Statistics of shock waves in a two-dimensional granular flow

We have investigated the dynamics of shock waves in a single layer of uniform balls in a small-angle two-dimensional funnel. When the funnel half-angle 0 degrees < or approximately beta < or approximately 2 degrees, the flow is intermittent and kinematic shock waves are observed to propagate against the flow. We have used fast video equipment and image analysis methods to study the statistics of the shock waves. It is found that their speed and frequency increase with the distance from the outlet. In particular, the shock speed scales as the ratio of the local funnel width to the width of the funnel outlet. Various kinds of interactions between shock waves are observed, including repulsion. New shock waves are only created at those sites where a close-packed triangular packing of the monodisperse balls fits across the funnel.     

Nonlinear dynamics of density waves in granular flows through narrow vertical channels

We study granular flows through narrow channels driven by gravity in the framework of the kinetic theory for dissipative dense gases. We derive equations of motion for quasi-one-dimensional systems. In a certain range of flow density, the steady homogeneous regime is found to be unstable against the formation of density waves. We show moreover that near the onset of the instability, the governing equation for the flow density is a mixture of the Korteweg-de-Vries equation, which leads to soliton, and the Bürger equation which exhibits spatio-temporal chaos. The competition between chaos and solitons may lead either to regular spatially ordered density waves or to chaotic dynamics. We argue that these two types of dynamics can be encountered experimentally according to the channel width and the dissipative properties of the granular media. Received: 11 March 1998 / Revised and Accepted: 3 July 1998     

Monodisperse dry granular flows on inclined planes: Role of roughness

Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that there exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the slope angle. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 m to 2 mm. The relative roughness corresponding to the maximum of the friction can be predicted with a geometrical model of stability of one single bead on the plane. The main parameters are the size of the bumps and the size of the flowing beads. In order to obtain a higher precision, the model also takes into account the spacing between the bumps of the rough plane. Experimental results and model are in good agreement for all the planes we studied. Other parameters, like the sphericity of the beads, or irregularities in the thickness of the layer of glued particles, are shown to be of influence on the friction.     

Modeling film flows down inclined planes

A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations. Received: 16 April 1998 / Revised: 29 June 1998 / Accepted: 2 July 1998     

Spatio-temporal patterns in the thermoconvection of a planar nematic layer: I. Weakly nonlinear models

We study theoretically the formation of convection patterns in a laterally extended planar nematic layer heated from below, in the linear and weakly nonlinear regimes. By reformulating the viscous coupling terms of the basic nematohydrodynamic equations, a simple interpretation of the flow effects on the director dynamics can be proposed. A detailed linear analysis of the problem is presented. A systematic method to investigate nonlinear mechanisms is developed, and exemplified by the study of the nonlinear saturation in rolls. The extension of the roll amplitude equation with the envelope formalism is used to characterize the dynamics of the roll modulations near threshold. Coupled envelope equations are shown to describe the structure of the point defects in zig-zags observed experimentally. Finally the bifurcation to the bimodal varicose is studied. The secondary wavevector in the bimodal appears to be selected by a rotation of the director in the horizontal plane. Quantitative predictions concerning the amplitude of this rotation are given. Received: 1st December 1997 / Revised: 25 May 1998 / Accepted: 2 June 1998     

Statistical analysis of the transition to turbulence in plane Couette flow

We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical level. We present such a statistical analysis of experimental data guided by a parallel investigation of a simple coupled map lattice model for spatiotemporal intermittency. We confirm that this generic type of spatiotemporal chaos is relevant in the context of plane Couette flow, where the linear stability of the laminar regime at all Reynolds numbers insures the necessary local subcriticality. Using large ensembles of similar experiments, we show the existence of a well-defined threshold Reynolds number above which a unique, turbulent, intermittent attractor coexists with the laminar flow. Furthermore, our data reveals that this transition to spatiotemporal intermittency is discontinuous, i.e. akin to a first-order phase transition. Received: 10 April 1998 / Revised: 22 June 1998 / Accepted: 24 June 1998     

