Theoretical analysis on hydraulic transient resulted by sudden increase of inlet pressure for laminar pipeline flow

Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.     

一类非自治动力系统超次谐周期解的不存在性

在非线性动力系统的研究中， Melnikov函数被广泛地用来作为微扰哈密顿系统是否发生次谐或超次谐分岔乃至混沌的判 据. 但是在大多数情况下，经典的Melnikov方法往往只给出存在次谐周期解的结论. 产生 该结果的原因被归之为在经典的Melnikov方法中只采取了一阶近似，因而高阶Melnikov方 法被发展用来判断超次谐周期解的存在性. 本文对一类非自治微分动力系统进行了研究，证 明了在这样一类系统中如果存在周期解则只可能是次谐周期解，超次谐周期解不可能存在， 并进一步证明了在一类平面问题中所定义的旋转(R)型超次谐周期解同样不可能存在.作为 该结论的一个应用，文中考察了几个典型的算例，结果表明现有的二阶Melnikov方法判断 平面扰动系统是否存在超次谐周期解的结论是不恰当的，并提供了一个简单的几何上的解释.     

Analytic solutions of incompressible laminar flow in the inlet region of a pipe

The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.     

On the existence of periodic solutions to higher dimensional periodic system with delay

Ｃｏｎｓｉｄｅｒｉｎｇｔｈｅｈｉｇｈｅｒｄｉｍｅｎｓｉｏｎａｌｐｅｒｉｏｄｉｃｓｙｓｔｅｍｓｗｉｔｈｄｅｌａｙｏｆｔｈｅｆｏｒｍｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－τ））,（１）ｘ′（ｔ）＝ｇｒａｄＧ（ｘ（ｔ））＋ｆ（ｔ,ｘ（ｔ－...     

On the asymptotic solutions for a class of second order differential equations with slowly varying coefficients

In this paper we study the asymptotic expansions of the solutions for a class of secondorder ordinary differential equations with slowly varying coefficients.The defect of theknown works on these problems is noted,and the results in[1—4]are improved andextended by means of the modified method of multiple scales.     

On the Jacobian conjecture for global asymptotic stability

An old conjecture says that, for the two-dimensional system of ordinary differential equationsx=f(x), wheref: ^{2 2},f C ¹, andf(0)=0 the originx=0 should beglobally asymptotically stable (i.e., a stable equilibrium and all trajectoriesx(t) converge to it ast +) whenever the following conditions on the Jacobian matrixJ(x) off hold: trJ(x) < 0, detJ(x) > 0, x ² It is known that if such anf is globallyone-to-one as a mapping of the plane into itself, then the origin is a globally asymptotically stable equilibrium point for the systemx =f(x). In this paper we outline a new strategy to tackle the injectivity off, based on anauxiliary boundary value problem. The strategy is shown to be successful if the norm of the matrixJ(x) ^T J(x)t/det J(x) is bounded or, at least, grows slowly (for instance, linearly) as ¦x¦ t.     

Local Hopf bifurcation and global existence of periodic solutions in TCP system

This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu （Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350（12）, 4799-4838 （1998））.     

On the existence of periodic solutions for nonlinear system with multiple delays

IntroductionInthispaper,westudyT_periodicsolutionsofthefollowingnonlinearsystemwithmultipledelays x(t) =f(t,x(t) ,x(t-τ1(t) ) ,… ,x(t -τm(t) ) ) ,(1 )wherex(t) ∈C(R ,R) ,fiscontinuous,f(t+T ,·) =f(t,·) ,τi(t) (i=1 ,2 ,… ,m)arecontinuousperiodicfunctionsofperiodT .AlemmaisintroducedfordiscussingtheexistenceofT_periodicsolutionofsystem (1 ) .LetXbeaBanachSpace ,considerthefollowingoperatorequation :Lx =λNx　　 (λ∈ [0 ,1 ] ) ,whereL :DomL∩X→Xisalinearoperator,λ∈ [0 ,1 ]isapa…     

Conjugated laminar forced convection in ducts with periodic variation of inlet temperature

Conjugated laminar forced convection with parabolic velocity is studied for flow inside both parallel-plate and circular ducts subjected to a periodically varying inlet temperature. The analysis of this classs of problems lead to a Sturm-Liouville type complex eigenvalue problem for which no known solution is available. In this work, a new methodology is presented for a direct solution of such complex eigenvalue problems in the complex domain using the shooting method along with the Runge-Kutta method. The methodology is applicable for solving both laminar and turbulent flow problems; here we consider only the laminar flow with a parabolic velocity profile. The results clearly show that the slug-flow assumption overestimates the phase lag and the Nusselt number. Some benchmark results are also presented for the eigenquantities in tabular form.     

