115 research outputs found
Roughness of moving elastic lines - crack and wetting fronts
We investigate propagating fronts in disordered media that belong to the
universality class of wetting contact lines and planar tensile crack fronts. We
derive from first principles their nonlinear equations of motion, using the
generalized Griffith criterion for crack fronts and three standard mobility
laws for contact lines. Then we study their roughness using the self-consistent
expansion. When neglecting the irreversibility of fracture and wetting
processes, we find a possible dynamic rough phase with a roughness exponent of
and a dynamic exponent of z=2. When including the irreversibility,
we conclude that the front propagation can become history dependent, and thus
we consider the value as a lower bound for the roughness exponent.
Interestingly, for propagating contact line in wetting, where irreversibility
is weaker than in fracture, the experimental results are close to 0.5, while
for fracture the reported values of 0.55--0.65 are higher.Comment: 15 pages, 6 figure
Scaling of the buckling transition of ridges in thin sheets
When a thin elastic sheet crumples, the elastic energy condenses into a
network of folding lines and point vertices. These folds and vertices have
elastic energy densities much greater than the surrounding areas, and most of
the work required to crumple the sheet is consumed in breaking the folding
lines or ``ridges''. To understand crumpling it is then necessary to understand
the strength of ridges. In this work, we consider the buckling of a single
ridge under the action of inward forcing applied at its ends. We demonstrate a
simple scaling relation for the response of the ridge to the force prior to
buckling. We also show that the buckling instability depends only on the ratio
of strain along the ridge to curvature across it. Numerically, we find for a
wide range of boundary conditions that ridges buckle when our forcing has
increased their elastic energy by 20% over their resting state value. We also
observe a correlation between neighbor interactions and the location of initial
buckling. Analytic arguments and numerical simulations are employed to prove
these results. Implications for the strength of ridges as structural elements
are discussed.Comment: 42 pages, latex, doctoral dissertation, to be submitted to Phys Rev
Effective interactions between inclusions in complex fluids driven out of equilibrium
The concept of fluctuation-induced effective interactions is extended to
systems driven out of equilibrium. We compute the forces experienced by
macroscopic objects immersed in a soft material driven by external shaking
sources. We show that, in contrast with equilibrium Casimir forces induced by
thermal fluctuations, their sign, range and amplitude depends on specifics of
the shaking and can thus be tuned. We also comment upon the dispersion of these
shaking-induced forces, and discuss their potential application to phase
ordering in soft-materials.Comment: 10 pages, 8 figures, to appear in PR
Minimal surfaces and Reggeization in the AdS/CFT correspondence
We address the problem of computing scattering amplitudes related to the
correlation function of two Wilson lines and/or loops elongated along
light-cone directions in strongly coupled gauge theories. Using the AdS/CFT
correspondence in the classical approximation, the amplitudes are shown to be
related to minimal surfaces generalizing the {\em helicoid} in various
backgrounds. Infra-red divergences appearing for Wilson lines can be factorized
out or can be cured by considering the IR finite case of correlation functions
of two Wilson loops. In non-conformal cases related to confining theories,
reggeized amplitudes with linear trajectories and unit intercept are obtained
and shown to come from the approximately flat metrics near the horizon, which
sets the scale for the Regge slope. In the conformal case the absence of
confinement leads to a different solution. A transition between both regimes
appears, in a confining theory, when varying impact parameter.Comment: 22 pages, 2 eps figures, expanded discussion, conclusions unchanged,
version to be published in Nuclear Physics
Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators
Spatially confined rigid membranes reorganize their morphology in response to
the imposed constraints. A crumpled elastic sheet presents a complex pattern of
random folds focusing the deformation energy while compressing a membrane
resting on a soft foundation creates a regular pattern of sinusoidal wrinkles
with a broad distribution of energy. Here, we study the energy distribution for
highly confined membranes and show the emergence of a new morphological
instability triggered by a period-doubling bifurcation. A periodic
self-organized focalization of the deformation energy is observed provided an
up-down symmetry breaking, induced by the intrinsic nonlinearity of the
elasticity equations, occurs. The physical model, exhibiting an analogy with
parametric resonance in nonlinear oscillator, is a new theoretical toolkit to
understand the morphology of various confined systems, such as coated materials
or living tissues, e.g., wrinkled skin, internal structure of lungs, internal
elastica of an artery, brain convolutions or formation of fingerprints.
