An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for ...An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.展开更多
This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commens...This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.展开更多
In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations(PDEs). The solution of this kind of PDEs may encoun...In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations(PDEs). The solution of this kind of PDEs may encounter smooth transitions, or there can be large gradients of the field variables. The numerical challenge posed in a shock situation is that high-order finite difference schemes lead to significant oscillations in the vicinity of shocks despite that such schemes result in higher accuracy in smooth regions. On the other hand, first-order methods provide monotonic solution convergences near the shocks,while giving poorer accuracy in the smooth regions.Accurate numerical simulation of such systems is a challenging task using conventional numerical methods. In this paper, we investigate several shock-capturing schemes.The competency of each scheme was tested against onedimensional benchmark problems as well as published numerical experiments. The numerical results have shown good performance of high-resolution finite volume methods in capturing shocks by resolving discontinuities while maintaining accuracy in the smooth regions. Thesemethods along with Godunov splitting are applied to model proppant transport in fractures. It is concluded that the proposed scheme produces non-oscillatory and accurate results in obtaining a solution for proppant transport problems.展开更多
We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic...We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic Crank-Nicolson approximations in order to improve the time convergence. Schemes are proved to be unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to [（√17- 1）/2, 2] using the maximum modulus principle. A numerical example is given to confirm the theoretical analysis result.展开更多
With the characteristics such as low porosity, low permeability and low gas saturation, tight sandstone reservoirs almost have no natural capacity and need to be fractured (or fracturing) for productivity. Therefore, ...With the characteristics such as low porosity, low permeability and low gas saturation, tight sandstone reservoirs almost have no natural capacity and need to be fractured (or fracturing) for productivity. Therefore, fracturing capacity prediction is very necessary. However there were so many factors, and the relations between the factor and the post-frac productivity are complex. In this study, first of all factors are concluded from the gas well stable productivity formula, then I used factor analysis to look for the main factors from the logging parameters and fracturing parameters in SULIGE area. This study could provide basal references for the gas post-frac productivity prediction in tight sandstone reservoirs.展开更多
In this paper, woven fabrics of glass fiber/carbon fiber intra-hybrid in plain structure were used to fabricate fiber reinforced plastic (FRP) composite by hand lay-up method. The investigation on tensile property was...In this paper, woven fabrics of glass fiber/carbon fiber intra-hybrid in plain structure were used to fabricate fiber reinforced plastic (FRP) composite by hand lay-up method. The investigation on tensile property was carried out on specimens in 7 orientations including 0°/5°/15°/75°/85°/90° in previous works. With the specimen parameters and experimental data, FEM model was built by the software of Marc. By combining the experimental results and finite element analysis, the modulus was simulated and calculated at the first stage. Then interfacial stress of the 0 degree and 90 degree was also calculated. By the initial fracture stress data from experiment as well as the simulation value of interfacial strength of 0 and 90 degree, the initial fracture stress of the off-axial specimens wascalculated and predicted. The result shows that the interfacial strength of the glass fiber bundle is higher than that of the carbon fiber bundle in transverse direction. By using the interfacial strength and according to the Von Mises yielding criterion, the initial fracture stress was predicted, which can be a contribution to the design or predict of the material properties.展开更多
The FRACS parameterizations,labeled as FRACS-C,have been improved in order to predict the presence of isotopes near the proton drip line produced in projectile fragmentation reactions.By investigating the cross sectio...The FRACS parameterizations,labeled as FRACS-C,have been improved in order to predict the presence of isotopes near the proton drip line produced in projectile fragmentation reactions.By investigating the cross sections for proton-rich isotopes in a series of reactions with energies ranging from intermediate to relativistic,it is shown that the FRACS-C parameterizations can predict isotopes near the proton drip line considerably well.The FRACS-C parameterizations are suggested to serve as an effective tool for predicting the presence of proton-rich isotopes with large asymmetry in a projectile fragmentation reaction.Different reactions have been investigated to check these results.展开更多
In this paper, we introduce the fractional wavelet transformations （FrWT） involving Han- kel-Clifford integral transformation （HCIIT） on the positive half line and studied some of its basic properties. Also we obt...In this paper, we introduce the fractional wavelet transformations （FrWT） involving Han- kel-Clifford integral transformation （HCIIT） on the positive half line and studied some of its basic properties. Also we obtain Parseval＇s relation and an inversion formula. Examples of fractional powers of Hankel-Clifford integral transformation （FrHClIT） and FrWT are given. Then, we introduce the concept of fractional wavelet packet transformations FrBWPT and FrWPIT, and investigate their properties.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11171193 and11371229)the Natural Science Foundation of Shandong Province(No.ZR2014AM033)the Science and Technology Development Project of Shandong Province(No.2012GGB01198)
文摘An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.
