258 research outputs found
Thin front propagation in steady and unsteady cellular flows
Front propagation in two dimensional steady and unsteady cellular flows is
investigated in the limit of very fast reaction and sharp front, i.e., in the
geometrical optics limit. In the steady case, by means of a simplified model,
we provide an analytical approximation for the front speed,
, as a function of the stirring intensity, , in good
agreement with the numerical results and, for large , the behavior
is predicted. The large scale of the
velocity field mainly rules the front speed behavior even in the presence of
smaller scales. In the unsteady (time-periodic) case, the front speed displays
a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is
chaotic, chaos in front dynamics only survives for a transient. Asymptotically
the front evolves periodically and chaos manifests only in the spatially
wrinkled structure of the front.Comment: 12 pages, 13 figure
Capillary buckling of a thin film adhering to a sphere
We present a combined theoretical and experimental study of the buckling of a
thin film wrapped around a sphere under the action of capillary forces. A rigid
sphere is coated with a wetting liquid, and then wrapped by a thin film into an
initially cylindrical shape. The equilibrium of this cylindrical shape is
governed by the antagonistic effects of elasticity and capillarity: elasticity
tends to keep the film developable while capillarity tends to curve it in both
directions so as to maximize the area of contact with the sphere. In the
experiments, the contact area between the film and the sphere has cylindrical
symmetry when the sphere radius is small, but destabilises to a non-symmetric,
wrinkled configuration when the radius is larger than a critical value. We
combine the Donnell equations for near-cylindrical shells to include a
unilateral constraint with the impenetrable sphere, and the capillary forces
acting along a moving edge. A non-linear solution describing the axisymmetric
configuration of the film is derived. A linear stability analysis is then
presented, which successfully captures the wrinkling instability, the symmetry
of the unstable mode, the instability threshold and the critical wavelength.
The motion of the free boundary at the edge of the region of contact, which has
an effect on the instability, is treated without any approximation
Cracks in Tension-Field Elastic Sheets
International audienceWe consider the deformation of a thin elastic sheet which is stiff in traction but very soft in compression, as happens in presence of wrinkling. We use the tension-field material model and explore numerically the response of a thin sheet containing multiple cracks of different geometries, when subjected to applied tension. With a single crack, the stress concentrates along a St-Andrew's cross-shaped pattern, whose branches extend from the crack tips to the corners of the domain; at a (small) distance r from the crack tip, the stress displays the usual stress singularity but with an unusual and non-universal angular dependence. A strong interaction between multiple cracks is reported and discussed: in particular, for certain configurations of the cracks, the tensile stiffness of a cracked sheet can be zero even though the sheet is made up of a single component
Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots
Article / Letter to editorLeids Instituut Onderzoek Natuurkund
Oscillatory fracture path in thin elastic sheet
We report a novel mode of oscillatory crack propagation when a cutting tip is
driven through a thin brittle polymer film. The phenomenon is so robust that it
can easily be reproduced at hand (using CD packaging material for example).
Careful experiments show that the amplitude and wavelength of the oscillatory
crack path scale lineraly with the width of the cutting tip over a wide range
of lenghtscales but are independant of the width of thje sheet and the cutting
speed. A simple geometric model is presented, which provides a simple but
thorough interpretation of the oscillations.Comment: 6 pages, submitted to Comptes Rendus Academie des Sciences. Movies
available at http://www.lmm.jussieu.fr/platefractur
Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots
We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to quantify the dependence of the mechanical response of the knot as a function of the geometry of the self-contacting region, and for different topologies as measured by their crossing number. An analytical model based on the nonlinear theory of thin elastic rods is then developed to describe how the physical and topological parameters of the knot set the tensile force required for equilibrium. Excellent agreement is found between theory and experiments for overhand knots over a wide range of crossing numbers.National Science Foundation (U.S.) (CMMI-1129894
Recommended from our members
From discrete to continuum models of three-dimensional deformations in epithelial sheets
International audienceEpithelial tissue, in which cells adhere tightly to each other and to theunderlying substrate, is one of the four major tissue types in adultorganisms. In embryos, epithelial sheets serve as versatile substratesduring the formation of developing organs. Some aspects of epithelialmorphogenesis can be adequately described using vertex models, in which thetwo-dimensional arrangement of epithelial cells is approximated by apolygonal lattice with an energy that has contributions reflecting theproperties of individual cells and their interactions. Previous studieswith such models have largely focused on dynamics confined to two spatialdimensions and analyzed them numerically. We show how these models can beextended to account for three-dimensional deformations and studiedanalytically. Starting from the extended model, we derive a continuumplate description of cell sheets, in which the effective tissue properties,such as bending rigidity, are related explicitly to the parameters of thevertex model. To derive the continuum plate model, we duly take intoaccount a microscopic shift between the two sublattices of the hexagonalnetwork, which has been ignored in previous work. As an application of thecontinuum model, we analyze tissue buckling by a line tension applied alonga circular contour, a simplified set-up relevant to several situations inthe developmental context. The buckling thresholds predicted by thecontinuum description are in good agreement with the results of directstability calculations based on the vertex model. Our results establish adirect connection between discrete and continuum descriptions of cellsheets and can be used to probe a wide range of morphogenetic processes inepithelial tissues
Thin front propagation in random shear flows
Front propagation in time dependent laminar flows is investigated in the
limit of very fast reaction and very thin fronts, i.e. the so-called
geometrical optics limit. In particular, we consider fronts evolving in time
correlated random shear flows, modeled in terms of Ornstein-Uhlembeck
processes. We show that the ratio between the time correlation of the flow and
an intrinsic time scale of the reaction dynamics (the wrinkling time ) is
crucial in determining both the front propagation speed and the front spatial
patterns. The relevance of time correlation in realistic flows is briefly
discussed in the light of the bending phenomenon, i.e. the decrease of
propagation speed observed at high flow intensities.Comment: 5 Revtex4 pages, 4 figures include
Pulsating Front Speed-up and Quenching of Reaction by Fast Advection
We consider reaction-diffusion equations with combustion-type non-linearities
in two dimensions and study speed-up of their pulsating fronts by general
periodic incompressible flows with a cellular structure. We show that the
occurence of front speed-up in the sense ,
with the amplitude of the flow and the (minimal) front speed, only
depends on the geometry of the flow and not on the reaction function. In
particular, front speed-up happens for KPP reactions if and only if it does for
ignition reactions. We also show that the flows which achieve this speed-up are
precisely those which, when scaled properly, are able to quench any ignition
reaction.Comment: 16p
- …