Hysteresis and elastic interactions of microasperities in dry friction

Velocity independent dry friction of a slider upon a base is due to an hysteretic response of relative displacement to a tangential driving force F. We show that the purely elastic model for multistability considered in a previous publication is in no way essential: multistability arises just as well from adhesion. We emphasize the physical consequences of multistability for dynamic/static, a.c./d.c. friction. When the slider is moved from rest by an amount the transition from the zero force static configuration to dynamic behaviour is progressive, spreading on a range equal to the width of the hysteresis cycle. When is small, an elastic restoring force ensues, in agreement with observations. The competition of that elastic pinning with bulk elasticity generates a screening length which we believe is the natural size of Burridge Knopoff blocks. We then study the effect of elastic interactions between asperities: it is weak for dilute asperities, but its long range makes it important. In lowest order the interaction mediated displacement of a given asperity has logarithmically divergent fluctuations: they become comparable to the asperity radius when the slider size reaches another characteristic “Larkin length”, which for dilute micronic asperities is exponentially large. We give arguments suggesting that individually monostable asperities display collective multistability on scales larger than . For individually multistable sites we show that elastic interactions give rise to cascade processes in which the spinodal jump of a given asperity triggers the jump of others. We estimate the size of these cascades that should show up in the noise spectrum. Received: 3 February 1998 / Accepted: 19 March 1998     

Rheological aging and rejuvenation in solid friction contacts

We study the low-velocity (0.1-100 μm s^-1) frictional properties of interfaces between a rough glassy polymer and smooth silanized glass, a configuration which gives direct access to the rheology of the adhesive joints in which shear localizes. We show that these joints exhibit the full phenomenology expected for confined quasi-2D soft glasses: they strengthen logarithmically when aging at rest, and weaken (rejuvenate) when sliding. Rejuvenation is found to saturate at large velocities. Moreover, aging at rest is shown to be strongly accelerated when waiting under finite stress below the static threshold. Received 20 February 2002 and Received in final form 16 May 2002     

Zero temperature phase transitions in spin-ladders: Phase diagram and dynamical studies of Cu2(C5H12N2)2Cl4>

In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields H_c1 and H_c2. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in one-dimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understanding of a broad class of quantum magnets in their gapless phase (between H_c1 and H_c2). In this phase, the low temperature divergence of the NMR relaxation demonstrates its Luttinger liquid nature as well as the novel quantum critical regime at higher temperature. The general behavior close these quantum critical points can be tied to known models of quantum magnetism. Received: 13 March 1998 / Received in final form and Accepted: 21 July 1998     

Dynamics of polymeric manifolds in melts: the Hartree approximation

The Martin-Siggia-Rose functional technique and the selfconsistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds. The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension, d _uc =2D/(2-D), discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, , discriminates between Rouse- and renormalized-Rouse behavior. The Rouse modes correlation function in a stretched exponential form and the dynamical exponents are calculated explicitly. The special case of linear chains D=1 shows agreement with Monte-Carlo simulations. Received: 22 May 1998 / Received in final form: 31 August 1998 / Accepted: 8 September 1998     

Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution

We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to the recently introduced nonextensive thermostatistics. The scenario which here emerges without tuning strongly reminds of that of the tuned onset of chaos in say logistic-like one-dimensional maps. We also calculate the dynamical exponent z. Received: 5 November 1997 / Received in final form: 11 November 1997 / Accepted: 19 November 1997     

Two-variable macroscopic model for spin-crossover solids: Static and dynamic effects of the correlations

In order to investigate the role of nearest neighbors correlations in the relaxation of the High Spin fraction in spin crossover compounds, we have developed a two macro-variable dynamical model based on Kubo's treatement of the master equation. This is compared to the local equilibrium approach, where short-range correlations are assumed to follow adiabatically the long range-order parameter. The sigmoidal shape of the relaxation, previously associated with the effects of interactions, and the so-called “tail effect”, i.e. the extra-slowing down at long times due to the correlations are obtained. The accurate comparison to experimental relaxation data confirms the coexistence of short-range and long-range interactions in spin-crossover solids. Received 20 April 2000     

Static electric dipole polarizabilities of Na clusters

The static electric dipole polarizability of Na _N clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for , including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments. Received 8 November 1999     

The temperature dependence of the perpendicular giant magnetoresistance in Co/Cu multilayered nanowires

