Improved modeling of flows down inclined planes

New models of film flows down inclined planes have been derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions. The two-dimensional formulation has been extended to account for three-dimensional flows as well. The full second-order two-dimensional model can be expressed as a set of four coupled evolution equations for four slowly varying fields, the thickness h, the flow rate q and two other quantities measuring the departure from the flat-film semi-parabolic velocity profile. A simplified model has been obtained in terms of h and q only. Including viscous dispersion effects properly, it closely sticks to the asymptotic expansion in the appropriate limit. Our new models improve over previous ones in that they remain valid deep into the strongly nonlinear regime, as shown by the comparison of our results relative to travelling-wave and solitary-wave solutions with those of both direct numerical simulations and experiments. Received 14 September 1999 and Received in final form 6 January 2000     

Interface dynamics in liquid crystals

We have experimentally observed the pattern instabilities of an Ising wall formed in a nematic or cholesteric liquid crystal layer. We have deduced an envelope equation, relevant close to the Fréedericksz transition, from which we derived an equation for the dynamics of the interface in the vicinity of its bifurcation. In the case of the zig-zag instability, this model is characterized by a conservative and variational order parameter whose gradient satisfies a Cahn-Hilliard equation. We have also investigated the influence of slightly broken symmetries on the dynamical behaviour of the system. The disappearance of the interface translational invariance or of the reflection symmetry along the wall axis may induce new interfacial patterns which have been both experimentally and theoretically pointed out. Received 5 August 1999 and Received in final form 13 September 1999     

Phase-ordering dynamics of binary mixtures with field-dependent mobility in shear flow

The effect of shear flow on the phase-ordering dynamics of a binary mixture with field-dependent mobility is investigated. The problem is addressed in the context of the time-dependent Ginzburg-Landau equation with an external velocity term, studied in self-consistent approximation. Assuming a scaling ansatz for the structure factor, the asymptotic behavior of the observables in the scaling regime can be analytically calculated. All the observables show log-time periodic oscillations which we interpret as due to a cyclical mechanism of stretching and break-up of domains. These oscillations are damped as consequence of the vanishing of the mobility in the bulk phase. Received 13 April 1999     

Flame spreading over liquid ethanol

Flame spreading over liquid ethanol has been experimentally characterized for ethanol for subflash temperatures, in two different channels. Three different spreading regimes have been observed. A uniform region (with flame velocities close to 10 cm/s) appears for values of the initial surface liquid temperature above a critical value . For values an oscillatory regime occurs. For very low temperatures, , a new uniform regime appears with slow propagation velocities (close to 1 cm/s). The critical point has been described as a Hopf bifurcation, while resembles a homoclinic connection. Received 16 October 1998 and Received in final form 23 June 1999     

Statics and dynamics of a single ferrofluid-peak

We consider a single peak of a ferrofluid resulting from the Rosensweig instability for a small fluid container. Minimizing the total energy of the system by a variational method we determine the shape of the peak in a static field as well as the characteristics of the subcritical bifurcation leading to its formation. The latter are in very good agreement with experiment. Generalizing the approach to dynamic situations we qualitatively reproduce the complicated subharmonic response of the peak to an oscillating part in the external magnetic field found in recent experiments. Received 14 December 1999 and Received in final form 31 May 2000     

Pattern Formation in the Turing-Hopf Codimension-2 Phase Space in a Reaction-Diffusion System

We systematicaily investigate the behaviour of pattern formation in a reaction-diffusion system when the system is located near the Turing-Hopf codimension-2 point in phase space. The chloride-iodide-malonic acid （CIMA） reaction is used in this study. A phase diagram is obtained using the concentration of polyvinyl alcohol （PVA ） and malonic acid （MA） as control parameters. It is found that the Turing-Hopf mixed state appears only in a small vicinity near the codimension-2 point, and has the form of hexagonal pattern overlapped with anti-target wave; the boundary line separating the Taring state and the wave state is independent of the concentration of MA, only relies on the concentration of PVA. The corresponding numerical simulation using the Lengyel-Epstein （LE） model gives a similar phase diagram as the experiment; it reproduces most patterns observed in the experiment. However, the mixed state we obtain in simulation only appears in the anti-wave tip area, implying that the 3-D effect in the experiments may change the pattern forming behaviour in the codimension-2 regime.     

