Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system ...Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system of the ARPS（Advanced Regional Prediction System） model.A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures.Results indicate that,compared with calculating the results using two previous methods,the lightning density calculated using the new method presented in this study is in better accordance with observations.Based on the calculated lightning densities using the new method,it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs,where the surface wind field converged intensely.The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it,and their lightning events mainly occurred in regions with a large gradient of CAPE.Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions;the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different;and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.展开更多
The existing torque roll axis(TRA) decoupling theories for a powertrain mounting system assume that the stiffness and viscous damping properties are constant. However, real-life mounts exhibit considerable spectrally ...The existing torque roll axis(TRA) decoupling theories for a powertrain mounting system assume that the stiffness and viscous damping properties are constant. However, real-life mounts exhibit considerable spectrally varying stiffness and damping characteristics, and the influence of the spectrally-varying properties of the hydraulic mounts on the powertrain system cannot be ignored. To overcome the deficiency, an analytical quasi-linear model of the hydraulic mount and the coupled properties of the powertrain and hydraulic mounts system are formulated. The influence of the hydraulic mounts on the TRA decoupling of a powertrain system is analytically examined in terms of eigensolutions, frequency, and impulse responses, and then a new analytical axiom is proposed based on the TRA decoupling indices. With the experimental setup of a fixed decoupler hydraulic mount in the context of non-resonant dynamic stiffness testing procedure, the quasi-linear model of the hydraulic mount is verified by comparing the predictions with the measurement. And the quasi-linear formulation of the coupled system is also verified by comparing the frequency responses with the numerical results obtained by the direct inversion method. Finally, the mounting system with a combination of hydraulic mounts is redesigned in terms of the stiffness, damping and mount locations by satisfying the new axiom. The frequency and time domain results of the redesigned system demonstrate that the torque roll axis of the redesigned powertrain mounting system is indeed decoupled in the presence of hydraulic mounts (given oscillating torque or impulsive torque excitation). The proposed research provides an important basis and method for the research on a powertrain system with spectrally-varying mount properties, especially for the TRA decoupling.展开更多
In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interfa...In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.展开更多
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ...In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.展开更多
In this paper, we prove a new fixed point theorem in cones and obtain the existence of triple positive solutions for a class of quasi-linear three-point boundary value problems.
In this paper, we investigate the perturbation problem for the Moore-Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysi...In this paper, we investigate the perturbation problem for the Moore-Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysis of bounded quasi-linear operators, we obtain an explicit perturbation theorem and error estimates for the Moore-Penrose bounded quasi-linear generalized inverse of closed linear operator under the T-bounded perturbation, which not only extend some known results on the perturbation of the oblique projection generalized inverse of closed linear operators, but also extend some known results on the perturbation of the Moore-Penrose metric generalized inverse of bounded linear operators in Banach spaces.展开更多
We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the ...We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.展开更多
The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radia...The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.展开更多
The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions...The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions of the nonlinear difference system with intrinsic parallelism are proved The limiting vector function is just the unique generalized solution of the original problem for the parabolic system展开更多
In this study,we have analyzedfluid mobility and thermal transport of the SiO_(2)/kerosene nanofluid within two rotating stretchable disks.The top disk is simulated to be oscil-lating with a periodic velocity and sque...In this study,we have analyzedfluid mobility and thermal transport of the SiO_(2)/kerosene nanofluid within two rotating stretchable disks.The top disk is simulated to be oscil-lating with a periodic velocity and squeezing continuously the nanofluid within a porous me-dium and making thefluid toflow perpendicularly to the situated magneticfield.Thermal radiation effects are considered in the heat transfer model.The non-linear(NL)PDEs that describe the nanofluid mobility structure and thermal transport are transformed into system of NL-ODEs by introducing adequately suitable non-dimensional variables after which the NL-ODEs were numerically solved via spectral quasi-linearization method(SQLM)on over-lapping grids.The consequences of several pertinent parameters of the model on pressure,tem-perature,velocity,skin drag coefficient and thermal transport rate are examined and elucidated in detail with the aid offigures and tables.It was found that theflow structure with prescribing conditions develops negative pressure situation which has vast applications in modern day medical engineering,especially in the construction of air pressure stabilizers used in medical isolation and wound therapy physiology.展开更多
基金supported jointly by the National Key Basic Research and Development (973) Program of China (Grant No. 2014CB441401)the National Natural Science Foundation of China (Grant Nos. 41405007, 41175043, 41475002, and 41205027)
文摘Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system of the ARPS（Advanced Regional Prediction System） model.A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures.Results indicate that,compared with calculating the results using two previous methods,the lightning density calculated using the new method presented in this study is in better accordance with observations.Based on the calculated lightning densities using the new method,it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs,where the surface wind field converged intensely.The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it,and their lightning events mainly occurred in regions with a large gradient of CAPE.Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions;the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different;and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.
