Settling of an asymmetric dumbbell in a quiescent fluid

We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal then fluid inertia causes the dumbbell to settle in a horizontal orientation.Comment: 11 pages, 1 figure, as publishe

Journey of an intruder through the fluidisation and jamming transitions of a dense granular media

We study experimentally the motion of an intruder dragged into an amorphous monolayer of horizontally vibrated grains at high packing fractions. This motion exhibits two transitions. The first transition separates a continuous motion regime at comparatively low packing fractions and large dragging force from an intermittent motion one at high packing fraction and low dragging force. Associated to these different motions, we observe a transition from a linear rheology to a stiffer response. We thereby call "fluidisation" this first transition. A second transition is observed within the intermittent regime, when the intruder's motion is made of intermittent bursts separated by long waiting times. We observe a peak in the relative fluctuations of the intruder's displacements and a critical scaling of the burst amplitudes distributions. This transition occurs at the jamming point characterized in a previous study and defined as the point where the static pressure (i.e. the pressure measured in the absence of vibration) vanishes. Investigating the motion of the surrounding grains, we show that below the fluidisation transition, there is a permanent wake of free volume behind the intruder. This transition is marked by the evolution of the reorganization patterns around the intruder, which evolve from compact aggregates in the flowing regime to long-range branched shapes in the intermittent regime, suggesting an increasing role of the stress fluctuations. Remarkably, the distributions of the kinetic energy of these reorganization patterns also exhibits a critical scaling at the jamming transition.Comment: 12 pages, 11 figure

Note on the method of matched-asymptotic expansions for determining the force acting on a particle

This paper is an addendum to the article by Candelier, Mehaddi & Vauquelin (2013) where the motion of a particle in a stratified fluid is investigated theoretically, at small Reynolds and P\'eclet numbers. We review briefly the method of matched asymptotic expansions which is generally used in order to determine the force acting on a particle embedded in a given flow, in order to account for small, but finite, inertia effects. As part of this method, we present an alternative matching procedure, which is based on a series expansion of the far-field solution of the problem, performed in the sense of generalized functions. The way to perform such a series is presented succinctly and a simple example is provided.Comment: 8 page

Movimientos literarios en América y la visión de la independencia / Literary movements in America and the vision for independence

realización de esa empresa libertaria, fueron necesarias acciones heroicas que demandaron la participación de los próceres de la sociedad, así como de sus líderes, pensadores y escritores, razón por la cual la literatura fue una valiosa arma de combate intelectual que atizó las aspiraciones y los ideales separatistas en los diferentes pueblos del Continente americano. La vocación de autonomía política a la que aspiraban los escritores hispanoamericanos del siglo XIX motorizó la primera generación de literatos que en América hicieron uso de la palabra al calor de las rebeliones que implicaba la Independencia Nacional. Políticos, intelectuales, escritores, maestros, sacerdotes y periodistas se alinearon en esa meta separatista que encendió la vocación literaria y el activismo social, político y cultural en las capas pensantes de los pueblos americanos. Al tiempo que describe facetas de la realidad natural, la realidad histórica y la realidad social, la literatura perfila el talante interpretativo, imaginativo y cultural de los países hispanoamericanos. Fueron narradores, poetas y dramaturgos, los abanderados del ideal independentista que asumieron la vanguardia política, social y cultural en los pueblos de habla hispana en nuestra América. La narrativa indianista, la poesía patriótica y el teatro popular fueron tres vertientes claves de la creatividad literaria que dieron cauce y brillantez al proyecto nacionalista de las diversas poblaciones de la América hispana durante el siglo XIX. Concitados por el Romanticismo, el Realismo y el Modernismo, tres corrientes estéticas de inspiración francesa, las naciones americanas de habla hispana desarrollaron sus inclinaciones intelectuales, morales, estéticas y espirituales, mientras prohijaban el ideal de independencia política bajo la llama del sueño libertario y la utopía. De ahí el rol estimulador de la literatura, que la poesía, la narrativa, el teatro, el periodismo y la oratoria encauzaron en diferentes escenarios y tribunas, desde las aulas del magisterio universitario hasta el púlpito de los templos sagrados, haciendo de la palabra el arma espiritual en las treguas del combate y la esperanza.In the nineteenth century occurring struggles for independence of Latin American nations. For the realization of this libertarian company heroic actions were necessary, participation was demanded of dignitaries of the society and its leaders, thinkers and writers. This is why literature was a valuable intellectual weapon that fueled the aspirations and separatist ideology in the various countries of the American Continent. Were the storytellers, poets and playwrights and torchbearers of independence ideal who assumed the political, social and cultural vanguard in the towns of Spanish speaking in our American nations. The native Indian narrative, patriotic poetry and popular theater were three key aspects of literary creativity that gave means and brilliance to the nationalistic project of diverse populations of Hispanic America during the nineteen century. Aroused by Romanticism, Realism and Modernism three aesthetic currents of French decent, America’s Spanish-speaking nations developed their intellectual, moral, aesthetic and spiritual inclinations, while prohibiting the ideal of political independence under the name of libertarian dream and utopia. Hence the stimulatory role of literature, poetry, fiction, drama, journalism and oratory channeled in different scenarios and galleries , from the university classroom to the pulpit teaching in sacred temples, making the word the spiritual weapon in the fight and hope

Super-diffusion around the rigidity transition: Levy and the Lilliputians

By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a genuine Levy flight, but with `jump' size very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.Comment: 7 pages, 6 figure

The history force on a small particle in a linearly stratified fluid

The hydrodynamic force experienced by a small spherical particle undergoing an arbitrary time-dependent motion in a density-stratified fluid is investigated theoretically. The study is carried out under the Oberbeck-Boussinesq approximation, and in the limit of small Reynolds and small P\'eclet numbers. The force acting on the particle is obtained by using matched asymptotic expansions in which the small parameter is given by a/l where a is the particle radius and l is the stratification length defined by Ardekani & Stocker (2010), which depends on the Brunt-Vaisala frequency, on the fluid kinematic viscosity and on the thermal or the concentration diffusivity (depending on the case considered). The matching procedure used here, which is based on series expansions of generalized functions, slightly differs from that generally used in similar problems. In addition to the classical Stokes drag, it is found the particle experiences a memory force given by two convolution products, one of which involves, as usual, the particle acceleration and the other one, the particle velocity. Owing to the stratification, the transient behaviour of this memory force, in response to an abrupt motion, consists of an initial fast decrease followed by a damped oscillation with an angular-frequency corresponding to the Brunt-Vaisala frequency. The perturbation force eventually tends to a constant which provides us with correction terms that should be added to the Stokes drag to accurately predict the settling time of a particle in a diffusive stratified-fluid.Comment: 16 page

Effect of weak fluid inertia upon Jeffery orbits

We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the "Jeffery orbits". We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyse how the linear stability of the \lq log-rolling\rq{} orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general both unsteady and non-linear terms in the Navier-Stokes equations are important.Comment: 5 pages, 2 figure