The asymptotic behavior of solutions of a similarity equation for the laminar flow in a porous channel with suction at both expanding and contracting walls has been obtained by using a singular perturbation method.How...The asymptotic behavior of solutions of a similarity equation for the laminar flow in a porous channel with suction at both expanding and contracting walls has been obtained by using a singular perturbation method.However,in the matching process,this solution neglects exponentially small terms.To take into account these exponentially small terms,a method involving the inclusion of exponentially small terms in a perturbation series was used to find two of the solutions analytically.The series involving the exponentially small terms and expansion ratio predicts dual solutions.Furthermore,the result indicates that the expansion ratio has much important influence on the solutions.展开更多
The maximum bending moment or curvature in the neighborhood of the touch down point(TDP)and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure...The maximum bending moment or curvature in the neighborhood of the touch down point(TDP)and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure the safety of the pipe-laying operation and the normal operation of the pipelines.In this paper,the non-linear governing differential equation for getting the two parameters during J-lay installation is proposed and solved by use of singular perturbation technique,from which the asymptotic expression of stiffened catenary is obtained and the theoretical expression of its static geometric configuration as well as axial tension and bending moment is derived.Finite element results are applied to verify this method.Parametric investigation is conducted to analyze the influences of the seabed slope,unit weight,flexural stiffness,water depth,and the pipe-laying tower angle on the maximum tension and moment of pipeline by this method,and the results show how to control the installation process by changing individual parameters.展开更多
We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the f...We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the flux terms. We present a concrete example occurring in flow of steam, nitrogen and water in porous media and an abstract example for a class of systems of three equations. In the concrete example the zero-order equations resulting from the expansion yield a type of conservation law system called compositional model in Petroleum Engineering. In this work we show how compositional models originate from physically more fundamental systems of balance laws. Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.展开更多
In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed ...In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters. The asymptotic solutions of the problem are given.展开更多
Time-delay efects on the dynamics of Li′enard type equation with one fast variable and one slow variable are investigated in the present paper.By using the methods of stability switch and geometric singular perturbat...Time-delay efects on the dynamics of Li′enard type equation with one fast variable and one slow variable are investigated in the present paper.By using the methods of stability switch and geometric singular perturbation,time-delay-induced complex oscillations and bursting are investigated,and in several case studies,the mechanism of the generation of the complex oscillations and bursting is illuminated.Numerical results demonstrate the validity of the theoretical results.展开更多
The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement of the asset price and real market data can find a non-flat structure...The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement of the asset price and real market data can find a non-flat structure of the implied volatility surface. So, in this paper, we formulate an underlying asset model by adding a delayed structure to the constant elasticity of variance(CEV) model that is one of renowned alternative models resolving the geometric issue. However, it is still one factor volatility model which usually does not capture full dynamics of the volatility showing discrepancy between its predicted price and market price for certain range of options. Based on this observation we combine a stochastic volatility factor with the delayed CEV structure and develop a delayed hybrid model of stochastic and local volatilities. Using both a martingale approach and a singular perturbation method, we demonstrate the delayed CEV correction effects on the European vanilla option price under this hybrid volatility model as a direct extension of our previous work [12].展开更多
文摘The asymptotic behavior of solutions of a similarity equation for the laminar flow in a porous channel with suction at both expanding and contracting walls has been obtained by using a singular perturbation method.However,in the matching process,this solution neglects exponentially small terms.To take into account these exponentially small terms,a method involving the inclusion of exponentially small terms in a perturbation series was used to find two of the solutions analytically.The series involving the exponentially small terms and expansion ratio predicts dual solutions.Furthermore,the result indicates that the expansion ratio has much important influence on the solutions.
基金financially supported by the National Basic Research Program of China(Grant No.2011CB013702)the National Natural Science Foundation of China(Grant No.50979113).1
文摘The maximum bending moment or curvature in the neighborhood of the touch down point(TDP)and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure the safety of the pipe-laying operation and the normal operation of the pipelines.In this paper,the non-linear governing differential equation for getting the two parameters during J-lay installation is proposed and solved by use of singular perturbation technique,from which the asymptotic expression of stiffened catenary is obtained and the theoretical expression of its static geometric configuration as well as axial tension and bending moment is derived.Finite element results are applied to verify this method.Parametric investigation is conducted to analyze the influences of the seabed slope,unit weight,flexural stiffness,water depth,and the pipe-laying tower angle on the maximum tension and moment of pipeline by this method,and the results show how to control the installation process by changing individual parameters.
基金supported in part by: CNPq under grant 141573/2002-3,ANP/PRH-32CNPq under Grant 301532/2003-6+2 种基金FAPERJ under Grant E-26/152.163/2002FINEP underCTPETRO Grant 21.01.0248.00PETROBRAS under CTPETRO Grant 650.4.039.01.0, Brazil
文摘We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the flux terms. We present a concrete example occurring in flow of steam, nitrogen and water in porous media and an abstract example for a class of systems of three equations. In the concrete example the zero-order equations resulting from the expansion yield a type of conservation law system called compositional model in Petroleum Engineering. In this work we show how compositional models originate from physically more fundamental systems of balance laws. Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.
基金supported by the National Natural Science Foundation of China (Nos. 40676016, 40876010)the Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+1 种基金the LASG State Key Laboratory Special Fundthe E-Institute of Shanghai Municipal Education Commission (No. E03004)
文摘In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters. The asymptotic solutions of the problem are given.
基金supported by the National Natural Science Foundation of China(11102078 and 11032009)Foundation of Jiangxi Education Committee of China(GJJ1169)
文摘Time-delay efects on the dynamics of Li′enard type equation with one fast variable and one slow variable are investigated in the present paper.By using the methods of stability switch and geometric singular perturbation,time-delay-induced complex oscillations and bursting are investigated,and in several case studies,the mechanism of the generation of the complex oscillations and bursting is illuminated.Numerical results demonstrate the validity of the theoretical results.
基金supported by the National Research Foundation of Korea NRF-2013R1A1A2A10006693
文摘The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement of the asset price and real market data can find a non-flat structure of the implied volatility surface. So, in this paper, we formulate an underlying asset model by adding a delayed structure to the constant elasticity of variance(CEV) model that is one of renowned alternative models resolving the geometric issue. However, it is still one factor volatility model which usually does not capture full dynamics of the volatility showing discrepancy between its predicted price and market price for certain range of options. Based on this observation we combine a stochastic volatility factor with the delayed CEV structure and develop a delayed hybrid model of stochastic and local volatilities. Using both a martingale approach and a singular perturbation method, we demonstrate the delayed CEV correction effects on the European vanilla option price under this hybrid volatility model as a direct extension of our previous work [12].
