Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses

Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal pressure have emerged as a theoretical and experimental paradigm for the study of dynamic buckling with controlled loads. Experimentally, an elastic ring is placed within a soap film. When the film outside the ring is removed, surface tension pulls the ring inward, mimicking an external pressurization. Here we present a theoretical analysis of this process by performing a post-bifurcation analysis of an elastic ring under pressure. This analysis allows us to understand how inertia, material properties, and loading affect the observed shape. In particular, we combine direct numerical solutions with a post-bifurcation asymptotic analysis to show that inertia drives the system towards higher modes that cannot be selected in static buckling. Our theoretical results explain experimental observations that cannot be captured by a standard linear stability analysis.Comment: 18 pages, 10 figure

Lubricated wrinkles: imposed constraints affect the dynamics of wrinkle coarsening

We study the dynamic coarsening of wrinkles in an elastic sheet that is compressed while lying on a thin layer of viscous liquid. When the ends of the sheet are instantaneously brought together by a small distance, viscous resistance initially prevents the sheet from adopting a globally buckled shape. Instead, the sheet accommodates the compression by wrinkling. Previous scaling arguments suggested that a balance between the sheet's bending stiffness and viscous effects lead to a wrinkle wavelength $\lambda$ that increases with time $t$ according to $\lambda\propto t^{1/6}$. We show that taking proper account of the compression constraint leads to a logarithmic correction of this result, $\lambda\propto (t/\log t)^{1/6}$. This correction is significant over experimentally observable time spans, and leads us to reassess previously published experimental data.Comment: 12 pages. Version accepted in Phys. Rev. Fluids (with small correction to bibliography

Institutional histories, seasonal floodplains (mares), and livelihood impacts of fish stocking in the Inner Niger River Delta of Mali

The Community-based Fish Culture in Seasonal Floodplains and Irrigation Systems (CBFC) project is a five year research project supported by the Challenge Program on Water and Food (CPWF), with the aim of increasing productivity of seasonally occurring water bodies through aquaculture. The project has been implemented in Bangladesh, Cambodia, China, Mali and Vietnam, where technical and institutional options for community based aquaculture have been tested. The project began in 2005 and was completed in March 2010. The seasonally flooded depressions in the Inner Niger Delta (known as mares) represent a critical fishery resource for the inhabitants of the village of Komio, and at present, access is open to all residents. A proposal to build stocked fish enclosures in the main village mare presents potential benefits and risks. On one hand, overall productivity in the mare could be significantly increased, providing important sources of protein and cash during the annual drought period, when few livelihood activities can be performed and when village livelihoods are at their most vulnerable. Enhanced productivity in mares may also decrease local household pressures for seasonal labor migration. On the other hand, a resulting increase in the value of these mares may encourage elite capture of project benefits or rentseeking by certain village leaders of the landowning Marka ethnic group. Using qualitative interviews and focus group discussions, the study provides evidence of how local institutional and leadership capacity for equitable common property resource management have evolved since the introduction of irrigated farming systems (known as PΘrimΦtres IrriguΘs Villageois or PIVs) in the 1990s.Fishing rights, River fisheries, Livelihoods

Dynamics of wrinkling in ultrathin elastic sheets

The wrinkling of thin elastic objects provides a means of generating regular patterning at small scales in applications ranging from photovoltaics to microfluidic devices. Static wrinkle patterns are known to be governed by an energetic balance between the object's bending stiffness and an effective substrate stiffness, which may originate from a true substrate stiffness or from tension and curvature along the wrinkles. Here we investigate dynamic wrinkling, induced by the impact of a solid sphere onto an ultra-thin polymer sheet floating on water. The vertical deflection of the sheet's centre induced by impact draws material radially inwards, resulting in an azimuthal compression that is relieved by the wrinkling of the entire sheet. We show that this wrinkling is truly dynamic, exhibiting features that are qualitatively different to those seen in quasi-static wrinkling experiments. Moreover, we show that the wrinkles coarsen dynamically because of the inhibiting effect of the fluid inertia. This dynamic coarsening can be understood heuristically as the result of a dynamic stiffness, which dominates the static stiffnesses reported thus far, and allows new controls of wrinkle wavelength.Comment: 8 pages, 4 figures. Please see published version for supplementary movies and SI Appendi

How Could Judges Ignore the Audi Et Alteram Partem Principle in a Criminal Case Trial?

