264 research outputs found
Nonlinear evolution of step meander during growth of a vicinal surface with no desorption
Step meandering due to a deterministic morphological instability on vicinal
surfaces during growth is studied. We investigate nonlinear dynamics of a step
model with asymmetric step kinetics, terrace and line diffusion, by means of a
multiscale analysis. We give the detailed derivation of the highly nonlinear
evolution equation on which a brief account has been given [Pierre-Louis et.al.
PRL(98)]. Decomposing the model into driving and relaxational contributions, we
give a profound explanation to the origin of the unusual divergent scaling of
step meander ~ 1/F^{1/2} (where F is the incoming atom flux). A careful
numerical analysis indicates that a cellular structure arises where plateaus
form, as opposed to spike-like structures reported erroneously in Ref.
[Pierre-Louis et.al. PRL(98)]. As a robust feature, the amplitude of these
cells scales as t^{1/2}, regardless of the strength of the Ehrlich-Schwoebel
effect, or the presence of line diffusion. A simple ansatz allows to describe
analytically the asymptotic regime quantitatively. We show also how
sub-dominant terms from multiscale analysis account for the loss of up-down
symmetry of the cellular structure.Comment: 23 pages, 10 figures; (Submitted to EPJ B
Dynamics of aeolian sand ripples
We analyze theoretically the dynamics of aeolian sand ripples. In order to
put the study in the context we first review existing models. We argue on the
local character of sand ripple formation. Using a hydrodynamical model we
derive a nonlinear equation for the sand profile. We show how the
hydrodynamical model may be modified to recover the missing terms that are
dictated by symmetries. The symmetry and conservation arguments are powerful in
that the form of the equation is model-independent. We then present an
extensive numerical and analytical analysis of the generic sand ripple
equation. We find that at the initial stage the wavelength of the ripple is
that corresponding to the linearly most dangerous mode. At later stages the
profile undergoes a coarsening process leading to a significant increase of the
wavelength. We find that including the next higher order nonlinear term in the
equation, leads naturally to a saturation of the local slope. We analyze both
analytically and numerically the coarsening stage, in terms of a dynamical
exponent for the mean wavelength increase. We discuss some future lines of
investigations.Comment: 22 pages and 10 postscript figure
New analytical progress in the theory of vesicles under linear flow
Vesicles are becoming a quite popular model for the study of red blood cells
(RBCs). This is a free boundary problem which is rather difficult to handle
theoretically. Quantitative computational approaches constitute also a
challenge. In addition, with numerical studies, it is not easy to scan within a
reasonable time the whole parameter space. Therefore, having quantitative
analytical results is an essential advance that provides deeper understanding
of observed features and can be used to accompany and possibly guide further
numerical development. In this paper shape evolution equations for a vesicle in
a shear flow are derived analytically with precision being cubic (which is
quadratic in previous theories) with regard to the deformation of the vesicle
relative to a spherical shape. The phase diagram distinguishing regions of
parameters where different types of motion (tank-treading, tumbling and
vacillating-breathing) are manifested is presented. This theory reveals
unsuspected features: including higher order terms and harmonics (even if they
are not directly excited by the shear flow) is necessary, whatever the shape is
close to a sphere. Not only does this theory cure a quite large quantitative
discrepancy between previous theories and recent experiments and numerical
studies, but also it reveals a new phenomenon: the VB mode band in parameter
space, which is believed to saturate after a moderate shear rate, exhibits a
striking widening beyond a critical shear rate. The widening results from
excitation of fourth order harmonic. The obtained phase diagram is in a
remarkably good agreement with recent three dimensional numerical simulations
based on the boundary integral formulation. Comparison of our results with
experiments is systematically made.Comment: a tex file and 6 figure
Hydrodynamic lift of vesicles under shear flow in microgravity
The dynamics of a vesicle suspension in a shear flow between parallel plates
has been investigated under microgravity conditions, where vesicles are only
submitted to hydrodynamic effects such as lift forces due to the presence of
walls and drag forces. The temporal evolution of the spatial distribution of
the vesicles has been recorded thanks to digital holographic microscopy, during
parabolic flights and under normal gravity conditions. The collected data
