2010 Vol. 31, No. 6

Display Method:
Riemann Problem for the Nonlinear Degenerate Wave Equations
SUN Wen-hua, SHENG Wan-cheng
2010, 31(6): 639-648. doi: 10.3879/j.issn.1000-0887.2010.06.001
Abstract(1578) PDF(774)
Abstract:
The Riemann problem for a non linear degenerate wave equation system in elasticity was considered. Since the stress function was not convex or concave, the shock condition was degenerate. By in troducing a degenerate shock under the generalized shock condition, the global solutions were constructively obtained case by case.
Influence of Chemical Reaction on Heat and Mass Transfer of Non-Newtonian Fluid With Yield Stress by Free Convection From a Vertical Surface in Porous Medium Considering Soret Effect
F. S. Ibrahim, F. M. Hady, S. M. Abdel-Gaied, Mohamed R. Eid
2010, 31(6): 649-658. doi: 10.3879/j.issn.1000-0887.2010.06.002
Abstract(1352) PDF(813)
Abstract:
The effect of chemical reaction on free convection heat and mass trans fer for non-New tonian power law fluid overa vertical flat plate embedded in a fluid saturated porous medium was studied in the presence of yield stress and Soreteffect. The governing boundary layer equations and boundary conditions were cast in to a dimension less form by smiilarity tran sformations and the resulting system of equations was solved by a finite difference method. Results are presented and discussed for concentration profiles, as well as the Nusselt and Sherwood numbers for various values of the parameters, which govern the problem. The results obtained show that the flow field is in fluenced appreciably by the presence of chemical reaction parameter, order of chemical reaction parameterm, Soret number Sr, buoyancy ratio N, Lew is number Le, and dmiension less rheological parameter.
Investigation Over the Recirculation Influence on the Combustion of Micro Organic Dust Particles
Mehdi Bidabadi, Aboozar Fanaee, Alireza Rahbari
2010, 31(6): 659-669. doi: 10.3879/j.issn.1000-0887.2010.06.003
Abstract(1344) PDF(766)
Abstract:
The role of recirculation and non-unity Lew is number on the combustion of organic dust particles were investigated. Since recirculation effect is more no ticeable in micro-combustors, it is necessary to propose a modeling approach of this phenomenon to better simulate the perform anceofmicro-combustors. In this research, in order to model the combustion of organic dust particles, it was assumed that the dust particles vaporize first to yield a known chemical structure which was oxidized in the gas phase, and the chemical structure of this gaseous fuel was assumed methane. To study the flame structure and solve the governing equations, it was considered that the flame structure consists of three zonestitled the prehea-tvaporization zone, the narrow reaction zone and finally the post flame zone. The recircu lation phenom enon was evaluated by entering the exhausted heat from the post flame zone in to the preheat zone. The solution was based on the following approach. First, the governing equations in each zone were nond imensionalized. Then the needed boundary and matching conditions were applied in each zone. A fter that, these equations and the required boundary and matching conditions were simultaneously solved with the analytical model. Consequently, the remarkable effects of recirculation and nonunity Lew is number on the combustion characteristics of the organic dust particles such as burning velocity and temperature profiles for different particle radiiare obtained. The results show reasonable agreement with published experimental data.
Pullback Attractor of 2D Non-Autonomous g-Navier-Stokes Equations on Some Bounded Domains
JIANG Jin-ping, HOU Yan-ren
2010, 31(6): 670-680. doi: 10.3879/j.issn.1000-0887.2010.06.004
Abstract(1353) PDF(847)
Abstract:
The existence of pullback attractors for the 2D non-autonomous g-Navier-Stokes equations on some bounded domains were inves tigated under the general assumptions of pull back asym ptotic compactness, and a new method to prove the existence of pullback attractors for the 2D g-Navier-Stokes equations was given.
Study on the Secondary Flow Coefficient of Overbank Flow
YANG Zhong-hua, GAO Wei, HUAI Wen-xin
2010, 31(6): 681-689. doi: 10.3879/j.issn.1000-0887.2010.06.005
Abstract(1490) PDF(969)
Abstract:
The 2-D analytical solution for tran sverse velocity distribution in compound open channels was presented based on the Shiono and Knight method, in which the secondary flow coefficient was introduced to take account in to the effect of the secondary flow. The modeling results agree well with the expermiental results from science and engineering research council-flood channel facility (SERC-FCF), based on which the effect of geography on the secondary flow coefficient is analyzed, as well as the essential reason for such effects. The modeling results show that the in tensity of the secondary flow is related with the geometry of the compound channel section, and the sign of Kvalue is related with the rotating direction of the secondary flow cell, which proposes scien tific reference for the selecting of Kvalue.
