By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square ...By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.展开更多
We investigate the interactions of lattice phonons with Frenkel exciton, which has a small radius in a twodimensional discrete molecular lattice, by the virtue of the quasi-discreteness approximation and the method of...We investigate the interactions of lattice phonons with Frenkel exciton, which has a small radius in a twodimensional discrete molecular lattice, by the virtue of the quasi-discreteness approximation and the method of multiplescale, and obtain that the self-trapping can also appear in the two-dimensional discrete molecular lattice with harmonic and nonlinear potential. The excitons＇ effect on the molecular lattice does not distort it but only causes it to localize which enables it to react again through phonon coupling to trap the energy and prevent its dispersion.展开更多
We investigate the effect of photons and phonons on Frenkel exciton spectrum. The Hamilto nian for a coupled system of the Frenkel excitons. the photons and the phonons is derived. The phonon-exciton interaction makes...We investigate the effect of photons and phonons on Frenkel exciton spectrum. The Hamilto nian for a coupled system of the Frenkel excitons. the photons and the phonons is derived. The phonon-exciton interaction makes the energy band of the Frenkel excitons narrow. The photons and the Frenkel excitons make up Frenkel exciton polaritons which are quasi-particles. The Frenkel exciton polariton spectrum consists of two branches. It is found that the photon-exciton interaction makes the ground energy of the Frenkel excitons increase.展开更多
篧ithin the Kinchin and Pease’s model, the author has derived a formula of Frenkel-pair production by using a new scattering cross section proposed recently. The formula, on the one hand, has confirmed Lindhard’s st...篧ithin the Kinchin and Pease’s model, the author has derived a formula of Frenkel-pair production by using a new scattering cross section proposed recently. The formula, on the one hand, has confirmed Lindhard’s statement, on the other hand, has removed the limitation of hard-sphere scattering model pointed out by Sigmund.展开更多
The dry friction force between two contacting surface layers is studied.The upper layer is arrangedon a two-dimensional square lattice and driven by an external driving force.The lower layer is approximated by atwo-di...The dry friction force between two contacting surface layers is studied.The upper layer is arrangedon a two-dimensional square lattice and driven by an external driving force.The lower layer is approximated by atwo-dimensional periodic substrate potential.This model,usually called two-dimensional Frenkel-Kontorova model,isapplied to study the friction forces in this paper.The behaviors of different substrate potential strongly affect the staticfriction force.It is found that the system has strong anisotropic character.The possibility to obtain superlubricity issuggested.展开更多
We report the oscillating propagation of kink in a nondissipative Frenkel-Kontorova （FK） chain driven by external DC force, which is different from the usual propagation of localized modes with equal speed. When the...We report the oscillating propagation of kink in a nondissipative Frenkel-Kontorova （FK） chain driven by external DC force, which is different from the usual propagation of localized modes with equal speed. When the kink moves in the opposite direction of the external DC force, the kink will be accelerated and the potential of the FK chain in the external force field is transformed to be the kinetic energy of the kink. If the kink reaches the boundary of the FK chain, the kink will be bounced back and moves in the opposite direction, then the kink will be decelerated gradually and the kinetic energy of the kink ＆ transformed to be the potential of the FK chain in the external force field. If the speed of the kink reaches zero, the kink will move in the opposite direction again driven by the external DC force, and a new oscillating cycle begins. Simulation result demonstrates exactly the transformation between the kinetic energy of the kink and the potential of the FK chain in the external force field. The interesting energy exchange is induced by the special topology of kinks, and other localized modes, such as breathers and envelope solitons, have no the interesting phenomenon.展开更多
A one-dimensional （1D） Frenkel-Kontorova （FK） model is studied numerically in this paper, and two new analytical solutions （a supersonic kink and a nonlinear periodic wave） of the Sine-Gordon （SG） equation （c...A one-dimensional （1D） Frenkel-Kontorova （FK） model is studied numerically in this paper, and two new analytical solutions （a supersonic kink and a nonlinear periodic wave） of the Sine-Gordon （SG） equation （continuum limit approximation of the FK model） are obtained by using the Jacobi elliptic function expansion method. Taking these new solutions as initial conditions for the FK model, we numerically find there exist the supersonic kink and the nonlinear periodic wave in these systems and obtain a lot of interesting and significant results. Moreover, we also investigate the subsonic kink and the breather in these systems and obtain some new feature.展开更多
The transport properties in a kind of simple system are studied within the framework of a generalized Frenkel Kontorova model where the chain is composed of two kinds of atoms. Its studied mobility includes two aspect...The transport properties in a kind of simple system are studied within the framework of a generalized Frenkel Kontorova model where the chain is composed of two kinds of atoms. Its studied mobility includes two aspects: the velocity mobility B v and the momentum mobility B m . The effective system temperatures for the two subchains, T e 1 and T e 2 are defined, respectively. For the underdamped case, the regime of nonlinear response becomes wider and more "steps" occur when the value of m increases. For m = 1, T e 1(F) = T e 2(F) . For m >1, T e 1(F) > T e 2(F) and the difference increases with the increase of m . The momentum transportation shows very different behavior from that of the velocity transportation. Within a prescribed intermediate "steps" of B v(F) or B m(F) , both of them decrease with the increase of F and B m(F) decreases more quickly. For the case of overdamping and nonzero temperature, the hysteresis interval becomes thinner and the transitions become smoother. The increase of m makes the hysteresis thinner and the transitions smoother. When T is high, all the transitions are smeared out, and the diatomic effects become unimportant. We expect these results contribute to the understanding of the atomic processes occurring at the interface of two materials when they are brought together and moved with respect to one another.展开更多
基金supported by the National Natural Science Foundation of China (Grand Nos. 50575217, 10875098 and 50421502)the Natural Science Foundation of Northwest Normal University (Grant Nos. NWNU-KJCXGC-03-17 and NWNU-KJCXGC-03-48)
文摘By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.
