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 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
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
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 dynamics of a certain density of interacting atoms arranged on a two-dimensional square lattice, which is made to slide over a two-dimensional periodic substrate potential with also the quare lattice symmetry, in ...The dynamics of a certain density of interacting atoms arranged on a two-dimensional square lattice, which is made to slide over a two-dimensional periodic substrate potential with also the quare lattice symmetry, in the presence of dissipation, by an externally applied driving force, is studied. By rotating the misfit angle θ, the dynamical behaviour displays two different tribological regimes： one is smooth, the other becomes intermittent. We comment both on the nature of the atomic dynamics in the locked-to-sliding transition, and on the dynamical states displayed during the atom motion at different values of the driving force. In tribological applications, we also investigate how the main model parameters such as the stiffness strength and the magnitude of the adhesive force affect the static friction of the system. In particular, our simulation indicates that the superlubricity will appear.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
The role of interface couplings on the energy transport of two coupled Frenkel-Kontorova （FK） chains is explored through numerical simulations. In general, it is expected that the interface cou- plings result in the...The role of interface couplings on the energy transport of two coupled Frenkel-Kontorova （FK） chains is explored through numerical simulations. In general, it is expected that the interface cou- plings result in the suppression of heat conduction through the coupled system due to the additional interface phonon-phonon scattering. In the present paper, it is found that the thermal conductivity increases with increasing intensity of interface interactions for weak inter-chain couplings, whereas the heat conduction is suppressed by the interface interaction in the case of strong inter-chain couplings. Based on the phonon spectral energy density method, we demonstrate that the enhance- ment of energy transport results from the excited phonon modes （in addition to the intrinsic phonon modes）, while the strong interface phonon-phonon scattering results in the suppressed energy transport.展开更多
Dynamical behaviours of the motion of particles in a periodic potential under a constant driving velocity by a spring at one end are explored. In the stationary case, the stable equilibrium position of the particle ex...Dynamical behaviours of the motion of particles in a periodic potential under a constant driving velocity by a spring at one end are explored. In the stationary case, the stable equilibrium position of the particle experiences an elasticity instability transition. When the driving velocity is nonzero, depending on the elasticity coefficient and the pulling velocity, the system exhibits complicated and interesting dynamics, such as periodic and chaotic motions. The results obtained here may shed light on studies of dynamical processes in sliding friction.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 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 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 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Project supported by the National Natural Science Foundation of China(Grant No.10875098)the Natural Science Foundation of Northwest Normal University,China(Grant Nos.NWNU-KJCXGC-03-48and NWNU-KJCXGC-03-17)the Domestic Visiting Scholars Program of the Doctoral Candidates of Northwest Normal University,China
文摘The dynamics of a certain density of interacting atoms arranged on a two-dimensional square lattice, which is made to slide over a two-dimensional periodic substrate potential with also the quare lattice symmetry, in the presence of dissipation, by an externally applied driving force, is studied. By rotating the misfit angle θ, the dynamical behaviour displays two different tribological regimes： one is smooth, the other becomes intermittent. We comment both on the nature of the atomic dynamics in the locked-to-sliding transition, and on the dynamical states displayed during the atom motion at different values of the driving force. In tribological applications, we also investigate how the main model parameters such as the stiffness strength and the magnitude of the adhesive force affect the static friction of the system. In particular, our simulation indicates that the superlubricity will appear.
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.
文摘The role of interface couplings on the energy transport of two coupled Frenkel-Kontorova （FK） chains is explored through numerical simulations. In general, it is expected that the interface cou- plings result in the suppression of heat conduction through the coupled system due to the additional interface phonon-phonon scattering. In the present paper, it is found that the thermal conductivity increases with increasing intensity of interface interactions for weak inter-chain couplings, whereas the heat conduction is suppressed by the interface interaction in the case of strong inter-chain couplings. Based on the phonon spectral energy density method, we demonstrate that the enhance- ment of energy transport results from the excited phonon modes （in addition to the intrinsic phonon modes）, while the strong interface phonon-phonon scattering results in the suppressed energy transport.
基金Project supported in part by the National Natural Science Foundation of China （Grant Nos 70431002 and 10575010）, the Foundation for the Author of National Excellent Doctoral Dissertation of China （Grant No 200120）, and the Teaching and Research Award Program for 0utstanding Young Teachers in Higher Education Institutions, Ministry of Education of China （Grant No 209）.
文摘Dynamical behaviours of the motion of particles in a periodic potential under a constant driving velocity by a spring at one end are explored. In the stationary case, the stable equilibrium position of the particle experiences an elasticity instability transition. When the driving velocity is nonzero, depending on the elasticity coefficient and the pulling velocity, the system exhibits complicated and interesting dynamics, such as periodic and chaotic motions. The results obtained here may shed light on studies of dynamical processes in sliding friction.