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     

Critical dynamics in clusters of noble gas atoms

The multi-fragmentation dynamics of noble gas atomic clusters is considered for different statistically distributed deposited energies. The conditions giving rise to the development of criticality in the cluster evolution are revealed from an analysis of the signals in the fragment mass distribution. The time dependence of the observables related to critical exponents is studied. It is demonstrated that in a certain regime the cluster exhibits a behavior which can be identified as the precursor of a second-order liquid-gas phase transition. Received 1st September 1998 and Received in final form 14 January 1999     

Heteroclinic behavior in rotating Rayleigh-Bénard convection

We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle. Received 10 June 1999     

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     

Geometrical frustration in 2D optical patterns

In the case of 2D optical patterns, frustration comes from the interplay between the physical constraints (light-matter interaction) and the geometrical constraints (cavity length and structure). Depending on the dynamical parameters, we are able to single out two distinct behaviors. For small diffusion and close to threshold, the system is forced to fulfill the geometrical constraints giving rise to a phase dynamics of quasicrystals. For larger diffusion, the system fragmentates into spatial domains giving rise to a competition between different patterns. By means of a geometrical argument, we show that the spatial distribution of domains is related to the symmetry imposed by the geometrical constraint and that the domain borders are disinclination defects. These defects being the nucleation centers of spatial domains, they trigger the onset of pattern competition. Received 27 December 1999 and Received in final form 29 March 2000     

Spontaneous alloying of tin atoms into nanometer-sized gold clusters and phase stability in the resultant alloy clusters

Alloying behavior and phase stability has been studied in situ by transmission electron microscopy using clusters in the Au-Sn system. When tin atoms are vapor-deposited onto nm-sized gold clusters, rapid dissolution of tin atoms into gold clusters takes place and as a result Au-rich solid solution, amorphous-like Au-Sn alloy and AuSn compound clusters are formed depending upon the concentration of tin. The remarkable enhancement of solubility has been observed in Au-rich solid solution and AuSn compound. It becomes more difficult to form two phases in the interior of individual clusters even if the composition of alloy clusters falls in the two-phase region in the phase diagram for the bulk alloy and as a result amorphous-like phase is stabilized in nm-sized Au-Sn alloy clusters. Received 2 August 1999 and Received in final form 8 November 1999     

Convection in horizontally shaken granular material

In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically. Using two dimensional molecular dynamics we show that the convection pattern depends crucially on the inelastic properties of the material. The concept of restitution coefficient provides arguments for the change of the behaviour with varying inelasticity. Received 3 March 1999     

A small-angle X-ray scattering study of the isotropic and nematic phases of V2O5 suspensions

We report small-angle X-ray scattering experiments performed in both the isotropic and nematic phases of aqueous V₂O₅ suspensions. We show that the scattering in the isotropic phase can be well described in the whole accessible q-range by only considering the form factor of non-interacting ribbons. We investigate the influence of concentration and pH on the dimensions of V₂O₅ ribbons and show that these parameters do not have any significant effect, as long as the system stays well within the chemical stability domain of the ribbons. We then show that nematic single domains display an anisotropic small-angle scattering pattern, even at scattering vectors small compared to that at which a characteristic correlation peak is observed. This feature is expected for a nematic phase, but was rarely observed. We finally try to describe this scattering within the framework of theories developed for the structure factor of a nematic polymer, and we reach the conclusion that chain ends are certainly important to understand this pattern. Received 21 July 1999 and Received in final form 17 December 1999     

Elastic neutron scattering and dielectric behaviour of 4% brominated betaine calcium chloride dihydrate (BCCD)