基金supported by the National Natural Science Foundation of China (Grant No 1057400)the Natural Science Foundation of Heilongjiang Province of China (Grant No A200506)
文摘We investigate the interactions of lattice phonons with Frenkel exciton, which has a small radius in a twodimensional discrete molecular lattice, by the virtue of the quasi-discreteness approximation and the method of multiplescale, and obtain that the self-trapping can also appear in the two-dimensional discrete molecular lattice with harmonic and nonlinear potential. The excitons＇ effect on the molecular lattice does not distort it but only causes it to localize which enables it to react again through phonon coupling to trap the energy and prevent its dispersion.
文摘We investigate the effect of photons and phonons on Frenkel exciton spectrum. The Hamilto nian for a coupled system of the Frenkel excitons. the photons and the phonons is derived. The phonon-exciton interaction makes the energy band of the Frenkel excitons narrow. The photons and the Frenkel excitons make up Frenkel exciton polaritons which are quasi-particles. The Frenkel exciton polariton spectrum consists of two branches. It is found that the photon-exciton interaction makes the ground energy of the Frenkel excitons increase.
文摘篧ithin the Kinchin and Pease’s model, the author has derived a formula of Frenkel-pair production by using a new scattering cross section proposed recently. The formula, on the one hand, has confirmed Lindhard’s statement, on the other hand, has removed the limitation of hard-sphere scattering model pointed out by Sigmund.
基金Supported by the National Natural Science Foundation of China under Grant Nos.50575217,10875098,and 50421502NWNUKJCXGC-03-17NWNU-KJCXGC-03-48
文摘The dry friction force between two contacting surface layers is studied.The upper layer is arrangedon a two-dimensional square lattice and driven by an external driving force.The lower layer is approximated by atwo-dimensional periodic substrate potential.This model,usually called two-dimensional Frenkel-Kontorova model,isapplied to study the friction forces in this paper.The behaviors of different substrate potential strongly affect the staticfriction force.It is found that the system has strong anisotropic character.The possibility to obtain superlubricity issuggested.
基金supported by Scientific Research Fund of Hunan Provincial Education Department under Grant No. 07B075Interactive Project Fund of Xiangtan University under Grant No. 061ND09Dr. Shangyou Zeng's Initial Scientific Research Fund of Xiangtan University
文摘We report the oscillating propagation of kink in a nondissipative Frenkel-Kontorova （FK） chain driven by external DC force, which is different from the usual propagation of localized modes with equal speed. When the kink moves in the opposite direction of the external DC force, the kink will be accelerated and the potential of the FK chain in the external force field is transformed to be the kinetic energy of the kink. If the kink reaches the boundary of the FK chain, the kink will be bounced back and moves in the opposite direction, then the kink will be decelerated gradually and the kinetic energy of the kink ＆ transformed to be the potential of the FK chain in the external force field. If the speed of the kink reaches zero, the kink will move in the opposite direction again driven by the external DC force, and a new oscillating cycle begins. Simulation result demonstrates exactly the transformation between the kinetic energy of the kink and the potential of the FK chain in the external force field. The interesting energy exchange is induced by the special topology of kinks, and other localized modes, such as breathers and envelope solitons, have no the interesting phenomenon.
基金supported by the National Natural Science Foundation of China (Grant No 10575082)the Natural Science Foundation of Gansu Province of China (Grant No 3ZS061-A25-013)the Natural Science Foundation of Northwest Normal University of China(Grant No NWNU-KJCXGC-03-17)
文摘A one-dimensional （1D） Frenkel-Kontorova （FK） model is studied numerically in this paper, and two new analytical solutions （a supersonic kink and a nonlinear periodic wave） of the Sine-Gordon （SG） equation （continuum limit approximation of the FK model） are obtained by using the Jacobi elliptic function expansion method. Taking these new solutions as initial conditions for the FK model, we numerically find there exist the supersonic kink and the nonlinear periodic wave in these systems and obtain a lot of interesting and significant results. Moreover, we also investigate the subsonic kink and the breather in these systems and obtain some new feature.
基金NationalNatureScienceFoundationofChina (No .19775 0 0 8)
文摘The transport properties in a kind of simple system are studied within the framework of a generalized Frenkel Kontorova model where the chain is composed of two kinds of atoms. Its studied mobility includes two aspects: the velocity mobility B v and the momentum mobility B m . The effective system temperatures for the two subchains, T e 1 and T e 2 are defined, respectively. For the underdamped case, the regime of nonlinear response becomes wider and more "steps" occur when the value of m increases. For m = 1, T e 1(F) = T e 2(F) . For m >1, T e 1(F) > T e 2(F) and the difference increases with the increase of m . The momentum transportation shows very different behavior from that of the velocity transportation. Within a prescribed intermediate "steps" of B v(F) or B m(F) , both of them decrease with the increase of F and B m(F) decreases more quickly. For the case of overdamping and nonzero temperature, the hysteresis interval becomes thinner and the transitions become smoother. The increase of m makes the hysteresis thinner and the transitions smoother. When T is high, all the transitions are smeared out, and the diatomic effects become unimportant. We expect these results contribute to the understanding of the atomic processes occurring at the interface of two materials when they are brought together and moved with respect to one another.
