Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-...Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.展开更多
The authors consider the complex Monge-Ampere equation det（uij） = ψ（z, u, △↓u） in bounded strictly pseudoconvex domains Ω, subject to the singular boundary condition u =∞ on δΩ. Under suitable conditions on...The authors consider the complex Monge-Ampere equation det（uij） = ψ（z, u, △↓u） in bounded strictly pseudoconvex domains Ω, subject to the singular boundary condition u =∞ on δΩ. Under suitable conditions on ψ, the existence, uniqueness and the exact asymptotic behavior of solutions Monge-Ampere equations are established to boundary blow-up problems for the complex展开更多
基金Supported by Natural Science Foundation of Shaanxi Province under Grant No. 2007A02the Science Foundation of Baoji University of Science and Arts of China under Grant No. ZK0914
文摘Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.
基金Project supported by the Tianyuan Foundation of Mathematics (No. 10926164)
文摘The authors consider the complex Monge-Ampere equation det（uij） = ψ（z, u, △↓u） in bounded strictly pseudoconvex domains Ω, subject to the singular boundary condition u =∞ on δΩ. Under suitable conditions on ψ, the existence, uniqueness and the exact asymptotic behavior of solutions Monge-Ampere equations are established to boundary blow-up problems for the complex
