Nonlinear friction of a damped dimer sliding on a periodic substrate

Gonçalves, Sebastián; Kenkre, V. M.; Bishop, A. R.

doi:10.1103/physrevb.70.195415

Cited by 13 publications

(11 citation statements)

References 17 publications

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“…At zero temperature, the equations of motion for the two particles constituting the dimer sliding over a periodic potential, in the presence of external force F, are 12,13 …”

Section: Model and Simulation Resultsmentioning

confidence: 99%

“…We integrate these coupled equations numerically using the algorithm of Verlet modified to allow for velocity-dependent forces. 13 The underlying characteristic physical quantities in this system are the equilibrium dimer length a, the substrate wavelength b, the free dimer characteristic time 1/ 0 = ͱ m /2k, and an energy that describes the dimer oscillation such as kb 2 . In our numerical integrations we use a time step ⌬t equal to 0.03 0 −1 .…”

Section: Model and Simulation Resultsmentioning

confidence: 99%

“…13. Contrary to that analysis, however, here our interest lies in the steady state reached after the application of the external force.…”

Section: Simple Theoretical Considerationsmentioning

confidence: 88%

“…The latter phenomenon was also studied by Braun et al 8,10 More recently, Fusco and Fasolino 11,12 have identified the same resonance phenomenon in the friction of a smaller object, a dimer moving over a periodic substrate. Goncalves et al 13 have analyzed a closely related system in the relaxation regime, i.e., in the absence of external forces, and have given a simple physical explanation of the observed results. Persson 14 has predicted that a friction force proportional to −3 is to be expected ͑in addition to the linear one͒ in the large-force regime for a sliding system of any size, ranging from a single atom to an infinite chain.…”

Section: Introductionmentioning

confidence: 99%

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Bistability and hysteresis in the sliding friction of a dimer

et al. 2005

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The sliding friction of a dimer moving over a periodic substrate and subjected to an external force is studied in the steady state for arbitrary temperatures within a one-dimensional model. Nonlinear phenomena that emerge include dynamic bistability and hysteresis, and can be related to earlier observations for extended systems such as the Frenkel-Kontorova model. Several observed features can be satisfactorily explained in terms of the resonance of a driven-damped nonlinear oscillator. Increasing temperature tends to lower the resonant peak and wash out the hysteresis.

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“…At zero temperature, the equations of motion for the two particles constituting the dimer sliding over a periodic potential, in the presence of external force F, are 12,13 …”

Section: Model and Simulation Resultsmentioning

confidence: 99%

Section: Model and Simulation Resultsmentioning

confidence: 99%

“…13. Contrary to that analysis, however, here our interest lies in the steady state reached after the application of the external force.…”

Section: Simple Theoretical Considerationsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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Bistability and hysteresis in the sliding friction of a dimer

et al. 2005

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“…15,16 For the latter system the friction due to vibrations is maximum for a commensuration ratio a / b =2/3. However, such a friction is due to resonance of the internal oscillation of the dimer that happens at much higher sliding velocities than the ones used here, since our purpose is to compare to typical experimental setups.…”

Section: Discussionmentioning

confidence: 99%

Nanoscale sliding friction versus commensuration ratio: Molecular dynamics simulations

et al. 2006

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The pioneer work of Krim and Widom ͓Phys. Rev. B 38, 12184 ͑1988͔͒ unveiled the origin of the viscous nature of friction at the atomic scale. This generated extensive experimental and theoretical activity. However, fundamental questions remain open like the relation between sliding friction and the topology of the substrate, as well as the dependence on the temperature of the contact surface. Here we present results, obtained using molecular dynamics, for the phononic friction coefficient ͑ ph ͒ for a one-dimensional model of an adsorbatesubstrate interface. Different commensuration relations between adsorbate and substrate are investigated as well as the temperature dependence of ph . In all the cases we studied ph depends quadratically on the substrate corrugation amplitude, but is a nontrivial function of the commensuration ratio between substrate and adsorbate. The most striking result is a deep and wide region of small values of ph for substrate-adsorbate commensuration ratios between Ϸ0.65 and 0.9. Our results shed some light on contradictory results for the relative size of phononic and electronic friction found in the literature.

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Nonlinear Dynamics and Surface Diffusion of Diatomic Molecules

Fusco

Fasolino

2005

ChemPhysChem

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The surface diffusion of single adatoms has been intensively studied over the last decades, [1][2][3] due to its importance in thin film and crystal growth. [4] Once individual atoms are adsorbed on a surface they can meet, thus forming larger clusters. However, the diffusion of even the simplest cluster, a dimer, on a surface is by far not yet understood. [5][6][7][8][9][10][11][12][13] The diffusion dynamics can be strongly affected by the coupling of the intramolecular motion to the translational motion of the centre of mass (CM) of the cluster. [12][13][14][15] Herein, we present a simple, one-dimensional model for studying the Hamiltonian and diffusive dynamics of a dimer, which is relevant to systems where quasione-dimensional motion takes place.[16] The deterministic dynamics of this model is characterized by a complex behavior, dominated by nonlinear effects, parametric resonances and chaotic features. At variance with the case of a single atom, at T ¼ 6 0 the role of the internal degrees of freedom of the dimer is responsible for deviations from activated behavior of the diffusion coefficient. In Section 1, we briefly outline our model. In Sections 2 and 3, we discuss the nonlinear deterministic and thermal dynamics, respectively, and compare the two situations in Section 4. Concluding remarks are given in Section 5. ModelWe consider the deterministic and thermal dynamics of a dimer moving on a periodic one-dimensional substrate. The particle-substrate interaction is a sinusoidal function of amplitude 2 U 0 and period a, and the interparticle interaction is given by a harmonic potential with spring constant K and equilibrium length l. We use Langevin dynamics to deal with finite temperature T. The equations of motion for the two atoms of mass m and of coordinates x 1 and x 2 composing the dimer are given by Equation (1):where the effect of finite temperature T is taken into account by the stochastically fluctuating forces f i , satisfying the conditions hf i (t)i = 0 and hf i (t)f j (0)i = 2mhk B Td ij d(t), and by the damping term mhẋ i . In the following, we will use representative[a] C.

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Nonlinear friction of a damped dimer sliding on a periodic substrate

Cited by 13 publications

References 17 publications

Bistability and hysteresis in the sliding friction of a dimer

Bistability and hysteresis in the sliding friction of a dimer

Nanoscale sliding friction versus commensuration ratio: Molecular dynamics simulations

Nonlinear Dynamics and Surface Diffusion of Diatomic Molecules

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