Large droplet impact on water layers

The impact of large droplets onto an otherwise undisturbed layer of water is considered. The work, which is motivated primarily with regard to aircraft icing, is to try and help understand the role of splashing on the formation of ice on a wing, in particular for large droplets where splash appears, to have a significant effect. Analytical and numerical approaches are used to investigate a single droplet impact onto a water layer. The flow for small times after impact is determined analytically, for both direct and oblique impacts. The impact is also examined numerically using the volume of fluid (VOF) method. At small times there are promising comparisons between the numerical results, the analytical solution and experimental work capturing the ejector sheet. At larger times there is qualitative agreement with experiments and related simulations. Various cases are considered, varying the droplet size to layer depth ratio, including surface roughness, droplet distortion and air effects. The amount of fluid splashed by such an impact is examined and is found to increase with droplet size and to be significantly influenced by surface roughness. The makeup of the splash is also considered, tracking the incoming fluid, and the splash is found to consist mostly of fluid originating in the layer

Response properties in a model for granular matter

We investigate the response properties of granular media in the framework of the so-called {\em Random Tetris Model}. We monitor, for different driving procedures, several quantities: the evolution of the density and of the density profiles, the ageing properties through the two-times correlation functions and the two-times mean-square distance between the potential energies, the response function defined in terms of the difference in the potential energies of two replica driven in two slightly different ways. We focus in particular on the role played by the spatial inhomogeneities (structures) spontaneously emerging during the compaction process, the history of the sample and the driving procedure. It turns out that none of these ingredients can be neglected for the correct interpretation of the experimental or numerical data. We discuss the problem of the optimization of the compaction process and we comment on the validity of our results for the description of granular materials in a thermodynamic framework.Comment: 22 pages, 35 eps files (21 figures

Long range correlations in the non-equilibrium quantum relaxation of a spin chain

We consider the non-stationary quantum relaxation of the Ising spin chain in a transverse field of strength h. Starting from a homogeneously magnetized initial state the system approaches a stationary state by a process possessing quasi long range correlations in time and space, independent of the value of $h$. In particular the system exhibits aging (or lack of time translational invariance on intermediate time scales) although no indications of coarsening are present.Comment: 4 pages RevTeX, 2 eps-figures include

Phase transitions and the internal noise structure of nonlinear Schr\"odi nger equation solitons

We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schr\"odinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude. These phase-transitions are robust with respect to Raman noise and scattering losses. We also describe the rich internal quantum noise structure of the solitonic fields in the vicinity of the phase-transition. For optical coherent quantum solitons, this leads to the prediction that eliminating the peak side-band noise due to the electronic nonlinearity of silica fiber by spectral filtering leads to the optimal photon-number noise reduction of a fundamental soliton.Comment: 10 pages, 5 figure

On-column conductivity detection in capillary-chip electrophoresis

On-column conductivity detection in capillary-chip electrophoresis was achieved by actively coupling the high electric field with two sensing electrodes connected to the main capillary channel through two side detection channels. The principle of this concept was demonstrated by using a glass ch p with a separation channel incorporating two double-Ts. One double-T was used for sample introduction, and the other for detection. The two electrophoresis electrodes apply the high voltage and provide the current, and the two sensing electrodes connected to the separation channel through the second double-T and probe a potential difference. This potential difference is directly related to the local resistance or the conductivity of the solution defined by the two side channels on the main separation channel. A detection limit of 15 mM (600 ppb or 900 fg) was achieved for potassium ion in a 2 mM Tris-HCl buffer (pH 8.7) with a linear range of 2 orders of magnitude without any stacking. The proposed detection method avoids integrating the sensing electrodes directly within the separation channel and prevents any direct contact of the electrodes with the sample. The baseline signal can also be used for online monitoring of the electric field strength and electroosmosis mobility characterization in the separation channel

Dynamic instability of a rotating Bose-Einstein condensate

We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the non-linear Schr\"odinger equation to determine almost analytically the evolution of the condensate. We predict that this evolution can exhibit dynamical instabilities, for the stirring procedure previously demonstrated at ENS and for a new stirring procedure that we put forward. These instabilities take place within the range of stirring frequency and amplitude for which vortices are produced experimentally. They provide therefore an initiating mechanism for vortex nucleation.Comment: 4 pages, 3 figures, last version including comparison with experiment

Memory Effects in Granular Material

We present a combined experimental and theoretical study of memory effects in vibration-induced compaction of granular materials. In particular, the response of the system to an abrupt change in shaking intensity is measured. At short times after the perturbation a granular analog of aging in glasses is observed. Using a simple two-state model, we are able to explain this short-time response. We also discuss the possibility for the system to obey an approximate pseudo-fluctuation-dissipation theorem relationship and relate our work to earlier experimental and theoretical studies of the problem.Comment: 5 pages, 4 figures, reference list change

Rheophysics of dense granular materials : Discrete simulation of plane shear flows

We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasi-static regime of soil mechanics, while large values of I correspond to the collisional regime of the kinetic theory. Those shear states are homogeneous, and become intermittent in the quasi-static regime. When I increases in the intermediate regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. We also show that the relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains (restitution, friction and elasticity) have a very small influence in this intermediate regime. Then, we explain how the friction law is related to the angular distribution of contact forces, and why the local frictional forces have a small contribution to the macroscopic friction. At the end, as an example of heterogeneous stress distribution, we describe the shear localization when gravity is added.Comment: 24 pages, 19 figure

A system of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify a system of ODEs similar to those from Comech and Pelinovsky (2003), which model the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, which is in accord with the conclusions of Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a soliton structure, a generic initial perturbation oscillates around the stable family of solitons. For initial data which is expected to disperse, the finite dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit

Signatures of granular microstructure in dense shear flows

Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion leaving adjacent regions essentially rigid[1,2,3,4,5]. Since shear bands mark areas of flow, material failure and energy dissipation, they play a crucial role for many industrial, civil engineering and geophysical processes[6]. They also appear in related contexts, such as in lubricating fluids confined to ultra-thin molecular layers[7]. Detailed information on motion within a shear band in a three-dimensional geometry, including the degree of particle rotation and inter-particle slip, is lacking. Similarly, only little is known about how properties of the individual grains - their microstructure - affect movement in densely packed material[5]. Combining magnetic resonance imaging, x-ray tomography, and high-speed video particle tracking, we obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.Comment: 5 pages, incl. 4 figure