Envelope solitary waves on two-dimensional lattices with in-plane displacements

We investigate envelope solitary waves on square lattices with two degrees of freedom and nonlinear nearest and next-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their motion and periodically modulated along the perpendicular direction. In the quasi-monochromatic approximation and low-amplitude limit a system of two coupled nonlinear Schr?dinger equations (CNLS) is obtained for the envelopes of the longitudinal and transversal displacements. For the case of bright envelope solitary waves the solvability condition is discussed, also with respect to the modulation. The stability of two special solution classes (type-I and type-II) of the CNLS equations is tested by molecular dynamics simulations. The shape of type-I solitary waves does not change during propagation, whereas the width of type-II excitations oscillates in time. Received: 4 December 1997 / Revised: 6 June 1998 / Accepted: 7 July 1998     

Collision of a 1-D column of beads with a wall

An experimental study of the collision of a column of N beads () with a fixed wall is presented. For a fixed height of fall and a rigid wall, we show that the maximum force felt by the wall is independent of the number of beads N. The duration of impact, the velocity of the deformation wave in the column and an effective restitution coefficient of the column are also measured as a function of N. For a soft wall, we show that the maximum force depends on N. A non-dissipative numerical model, based on a nonlinear interaction law between nearest neighbours, gives results in agreement with the experimental data. Moreover, we show that, after the compression phase, the beads of the top of the column separate one after the other from the column with a velocity greater than the initial one. The beads at the bottom then bounce upwards in block, with a velocity smaller than the initial one. We emphasize that this detachment effect results from the energy redistribution within the whole system during the collision and not from any dissipative effect. Received: 6 February 1998 / Revised and accepted: 26 May 1998     

Phase dynamics of Bose-Einstein condensates: Losses versus revivals

In the absence of losses the phase of a Bose-Einstein condensate undergoes collapses and revivals in time due to elastic atomic interactions. As experiments necessarily involve inelastic collisions, we develop a model to describe the phase dynamics of the condensates in presence of collisional losses. We find that a few inelastic processes are sufficient to damp the revivals of the phase. For this reason the observability of phase revivals for present experimental conditions is limited to condensates with a few hundreds of atoms. Received: 23 February 1998 / Revised: 21 July 1998 / Accepted: 23 July 1998     

Invariable-profile wavefunctions and Brittingham's focus wave modes

A family of invariable-profile wavefunctions is constructed. The relations found describe both transient and steady-state waves. The Gauss and Bessel-Gauss focused waves of order m can be obtained from these steady-state waves via Bateman's transformation. Received: 14 May 1998 / Accepted: 22 August 1998     

Configuration space for random walk dynamics

Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a configuration to be sampled depends on a number of unusual quantities, which are explained in this paper. This has been overlooked in recent literature, where the method is advertised for the calculation of canonical expectation values. We illustrate these points for the 2d Ising model. In addition, we prove a previously conjectured equation which relates microcanonical expectation values to the spectral density. Received: 13 May 1998 / Received in final form and Accepted: 26 May 1998     

Logarithmic islanding in submonolayer epitaxial growth

We investigate submonolayer epitaxial growth with a fixed monomer flux and irreversible aggregation of adatom islands due to an effective island diffusion, with a diffusivity for an mass k island proportional to . For , there is a steady state, while for , continuously evolving logarithmic islanding occurs in which the island density grows extremely slowly, as . In the latter regime, the island size distribution exhibits complex, but universal, multiple-scale mass dependence which we account for theoretically. Received: 3 June 1998 / Accepted: 13 July 1998     

Photodissociation dynamics of Cl in a xenon cluster

The photodissociation of a chlorine molecule in the environment of a xenon cluster has been studied experimentally using the real time pump and probe technique through the formation of an XeCl reaction product. The photodissociating system is probed in such a way that the movement of a single chlorine atom in the xenon environment is detected. Various Xe_nCl₂ cluster sizes have been investigated leading to the distinction between uncapped, half-capped and doubly capped structures for these clusters. These structures have a profound influence on the photodissociation dynamics. Retrapping of one chlorine atomic fragment and stabilization of the XeCl reaction product is only observed for the half and doubly capped clusters. The experimental work is complemented by classical molecular dynamics calculations to get a full picture of the photodissociation. Received: 17 February 1998 / Received in final form and Accepted: 28 July 1998     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

