By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong...By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong inhibition of the same time, support the weak” (抑强扶弱) based on “Yin Yang Wu Xing” Theory in image mathematics of Traditional Chinese Mathematics (TCMath). We defined generalized relations and generalized reasoning, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the intervention principle in image mathematics of TCMath and treated the research object of the image mathematics as a steady multilateral system, it has been proved that the mathematical intervening principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.展开更多
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equa- tions, which can be called attractor bifurcation. It is proved that as the control pa- rameter crosses certain critical value, the sy...The authors introduce a notion of dynamic bifurcation for nonlinear evolution equa- tions, which can be called attractor bifurcation. It is proved that as the control pa- rameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a uni?ed point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.展开更多
This present paper describes three dimensional computational analysis of complex internal flow in a cross flow fan. A commercial computational fluid dynamics (CFD) software code CFX was used for the computation. RNG k...This present paper describes three dimensional computational analysis of complex internal flow in a cross flow fan. A commercial computational fluid dynamics (CFD) software code CFX was used for the computation. RNG k-ε two equation turbulence model was used to simulate the model with unstructured mesh. Sliding mesh interface was used at the interface between the rotating and stationary domains to capture the unsteady interactions. An accurate assessment of the present investigation is made by comparing various parameters with the available experimental data. Three impeller geometries with different blade angles and radius ratio are used in the present study. Maximum energy transfer through the impeller takes place in the region where the flow follows the blade curvature. Radial velocity is not uniform through blade channels. Some blades work in turbine mode at very low flow coefficients. Static pressure is always negative in and around the impeller region.展开更多
An iterative optimization strategy is proposed and applied to the steady state optimizing control of the bio-dissimilation process of glycerol to 1,3-propanediol in the presence of model-plant mismatch and input const...An iterative optimization strategy is proposed and applied to the steady state optimizing control of the bio-dissimilation process of glycerol to 1,3-propanediol in the presence of model-plant mismatch and input constraints. The scheme is based on the Augmented Integrated System Optimization and Parameter Estimation （AI- SOPE） technique, but a linearization of some performance function in the modified model-based optimization problem of AISOPE is introduced to overcome the difficulty of determining an appropriate penalty parameter. When carrying out the iterative optimization, the penalty coefficient is set to a larger value at the current iteration than at the previous iteration, which can promote the evolution rate of the iterative optimization. Simulation studies illustrate the potential ofthe approach presented for the optimizing control of the bioTdissimilation process of glycerol to 1,3-propanediol. The effects of measurement noise, measured and unmeasured disturbances on the proposed algorithm are also investigated.展开更多
The effect of cooling rate during quenching on the microstructure and creep property of nickel-based superalloy FGH96 was investigated. Three groups of samples were quenched continuously with three fixed cooling rates...The effect of cooling rate during quenching on the microstructure and creep property of nickel-based superalloy FGH96 was investigated. Three groups of samples were quenched continuously with three fixed cooling rates, respectively, then subjected to a creep test under a constant load of 690 MPa at 700℃. Clear differences in size of secondary γ′ precipitates, creep properties and substructure of creep-tested samples were observed. The quantitative relationship among cooling rate, the size of secondary γ′ precipitates, and steady creep rate was constructed. It was found that with increasing cooling rate, the size of secondary γ′ precipitates decreases gradually, showing that the relationship between the size of secondary γ′ precipitates and the cooling rate obeys a power law, with an exponent of about –0.6, and the creep rate of steady state follows a good parabola relationship with cooling γ′ precipitate size. For 235℃/min, FGH96 alloy exhibited very small steady creep rate. The density of dislocation was low, and the isolated stacking fault was the dominant deformation mechanism. With decreasing cooling rates, the density of dislocation increased remarkably, and deformation microtwinning was the dominant deformation process. Detailed mechanisms for different cooling rate were discussed.展开更多
In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of th...In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.展开更多
文摘By using mathematical reasoning, this paper demonstrates the mathematical intervening principle: “Virtual disease is to fill his mother but real disease is to rush down his son” (虚则补其母, 实则泄其子) and “Strong inhibition of the same time, support the weak” (抑强扶弱) based on “Yin Yang Wu Xing” Theory in image mathematics of Traditional Chinese Mathematics (TCMath). We defined generalized relations and generalized reasoning, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the intervention principle in image mathematics of TCMath and treated the research object of the image mathematics as a steady multilateral system, it has been proved that the mathematical intervening principle is true. The kernel of this paper is the existence and reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.
