Asymmetric frictional sliding between incommensurate surfaces

We study the frictional sliding of two ideally incommensurate surfaces with a third incommensurate sheet - a sort of extended lubricant - in between. When the mutual ratios of the three periodicities in this sandwich geometry are chosen to be the golden mean , this system is believed to be statically pinned for any choice of system parameters. In the present study we overcome this pinning and force the two “substrates” to slide with a mutual velocity V_ext, analyzing the resulting frictional dynamics. An unexpected feature is an asymmetry of the relative sliding velocity of the intermediate lubricating sheet relative to the two substrates. Strikingly, the velocity asymmetry takes an exactly quantized value which is uniquely determined by the incommensurability ratio, and absolutely insensitive to all other parameters. The reason for quantization of the velocity asymmetry will be addressed. This behavior is compared and contrasted to the corresponding one obtained for a representative cubic irrational, the spiral mean ω.     

Onset temperature of Bose-Einstein condensation in incommensurate solid (4)He

The temperature dependence of the one-body density matrix in (4)He crystals presenting vacancies is computed with path integral Monte Carlo simulations. The main purpose of this study is to estimate the onset temperature T(0) of Bose-Einstein condensation in these systems. We see that T(0) depends on the vacancy concentration X(v) of the simulated system, but not following the law T(0) ~ X(v)(2/3) obtained assuming noninteracting vacancies. For the lowest X(v) we study, that is X(v)= 1/256, we get T(0) = 0.15 ± 0.05 K, close to the temperatures at which a finite fraction of nonclassical rotational inertia is experimentally observed. Below T(0), vacancies do not act as classical point defects becoming completely delocalized entities.     

Chaotic attractors in incommensurate fractional order systems

In this paper, based on the stability theorems in fractional differential equations, a necessary condition is given to check the existence of 1-scroll, 2-scroll or multi-scroll chaotic attractors in a fractional order system. This condition is proposed for incommensurate order systems in general, but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems. Though the presented condition is only a necessary (and not sufficient) condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system, chaotic attractors can not be observed and for what parameters and orders, the system may generate chaos. It can also be used as a tool to confirm or reject results of a numerical simulation. Some of the numerical results reported in the previous literature are confirmed by this tool.     

Synchronization in coupled nonidentical incommensurate fractional-order systems

Synchronization of fractional-order nonlinear systems has received considerable attention for many research activities in recent years. In this Letter, we consider the synchronization between two nonidentical fractional-order systems. Based on the open-plus-closed-loop control method, a general coupling applied to the response system is proposed for synchronizing two nonidentical incommensurate fractional-order systems. We also derive a local stability criterion for such synchronization behavior by utilizing the stability theory of linear incommensurate fractional-order differential equations. Feasibility of the proposed coupling scheme is illustrated through numerical simulations of a limit cycle system, a chaotic system and a hyperchaotic system.     

Temperature dependence of hyperfine interactions in incommensurate systems

One investigates the influence of thermally excited collective modes in incommensurate systems on the temperature dependence of hyperfine interactions. The observed hyperfine fields are reduced by a temperature-dependent Debye-Waller factor and the hyperfine field amplitude can eventually decrease to zero well below the transition temperature.     

Phasons, sliding modes and friction

Aperiodic crystals may have additional low frequency modes related to the possibility to describe them in a higher-dimensional space. Dynamics associated with these degrees of freedom is called phasonic, but there are very different phenomena of this type. A discussion is given of the use of the term. The relation between phason modes, the crystal structure, and the modulation and sliding modes is discussed. Finally a relation with frictionless motion is studied. Received 4 April 2002 / Received in final form 22 July 2002 Published online 17 September 2002     

Kinetics of capillary condensation in nanoscopic sliding friction

The velocity and humidity dependence of nanoscopic sliding friction has been studied on CrN and diamondlike carbon surfaces with an atomic force microscope. The surface wettability is found to be decisive. Partially hydrophilic surfaces show a logarithmic decrease of friction with increasing velocity, the slope of which varies drastically with humidity, whereas on partially hydrophobic surfaces we confirm the formerly reported logarithmic increase. A model for the thermally activated nucleation of water bridges between tip and sample asperities fully reproduces the experimental data.     

Prediction of dynamic friction forces in spur gears using alternate sliding friction formulations

In this communication, several sliding friction formulations used in spur gear dynamics are examined and compared in terms of the predictions of interfacial friction forces and off-line-of-action motions. Competing friction formulations include Coulomb models with time-varying friction coefficients and empirical expressions based on elasto-hydrodynamic and/or boundary lubrication regime principles. Predicted results compare well with friction force measurements.     

Spectral properties of incommensurate charge-density wave systems

The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the high T _c cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional “eggbox type” charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments. Received 14 June 1999     

滑动摩擦力作用下弹簧振子的振动

对在粗糙水平面上作振动的弹簧振子进行研究,探讨该弹簧振子最后停止的位置,估算了弹簧振子的振动总次数,得出弹簧振子的相轨迹.     

Magnetic resonance and relaxation in structurally incommensurate systems

The present state of theoretical and experimental magnetic resonance investigations of structurally incommensurate systems is reviewed. The magnetic resonance lineshapes and the temperature and frequency dependences of the spin-lattice relaxation rates are evaluated in the plane wave and multisoliton limits. In contrast to translationally periodic systems, the spin-lattice relaxation rate is shown to vary over the incommensurate resonance line and is determined by phason and amplitudon fluctuations. The variation of the relaxation rate over the incommensurate line allows for a separate determination of the amplitudon and phason contributions as well as a discrimination between direct and Raman processes. The results further demonstrate that the soliton width is large as compared to the intersoliton spacing over most of the incommensurate phase.     

Giant wave-drag enhancement of friction in sliding carbon nanotubes

Molecular dynamics simulations of coaxial carbon nanotubes in relative sliding motion reveal a striking enhancement of friction when phonons whose group velocity is close to the sliding velocity of the nanotubes are strongly excited. The effect is analogous to the dramatic increase in air drag experienced by aircraft flying close to the speed of sound but differs in that it can occur in multiple velocity ranges with varying magnitude, depending on the atomic level structures of the nanotubes. The phenomenon is a general one that may occur in other nanoscale mechanical systems.     

Dynamic sliding friction between concentric carbon nanotubes

Molecular dynamics simulations are used to study mechanical energy dissipation in carbon nanotube oscillators of lengths of tens of nanometers. The principal source of friction is found to be the ends of the tubes and hence dynamical friction is virtually independent of the overlap area between tubes. As a result of this, tube commensuration does not lead to significantly increased frictional forces. The friction force is found to depend strongly and nonlinearly on the relative velocity of the tubes. It is suggested that a strong velocity dependence and strong contributions from surface edges may be quite general features of friction at the nanoscale.     

用DIS探究影响滑动摩擦力的因素

利用DIS,定量地探究滑动摩擦力在正压力、接触面积、接触面性质以及物体间相对运动速度变化时的变化情况,加深学生对滑动摩擦力的理解,弥补了传统课堂实验只做定性分析的不足.