Clusters in an assembly of globally coupled bistable oscillators

We study the dynamics of an assembly of globally coupled bistable elements. We show that bistability of elements results in some new features of clustering in the assembly when there is global coupling. We provide conditions for the existence of stable amplitude-phase clusters and splay-phase states. Received 12 June 1998 and Received in final form 30 November 1998     

Dissipation, decoherence and preparation effects in the spin-boson system

The dynamics of the reduced density matrix of the driven dissipative two-state system is studied for a general diagonal/off-diagonal initial state. We derive exact formal series expressions for the populations and coherences and show that they can be cast into the form of coupled nonconvolutive exact master equations and integral relations. We show that neither the asymptotic distributions, nor the transition temperature between coherent and incoherent motion, nor the dephasing rate and relaxation rate towards the equilibrium state depend on the particular initial state chosen. However, in the underdamped regime, effects of the particular initial preparation, e.g. in an off-diagonal state of the density matrix, strongly affect the transient dynamics. We find that an appropriately tuned external ac-field can slow down decoherence and thus allow preparation effects to persist for longer times than in the absence of driving. Received 23 October 1998 and Received in final form 26 February 1999     

Anomalous viscosity exponent in a discretized model for a chain diffusion in one dimension

We present a one-dimensional Monte Carlo simulation for the diffusion motion of a chain of N beads. We found that the scaling exponent for the viscosity can be smaller or greater than 3. This anomalous behavior cannot be attributed to the diffusivity scaling or the length fluctuations but is due to the chain dynamics details during diffusion in which the end beads play the key role. The viscosity exponent 3 and its expected relation with the diffusivity exponent are recovered in the asymptotic regime (N ↦∞). Received 24 September 2001 and Received in final form 28 January 2002     

Effect of hydrodynamic flow on kinetics of nematic-isotropic transition in liquid crystals

We investigate kinetics of nematic-isotropic transition by solving the hydrodynamic equations for the nematic tensor order parameter and the fluid velocity in two space dimension (x-y plane). Numerical results indicate that nematic directors tend to align parallel to the x-y plane when hydrodynamic flow is incorporated. Late stage growth exponents, for the correlation length and for the number of topological defects, are not significantly altered by hydrodynamic flow. However, in contrast to the case without flow, the relation holds well, which may indicate the validity of dynamical scaling for the case with hydrodynamic flow. Received: 8 September 1997 / Received in final form: 23 October 1997 /Accepted: 3 November 1997     

Pulses of tunable size near a subcritical bifurcation

We show that a nonlinear gradient term can be used to tune the width of pulse-like solutions to a generalized quintic Ginzburg-Landau equation. We investigate the dynamics of these solutions and show that weakly turbulent patches can persist for long times. Analogies with turbulent spots in plane Couette flows are discussed. Received: 29 May 1997 / Revised: 16 March 1998 / Accepted: 30 April 1998     

Influence of hydrodynamics on the dynamics of a homopolymer

We present an analytical approach of the dynamics of a polymer when it is quenched from a solvent into a good or bad solvent. The dynamics is studied by means of a Langevin equation, first in the absence of hydrodynamic effect, then taking into account the hydrodynamic interactions with the solvent. The variation of the radius of gyration is studied as a function of time. In both cases, for the first stage of collapse or swelling, the evolution is described by a power law with a characteristic time proportional to N ^4/3 (N), where N is the number of monomers, without (with) hydrodynamic interactions. At larger times, scaling laws are derived for the diffusive relaxation time. Received: 10 March 1998 / Received in final form: 15 September 1998 / Accepted: 25 September 1998