In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for ...In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.展开更多
An experimental investigation was performed for active control of coherent structure bursting in the near-wall region of the turbulent boundary layer. By means of synchronous and asynchronous vibrations with double pi...An experimental investigation was performed for active control of coherent structure bursting in the near-wall region of the turbulent boundary layer. By means of synchronous and asynchronous vibrations with double piezoelectric vibrators, the influence of periodic vibration of the double piezoelectric vibrators on the mean velocity profile, drag reduction rate, and coherent structure bursting is analyzed at Reo = 2766. The case with 100 V/160 Hz-ASYN is superior to other conditions in the experiment and a relative drag reduction rate of 18.54% is exciting. Asynchronous vibration is more effective than synchronous vibration in drag reduction at the same voltage and frequency. In all controlled cases, coherent structures at large scales are regulated while the small-scale structures are stimulated. The fluctuating velocity increases significantly. A periodic regulating effect on the coherent structure can be seen in the ASYN control conditions at the frequency of 160 Hz.展开更多
Error estimates of Galerkin method for Kuramoto-Sivashingsky (K-S) equation in space dimension ≥3 are derived in the paper. These results furnish strong evidence for the computation of the solutions.
In this paper we prove that the asymptotic rate of convergence of the mod-ified Gauss-Seidel method of a non-singular M-matrix is a monotonic function for precondition parameters 0 ≤ αi ≤ 1-2,(i = 1,2,… ,n- 1).
Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or (S F , S F ) are function P-sets. Function P-sets have dynamic characteristics and law charac...Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or (S F , S F ) are function P-sets. Function P-sets have dynamic characteristics and law characteristics. Based on function P-sets, P-information law discovery theorems which has attribute supplementing-deleting are given. Mining-discovery and mining-discovery theorems of unknown information law are proposed. Function P-sets are a new theory and new method to research dynamic information laws for information systems.展开更多
In this paper,we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition.The main idea is to use traditional finite element method on se...In this paper,we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition.The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton’s method to handle nonlinearity.It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem.Numerical experiments show that our method is about second order accurate in the L1 norm.展开更多
In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.T...In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.The manufacturer needs to determine which jobs should be produced in-house and which jobs should be subcontracted.Furthermore,it needs to determine a production schedule for jobs to be produced in-house.We discuss five classical scheduling objectives as production costs.For each problem with different objective functions,we give optimality conditions and propose dynamic programming algorithms.展开更多
The numerical methods for miscible displacment in aggregated or sorbing medium are considered. A mixed finite element method is adopted for the pressure equation. The concentration in the mobile water is approximated ...The numerical methods for miscible displacment in aggregated or sorbing medium are considered. A mixed finite element method is adopted for the pressure equation. The concentration in the mobile water is approximated by a combination of a Galerkin finite element method and the method of characteristics and the concentration in immobile water is approximated by a standard Galerkin method. The moving mesh technique which depends on time t is adopted here. The moving meshes can vary in different spacial domains with different variable times. Optima error estimates in energy norm and L2 norm are obtained under certain constraints.展开更多
It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of s...It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO.展开更多
A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method...A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implementation in a manner of p-adaptivity. A coarse solution is obtained from solving the model problem in the low order spline space, and the solution with higher accuracy are generated subsequently, via one step Newton or monidifed Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.展开更多
基金supported by the Zhejiang Natural Science Foundation of China(LQ13A010022)supported by the Qianjiang professorship of Zhejiang Province of Chinathe National Natural Science Foundation of China(11271105)
文摘In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11332006,11732010,11572221,and 11502066)
文摘An experimental investigation was performed for active control of coherent structure bursting in the near-wall region of the turbulent boundary layer. By means of synchronous and asynchronous vibrations with double piezoelectric vibrators, the influence of periodic vibration of the double piezoelectric vibrators on the mean velocity profile, drag reduction rate, and coherent structure bursting is analyzed at Reo = 2766. The case with 100 V/160 Hz-ASYN is superior to other conditions in the experiment and a relative drag reduction rate of 18.54% is exciting. Asynchronous vibration is more effective than synchronous vibration in drag reduction at the same voltage and frequency. In all controlled cases, coherent structures at large scales are regulated while the small-scale structures are stimulated. The fluctuating velocity increases significantly. A periodic regulating effect on the coherent structure can be seen in the ASYN control conditions at the frequency of 160 Hz.
文摘Error estimates of Galerkin method for Kuramoto-Sivashingsky (K-S) equation in space dimension ≥3 are derived in the paper. These results furnish strong evidence for the computation of the solutions.
文摘In this paper we prove that the asymptotic rate of convergence of the mod-ified Gauss-Seidel method of a non-singular M-matrix is a monotonic function for precondition parameters 0 ≤ αi ≤ 1-2,(i = 1,2,… ,n- 1).
基金Supported by the Elementary and Advanced Technology Foundation of Henan Province(082300410040, 102300410153)
文摘Function P-sets are a set pair which are composed of function internal packetsets S F and function outer packet sets S F or (S F , S F ) are function P-sets. Function P-sets have dynamic characteristics and law characteristics. Based on function P-sets, P-information law discovery theorems which has attribute supplementing-deleting are given. Mining-discovery and mining-discovery theorems of unknown information law are proposed. Function P-sets are a new theory and new method to research dynamic information laws for information systems.
基金L.Shi’s research is supported by National Natural Science Foundation of China(No.11701569)S.Hou’s research is supported by Dr.Walter Koss Professorship made available through Louisiana Board of RegentsL.Wang’s research is supported by Science Foundations of China University of Petroleum-Beijing(No.2462015BJB05).
文摘In this paper,we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition.The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton’s method to handle nonlinearity.It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem.Numerical experiments show that our method is about second order accurate in the L1 norm.
基金Supported by the National Natural Science Foundation of China(70731160015)Supported the National Natural Science Foundation of Jiangsu Province(yw06037)
文摘In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.The manufacturer needs to determine which jobs should be produced in-house and which jobs should be subcontracted.Furthermore,it needs to determine a production schedule for jobs to be produced in-house.We discuss five classical scheduling objectives as production costs.For each problem with different objective functions,we give optimality conditions and propose dynamic programming algorithms.
文摘The numerical methods for miscible displacment in aggregated or sorbing medium are considered. A mixed finite element method is adopted for the pressure equation. The concentration in the mobile water is approximated by a combination of a Galerkin finite element method and the method of characteristics and the concentration in immobile water is approximated by a standard Galerkin method. The moving mesh technique which depends on time t is adopted here. The moving meshes can vary in different spacial domains with different variable times. Optima error estimates in energy norm and L2 norm are obtained under certain constraints.
文摘It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO.
文摘A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implementation in a manner of p-adaptivity. A coarse solution is obtained from solving the model problem in the low order spline space, and the solution with higher accuracy are generated subsequently, via one step Newton or monidifed Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.