demonstrates that vesicles are pushed away from the walls with a lift velocity
proportional to where is the shear rate,
the vesicle radius and its distance from the wall. This scaling as well
as the dependence of the lift velocity upon vesicle aspect ratio are consistent
with theoretical predictions by Olla [J. Phys. II France {\bf 7}, 1533--1540
(1997)].Comment: 6 pages, 8 figure
Amplitude equations for systems with long-range interactions
We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review
Two-dimensional Vesicle dynamics under shear flow: effect of confinement
Dynamics of a single vesicle under shear flow between two parallel plates is
studied using two-dimensional lattice-Boltzmann simulations. We first present
how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using
an approach known from the immersed boundary method. The fluid flow is computed
on an Eulerian regular fixed mesh while the location of the vesicle membrane is
tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle
equilibrium shapes in a fluid at rest are found and the dynamical behavior of a
vesicle under simple shear flow is being reproduced. Further, we focus on
investigating the effect of the confinement on the dynamics, a question that
has received little attention so far. In particular, we study how the vesicle
steady inclination angle in the tank-treading regime depends on the degree of
confinement. The influence of the confinement on the effective viscosity of the
composite fluid is also analyzed. At a given reduced volume (the swelling
degree) of a vesicle we find that both the inclination angle, and the membrane
tank-treading velocity decrease with increasing confinement. At sufficiently
large degree of confinement the tank-treading velocity exhibits a
non-monotonous dependence on the reduced volume and the effective viscosity
shows a nonlinear behavior.Comment: 12 pages, 8 figure
Lateral migration of a 2D vesicle in unbounded Poiseuille flow
The migration of a suspended vesicle in an unbounded Poiseuille flow is
investigated numerically in the low Reynolds number limit. We consider the
situation without viscosity contrast between the interior of the vesicle and
the exterior. Using the boundary integral method we solve the corresponding
hydrodynamic flow equations and track explicitly the vesicle dynamics in two
dimensions. We find that the interplay between the nonlinear character of the
Poiseuille flow and the vesicle deformation causes a cross-streamline migration
of vesicles towards the center of the Poiseuille flow. This is in a marked
contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12,
435(1980)]according to which the droplet moves away from the center (provided
there is no viscosity contrast between the internal and the external fluids).
The migration velocity is found to increase with the local capillary number
(defined by the time scale of the vesicle relaxation towards its equilibrium
shape times the local shear rate), but reaches a plateau above a certain value
of the capillary number. This plateau value increases with the curvature of the
parabolic flow profile. We present scaling laws for the migration velocity.Comment: 11 pages with 4 figure
An analytical analysis of vesicle tumbling under a shear flow
Vesicles under a shear flow exhibit a tank-treading motion of their membrane,
while their long axis points with an angle < 45 degrees with respect to the
shear stress if the viscosity contrast between the interior and the exterior is
not large enough. Above a certain viscosity contrast, the vesicle undergoes a
tumbling bifurcation, a bifurcation which is known for red blood cells. We have
recently presented the full numerical analysis of this transition. In this
paper, we introduce an analytical model that has the advantage of being both
simple enough and capturing the essential features found numerically. The model
is based on general considerations and does not resort to the explicit
computation of the full hydrodynamic field inside and outside the vesicle.Comment: 19 pages, 9 figures, to be published in Phys. Rev.
The effect of shear stress reduction on endothelial cells : a microfluidic study of the actin cytoskeleton
Reduced blood flow, as occurring in ischemia or resulting from exposure to microgravity such as encountered in space flights, induces a decrease in the level of shear stress sensed by endothelial cells forming the inner part of blood vessels. In the present study, we use a microvasculature-on-a-chip device in order to investigate in vitro the effect of such a reduction in shear stress on shear-adapted endothelial cells. We find that, within 1 h of exposition to reduced wall shear stress, human umbilical vein endothelial cells undergo reorganization of their actin skeleton with a decrease in the number of stress fibers and actin being recruited into the cells' peripheral band, indicating a fairly fast change in the cells' phenotype due to altered flow
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