Static and dynamic properties of frictional phenomena in a one-dimensional system with randomness

Static and dynamic frictional phenomena at the interface with random impurities are investigated in a two-chain model with incommensurate structure. Static frictional force is caused by the impurity pinning and/or by the pinning due to the regular potential, which is responsible for the breaking of analyticity transition for impurity-free cases. It is confirmed that the static frictional force is always finite in the presence of impurities, in contrast to the impurity-free system. The nature of impurity pinning is discussed in connection with that in density waves. The kinetic frictional force of a steady sliding state is also investigated numerically. The relationship between the sliding velocity dependence of the kinetic frictional force and the strength of impurity potential is discussed.Comment: RevTex, 14 pages, 6 PostScript figures, to appear in Phys. Rev.

Breakdown of a conservation law in incommensurate systems

We show that invariance properties of the Lagrangian of an incommensurate system, as described by the Frenkel Kontorova model, imply the existence of a generalized angular momentum which is an integral of motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the system as floating (when it is conserved) or locked (when it is not). We find that, during the dynamics, the non-linear couplings of our model cause parametric phonon excitations which lead to the appearance of Umklapp terms and to a sudden deviation of the generalized momentum from a constant value, signalling a dynamical transition from a floating to a pinned state. We point out that this transition is related but does not coincide with the onset of sliding friction which can take place when the system is still floating.Comment: 7 pages, 6 figures, typed with RevTex, submitted to Phys. Rev. E Replaced 27-03-2001: changes to text, minor revision of figure

Depinning of elastic manifolds

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows to determine the critical manifold in finite samples for an arbitrary convex elastic energy. For a harmonic elastic energy, we find values of the roughness exponent between the one-loop and the two-loop functional renormalization group result, in good agreement with earlier cellular automata simulations. We find that the harmonic model is unstable with respect both to slight stiffening and to weakening of the elastic potential. Anharmonic corrections to the elastic energy allow us to obtain the critical exponents of the quenched KPZ class.Comment: 4 pages, 4 figure

Anomalous pinning behavior in an incommensurate two-chain model of friction

Pinning phenomena in an incommensurate two-chain model of friction are studied numerically. The pinning effect due to the breaking of analyticity exists in the present model. The pinning behavior is, however, quite different from that for the breaking of analyticity state of the Frenkel-Kontorova model. When the elasticity of chains or the strength of interchain interaction is changed, pinning force and maximum static frictional force show anomalously complicated behavior accompanied by a successive phase transition and they vanish completely under certain conditions.Comment: RevTex, 9 pages, 19 figures, to appear in Phys. Rev. B58 No.23(1998

Modified critical correlations close to modulated and rough surfaces

Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. The results, combined with a renormalization group around four dimensions, are also used to predict critical behavior near a self-affinely rough surface. We find that a large enough roughness exponent can modify surface critical behavior.Comment: 4 pages, 1 figure. Revised version as published in Phys. Rev. Lett. 86, 4596 (2001

Dynamical frictional phenomena in an incommensurate two-chain model

Dynamical frictional phenomena are studied theoretically in a two-chain model with incommensurate structure. A perturbation theory with respect to the interchain interaction reveals the contributions from phonons excited in each chain to the kinetic frictional force. The validity of the theory is verified in the case of weak interaction by comparing with numerical simulation. The velocity and the interchain interaction dependences of the lattice structure are also investigated. It is shown that peculiar breaking of analyticity states appear, which is characteristic to the two-chain model. The range of the parameters in which the two-chain model is reduced to the Frenkel-Kontorova model is also discussed.Comment: RevTex, 9 pages, 7 PostScript figures, to appear in Phys. Rev.

Simulations of the Static Friction Due to Adsorbed Molecules

The static friction between crystalline surfaces separated by a molecularly thin layer of adsorbed molecules is calculated using molecular dynamics simulations. These molecules naturally lead to a finite static friction that is consistent with macroscopic friction laws. Crystalline alignment, sliding direction, and the number of adsorbed molecules are not controlled in most experiments and are shown to have little effect on the friction. Temperature, molecular geometry and interaction potentials can have larger effects on friction. The observed trends in friction can be understood in terms of a simple hard sphere model.Comment: 13 pages, 13 figure

Nonmonotonic roughness evolution in unstable growth

The roughness of vapor-deposited thin films can display a nonmonotonic dependence on film thickness, if the smoothening of the small-scale features of the substrate dominates over growth-induced roughening in the early stage of evolution. We present a detailed analysis of this phenomenon in the framework of the continuum theory of unstable homoepitaxy. Using the spherical approximation of phase ordering kinetics, the effect of nonlinearities and noise can be treated explicitly. The substrate roughness is characterized by the dimensionless parameter $Q = W_0/(k_0 a^2)$, where $W_0$ denotes the roughness amplitude, $k_0$ is the small scale cutoff wavenumber of the roughness spectrum, and $a$ is the lattice constant. Depending on $Q$, the diffusion length $l_D$ and the Ehrlich-Schwoebel length $l_{ES}$, five regimes are identified in which the position of the roughness minimum is determined by different physical mechanisms. The analytic estimates are compared by numerical simulations of the full nonlinear evolution equation.Comment: 16 pages, 6 figures, to appear on Phys. Rev.

Strongly Temperature Dependent Sliding Friction for a Superconducting Interface

A sudden drop in mechanical friction, between an adsorbed nitrogen monolayer and a lead substrate, occurs when the lead passes through the superconducting transition temperature. We attribute this effect to a sudden drop at the superconducting transition temperature of the substrate Ohmic heating. The Ohmic heating is due to the electronic screening current that results from the sliding adsorbed film.Comment: Revte

The Palomar Testbed Interferometer

The Palomar Testbed Interferometer (PTI) is a long-baseline infrared interferometer located at Palomar Observatory, California. It was built as a testbed for interferometric techniques applicable to the Keck Interferometer. First fringes were obtained in July 1995. PTI implements a dual-star architecture, tracking two stars simultaneously for phase referencing and narrow-angle astrometry. The three fixed 40-cm apertures can be combined pair-wise to provide baselines to 110 m. The interferometer actively tracks the white-light fringe using an array detector at 2.2 um and active delay lines with a range of +/- 38 m. Laser metrology of the delay lines allows for servo control, and laser metrology of the complete optical path enables narrow-angle astrometric measurements. The instrument is highly automated, using a multiprocessing computer system for instrument control and sequencing.Comment: ApJ in Press (Jan 99) Fig 1 available from http://huey.jpl.nasa.gov/~bode/ptiPicture.html, revised duging copy edi