In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from ...In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.展开更多
The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interacti...The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.展开更多
In this paper, a novel unsteady fluid network simulation method to compute the air system of jet engine was coded to predict the characteristics of pressure, temperature and mass flow rate of the flow and the temperat...In this paper, a novel unsteady fluid network simulation method to compute the air system of jet engine was coded to predict the characteristics of pressure, temperature and mass flow rate of the flow and the temperature of the solid in the gas turbine engine. The fluid and solid areas are divided into the network comprised of branches and nodes, and the method solves transient mass, energy conservation equations at each node and momentum conservation equation at each branch by a newly deduced numerical method. With this method, to simulate complicated fluid and solid system in short time becomes possible. To verify the code developed, it has been applied to simulate a gas turbine model against the widely used commercial software Flowmaster. And the comparisons show that the two are in good agreement. Then the verified program is applied to the prediction of the characteristics of a designed turbine disk and air-cooling system associated to it, and useful information is obtained.展开更多
Power systems in Germany mainly containing intermittently operating renewable sources require load/frequency control which is performed up to now at the AC transmissioh and distribution levels. Frequency control can b...Power systems in Germany mainly containing intermittently operating renewable sources require load/frequency control which is performed up to now at the AC transmissioh and distribution levels. Frequency control can be achieved by employing short-and long-term storage plants buffering and complementing renewable energy sources. A representative grid consists of a natural-gas-fired plant serving as frequency leader, long-term storage plant, wind-power farm with associated short-term storage plantfor energy buffering, and photovoltaic farm with associated short-term storage plant interconnected by a long transmission line to two load circuits. Transient analysis is performed with Mathemafica solving the differential equation system for frequency variation. Powerflow through the AC transmission line is limited by its impedance. The long transmission line must be segmented to achieve stability and voltage control over an 800 km distance. The renewable plants must be operated together with the storage plants in order tominimize frequency variations by smoothing the power output of renewable plants, achieving step-wise control of the transmission-line power. Although to date only AC Iransmission lines in Germany exist, it is anticipated that within the next 10 years these will beaugmented by DC high-voltage lines.展开更多
In this paper we give an appropriate energy equation considering the diffusion and the energy production contributions of species for a complex coupled system with chemical reaction. It is shown that the contribution ...In this paper we give an appropriate energy equation considering the diffusion and the energy production contributions of species for a complex coupled system with chemical reaction. It is shown that the contribution of the mass diffusion on the internal energy is the same whether it is introduced by the mass flow through the outer boundary or by the inner chemical reaction. In addition, the diffusion is a purely irreversible process and does not produce reversible entropy or entropy flow. Based on this theory a new entropy production rate equation is derived for the coupled thermal diffusive chemical heterogeneous system. The evolution equations of the heat conduction and the mass diffusion derived from this theory are fully consistent with the Fourier and Fick＇s laws.展开更多
基金Supported by National Nature Science Foundation of China under Grant No. 10701081
文摘In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.
基金Supported by the Natural Science Foundation of China under Grant Nos. 50831003, 50571037, and 10774041
文摘The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.
文摘In this paper, a novel unsteady fluid network simulation method to compute the air system of jet engine was coded to predict the characteristics of pressure, temperature and mass flow rate of the flow and the temperature of the solid in the gas turbine engine. The fluid and solid areas are divided into the network comprised of branches and nodes, and the method solves transient mass, energy conservation equations at each node and momentum conservation equation at each branch by a newly deduced numerical method. With this method, to simulate complicated fluid and solid system in short time becomes possible. To verify the code developed, it has been applied to simulate a gas turbine model against the widely used commercial software Flowmaster. And the comparisons show that the two are in good agreement. Then the verified program is applied to the prediction of the characteristics of a designed turbine disk and air-cooling system associated to it, and useful information is obtained.
文摘Power systems in Germany mainly containing intermittently operating renewable sources require load/frequency control which is performed up to now at the AC transmissioh and distribution levels. Frequency control can be achieved by employing short-and long-term storage plants buffering and complementing renewable energy sources. A representative grid consists of a natural-gas-fired plant serving as frequency leader, long-term storage plant, wind-power farm with associated short-term storage plantfor energy buffering, and photovoltaic farm with associated short-term storage plant interconnected by a long transmission line to two load circuits. Transient analysis is performed with Mathemafica solving the differential equation system for frequency variation. Powerflow through the AC transmission line is limited by its impedance. The long transmission line must be segmented to achieve stability and voltage control over an 800 km distance. The renewable plants must be operated together with the storage plants in order tominimize frequency variations by smoothing the power output of renewable plants, achieving step-wise control of the transmission-line power. Although to date only AC Iransmission lines in Germany exist, it is anticipated that within the next 10 years these will beaugmented by DC high-voltage lines.
文摘In this paper we give an appropriate energy equation considering the diffusion and the energy production contributions of species for a complex coupled system with chemical reaction. It is shown that the contribution of the mass diffusion on the internal energy is the same whether it is introduced by the mass flow through the outer boundary or by the inner chemical reaction. In addition, the diffusion is a purely irreversible process and does not produce reversible entropy or entropy flow. Based on this theory a new entropy production rate equation is derived for the coupled thermal diffusive chemical heterogeneous system. The evolution equations of the heat conduction and the mass diffusion derived from this theory are fully consistent with the Fourier and Fick＇s laws.