A theory, based on earlier work by Valet and Fert, is first presented to describe the influence of temperature on the perpendicular giant magnetoresistance (GMR) in multilayers. Then we present GMR measurements performed at T=77 K and at room temperature on Co/Cu multilayered nanowires with layer thicknesses ranging from a few nm to 1 μm. We use our model to obtain a good quantitative fit to the experimental results in both the short spin diffusion length limit and out of this limit. We discuss the temperature dependence of the bulk parameters, the scattering spin asymmetry coefficient and spin diffusion length in the Co layers. Received: 25 January 1998 / Accepted: 6 May 1998     

Self-healing slip pulses and the friction of gelatin gels

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity V = V _c. For V > V _c, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a solution of polymer chain ends hanging from the network. In spite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than V _c, hence with the existence of the healing instability. Received: 7 March 2003 / Accepted: 2 May 2003 / Published online: 11 June 2003 RID="b" ID="b"e-mail: ronsin@gps.jussieu.fr     

Slow nucleic acid unzipping kinetics from sequence-defined barriers

Recent experiments on unzipping of RNA helix-loop structures by force have shown that ≈40-base molecules can undergo kinetic transitions between two well-defined “open” and “closed” states, on a timescale ≈1 sec [Liphardt et al., Science 297, 733-737 (2001)]. Using a simple dynamical model, we show that these phenomena result from the slow kinetics of crossing large free energy barriers which separate the open and closed conformations. The dependence of barriers on sequence along the helix, and on the size of the loop(s) is analyzed. Some DNA and RNA sequences that could show dynamics on different time scales, or three(or more)-state unzipping, are proposed. Our dynamical model is also applied to the unzipping of long (kilo-basepair) DNA molecules at constant force. Received 29 July 2002 / Received in final form 5 February 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: cocco@ldfc.u-strasbg.fr RID="b" ID="b"e-mail: jmarko@uic.edu RID="c" ID="c"e-mail: monasson@lpt.ens.fr     

Dynamics of selfavoiding tethered membranes. I. Model A dynamics (Rouse model)

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D are studied using model A dynamics. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by . This result applies especially to membranes (D=2) but also to polymers (D=1). Received: 5 September 1997 / Accepted: 17 November 1997     

Spherical averaged jellium model with norm-conserving pseudopotentials

The effect of non-local norm-conserving pseudo-potentials on the static and dynamic properties of Na_n and Li_n cluster with n=6,8 is investigated in the frame of self-consistent LDA calculations with spherically averaged ionic density (SAPS model). A comparison with previous calculations which use local pseudo-potentials as well with uniform averaged non-local pseudo-jellium calculation has been carried out. A better quantitative agreement with experiments has been found in the calculation of the photoresponse cross-section with respect to either simple jellium or pseudo-jellium model, even in very small clusters, where deviations from sphericity are not negligible. Received: 3 March 1998 / Received in final form and Accepted: 2 June 1998     

Quantum XY spin glass model with planar Dzyaloshinskii-Moriya interactions in longitudinal field

In the replica symmetric approximation and static limit in Matsubara “imaginary time”, the quantum XY spin glass model with planar Dzyaloshinskii-Moriya interaction in longitudinal field is investigated. Several thermodynamic quantities are calculated numerically as well as spin self-interaction and spin glass order parameter for spin S=1/2. It is shown that the entropy is not independent of the field. A crossover behavior of the specific heat depending on temperature is found. There is a deviation from the parabolic approximation, C/T=A+Bh ² . Received 11 March 1998     

Creation and manipulation of coherences in molecules with a pulsed magnetic field

We demonstrate the application of a pulsed magnetic field for the creation and manipulation of coherences in molecular systems, using quantum beat spectroscopy for the detection of the dynamics of the molecular superposition states. In all cases, the experiments are performed on energy levels in electronically excited states of the (jet-cooled) CS₂ molecule populated by a short laser pulse. In the basic experiment, following excitation of initially degenerate Zeeman sublevels under zero field conditions with suitable laser polarization, quantum beats are generated at the moment the magnetic field is switched on, even when the field is delayed by several excited state lifetimes. By quenching of the field, it is shown that the molecule may be “frozen” in any superposition state of the participating sublevels. Using a combination of static and pulsed fields with different orientations, the molecule can be prepared in a more general state, described by coherences among all Zeeman substrates. This is achieved by choosing an appropriate time delay for the switched field, without any change to the geometrical parameters of the experiment such as laser polarization or detection direction. Numerical simulations of these dynamical coherence phenomena have been performed to support assignment and interpretation of the experimental results. Received: 8 April 1998 / Accepted: 3 June 1998     

