Necessary conditions are proved for certain problems of optimal control of diffusions where hard end constraints occur. The main results apply to several dimensional problems, where some of the state equations involve...Necessary conditions are proved for certain problems of optimal control of diffusions where hard end constraints occur. The main results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time. The necessary conditions are stated in terms of weak variations. Two versions of necessary conditions are given, one version involving solutions of variational equations, the other one involving first order adjoint equations.展开更多
We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms （n = 1, 2, 3, 4, 5） fo...We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms （n = 1, 2, 3, 4, 5） for surface tension Sn （r）, r≥ d/2 with intermolecular separation r as a variable, where m is an arbitrary real number （pole）. Among the equations of state obtained in this way are Percus-Yevick, scaled particle theory and Carnahan-Starling equations of state. In addition, we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately. It is found that for both hard sphere fluids as well as Lennard-Jones fluids, with m = 3/4 the derived equation of state （EOS） gives results which are in good agreement with computer simulation results. Furthermore, this equation of state gives the Percus-Yevick （pressure） EOS for the m = 0, the Carnahan-Starling EOS for rn = 4/5, while for the value of m = 1 it corresponds to a scaled particle theory EOS.展开更多
The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state （EOS） for a mixture of hard sphere （HS）, Lennar-Jones （L J） fluids. A su...The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state （EOS） for a mixture of hard sphere （HS）, Lennar-Jones （L J） fluids. A suitable flexible functional form for the radial distribution function G（R） is assumed for the mixture, with R as a variable. The function G（R） has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics （MD） result for pure HS and LJ fluid respectively.展开更多
This paper has constructed two kinds of atomic and electronic models for hexagonal β-Mo2C and orthorhombic α-Mo2C. The optimized lattice parameters, elastic constant matrixes and overlap population for Mo2C crystal ...This paper has constructed two kinds of atomic and electronic models for hexagonal β-Mo2C and orthorhombic α-Mo2C. The optimized lattice parameters, elastic constant matrixes and overlap population for Mo2C crystal cells have been obtained to realize the characterization of the hardness and melting point of the two structures by the first-principles plane wave pseudo potential method based on the density functional theory. The results reveal that the calculated lattice parameters of the Mo2C crystal cells agree with the experimental and other calculated data. The calculated melting point/hardness are 2715 K/11.38 GPa for β-Mo2C and 2699 K/10.57-12.67 GPa for α-Mo2C, respectively. The calculated results from the density of states （DOS） demonstrate that the hybridization effect between Mo-3d and C-2p states in α-Mo2C crystal cell is much stronger than that in β-Mo2C one.展开更多
We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster. Efforts are made to estimate new physical parameter f in liqu...We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster. Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy. The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied. Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity（radial distribution function）.From the thermodynamic profile of the fluid, the model results are discussed in terms of the cavity due to the closed surface along with suitable energy. The present calculation is based upon the sample thermodynamic data for n-hexanol, such as the ultrasonic wave, density, volume expansion coefficient, and ratio of specific heat in the liquid state, and it is consistent with the thermodynamic relations containing physical parameters such as size and energy. Since the data is restricted to n-hexanol, we avoid giving the physical meaning of f, which is the key parameter studied in the present work.展开更多
In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state （EOS） for a hard sphere （HS） ...In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state （EOS） for a hard sphere （HS） and Lennard Jones （L J） fluids. A suitable axiomatic form for surface tension S（r） is assumed for the pure fluid, with r as a variable. The function S（r） has an arbitrary parameter rn. S（r） = A ＋ B（d/r）/[1 ＋ m（d/r）]. We use the condition in terms of radial distribution function G（λd,η） containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of rn and the EOS has a lower root-mean-square deviation than that of Barker-Henderson BH2 for LJ fluids.展开更多
本文较为详细地介绍了自Van der Waals状态方程以来所发展的若干典型的状态方程,并对各类型的状态方程进行了评价。但到目前为止还没有一种状态方程能对任何物质在很大范围内都是通用的。特别对量子流体及某些强极性物质,任何状态方程...本文较为详细地介绍了自Van der Waals状态方程以来所发展的若干典型的状态方程,并对各类型的状态方程进行了评价。但到目前为止还没有一种状态方程能对任何物质在很大范围内都是通用的。特别对量子流体及某些强极性物质,任何状态方程都还有困难。当前的办法仍是将若干类状态方程同时并用,在不同场合选择最合适的方程使用。因此本文对于状态方程的详细的综述可以为工程设计及从事这方面研究的人员提供有价值的参考。展开更多
文摘Necessary conditions are proved for certain problems of optimal control of diffusions where hard end constraints occur. The main results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time. The necessary conditions are stated in terms of weak variations. Two versions of necessary conditions are given, one version involving solutions of variational equations, the other one involving first order adjoint equations.
