In this paper we prove Phragmen-Lindelof type alternative.for foe initial boundaryproblem of Stokes equation, i. e. we show that the energy expression for the solutionof the initial boundary problem must either grow e...In this paper we prove Phragmen-Lindelof type alternative.for foe initial boundaryproblem of Stokes equation, i. e. we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentiallywilh axial distance from the end of a semi-infinite strip. For the case of decay, we alsoestablish the pointwise estimate for the maximum module of the Stokes .flow andpresent a method for obtaining explicit bounds for the total energy.展开更多
Following Bagnold's approach, a relationship between sediment transport and energy dissipation is developed. The major assumption made in the study is that the near bed velocity plays a dominant role in the proces...Following Bagnold's approach, a relationship between sediment transport and energy dissipation is developed. The major assumption made in the study is that the near bed velocity plays a dominant role in the process of sediment transport. A general relationship between energy dissipation and sediment transport is first proposed. Then the equations for total sediment transport are derived by introducing the appropriate expression of energy dissipation rate under different conditions, such as open channel flows, combination of wave and current, as well as longshore sediment transport. Within the flows investigated, the derived relationships are fairly consistent with the available data over a wide range of conditions.展开更多
According to the analysis results of risk,economy and practical experiences for many years,the paper demonstrates that the great economic benifits can be got by reducing the design flood standard of energy dissipators...According to the analysis results of risk,economy and practical experiences for many years,the paper demonstrates that the great economic benifits can be got by reducing the design flood standard of energy dissipators and that the reduction of design flood standard is significant for reducing project investment and speeding project construction.展开更多
In this paper, we propose a class of stable finite difference schemes for the initial-boundary value problem of the Cahn-Hilliard equation. These schemes are proved to inherit the total mass conservation and energy di...In this paper, we propose a class of stable finite difference schemes for the initial-boundary value problem of the Cahn-Hilliard equation. These schemes are proved to inherit the total mass conservation and energy dissipation in the discrete level. The dissipation of the total energy implies boundness of the numerical solutions in the discrete H1 norm. This in turn implies boundedness of the numerical solutions in the maximum norm and hence the stability of the difference schemes. Unique existence of the numerical solutions is proved by the fixed-point theorem. Convergence rate of the class of finite difference schemes is proved to be O（h2 ＋ r2） with time step T and mesh size h. An efficient iterative algorithm for solving these nonlinear schemes is proposed and discussed in detail.展开更多
Damage zones of brittle-ductile (B-D) transition in PP/EPDM blends are studied in this paper. The contribution of crazing and shear yielding zones in damage zones to energy dissipation of blends was measured with comp...Damage zones of brittle-ductile (B-D) transition in PP/EPDM blends are studied in this paper. The contribution of crazing and shear yielding zones in damage zones to energy dissipation of blends was measured with computer image analysis (CIA) and the transition of shear yielding zone (A_(sh)) with rubber volume fraction (V_f) was also manipulated. Results showed that the B-D transition of impact strength of blends corresponded to the fracture mechanism in PP/EPDM blends, from matrix crazing to matrix shear yielding. In addition, two new parameters, density of energy dissipation for crazing zone (F_(cz)) and for shear yielding zone (F_(sh)), are first obtained in this paper. The value of F_(sh) is about four times larger than that of F_(cz) for PP/EPDM blends, which confirmed that the matrix shear yielding is a more effective way of energy dissipation in blends.展开更多
文摘In this paper we prove Phragmen-Lindelof type alternative.for foe initial boundaryproblem of Stokes equation, i. e. we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentiallywilh axial distance from the end of a semi-infinite strip. For the case of decay, we alsoestablish the pointwise estimate for the maximum module of the Stokes .flow andpresent a method for obtaining explicit bounds for the total energy.
文摘Following Bagnold's approach, a relationship between sediment transport and energy dissipation is developed. The major assumption made in the study is that the near bed velocity plays a dominant role in the process of sediment transport. A general relationship between energy dissipation and sediment transport is first proposed. Then the equations for total sediment transport are derived by introducing the appropriate expression of energy dissipation rate under different conditions, such as open channel flows, combination of wave and current, as well as longshore sediment transport. Within the flows investigated, the derived relationships are fairly consistent with the available data over a wide range of conditions.
文摘According to the analysis results of risk,economy and practical experiences for many years,the paper demonstrates that the great economic benifits can be got by reducing the design flood standard of energy dissipators and that the reduction of design flood standard is significant for reducing project investment and speeding project construction.
基金Supported by National Natural Science Foundation of China(Nos.11201239,11571181)
文摘In this paper, we propose a class of stable finite difference schemes for the initial-boundary value problem of the Cahn-Hilliard equation. These schemes are proved to inherit the total mass conservation and energy dissipation in the discrete level. The dissipation of the total energy implies boundness of the numerical solutions in the discrete H1 norm. This in turn implies boundedness of the numerical solutions in the maximum norm and hence the stability of the difference schemes. Unique existence of the numerical solutions is proved by the fixed-point theorem. Convergence rate of the class of finite difference schemes is proved to be O（h2 ＋ r2） with time step T and mesh size h. An efficient iterative algorithm for solving these nonlinear schemes is proposed and discussed in detail.
基金Project supported by the National Natural Science Foundation of China.
文摘Damage zones of brittle-ductile (B-D) transition in PP/EPDM blends are studied in this paper. The contribution of crazing and shear yielding zones in damage zones to energy dissipation of blends was measured with computer image analysis (CIA) and the transition of shear yielding zone (A_(sh)) with rubber volume fraction (V_f) was also manipulated. Results showed that the B-D transition of impact strength of blends corresponded to the fracture mechanism in PP/EPDM blends, from matrix crazing to matrix shear yielding. In addition, two new parameters, density of energy dissipation for crazing zone (F_(cz)) and for shear yielding zone (F_(sh)), are first obtained in this paper. The value of F_(sh) is about four times larger than that of F_(cz) for PP/EPDM blends, which confirmed that the matrix shear yielding is a more effective way of energy dissipation in blends.