Moreover, it opens the way to new kind of microfabrication design of
multiperiodic or chaotic (aperiodic) surface topography via self-organization.Comment: Submitted for publicatio
Noise and Robustness in Phyllotaxis
A striking feature of vascular plants is the regular arrangement of lateral organs on the stem, known as phyllotaxis. The most common phyllotactic patterns can be described using spirals, numbers from the Fibonacci sequence and the golden angle. This rich mathematical structure, along with the experimental reproduction of phyllotactic spirals in physical systems, has led to a view of phyllotaxis focusing on regularity. However all organisms are affected by natural stochastic variability, raising questions about the effect of this variability on phyllotaxis and the achievement of such regular patterns. Here we address these questions theoretically using a dynamical system of interacting sources of inhibitory field. Previous work has shown that phyllotaxis can emerge deterministically from the self-organization of such sources and that inhibition is primarily mediated by the depletion of the plant hormone auxin through polarized transport. We incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis – the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles – and we investigated whether a secondary inhibitory field filters out defects. Our results are consistent with available experimental data and yield a prediction of the main source of stochasticity during organogenesis. Our model can be related to cellular parameters and thus provides a framework for the analysis of phyllotactic mutants at both cellular and tissular levels. We propose that secondary fields associated with organogenesis, such as other biochemical signals or mechanical forces, are important for the robustness of phyllotaxis. More generally, our work sheds light on how a target pattern can be achieved within a noisy background
A finite strain fibre-reinforced viscoelasto-viscoplastic model of plant cell wall growth
A finite strain fibre-reinforced viscoelasto-viscoplastic model implemented in a finite element (FE) analysis is presented to study the expansive growth of plant cell walls. Three components of the deformation of growing cell wall, i.e. elasticity, viscoelasticity and viscoplasticity-like growth, are modelled within a consistent framework aiming to present an integrative growth model. The two aspects of growth—turgor-driven creep and new material deposition—and the interplay between them are considered by presenting a yield function, flow rule and hardening law. A fibre-reinforcement formulation is used to account for the role of cellulose microfibrils in the anisotropic growth. Mechanisms in in vivo growth are taken into account to represent the corresponding biologycontrolled behaviour of a cell wall. A viscoelastic formulation is proposed to capture the viscoelastic response in the cell wall. The proposed constitutive model provides a unique framework for modelling both the in vivo growth of cell wall dominated by viscoplasticity-like behaviour and in vitro deformation dominated by elastic or viscoelastic responses. A numerical scheme is devised, and FE case studies are reported and compared with experimental data
Modified Rodrigues Parameters: An Efficient Representation of Orientation in 3D Vision and Graphics
Mechanical Stress Induces Remodeling of Vascular Networks in Growing Leaves
International audienceDifferentiation into well-defined patterns and tissue growth are recognized as key processes in organismal development. However, it is unclear whether patterns are passively, homogeneously dilated by growth or whether they remodel during tissue expansion. Leaf vascu-lar networks are well-fitted to investigate this issue, since leaves are approximately two-dimensional and grow manyfold in size. Here we study experimentally and computationally how vein patterns affect growth. We first model the growing vasculature as a network of viscoelastic rods and consider its response to external mechanical stress. We use the so-called texture tensor to quantify the local network geometry and reveal that growth is heterogeneous , resembling non-affine deformations in composite materials. We then apply mechanical forces to growing leaves after veins have differentiated, which respond by anisotropic growth and reorientation of the network in the direction of external stress. External mechanical stress appears to make growth more homogeneous, in contrast with the model with viscoelastic rods. However, we reconcile the model with experimental data by incorporating randomness in rod thickness and a threshold in the rod growth law, making the rods viscoelastoplastic. Altogether, we show that the higher stiffness of veins leads to their reorientation along external forces, along with a reduction in growth heterogeneity. This process may lead to the reinforcement of leaves against mechanical stress. More generally , our work contributes to a framework whereby growth and patterns are coordinated through the differences in mechanical properties between cell types
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