Lattice Boltzmann simulation of a binary fluid with different phase viscosities and its application to fingering in two dimensions

A thermodynamically consistent lattice Boltzmann scheme for simulating the flow of a binary fluid is extended to allow the fluid components to have different viscosities. The approach is tested for the shear and Poiseuille flow of layered immiscible fluids and for the dispersion relation and the damping of a capillary wave. We then consider the fingering that results when a fluid is displaced by a less viscous fluid in a two-dimensional channel. The finger widths obtained match the results of Reinelt and Saffman [#!Reinelt85!#], but differ somewhat from those of Halpern and Gaver [#!Halpern94!#] for capillary numbers above 2. A limiting finger width close to 1/2 is obtained for high capillary numbers and high viscosity ratios. Received 25 May 1999 and Received in final form 19 November 1999     

Anharmonic oscillators energies via artificial perturbation method

A new pseudoperturbative (artificial in nature) methodical proposal [#!ref15!#] is used to solve for Schr?dinger equation with a class of phenomenologically useful and methodically challenging anharmonic oscillator potentials . The effect of the [#!ref4!#,#!ref5!#] Padé approximant on the leading eigenenergy term is studied. Comparison with results from numerical (exact) and several eligible (approximation) methods is made. Received 2 July 1999 and Received in final form 18 November 1999     

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in [#!bcre!#] to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We relate the critical wave vector to the mean hopping length and to the ratio of the flight time to the `stick' time. We provide an intuitive interpretation of the instability. Received: 30 January 1998 / Revised: 12 May 1998 / Accepted: 8 June 1998     

Vesicles in haptotaxis with hydrodynamical dissipation

We analyze the problem of vesicle migration in haptotaxis (a motion directed by an adhesion gradient), though most of the reasoning applies to chemotaxis as well as to a variety of driving forces. A brief account has been published on this topic [#!Cantat99a!#]. We present an extensive analysis of this problem and provide a basic discussion of most of the relevant processes of migration. The problem allows for an arbitrary shape evolution which is compatible with the full hydrodynamical flow in the Stokes limit. The problem is solved within the boundary integral formulation based on the Oseen tensor. For the sake of simplicity we confine ourselves to 2D flows in the numerical analysis. There are basically two regimes (i) the tense regime where the vesicle behaves as a “droplet” with an effective contact angle. In that case the migration velocity is given by the Stokes law. (ii) The flask regime where the vesicle has a significant (on the scale of the vesicle size) contact curvature. In that case we obtain a new migration law which substantially differs from the Stokes law. We develop general arguments in order to extract analytical laws of migration. These are in good agreement with the full numerical analysis. Finally we mention several important future issues and open questions. Received 24 June 2002 and Received in final form 4 February 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: isabelle.cantat@univ-rennes1.fr     

Random inelasticity and velocity fluctuations in a driven granular gas

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the “stochastic thermostat” model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high-velocity stretched-exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics. Received: 27 May 2002 / Accepted: 6 May 2003 / Published online: 27 May 2003 RID="a" ID="a"e-mail: Alain.Barrat@th.u-psud.fr     

Dilatancy and friction in sheared granular media

We introduce a simple model to describe the frictional properties of granular media under shear. We model the friction force in terms of the horizontal velocity and the vertical position z of the slider, interpreting z as a constitutive variable characterizing the contact. Dilatancy is shown to play an essential role in the dynamics, inducing a stick-slip instability at low velocity. We compute the phase diagram, analyze numerically the model for a wide range of parameters and compare our results with experiments on dry and wet granular media, obtaining a good agreement. In particular, we reproduce the hysteretic velocity dependence of the frictional force. Received 16 November 1999     

Cluster formation, pressure and density measurements in a granular medium fluidized by vibrations

We report experimental results on the behavior of an ensemble of inelastically colliding particles, excited by a vibrated piston in a vertical cylinder. When the particle number is increased, we observe a transition from a regime where the particles have erratic motions (“granular gas”) to a collective behavior where all the particles bounce like a nearly solid body. In the gas-like regime, we measure the density of particles as a function of the altitude and the pressure as a function of the number N of particles. The atmosphere is found to be exponential far enough from the piston, and the “granular temperature”, T, dependence on the piston velocity, V, is of the form , where is a decreasing function of N. This may explain previous conflicting numerical results. Received 1 February 1999     

Comment on “Growth of Molecular Superlattice in Fully Hydrated Dipalmitoylphosphatidylcholine during Subgel Phase Formation Process” by H. Takahashi, K. Hatta and I. Hatta

This comment shows that data recently reported [#!ref1!#] as being seemingly in conflict with earlier data [#!ref2!#] are, in fact, in excellent agreement. Together, both studies confirm that the kinetics of the subgel phase transformation in dipalmitoylphosphatidylcholine (DPPC) lipid bilayers obeys Kolmogorov-Avrami (K-A) theory [#!ref3!#,#!ref4!#] with an anomalously low effective dimensionality. Received: 11 December 1997 / Accepted: 28 January 1998     

“Linearized” dynamical mean-field theory for the Mott-Hubbard transition

The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are linearized, and the value for the critical Coulomb repulsion can be calculated analytically. For the symmetric single-band Hubbard model at zero temperature, the critical value is found to be given by 6 times the square root of the second moment of the free (U=0) density of states. This result is in good agreement with the numerical value obtained from the Projective Selfconsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generalization to more complicated lattices is discussed. The “linearized DMFT” yields plausible results for the complete geometry dependence of the critical interaction. Received 6 May 1999 and Received in final form 2 July 1999     

