135 research outputs found
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
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
Avalanches and Dynamical Correlations in supercooled liquids
We identify the pattern of microscopic dynamical relaxation for a two
dimensional glass forming liquid. On short timescales, bursts of irreversible
particle motion, called cage jumps, aggregate into clusters. On larger time
scales, clusters aggregate both spatially and temporally into avalanches. This
propagation of mobility, or dynamic facilitation, takes place along the soft
regions of the systems, which have been identified by computing
isoconfigurational Debye-Waller maps. Our results characterize the way in which
dynamical heterogeneity evolves in moderately supercooled liquids and reveal
that it is astonishingly similar to the one found for dense glassy granular
media.Comment: 4 pages, 3 figure
Rotation of a spheroid in a simple shear at small Reynolds number
We derive an effective equation of motion for the orientational dynamics of a
neutrally buoyant spheroid suspended in a simple shear flow, valid for
arbitrary particle aspect ratios and to linear order in the shear Reynolds
number. We show how inertial effects lift the degeneracy of the Jeffery orbits
and determine the stabilities of the log-rolling and tumbling orbits at
infinitesimal shear Reynolds numbers. For prolate spheroids we find stable
tumbling in the shear plane, log-rolling is unstable. For oblate particles, by
contrast, log-rolling is stable and tumbling is unstable provided that the
aspect ratio is larger than a critical value. When the aspect ratio is smaller
than this value tumbling turns stable, and an unstable limit cycle is born.Comment: 25 pages, 5 figure
The building blocks of dynamical heterogeneities in dense granular media
We investigate experimentally the connection between short time dynamics and
long time dynamical heterogeneities within a dense granular media under cyclic
shear. We show that dynamical heterogeneities result from a two timescales
process. Short time but already collective events consisting in clustered cage
jumps concentrate most of the non affine displacements. On larger timescales
such clusters appear aggregated both temporally and spatially in avalanches
which eventually build the large scales dynamical heterogeneities. Our results
indicate that facilitation plays an important role in the relaxation process
although it does not appear to be conserved as proposed in many models studied
in the literature.Comment: 4 pages, 4 figure
Hydrodynamic force on a small squirmer moving with a time-dependent velocity at small Reynolds numbers
We calculate the hydrodynamic force on a small spherical, unsteady squirmer
moving with a time-dependent velocity in a fluid at rest, taking into account
convective and unsteady fluid-inertia effects in perturbation theory. Our
results generalise those of Lovalenti and Brady (1993) from passive to active
spherical particles. We find that convective inertia changes the history
contribution to the hydrodynamic force, as it does for passive particles. We
determine how the hydrodynamic force depends on the swimming gait of the
unsteady squirmer. Since swimming breaks the spherical symmetry of the problem,
the force is not completely determined by the outer solution of the
asymptotic-matching problem, as it is for passive spheres. There are additional
contributions brought by the inhomogeneous solution of the inner problem. We
also compute the disturbance flow, illustrating convective and unsteady
fluid-inertia effects for a sudden start of the centre-of-mass motion, and for
swimming with a periodic gait. We discuss the implications of our findings for
small motile organisms in a marine environment.Comment: 16 pages, 4 figure
The role of inertia for the rotation of a nearly spherical particle in a general linear flow
We analyse the angular dynamics of a neutrally buoyant nearly spherical
particle immersed in a steady general linear flow. The hydrodynamic torque
acting on the particle is obtained by means of a reciprocal theorem, regular
perturbation theory exploiting the small eccentricity of the nearly spherical
particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur
Texture-induced modulations of friction force: the fingerprint effect
Dry solid friction is often accompanied by force modulations originating from
stick-slip instabilities. Here a distinct, quasi-static mechanism is evidenced
leading to quasi-periodic force oscillations during sliding contact between an
elastomer block, whose surface is patterned with parallel grooves, and finely
abraded glass slides. The dominant oscillation frequency is set by the ratio
between the sliding velocity and the period of the grooves. A mechanical model
is proposed that provides a quantitative prediction for the amplitude of the
force modulations as a function of the normal load, the period of the grooves
and the roughness characteristics of the substrate. The model's main ingredient
is the non-linearity of the friction law. Since such non-linearity is
ubiquitous for soft solids, this "fingerprint effect" should be relevant to a
large class of frictional configurations and might in particular have important
consequences in human (or humanoid) active digital touch.Comment: 4 page
Inertial drag on a sphere settling in a stratified fluid
We compute the drag force on a sphere settling slowly in a quiescent,
linearly stratified fluid. Stratification can significantly enhance the drag
experienced by the settling particle. The magnitude of this effect depends on
whether fluid-density transport around the settling particle is due to
diffusion, to advection by the disturbance flow caused by the particle, or due
to both. It therefore matters how efficiently the fluid disturbance is
convected away from the particle by fluid-inertial terms. When these terms
dominate, the Oseen drag force must be recovered. We compute by perturbation
theory how the Oseen drag is modified by diffusion and stratification. Our
results are in good agreement with recent direct-numerical simulation studies
of the problem at small Reynolds numbers and large (but not too large) Froude
numbers.Comment: 10 pages, 1 figur
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