基金supported by the National Natural Science Foundation of China(60674090)Shandong Natural Science Foundation(ZR2017QF016)
文摘This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.
基金the research funding for this study provided by NSERC through CRDPJ 387606-09
文摘In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations(PDEs). The solution of this kind of PDEs may encounter smooth transitions, or there can be large gradients of the field variables. The numerical challenge posed in a shock situation is that high-order finite difference schemes lead to significant oscillations in the vicinity of shocks despite that such schemes result in higher accuracy in smooth regions. On the other hand, first-order methods provide monotonic solution convergences near the shocks,while giving poorer accuracy in the smooth regions.Accurate numerical simulation of such systems is a challenging task using conventional numerical methods. In this paper, we investigate several shock-capturing schemes.The competency of each scheme was tested against onedimensional benchmark problems as well as published numerical experiments. The numerical results have shown good performance of high-resolution finite volume methods in capturing shocks by resolving discontinuities while maintaining accuracy in the smooth regions. Thesemethods along with Godunov splitting are applied to model proppant transport in fractures. It is concluded that the proposed scheme produces non-oscillatory and accurate results in obtaining a solution for proppant transport problems.
基金Supported by the National Natural Science Foundation of China(91330106,11171190,51269024,11161036)the National Nature Science Foundation of Ningxia(NZ14233)
文摘We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic Crank-Nicolson approximations in order to improve the time convergence. Schemes are proved to be unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to [（√17- 1）/2, 2] using the maximum modulus principle. A numerical example is given to confirm the theoretical analysis result.
文摘With the characteristics such as low porosity, low permeability and low gas saturation, tight sandstone reservoirs almost have no natural capacity and need to be fractured (or fracturing) for productivity. Therefore, fracturing capacity prediction is very necessary. However there were so many factors, and the relations between the factor and the post-frac productivity are complex. In this study, first of all factors are concluded from the gas well stable productivity formula, then I used factor analysis to look for the main factors from the logging parameters and fracturing parameters in SULIGE area. This study could provide basal references for the gas post-frac productivity prediction in tight sandstone reservoirs.
文摘In this paper, woven fabrics of glass fiber/carbon fiber intra-hybrid in plain structure were used to fabricate fiber reinforced plastic (FRP) composite by hand lay-up method. The investigation on tensile property was carried out on specimens in 7 orientations including 0°/5°/15°/75°/85°/90° in previous works. With the specimen parameters and experimental data, FEM model was built by the software of Marc. By combining the experimental results and finite element analysis, the modulus was simulated and calculated at the first stage. Then interfacial stress of the 0 degree and 90 degree was also calculated. By the initial fracture stress data from experiment as well as the simulation value of interfacial strength of 0 and 90 degree, the initial fracture stress of the off-axial specimens wascalculated and predicted. The result shows that the interfacial strength of the glass fiber bundle is higher than that of the carbon fiber bundle in transverse direction. By using the interfacial strength and according to the Von Mises yielding criterion, the initial fracture stress was predicted, which can be a contribution to the design or predict of the material properties.
基金partially supported by the National Natural Science Foundation of China(No.U1732135)the Key Research Program of Frontier Sciences of CAS(No.QYZDJSSW-SLH002)the Natural and Science Foundation in Henan Province(No.162300410179)
文摘The FRACS parameterizations,labeled as FRACS-C,have been improved in order to predict the presence of isotopes near the proton drip line produced in projectile fragmentation reactions.By investigating the cross sections for proton-rich isotopes in a series of reactions with energies ranging from intermediate to relativistic,it is shown that the FRACS-C parameterizations can predict isotopes near the proton drip line considerably well.The FRACS-C parameterizations are suggested to serve as an effective tool for predicting the presence of proton-rich isotopes with large asymmetry in a projectile fragmentation reaction.Different reactions have been investigated to check these results.
基金Supported by Govt. of India,Ministry of Science&Technology,DST(Grant No.DST/INSPIRE FELLOWSHIP/2012/479)
文摘In this paper, we introduce the fractional wavelet transformations （FrWT） involving Han- kel-Clifford integral transformation （HCIIT） on the positive half line and studied some of its basic properties. Also we obtain Parseval＇s relation and an inversion formula. Examples of fractional powers of Hankel-Clifford integral transformation （FrHClIT） and FrWT are given. Then, we introduce the concept of fractional wavelet packet transformations FrBWPT and FrWPIT, and investigate their properties.