Anisotropic velocity distributions in 3D dissipative optical lattices

We present a direct measurement of velocity distributions in two dimensions by using an absorption imaging technique in a 3D near resonant optical lattice. The results show a clear difference in the velocity distributions for the different directions. The experimental results are compared with a numerical 3D semi-classical Monte-Carlo simulation. The numerical simulations are in good qualitative agreement with the experimental results. Received 3 September 2002 / Received in final form 25 October 2002 Published online 11 February 2003     

Ab initio lattice dynamics and elastic constants of ZrC

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 222 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data. Received 2 July 1999 and Received in final form 26 November 1999     

High-pressure subsonic mode operation of chemical oxygen-iodine laser

A new regime of chemical oxygen-iodine laser (COIL), high-pressure subsonic mode operation, was demonstrated using a jet-type singlet oxygen generator (SOG). The laser output power of 342 W with chemical efficiency of 20.9% was obtained at the Cl₂ flow rate of 18 mmol/s and the operating pressure of 6.4 Torr in the laser cavity. The specific energy was 3.1 J/l which was four times higher than our supersonic device, and was comparable to the highest value for the supersonic regime. The experimental results were in good agreement with the numerical simulation results. Received: 26 February 1999 / Revised version: 13 July 1999 / Published online: 30 November 1999     

Granular flow from a silo: Discrete-particle simulations in three dimensions

Molecular (or granular) dynamics methods are used to study the gravity-driven flow of granular material through a horizontal aperture in three dimensions. The grains are spherical and modeled using a short-range repulsive interaction, together with normal and tangential frictional damping forces. The material is contained in a rough-walled cylindrical container with a circular hole in its base, and to permit flow measurements under steady-state conditions a continuous feed approach is employed in which exiting grains are replaced at the upper surface of the material. The dependence of flow velocity and discharge rate on aperture diameter is found to agree with experiment; other quantities such as the kinetic energy and pressure distributions are also examined. Received 5 June 2000 and Received in final form 21 September 2000     

Scaling approach of the convective drying of a porous medium

We propose a simplified, theoretical approach of the evolution of liquid distribution during the convective drying of a granular packing. In the absence of gravity effects three regimes are distinguished according to the relative importance of surface evaporation, capillarity or evaporation from the interior of the sample. The evolution of the drying rate as a function of the saturation can be inferred from the characteristic velocities associated to each of these effects. We also carried out drying experiments of bead packings saturated with ethanol, at four different velocities of the boundary convection current, and with bead size ranging from 4.5 to 100 μm. The drying curves exhibit different regimes with a scaling as a function of particle radius and current velocity as predicted by the theory. Received 7 June 1999 and Received in final form 25 October 1999     

The correlation length of commodity markets 2. Theoretical framework

The second of this series of two papers is devoted to a theoretical analysis of spatial interaction between commodity markets. The theoretical framework that we present is referred to as the stochastic spatial arbitrage model (SSAM); it accounts for most of the empirical regularities observed in the first paper. Two basic mechanisms are found to be responsible for spatial inter-market interaction, namely (i) spatial arbitrage and hedging conducted by traders, (ii) spatial correlation between local shocks; the latter is favored by a similar economic and cultural environment. The SSAM includes both effects and offers a wide range of predictions about price volatility, trade, price correlations, price differentials. Statistical tests display a convergent array of evidence in favor of the model. However several predictions cannot be tested by lack of statistical evidence, a circumstance which shows that yet additional “experimental” work is r! equired. Received 17 May 1999 and Received in final form 31 May 1999     

Steps and facets at the surface of soft crystals

We consider the shape of crystals which are soft in the sense that their elastic modulus μ is small compared to their surface tension γ, more precisely μa < γ where a is the lattice spacing. We show that their surface steps penetrate inside the crystal as edge dislocations. As a consequence, these steps are broad with a small energy which we calculate. We also calculate the elastic interaction between steps a distance d apart, which is a 1/d ² repulsion. We finally calculate the roughening temperatures of successive facets in order to compare with the remarkable shapes of lyotropic crystals recently observed by Pieranski et al. [#!Pieranski!#,#!EPJ!#]. Good agreement is found. Received 25 June 2001     

Nuclear spin conversion in CH F induced by an alternating electric field

The nuclear spin conversion in CH₃F molecules subjected to an alternating electric field was investigated experimentally. The conversion rate was found to be almost unaffected by low electric fields ( V/cm) but sharply increased tenfold when the electric field amplitude exceeds the values ( V/cm) sufficiently high to produce crossings of the ortho and para states of the molecule. A theoretical model for the molecular conversion in alternating electric field was developed. The results of the experiment were found to be in a good agreement with the theory. Received 23 July 1999 and Received in final form 7 September 1999     

Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected. Received 4 June 1999 and Received in final form 28 September 1999     

Stereoscopic flow-tagging velocimetry

A laser-based method for measuring the three components of the velocity in a plane simultaneously and instantaneously without seed particles is presented. This is achieved by combining a laser flow-tagging technique with stereoscopic detection, in which the tagged flow is viewed from two different directions. A single CCD camera is employed for this purpose by using a new optical detection system. The flow tagging is performed by two consecutive laser pulses, i.e., “write” and “read” laser pulses. The write laser creates a grid of tracer molecules (NO) by inducing a photodissociation process. The three-dimensional motion of the tracer molecules is measured by a thick read laser sheet. Received: 22 July 1999 / Revised version: 5 August 1999 / Published online: 30 September 1999