Phase transition and random-field induced domain wall response of SrTi O 3

The dielectric permittivity ε^′ - i of SrTi ¹⁸O ₃ (STO18) is studied under a dc electric field E as a function of the temperature, T. In ε^′ vs. T, a double-peak is found when 0 < E < 30 KV/m. While the peak at high-T is attributed to the smeared ferroelectric phase transition, the low-T one is induced by domain wall motion. The transverse Ising model including an external homogeneous and quenched random-fields is successfully used to describe both the smeared phase transition and the domain wall response in the low-T domain state. The calculations are in good agreement with the experimental results. Received 4 January 2002 / Received in final form 25 March 2002 Published online 19 July 2002     

Switching of banana liquid crystal mesophases under field

Taking advantage of the great number of bent-core or “banana" compounds synthesized and studied in the laboratory, we describe their behaviour under the application of an external electric field. If the field were a static one, we would work within the frame of an equilibrium phase diagram in a (field E, temperature T) space where some phases would be simple dielectrics and others ferroelectric ones with a macroscopic polarization, either spontaneous or induced by the field. In this paper, we deal with the basic responses of “banana” liquid crystals under the application of a low frequency (1 to 100 Hz) AC field. Firstly square-wave voltages allow us to locate the phase boundary between dielectric (at lower field) and ferroelectric phases (higher field) at a given temperature and field threshold. Then we apply slowly varying AC voltages with shapes like triangle or “triple-plateau” to check out the stability of the induced ferroelectric phase versus field removal. Three behaviours are encountered, the unstable one (short lifetime of the high-field ferroelectric phase) where the macroscopic polarization is destroyed and then rebuilt in the opposite direction during each half period and usually called “antiferroelectric”; the stable one (long lifetime) with a polarization that rotates at constant modulus which is labeled as “ferroelectric” and a new one where the macroscopic polarization is proportional to the applied fied, we named this behaviour as “superparaelectric”. Let us stress that these observations apply to the ferroelectric phases of the (E, T) phase diagram not to the zero field (0,T) phases observed in the usual phase characterization experiments except for an eventual spontaneous ferroelectric phase. Received 18 April 2002 and Received in final form 17 January 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: marcerou@crpp.u-bordeaux.fr RID="b" ID="b"URL: http://www.crpp-bordeaux.cnrs.fr     

On the connection between off-equilibrium response and statics in non disordered coarsening systems

The connection between the out of equilibrium linear response function and static properties established by Franz, Mezard, Parisi and Peliti for slowly relaxing systems is analyzed in the context of phase ordering processes. Separating the response in the bulk of domains from interface response, we find that in order for the connection to hold the interface contribution must be asymptotically negligible. How fast this happens depends on the competition between interface curvature and the perturbing external field in driving domain growth. This competition depends on space dimensionality and there exists a critical value d _c = 3 below which the interface response becomes increasingly important eventually invalidating the connection between statics and dynamics as the limit d = 1 is reached. This mechanism is analyzed numerically for the Ising model with d ranging from 1 to 4 and analytically for a continuous spin model with arbitrary dimensionality. Received 10 July 2001     

Interplay between chains of S = 5/2 localised spins and two-dimensional sheets of organic donors in the synthetically built magnetic multilayer λ ‒ (BETS)2FeCl4

In order to understand the magnetic field-induced restoration of a highly conductive state in , static (SQUID) and dynamic (ESR and AFR) magnetization measurements were performed on polycrystalline samples and single crystals, respectively. In addition, cantilever and resistivity measurements under steady fields were performed. While the metal-insulator transition curve of the () phase diagram exhibits a first order character, a “spin-flop” transition line divides the insulating state when the magnetic field is applied along the easy axis of magnetization. The effects of a RKKY-type indirect exchange and of applied magnetic field are described within the framework of a generalized Kondo lattice, namely two chains of localised spins coupled through the itinerant spins of the 2D sheets of BETS. The calculations, which can incorporate intramolecular electron correlations within a mean field theory, are in qualitative agreement with the field induced transition from the antiferromagnetic insulating ground state to a canted one, i.e. a not fully oriented paramagnetic, but metallic state. Received: 6 August 1997 / Received: 5 November 1997 / Accepted: 10 November 1997     

Temporal and spatial correlations in a viscoelastic model of heterogeneous faults

We study the temporal and spatial correlations in a one-dimensional model of a heterogeneous fault zone, in the presence of viscoelastic effects. As a function of dynamical weakening and of dissipation, the system exhibits three different “phases": one in which there are no time correlations between the events, a second, in which there are “Omori's law” type temporal correlations, and a third, runaway phase with quasiperiodic system size events. Received 30 May 2000 and Received in final form 7 September 2000