In this paper, we study solution structures of the following generalized Lennard-Jones system in R^n,x（-α/｜x｜α＋2＋β/｜x｜β＋2）xwith 0 〈 α 〈β. Considering periodic solutions with zero angular momentum, we ...In this paper, we study solution structures of the following generalized Lennard-Jones system in R^n,x（-α/｜x｜α＋2＋β/｜x｜β＋2）xwith 0 〈 α 〈β. Considering periodic solutions with zero angular momentum, we prove that the corre- sponding problem degenerates to I-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.展开更多
In this paper,we obtain the existence of non-planar circular homographic solutions and non-circular homographic solutions of the(2+N)-and(3+N)-body problems of the Lennard-Jones system.These results show the essential...In this paper,we obtain the existence of non-planar circular homographic solutions and non-circular homographic solutions of the(2+N)-and(3+N)-body problems of the Lennard-Jones system.These results show the essential difference between the Lennard-Jones potential and the Newton's potential of universal gravitation.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
Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rhe-ological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are...Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rhe-ological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic struc- ture of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here： First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase mono- tonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.展开更多
Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid are employed to describe the Helmholtz free energy of Lennard-...Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid are employed to describe the Helmholtz free energy of Lennard-Jones solid in the framework of the first order thermodynamic perturbation theory, which also is employed for the uniform LennardJones fluid. The dividing of the Lennard-Jones potential follows from the WCA prescription, but the specification of the equivalent hard sphere diameter is determined by a simple iteration procedure devised originally for liquid state, but extended to solid state in the present study. Two hundred sheiks are used in the rdf to get an accurate perturbation term.The present approach is very accurate for the description of excess Helmholtz free energy of LJ solid, but shows some deviation from the simulation for excess Helmholtz free energy of uniform LJ fluid when the reduced temperature kT/ε is higher then 5. The present approach is satisfactory for description of solid-liquid phase transition of the Lennard-Jones model.展开更多
基金partially supported by the Ph.D.Candidate Research Innovation Fund of Nankai University and NSFC(Grant Nos.11131004 and 11671215)partially supported by NSFC(Grant Nos.11131004 and 11671215)+3 种基金LPMC of MOE of ChinaNankai Universitythe BAICIT at Capital Normal Universitypartially supported by US NSF(Grant DMS-1362507)
文摘In this paper, we study solution structures of the following generalized Lennard-Jones system in R^n,x（-α/｜x｜α＋2＋β/｜x｜β＋2）xwith 0 〈 α 〈β. Considering periodic solutions with zero angular momentum, we prove that the corre- sponding problem degenerates to I-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.
基金Partially supported by NSFC(Grant Nos.11131004 and 11671215)Sino-German(CSC-DAAD)Postdoc Scholarship Program(Grant Nos.201800260010 and 91696544)funded by China Scholarship Council and Deutscher Akademischer Austausch Dienst。
文摘In this paper,we obtain the existence of non-planar circular homographic solutions and non-circular homographic solutions of the(2+N)-and(3+N)-body problems of the Lennard-Jones system.These results show the essential difference between the Lennard-Jones potential and the Newton's potential of universal gravitation.
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Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rhe-ological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic struc- ture of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here： First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase mono- tonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.
文摘Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid are employed to describe the Helmholtz free energy of Lennard-Jones solid in the framework of the first order thermodynamic perturbation theory, which also is employed for the uniform LennardJones fluid. The dividing of the Lennard-Jones potential follows from the WCA prescription, but the specification of the equivalent hard sphere diameter is determined by a simple iteration procedure devised originally for liquid state, but extended to solid state in the present study. Two hundred sheiks are used in the rdf to get an accurate perturbation term.The present approach is very accurate for the description of excess Helmholtz free energy of LJ solid, but shows some deviation from the simulation for excess Helmholtz free energy of uniform LJ fluid when the reduced temperature kT/ε is higher then 5. The present approach is satisfactory for description of solid-liquid phase transition of the Lennard-Jones model.