基金Project supported by the Office of Naval Research,the National Science Foundation,and the National Natural Science Foundation of China (No.19971062).
文摘The authors introduce a notion of dynamic bifurcation for nonlinear evolution equa- tions, which can be called attractor bifurcation. It is proved that as the control pa- rameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a uni?ed point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
文摘This present paper describes three dimensional computational analysis of complex internal flow in a cross flow fan. A commercial computational fluid dynamics (CFD) software code CFX was used for the computation. RNG k-ε two equation turbulence model was used to simulate the model with unstructured mesh. Sliding mesh interface was used at the interface between the rotating and stationary domains to capture the unsteady interactions. An accurate assessment of the present investigation is made by comparing various parameters with the available experimental data. Three impeller geometries with different blade angles and radius ratio are used in the present study. Maximum energy transfer through the impeller takes place in the region where the flow follows the blade curvature. Radial velocity is not uniform through blade channels. Some blades work in turbine mode at very low flow coefficients. Static pressure is always negative in and around the impeller region.
基金the State Science and Technology Project of China (No.2001BA204B01).
文摘An iterative optimization strategy is proposed and applied to the steady state optimizing control of the bio-dissimilation process of glycerol to 1,3-propanediol in the presence of model-plant mismatch and input constraints. The scheme is based on the Augmented Integrated System Optimization and Parameter Estimation （AI- SOPE） technique, but a linearization of some performance function in the modified model-based optimization problem of AISOPE is introduced to overcome the difficulty of determining an appropriate penalty parameter. When carrying out the iterative optimization, the penalty coefficient is set to a larger value at the current iteration than at the previous iteration, which can promote the evolution rate of the iterative optimization. Simulation studies illustrate the potential ofthe approach presented for the optimizing control of the bioTdissimilation process of glycerol to 1,3-propanediol. The effects of measurement noise, measured and unmeasured disturbances on the proposed algorithm are also investigated.
基金financially supported by the National Material Special Program of China (No. JPPT-F2008-5-1)
文摘The effect of cooling rate during quenching on the microstructure and creep property of nickel-based superalloy FGH96 was investigated. Three groups of samples were quenched continuously with three fixed cooling rates, respectively, then subjected to a creep test under a constant load of 690 MPa at 700℃. Clear differences in size of secondary γ′ precipitates, creep properties and substructure of creep-tested samples were observed. The quantitative relationship among cooling rate, the size of secondary γ′ precipitates, and steady creep rate was constructed. It was found that with increasing cooling rate, the size of secondary γ′ precipitates decreases gradually, showing that the relationship between the size of secondary γ′ precipitates and the cooling rate obeys a power law, with an exponent of about –0.6, and the creep rate of steady state follows a good parabola relationship with cooling γ′ precipitate size. For 235℃/min, FGH96 alloy exhibited very small steady creep rate. The density of dislocation was low, and the isolated stacking fault was the dominant deformation mechanism. With decreasing cooling rates, the density of dislocation increased remarkably, and deformation microtwinning was the dominant deformation process. Detailed mechanisms for different cooling rate were discussed.
基金the National Natural Science Foundation of China 10471022the Ministry of Education of China Science and Technology Major Projects Grant 104090the Foundation of Excellent Doctoral Disscrtation of Southeast University YBJJ0405
文摘In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.