We report a combined experimental study by means of elastic neutron scattering and dielectric measurements of a partially deuterated and brominated BCCD (Betaine Calcium Chloride Dihydrate) crystal. The lowest-temperature phase is one-dimensional modulated and characterized by the coexistence of different commensurate domains (with = 1/4, 4/17, 2/9 and 1/5 on cooling), but with a clear predominance of the five-fold phase. A huge global thermal hysteresis of the wave-vector of the modulation, attaining values of about 9 K in the incommensurate phase and up to 15 K in the “harmless” low temperature part of the phase diagram, is observed up to . The role of lattice defects on this phenomenon is discussed. Similarly to the behaviour of the pure compound, the structural modulation evolves on cooling towards a soliton regime (growth of third and fifth-order satellite peaks), probably with respect to a non-stabilized non-modulated ferroelectric phase. The critical temperatures deduced from dielectric constant and pyroelectric current measurements are in very good agreement with those obtained from neutron scattering. The dielectric anomaly observed in at K, and known as the “-anomaly”, could not be related with any special feature detected in the neutron data, and in particular no correlation between this anomaly and the appearance of the soliton regime can be established. Received 26 October 1998     

Nonlinear-driven instability of dynamical plasma in solids: Emergence of spatially self-organized order and chaotic-like behavior

We analyze in detail the nonlinear kinetics of a carrier system in a photoinjected plasma in semiconductors under the action of constant illumination with ultraviolet light. We show that the spatially homogeneous steady-state becomes unstable, and a charge density wave emerges after a critical intensity of the incident radiation is achieved. It is shown that this instability can only follow in doped p-type materials. In bulk systems the critical intensity was found to be too high making the phenomenon not observable under realistic experimental conditions. However, a more efficient electron excitation can be obtained in low dimensional p-type systems, like some molecular and biological polymers, where the interaction may follow by chemical interaction with the medium. We show that for intensities beyond the critical threshold an increasing number of modes provide further contributions (subharmonics) to the space inhomogeneity. It is conjectured that this process could lead the system to display chaotic-like behavior. Received 8 July 1998 and Received in final form 6 May 1999     

Experimental study of the porosity of loose stacks of stiff cylindrical fibres: Influence of the aspect ratio of fibres

The aim of this work is to study the porosity of three-dimensional and two-dimensional packing of stiff cylindrical fibres according to their aspect ratio. First, we have carried out an experimental study of the porosity for 3D and 2D packing. In this last case, the elementary representative surfaces have been determined. Then, an attempt of interpretation of the porosity variations for 2D stacks has been realized on the basis of the excluded volume theory and a variation law has been proposed. To conclude, we have studied the relevance of a simplified packing model based on a single geometry of the defects. Received 12 April 1999 and Received in final form 4 August 1999     

Microwave transport approach to the coherence of interchain hopping in (TMTSF)2PF6

We report a microwave study of the longitudinal and transverse transport properties of the quasi-one-dimensional organic conductor (TMTSF)₂PF₆ in its normal phase. The contactless technique have provided a direct measurement of the temperature profile of the resistivity along the b' direction and in magnetic fields up to 14 T. A characteristic energy scale ( K) has been observed which delimits a transient regime from an insulating to a metallic behavior. This anomalous profile is discussed in terms of the onset of coherent transport properties along the b' direction below 40 K. This is also supported by the observation of a finite longitudinal and transverse magnetoresistances only below 40 K, indicative of a two-dimensional regime. Below T_x, however, strong deviations with respect to a Fermi liquid behavior are evidenced. Received 27 January 1999     

Laser Doppler velocimetry analysis of transitional pipe flow

The objective of this study has been to experimentally analyze the correlation structure of the strong temporal intermittency which characterizes pipe flow close to the transition to turbulence. In doing so transitional pipe flow has been analyzed by Laser Doppler velocimetry and the Reynolds number dependence of the covariance function has been studied. The range which has been analyzed covers the transition to turbulence and moderately developed turbulence (Reynolds number from 1 500 to 5 000). The correlation structure which has been evidenced is generally in agreement with the deterministic, dynamical, interpretation of temporal intermittency which explains the intermittent behavior as a result of a saddle node bifurcation. However, the analysis has evidenced fluctuations even before the onset of turbulence. The structure of these fluctuations is perfectly autoregressive which leads us to conclude that the transition to turbulence can be viewed as a transition from linear randomness to (non-linear) homogeneity. Received 29 March 1999 and Received in final form 6 September 1999