil–Jacotin transformation
is used to transfer the original exponentially nonlinear boundary-value problem in an unknown domain into an algebraically
nonlinear boundary-value problem in a known domain. Convergent series solutions are obtained not only for small amplitude
water waves on a weak current but also for large amplitude waves on a strong current. The nonlinear wave-current interaction
is studied in detail. It is found that an aiding shear current tends to enlarge the wave phase speed, sharpen the wave crest,
but shorten the maximum wave height, while an opposing shear current has the opposite effect. Besides, the amplitude of waves
and fluid velocity decay over the depth more quickly on an aiding shear current but more slowly on an opposing shear current
than that of waves on still water. Furthermore, it is found that Stokes criteria of wave breaking is still valid for waves
on a shear current: a train of propagating waves on a shear current breaks as the fiuid velocity at crest equals the wave
phase speed. Especially, it is found that the highest waves on an opposing shear current are even higher and steeper than
that of waves on still water. Mathematically, this analytic method is rather general in principle and can be employed to solve
many types of nonlinear partial differential equations with variable coefficients in science, finance and engineering. 相似文献