arXiv subjects

Arezki Boudaoud

Publications and source records attributed to Arezki Boudaoud.

25 records · Page 2Linked to original sources

arXiv2008

Statistics of power injection in a plate set into chaotic vibration

A vibrating plate is set into a chaotic state of wave turbulence by either a periodic or a random local forcing. Correlations between the forcing and the local velocity response of the plate at the forcing point are studied. Statistical models with fairly good agreement with the experiments are proposed for each forcing. Both distributions of injected power have a logarithmic cusp for zero power, while the tails are Gaussian for the periodic driving and exponential for the random one. The distributions of injected work over long time intervals are investigated in the framework of the fluctuation theorem, also known as the Gallavotti-Cohen theorem. It appears that the conclusions of the theorem are verified only for the periodic, deterministic forcing. Using independent estimates of the phase space contraction, this result is discussed in the light of available theoretical framework.

cond-mat.stat-mech↗

arXiv2007

The buckling of a swollen thin gel layer bound to a compliant substrate

Gels are used to design bilayered structures with high residual stresses. The swelling of a thin layer on a compliant substrate leads to compressive stresses. The post-buckling of this layer is investigated experimentally; the wavelengths and amplitudes of the resulting modes are measured. A simplified model with a self-avoiding rod on a Winkler foundation is in semi-quantitative agreement with experiments and reproduces the observed cusp-like folds.

cond-mat.soft↗

arXiv2006

Non-Newtonian thin films with normal stresses: dynamics and spreading

The dynamics of thin films on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the thickness of the film and the shear rate are proposed within the lubrication approximation. This framework is applied to the motion of an advancing contact line. The apparent dynamic contact angle is found to depend logarithmically on a lengthscale determined solely by the rheological properties of the fluid and the velocity of the contact line.

physics.flu-dyn↗

arXiv2005

The Statistics of Crumpled Paper

A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles -- in which resides the elastic energy -- put in a confining potential. Many independent equilibrium configurations are generated numerically and their properties are investigated. At small confinement, the distribution of segment lengths is log-normal in agreement with previous predictions and experiments. At high confinement, the system approaches a jammed state with a critical behavior, whereas the length distribution follows a Gamma law which parameter is predicted as a function of the number of layers in the system.

cond-mat.soft↗

arXiv2005

Buckling of swelling gels

The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel. When the structure is immersed in water, the soft gel swells and bends out of plane leading to a wavy periodic pattern which wavelength is measured. The linear stability of the flat state is studied in the framework of linear elasticity using the equations for thin plates. The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment.

cond-mat.soft↗

arXiv2004

Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities

The stability of an evaporating thin liquid film on a solid substrate is investigated within lubrication theory. The heat flux due to evaporation induces thermal gradients; the generated Marangoni stresses are accounted for. Assuming the gas phase at rest, the dynamics of the vapour reduces to diffusion. The boundary condition at the interface couples transfer from the liquid to its vapour and diffusion flux. A non-local lubrication equation is obtained; this non-local nature comes from the Laplace equation associated with quasi-static diffusion. The linear stability of a flat film is studied in this general framework. The subsequent analysis is restricted to moderately thick films for which it is shown that evaporation is diffusion limited and that the gas phase is saturated in vapour in the vicinity of the interface. The stability depends only on two control parameters, the capillary and Marangoni numbers. The Marangoni effect is destabilising whereas capillarity and evaporation are stabilising processes. The results of the linear stability analysis are compared with the experiments of Poulard et al (2003) performed in a different geometry. In order to study the resulting patterns, the amplitude equation is obtained through a systematic multiple-scale expansion. The evaporation rate is needed and is computed perturbatively by solving the Laplace problem for the diffusion of vapour. The bifurcation from the flat state is found to be a supercritical transition. Moreover, it appears that the non-local nature of the diffusion problem unusually affects the amplitude equation.

cond-mat.soft↗

arXiv2002

On size and growth of cells

Understanding how growth induces form is a longstanding biological question. Many studies concentrated on the shapes of plant cells, fungi or bacteria. Some others have shown the importance of the mechanical properties of bacterial walls and plant tissues in pattern formation. Here I sketch a simple physical picture of cell growth. The study is focussed on isolated cells that have walls. They are modeled as thin elastic shells containing a liquid, which pressure drives the growth as generally admitted for bacteria or plant cells. Requiring mechanical equilibrium leads to estimations of typical cell sizes, in quantitative agreement with compiled data including bacteria, cochlear outer hair, fungi, yeast, root hair and giant alga cells.

physics.bio-ph↗