In this work,a system of three masses on the vertices of equilateral triangle is investigated.This system is known in the literature as a planar system.We first give a description to the system by constructing its cla...In this work,a system of three masses on the vertices of equilateral triangle is investigated.This system is known in the literature as a planar system.We first give a description to the system by constructing its classical Lagrangian.Secondly,the classical Euler-Lagrange equations(i.e.,the classical equations of motion)are derived.Thirdly,we fractionalize the classical Lagrangian of the system,and as a result,we obtain the fractional Euler-Lagrange equations.As the final step,we give the numerical simulations of the fractional model,a new model which is based on Caputo fractional derivative.展开更多
The formation mechanism for the equilateral triangle structure of the He-3(+) cluster is proposed. The curve of the total energy versus the internuclear distance R for this structure has been calculated by the method ...The formation mechanism for the equilateral triangle structure of the He-3(+) cluster is proposed. The curve of the total energy versus the internuclear distance R for this structure has been calculated by the method of a modified arrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a. u at R = 1.55 a(0). The binding energy of He-3(+) with respect to He+He++He was calculated to be 0.1064 a.u. (about 2.89 eV). This means that the He-3(+) cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two helium atoms.展开更多
The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Go...The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou＇s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 ao. The total energy of Lia when R approaches co has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Lia. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Lia is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82ao stably with a stronger binding from the symmetrical interaction among the three lithium atoms.展开更多
The formation mechanism for the equilateral triangle structure of the He3+ cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a...The formation mechanism for the equilateral triangle structure of the He3+ cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a modifiedarrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a.u at 1 = 1.55 a0.The binding energy of He3+ with respect to He+He+ +He was calculated to be 0.1064 a.u. (about 2.89 eV). This meansthat the He3+ cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two heliumatoms.展开更多
文摘In this work,a system of three masses on the vertices of equilateral triangle is investigated.This system is known in the literature as a planar system.We first give a description to the system by constructing its classical Lagrangian.Secondly,the classical Euler-Lagrange equations(i.e.,the classical equations of motion)are derived.Thirdly,we fractionalize the classical Lagrangian of the system,and as a result,we obtain the fractional Euler-Lagrange equations.As the final step,we give the numerical simulations of the fractional model,a new model which is based on Caputo fractional derivative.
文摘The formation mechanism for the equilateral triangle structure of the He-3(+) cluster is proposed. The curve of the total energy versus the internuclear distance R for this structure has been calculated by the method of a modified arrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a. u at R = 1.55 a(0). The binding energy of He-3(+) with respect to He+He++He was calculated to be 0.1064 a.u. (about 2.89 eV). This means that the He-3(+) cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two helium atoms.
文摘The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou＇s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 ao. The total energy of Lia when R approaches co has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Lia. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Lia is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82ao stably with a stronger binding from the symmetrical interaction among the three lithium atoms.
基金The project supported by National Natural Science Foundation of China under Grant No. 19974027
文摘The formation mechanism for the equilateral triangle structure of the He3+ cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a modifiedarrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a.u at 1 = 1.55 a0.The binding energy of He3+ with respect to He+He+ +He was calculated to be 0.1064 a.u. (about 2.89 eV). This meansthat the He3+ cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two heliumatoms.