文摘We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms （n = 1, 2, 3, 4, 5） for surface tension Sn （r）, r≥ d/2 with intermolecular separation r as a variable, where m is an arbitrary real number （pole）. Among the equations of state obtained in this way are Percus-Yevick, scaled particle theory and Carnahan-Starling equations of state. In addition, we have found a simple equation of state for the hard sphere fluid in the region that represents the simulation data accurately. It is found that for both hard sphere fluids as well as Lennard-Jones fluids, with m = 3/4 the derived equation of state （EOS） gives results which are in good agreement with computer simulation results. Furthermore, this equation of state gives the Percus-Yevick （pressure） EOS for the m = 0, the Carnahan-Starling EOS for rn = 4/5, while for the value of m = 1 it corresponds to a scaled particle theory EOS.
文摘The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state （EOS） for a mixture of hard sphere （HS）, Lennar-Jones （L J） fluids. A suitable flexible functional form for the radial distribution function G（R） is assumed for the mixture, with R as a variable. The function G（R） has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics （MD） result for pure HS and LJ fluid respectively.
文摘This paper has constructed two kinds of atomic and electronic models for hexagonal β-Mo2C and orthorhombic α-Mo2C. The optimized lattice parameters, elastic constant matrixes and overlap population for Mo2C crystal cells have been obtained to realize the characterization of the hardness and melting point of the two structures by the first-principles plane wave pseudo potential method based on the density functional theory. The results reveal that the calculated lattice parameters of the Mo2C crystal cells agree with the experimental and other calculated data. The calculated melting point/hardness are 2715 K/11.38 GPa for β-Mo2C and 2699 K/10.57-12.67 GPa for α-Mo2C, respectively. The calculated results from the density of states （DOS） demonstrate that the hybridization effect between Mo-3d and C-2p states in α-Mo2C crystal cell is much stronger than that in β-Mo2C one.
文摘We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster. Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy. The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied. Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity（radial distribution function）.From the thermodynamic profile of the fluid, the model results are discussed in terms of the cavity due to the closed surface along with suitable energy. The present calculation is based upon the sample thermodynamic data for n-hexanol, such as the ultrasonic wave, density, volume expansion coefficient, and ratio of specific heat in the liquid state, and it is consistent with the thermodynamic relations containing physical parameters such as size and energy. Since the data is restricted to n-hexanol, we avoid giving the physical meaning of f, which is the key parameter studied in the present work.
文摘In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state （EOS） for a hard sphere （HS） and Lennard Jones （L J） fluids. A suitable axiomatic form for surface tension S（r） is assumed for the pure fluid, with r as a variable. The function S（r） has an arbitrary parameter rn. S（r） = A ＋ B（d/r）/[1 ＋ m（d/r）]. We use the condition in terms of radial distribution function G（λd,η） containing the self-consistent parameter λ and the condition of continuity at r = d/2 to determine A and B. A different EOS can be obtained with a suitable choice of rn and the EOS has a lower root-mean-square deviation than that of Barker-Henderson BH2 for LJ fluids.
文摘本文较为详细地介绍了自Van der Waals状态方程以来所发展的若干典型的状态方程,并对各类型的状态方程进行了评价。但到目前为止还没有一种状态方程能对任何物质在很大范围内都是通用的。特别对量子流体及某些强极性物质,任何状态方程都还有困难。当前的办法仍是将若干类状态方程同时并用,在不同场合选择最合适的方程使用。因此本文对于状态方程的详细的综述可以为工程设计及从事这方面研究的人员提供有价值的参考。