Boundary-Layer Eigen Solutions for Multi-Field Coupled Equations in the Contact Interface
HOU Lei, LI Han-ling, ZHANG Jia-jian, LIN De-zhi, QIU Lin
2010, 31(6): 690-702. doi: 10.3879/j.issn.1000-0887.2010.06.006
Abstract(1541) PDF(630)
Abstract:
The dissipative equilibrium dynamics studied the law of fluid motion under constraints in the contact in terface of the coupling system. It needed to examine how constraints actupon the fluid movement, while the fluid movement reacted to the constraint field. It also needed to examine the coupling fluid field and media with in the contact in terface, and to use the multi-scale analys is to solve the regular and singular perturbation problems in micro-phenomen a of laboratories and macro-phenomena of nature. The field affected by the gravity constraints was described. A pplying the multi-scale analysis to the complex Fourier harmonic analysis, scale changes, and the in troduction of new parameters, the complex threed miensional coupling dynamic equations were trans formed in to a boundary layer problem in the one-dimensional complex space. Asymptotic analys is was carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples were given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further an alysis and calculation on non-lineare igenfunctions of the contact in terface dynamic problems by the eigenvalue relation, anasymptotic perturbation solution was obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact in terface was obtained by asymptotic estmiates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact in terface.
Lag Synchronization Between Discrete Chaotic Systems With Diverse Structure
CHAI Yuan, LÜ Ling, ZHAO Hong-yan
2010, 31(6): 703-709. doi: 10.3879/j.issn.1000-0887.2010.06.007
Abstract(1609) PDF(818)
Abstract:
A lag synchron ization controller was designed to discuss discrete chaotic systems with diverse structures and to realize syn chronization between Henon system and Ikeda system. The structure of the lag synchronization controller and the error equations of state variables between discrete chaotic systems were presented on the basis of stability theory. The designed controller had unique structures for different chaotic systems, and lagsynchronization between any discrete chaotic systems with diverse structures could be achieved. The artificial smiulation results show that this control method is effective and feasible.
Dynamic Bifurcation of the n-Dimensional Complex Swift-Hohenberg Equation
XIAO Qing-kun, GAO Hong-jun
2010, 31(6): 710-721. doi: 10.3879/j.issn.1000-0887.2010.06.008
Abstract(1394) PDF(767)
Abstract:
The bifurcation of the complex Swif-tHohenberg equation was considered. A ttractor bifurcation of the complex S wift-Hohenberg equation on a one-dmiensional domain (0, L) was investigated. It's also shown that then-dmiens ionalcomplex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general doma in and under the periodic boundary condition when the bifurcation parameter Kcrosses some critical value. The stability property of the bifurcation attractor is also analyzed.
On the Stability of Equilibria of Nonholonomic Systems With Nonlinear Constraints
V. Čović, M. Vesković, D. Djuri, A. Obradović
2010, 31(6): 722-723. doi: 10.3879/j.issn.1000-0887.2010.06.009
Abstract(1565) PDF(885)
Abstract:
Liapunov's first method, extended by Kozlov to non linearm echanical systems, was applied to the study of the in stability of the position of equilibrium of amechanical system moving in the field of conservative and dissipative forces. The motion of the system was lmiited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first non trivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of non linear nonholonomic constraints were analyzed. In the three cases the theoremon the instability of the position of equilibrium of non holonomic systems with linear homogeneous constraints (Kozlov (1986)) was generalized to the case of non linear nonhom ogeneous constraints. In the other two cases new theorems were setextending the result from Kozlov (1994) to nonholonomic systems with non linear constraints.
Weighted Estimates for Strongly Singular Integral Operators With Rough Kernels
HUANG Wen-li, TAO Xiang-xing, LI Sheng-hong
2010, 31(6): 731-738. doi: 10.3879/j.issn.1000-0887.2010.06.010
Abstract(1328) PDF(735)
Abstract:
The Fourier trans form and Little wood-Paley theory were used to give the weighted boundedness of the strongly singular in tegraloperator. It is shown that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.
Singularly Perturbed Reaction Diffusion Equations With Time Delay
MO Jia-qi, WEN Zhao-hui
2010, 31(6): 739-744. doi: 10.3879/j.issn.1000-0887.2010.06.011
Abstract(1685) PDF(777)
Abstract:
A class of differential difference reaction diffusion equations initial boundary problem with a small time delay was considered. Under suitable conditions and by using method of the stretched variable, the formal asymptotic solution was constructed. And then, by using the theory of differential inequalities, the uniformly validity of solution was proved.
Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System
XU Chang-jin, TANG Xian-hua, LIAO Mao-xin
2010, 31(6): 745-755. doi: 10.3879/j.issn.1000-0887.2010.06.012
Abstract(1355) PDF(844)
Abstract:
The dynamics of a TCP system described by a firs-torder non linear delay differential equations was investigated. Byanalyzing the associated characteristic tran scendental equation, the result thata sequence of Hopf bifurcations occurat the positive equilibrium as the delay passesth rough a sequence of critical values was obtained. Explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were derived by using the normal form theory and center manifold theory. Global existence of periodic solutions was also established by using the method of Wu [Trans Amer Math Soc, 1998, 350(12):4799-38].
Blow-up Rate Estimate for Degenerate Parabolic Equation With Nonlinear Gradient Term
ZHANG Zheng-ce, WANG Biao
2010, 31(6): 756-764. doi: 10.3879/j.issn.1000-0887.2010.06.013
Abstract(1451) PDF(739)
Abstract:
Blow-up rate was obtained for a porous medium equation with non linear gradient term and a non linear boundary flux. By using the scaling method and the regularity estmiates of parabolic equations, the blow-up rate which was deter mined by the interaction between the diffusion and the boundary flux was gotten. Interestingly, compared with the previous results, the gradientterm which exponent does not exceed 2 will not affect the blow-up rate for solutions.