Double method of characteristics to analyze hydraulic-thermal transients of pipeline flow

ＩｎｔｒｏｄｕｃｔｉｏｎＭｅｔｈｏｄｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｓ (ＭＯＣ)ｈａｓｓｔｉｌｌｂｅｅｎｔｈｅｐｏｗｅｒｆｕｌｔｏｏｌｔｏａｎａｌｙｚｅｈｙｄｒａｕｌｉｃｔｒａｎｓｉｅｎｔｏｆｐｉｐｅｌｉｎｅｆｌｏｗｓｉｎｃｅｔｈｅ 1 960ｓ.Ｓｅｌｄｏｍｈａｓｔｈｅｔｈｅｒｍａｌｔｒａｎｓｉｅｎｔｂｅｅｎｔａｋｅｎｉｎｔｏａｃｃｏｕｎｔ.Ｈｅａｔｄｕｅｔｏｆｒｉｃｔｉｏｎｖａｒｉｅｓｗｈｅｎｆｌｏｗｒａｔｅｃｈａｎｇｅｄｂｅｃａｕｓｅｏｆｖａｒｉｏｕｓｋｉｎｄｓｏｆｒｅａｓｏｎｓ,ｗｈｉｃｈｃａｕｓ…     

非线性电报方程组的3个双周期正解问题

This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.     

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｎｃｅｔｈｅｓｐｅｃｉａｌｓｕｐｅｒｉｏｒｉｔｙｏｆａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓｔｅｃｈｎｏｌｏｇｙｉｎｖａｒｉｏｕｓｅｎｇｉｎｅｅｒｉｎｇｔｅｃｈｎｉｑｕｅｓｆｉｅｌｄｓ,ｓｕｃｈａｓｏｐｔｉｍｉｚａｔｉｏｎ ,ａｓｓｏｃｉａｔｉｖｅｍｅｍｏｒｉｅｓ,ｐａｔｔｅｒｎｒｅｃｏｇｎｉｔｉｏｎ ,ｓｉｇｎａｌｐｒｏｃｅｓｓｉｎｇａｎｄａｕｔｏｍａｔｉｃｃｏｎｔｒｏｌ,ｔｈｅｒｅｈａｓｂｅｅｎｉｎｃｒｅａｓｉｎｇｉｎｔｅｒｅｓｔｉｎｔｈｅｉｎｖｅｓｔｉｇａｔｉ…     

Existence of periodic traveling wave solutions for a class of generalized BBM equation

In this paper, a new kind of generalized BBM equation is introduced and discussed. Some existence theorems of periodic traveling wave solutions for this kind generalized BBM equation are given.     

On the global solutions to two-phase nonequilibrium problems

In this paper, we consider a Stefan-like problem with a kinetic condition on the free boundary, i.e. a two-phase nonequilibrium problem in one dimension, and prove that it has a unique classical and global solution under some conditions. We also investigate the travelling wave solutions.

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Sommario In questo lavoro si considera un problema tipo Stefan con una condizione cinetica sul bordo libero, cioc' un problema di non equilibrio a due fasi in una dimensione. Si dimostra che, sotto opportune condizioni, il problema ammette una unica soluzione globale di tipo classico. Sono altresi' analizate soluzioni ad onde viaggianti.

     

Existence and uniqueness of almost periodic solution to a class of nonautonomous system

Ｈｉｇｈ＿ｔｅｎｓｉｏｎｅｌｅｃｔｒｉｃｉｔｙｎｅｔｗｏｒｋ,ｗｉｔｈｏｕｔｗｈｉｃｈｏｕｒｍｏｄｅｒｎｓｏｃｉｅｔｙｃａｎｎｅｖｅｒｌａｓｔｆｏｒａｄａｙ,ｍａｙｓｏｍｅｔｉｍｅｓｂｅｒｅａｌｌｙｕｎｓｔａｂｌｅ,ｄｕｅｔｏｖａｒｉｏｕｓｋｉｎｄｏｆｏｓｃｉｌｌａｔｉｏｎｓｏｆｃｕｒｒｅｎｔｉｎｔｅｎｓｉｔｙ．Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｐｅｒｉｏｄｉｃｏｓｃｉｌｌａｔｉｏｎｓｏｒａｌｍｏｓｔｐｅｒｉｏｄｉｃｏｓｃｉｌｌａｔｉｏｎｓｈａｖｅａｐｐｅａｒｅｄｉｎＣｅｎｔｒａｌｇｒｉｄａｎｄＮｏｒ…     

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＺｈａｏＪｉｅ－ｍｉｎ（赵杰民）;ＨｕａｎｇＫｅ－ｌｅｉ（黄克累）...     

On the periodic solutions of differential inclusions and applications

The periodic problem of evolution inclusion is studied and its results are used toestablish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given forthis class of semi-linear differential inclusion. An application to some feedback control systems isdiscussed.     

On the existence and the asymptotic stability of solutions for linearly viscoelastic solids

Communicated by C. Dafermos     

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.