基金supported by National Natural Science Foundation of China (Grant Nos. 51075112, 51175135)Fundamental Research Funds for the Central Universities of China (Grant Nos. 2012HGBZ0618,2013HGBH0008)
文摘The existing torque roll axis(TRA) decoupling theories for a powertrain mounting system assume that the stiffness and viscous damping properties are constant. However, real-life mounts exhibit considerable spectrally varying stiffness and damping characteristics, and the influence of the spectrally-varying properties of the hydraulic mounts on the powertrain system cannot be ignored. To overcome the deficiency, an analytical quasi-linear model of the hydraulic mount and the coupled properties of the powertrain and hydraulic mounts system are formulated. The influence of the hydraulic mounts on the TRA decoupling of a powertrain system is analytically examined in terms of eigensolutions, frequency, and impulse responses, and then a new analytical axiom is proposed based on the TRA decoupling indices. With the experimental setup of a fixed decoupler hydraulic mount in the context of non-resonant dynamic stiffness testing procedure, the quasi-linear model of the hydraulic mount is verified by comparing the predictions with the measurement. And the quasi-linear formulation of the coupled system is also verified by comparing the frequency responses with the numerical results obtained by the direct inversion method. Finally, the mounting system with a combination of hydraulic mounts is redesigned in terms of the stiffness, damping and mount locations by satisfying the new axiom. The frequency and time domain results of the redesigned system demonstrate that the torque roll axis of the redesigned powertrain mounting system is indeed decoupled in the presence of hydraulic mounts (given oscillating torque or impulsive torque excitation). The proposed research provides an important basis and method for the research on a powertrain system with spectrally-varying mount properties, especially for the TRA decoupling.
基金This work was supported by the Special Funds for Major State Basic Research Projects (Grant No.2005CB321703)the National Natural Science Foundation of China (Grant Nos. 10476002, 60533020)the Science Foundation of CAEP (Grant No. 20060649)
文摘In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.
文摘In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.
基金Supported by the National Natural Science Foundation of China （No. 10371006） and the Postdoctoral Foundation of China
文摘In this paper, we prove a new fixed point theorem in cones and obtain the existence of triple positive solutions for a class of quasi-linear three-point boundary value problems.
基金Supported by National Nature Science Foundation of China(Grant No.11471091)
文摘In this paper, we investigate the perturbation problem for the Moore-Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysis of bounded quasi-linear operators, we obtain an explicit perturbation theorem and error estimates for the Moore-Penrose bounded quasi-linear generalized inverse of closed linear operator under the T-bounded perturbation, which not only extend some known results on the perturbation of the oblique projection generalized inverse of closed linear operators, but also extend some known results on the perturbation of the Moore-Penrose metric generalized inverse of bounded linear operators in Banach spaces.
基金The first author is partly supported by National Natural Science Foundation of China （Grants Nos. 10801029 and 10911120384）, FANEDD, Shanghai Rising Star Program （10QA1400300）, SGST 09DZ2272900 and SRF for ROCS, SEM the second author is partly supported by an NSF grant the third author is partly supported by the National Natural Science Foundation of China （Crant No. 10728101）, the 973 project of the Ministry of Science and Technology of China, the Doctoral Program Foundation of the Ministry of Education of China, the ＂111＂ project （B08018） and SGST 09DZ2272900Acknowledgements Part of the work was carried out when Zhen Lei was visiting the Courant Institute. He would like to thank Professor Fanghua Lin for his hospitality.
文摘We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.
文摘The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.
基金Project supported by the National Natural Science Foundation of China and the Foundation of Chinese Academy of Engineering Physics.
文摘The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions of the nonlinear difference system with intrinsic parallelism are proved The limiting vector function is just the unique generalized solution of the original problem for the parabolic system
文摘In this study,we have analyzedfluid mobility and thermal transport of the SiO_(2)/kerosene nanofluid within two rotating stretchable disks.The top disk is simulated to be oscil-lating with a periodic velocity and squeezing continuously the nanofluid within a porous me-dium and making thefluid toflow perpendicularly to the situated magneticfield.Thermal radiation effects are considered in the heat transfer model.The non-linear(NL)PDEs that describe the nanofluid mobility structure and thermal transport are transformed into system of NL-ODEs by introducing adequately suitable non-dimensional variables after which the NL-ODEs were numerically solved via spectral quasi-linearization method(SQLM)on over-lapping grids.The consequences of several pertinent parameters of the model on pressure,tem-perature,velocity,skin drag coefficient and thermal transport rate are examined and elucidated in detail with the aid offigures and tables.It was found that theflow structure with prescribing conditions develops negative pressure situation which has vast applications in modern day medical engineering,especially in the construction of air pressure stabilizers used in medical isolation and wound therapy physiology.
