Transport and sedimentation of solid particles in Bénard hexagonal cells

The motion of particles moving under gravity in the velocity field of a liquid in a Bénard hexagonal cell is studied experimentally and numerically for Stokes flow conditions. We then explain the settlement of particles in the centers of cells to form a regular quincunx. It is found that sedimentation also occurs preferentially along the lines connecting the centers of adjacent cells to form a triangle deposition tessellation. Finally, it is explained why particles occupy the central part of each convective cell while the peripheral part of the cell quickly becomes limpid. Numerical results are in agreement with the experimental observations of Bénard and those of the present study.     

Development of an optical trap for microparticle clouds in dilute gases

Long-duration experiments with clouds of microparticles are planned for the ICAPS facility on board the International Space Station ISS. The scientific objectives of such experiments are widespread and are ranging from the simulation of aerosol behaviour in Earths atmosphere to the formation of planets in the early solar system. It is, however, even under microgravity conditions, impossible to sustain a cloud of free-floating, microscopic particles for an extended period of time, due to thermal diffusion and due to unavoidable external accelerations. Therefore, a trap for dust clouds is required which prevents the diffusion of the particles, which provides a source of relative velocities between the dust grains and which can also concentrate the dust to higher number densities that are otherwise not achievable. We are planning to use the photophoretic effect for such a particle trap. First short-duration microgravity experiments on the photophoretic motion of microscopic particles show that such an optical particle-cloud trap is feasible. First tests of a two-dimensional trap were performed in the Bremen drop tower.     

Network synthesis under survivability constraints

Telecommunication networks are subject to link and equipment failures. Since failures cannot be entirely avoided, networks have to be designed so as to survive failure situations. In this paper, we are interested in designing low cost survivable networks. Given point-to-point traffic demands and a cost/capacity function for each link, we aim at finding the minimum cost capacities satisfying the given demands and survivability requirements. A survivability model that reroutes interrupted traffic using all the available capacities on the network is presented and studied. In the proposed model, capacity and flow assignments for each network operating state are jointly optimized. We prove the -hardness of the optimisation problem defined by dual constraints. Then, we propose a polynomial relaxation along with a fast heuristic to compute a feasible solution of the problem from its relaxed optimal solution. Our solution approaches are tested on a set of problem instances.Received: September 2002, Revised: July 2003, AMS classification: 90C05     

An Incremental Algorithm for the Maximum Flow Problem

An incremental algorithm may yield an enormous computational time saving to solve a network flow problem. It updates the solution to an instance of a problem for a unit change in the input. In this paper we have proposed an efficient incremental implementation of maximum flow problem after inserting an edge in the network G. The algorithm has the time complexity of O((n)² m), where n is the number of affected vertices and m is the number of edges in the network. We have also discussed the incremental algorithm for deletion of an edge in the network G.     

Noise correlations in shear flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions. Received 26 February 2002 / Received in final form 11 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bruno.eckhardt@physik.uni-marburg.de RID="b" ID="b"Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India     

Pseudo-Anosov Flows and Incompressible Tori

We study incompressible tori in 3-manifolds supporting pseudo-Anosov flows and more generally ZZ subgroups of the fundamental group of such a manifold. If no element in this subgroup can be represented by a closed orbit of the pseudo-Anosov flow, we prove that the flow is topologically conjugate to a suspension of an Anosov diffeomorphism of the torus. In particular it is non singular and is an Anosov flow. It follows that either a pseudo-Anosov flow is topologically conjugate to a suspension Anosov flow, or any immersed incompressible torus can be realized as a free homotopy from a closed orbit of the flow to itself. The key tool is an analysis of group actions on non-Hausdorff trees, also known as R-order trees – we produce an invariant axis in the free action case. An application of these results is the following: suppose the manifold has an R-covered foliation transverse to a pseudo-Anosov flow. If the flow is not an R-covered Anosov flow, then it follows that the manifold is atoroidal.     

Invariant Metrics on Nilmanifolds with Positive Topological Entropy

Let T _n denote the group of real n × n upper-triangular matrices with 1s on the diagonal. This paper constructs left-invariant Riemannian and sub-Riemannian metrics on T ₃ T ₄ whose geodesic flow has a subsystem that factors onto a suspended horseshoe. As a corollary, left-invariant Riemannian metrics with positive topological entropy are constructed on all quotients DT _n where D is a discrete subgroup of T _n and n 7.     

Polymer and surface roughness effects on the drag crisis for falling spheres

We make time resolved velocity measurements of steel spheres in free fall through liquid using a continuous ultrasound technique. We explore two different ways to induce large changes in drag on the spheres: 1) a small quantity of viscoelastic polymer added to water and 2) altering the surface of the sphere. Low concentration polymer solutions and/or a pattern of grooves in the sphere surface induce an early drag crisis, which may reduce drag by more than 50% compared to smooth spheres in pure water. On the other hand, random surface roughness and/or high concentration polymer solutions reduce drag progressively and suppress the drag crisis. We also present a qualititative argument which ties the drag reduction observed in low concentration polymer solutions to the Weissenberg number and normal stress difference.     

Viscous potential flow analysis of Kelvin-Helmholtz instability with mass transfer and vaporization

Viscous potential flow analysis of Kelvin-Helmholtz instability with heat and mass transfer has been studied. A dispersion relation has been obtained. Stability criterion is given by a critical value of relative velocity. It has been found that heat and mass transfer has destabilizing effect on relative velocity when lower fluid viscosity is low while it has stabilizing effect when lower fluid viscosity is high. Various graphs have been plotted for relative velocity and growth rate. In statically unstable situation viscosity has stabilizing effect while in statically stable situation it has destabilizing effect.     

Unified semi‐analytical wall boundary conditions for inviscid,laminar or turbulent flows in the meshless SPH method

Wall boundary conditions in smoothed particle hydrodynamics (SPH) is a key issue to perform accurate simulations. We propose here a new approach based on a renormalising factor for writing all boundary terms. This factor depends on the local shape of a wall and on the position of a particle relative to the wall, which is described by segments (in two‐dimensions), instead of the cumbersome fictitious or ghost particles used in most existing SPH models. By solving a dynamic equation for the renormalising factor, we significantly improve traditional wall treatment in SPH, for pressure forces, wall friction and turbulent conditions. The new model is demonstrated for cases including hydrostatic conditions for still water in a tank of complex geometry and a dam break over triangular bed profile with sharp angle where significant improved behaviour is obtained in comparison with the conventional boundary techniques. The latter case is also compared with a finite volume and volume‐of‐fluid scheme. The performance of the model for a two‐dimensional laminar flow in a channel is demonstrated where the profiles of velocity are in agreement with the theoretical ones, demonstrating that the derived wall shear stress balances the pressure gradient. Finally, the performance of the model is demonstrated for flow in a schematic fish pass where both the velocity field and turbulent viscosity fields are satisfactorily reproduced compared with mesh‐based codes. Copyright © 2012 John Wiley & Sons, Ltd.