Buckling Cascade of Thin Plates: Forms, Constraints and Similarity

We experimentally study compression of thin plates in rectangular boxes with variable height. A cascade of buckling is generated. It gives rise to a self-similar evolution of elastic reaction of plates with box height which surprisingly exhibits repetitive vanishing and negative stiffness. These features are understood from properties of Euler's equation for elastica

Atypical Representations of Uq(sl(N))U_{q}(sl(N)) at Roots of Unity

We show how to adapt the Gelfand-Zetlin basis for describing the atypical representation of ${\cal U}_{\displaystyle{q}}(sl(N))$ when $q$ is root of unity. The explicit construction of atypical representation is presented in details for $N=3$.Comment: 18 pages, Tex-file and 2 figures. Uuencoded, compressed and tared archive of plain tex file and postscript figure file. Upon uudecoding, uncompressing and taring, tex the file atypique.te

Coiling Instabilities in Multilamellar Tubes

Myelin figures are densely packed stacks of coaxial cylindrical bilayers that are unstable to the formation of coils or double helices. These myelin figures appear to have no intrinsic chirality. We show that such cylindrical membrane stacks can develop an instability when they acquire a spontaneous curvature or when the equilibrium distance between membranes is decreased. This instability breaks the chiral symmetry of the stack and may result in coiling. A unilamellar cylindrical vesicle, on the other hand, will develop an axisymmetric instability, possibly related to the pearling instability.Comment: 6 pages, 2 figure

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

Role of boundary conditions on mode selection in a buckling instability

We present an experimental study on the selection of the wave number in the buckling of a thin elastic rectangular plate, subjected to a compressive force while being held laterally. Boundary conditions act selectively through non-linear mechanisms to restrict the accessible states above threshold.En variant les conditions aux bords chargés, on sélectionne de façon différente les modes instables accessibles. La sélection de modes est reliée à des analyses non linéaires de ces problèmes. Une comparaison est établie avec la sélection des modes dans des instabilités convectives

Hollow Fiber Membrane Contactor for Hydrogen Sulfide Odor Control

International audienceHollow fiber membrane modules are extensively used as gas-liquid contactors for acid gas removal from waste gas streams. Hydrogen sulfide is an important indoor and outdoor contaminant, but, given its toxicity, a limited number of experimental results have been reported for this compound. Moreover, chemical absorption has been exclusively investigated. In this study, hydrogen sulfide odor control by absorption in water thanks to a hollow fiber contactor has been studied both experimentally and theoretically. The scrubbing of hydrogen sulfide from air gas mixture is investigated in two porous polypropylene (PP) hollow fiber modules of different contact area and fiber packing fraction. The gas phase is circulated in the lumen of the fiber bore and the liquid phase in the shell in a nonwetted mode, i.e. the membrane pores being filled with gas. The gas phase was run in countercurrent contact with the liquid phase at constant pressure. A laminar parabolic velocity has been employed to describe the convective diffusive mass transport equation which has been solved analytically and numerically. The calculated extents of hydrogen sulfide depletion reasonably compare with the generated experimental results for both membrane modules. Up to 85% of acid gas could be removed at gaseous flowrates of 200 cm3/min for the large module and removals as high as 89% at 10 cm3/min have been observed for the smaller one. The overall mass-transfer coefficients calculated from the experimental data, agree satisfactorily with those generated by the mathematical model. The relation of the dimensionless Sherwood number to the Graetz number is in a good agreement with the Leveque semianalytical solution