In a judge's decision, legal considerations aim to delve into the facts revealed at trials based on the audi et alteram partem principle, which must exist and become a foundation. The philosophy of the audi et alteram partem principle is essentially the values of justice and balance. In applying the audi et alteram partem principle in a criminal case, although the judges have judicial power, they should consider the evidence and facts that are not only submitted by the public Prosecutor but also have to consider the evidence and facts submitted by the defendant. In decision Number 123/Pid.B/2022/PN Yyk, the panel of examining judges rejected the explanation of the witness a de-charge  which was not based on a clear reason, so it was felt that the panel of judges examining the case did not consider the explanation of the witness which was mitigating for the defendant and violated the principle of audi et alteram. Therefore, this study aims to elaborate on how the judicial panel examined the case by applying the audi et alteram partem principle. To answer these legal issues, this study uses combined research methods of normative and empirical data with data collection methods by conducting interviews and literature reviews as well as using descriptive qualitative data analysis methods. The result of this study showed that the judicial panel examining case number 123/Pid.B/2022/PN Yyk did not consider the audi et alteram partem principle for the judgment because the judges were not balanced by only considering the prosecutor's explanation and rejecting the testimony of the defendant's witnesses and ignoring material truth of defendant's proof

Self-Ordering of Buckling, Bending, Bumping Beams

A collection of thin structures buckle, bend, and bump into each-other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will fold in on itself, forming a maze of interleaved sheets. This pattern formation changes how densely the structures can pack, as well as the mechanical properties of the system. How and when these patterns form, as well as the force required to pack these structures is not currently understood. Here we study the emergence of order in a canonical example of packing in slender-structures, i.e. a system of parallel growing elastic beams. Using experiments, simulations, and simple theory from statistical mechanics, we predict the amount of growth (or, equivalently, the amount of compression) of the beams that will guarantee a global system order, which depends only on the initial geometry of the system. Furthermore, we find that the compressive stiffness and stored bending energy of this meta-material is directly proportional to the number of beams that are geometrically frustrated at any given point. We expect these results to elucidate the mechanisms leading to pattern formation in these kinds of systems, and to provide a new mechanical meta-material, with a tunable resistance to compressive force

Structure d'âge et croissance de Clarias anguillaris (Pisces, Clariidae) dans le Delta Central du Niger au Mali (Afrique de l’Ouest)

L’étude de l’âge et de la croissance de C. anguillaris dans le Delta Central du Niger a porté sur 390 individus, de taille comprise entre 144 et 670 mm et échantillonnés sur un cycle annuel. L'âge individuel des poissons a été déterminé par squelettochronologie au moyen des coupes transversales de rayons épineux pectoraux dont l'épaisseur était de 100 μm. La validité des lectures d'âge a été appréciée par le calcul des indices de cohérence inter-lecteurs. L’évolution mensuelle de la marge relative du diamètre (dr) de la coupe du rayon épineux a été utilisée pour déterminer la périodicité de formation des marques de croissance et le cycle saisonnier de croissance. Ce dernier se caractérise par l'absence d'une période tranchée d'arrêt de croissance même si une reprise précoce, dès l'étiage, liée à une amélioration des conditions physico-chimiques et alimentaires, est observée. La longévité au sein de la population est de 4 ans bien qu’une forte proportion soit pêchée avant 2 ans d’âge. Le modèle théorique de croissance révèle, outre la grande taille que pourraient atteindre certains individus, une très importante croissance linéaire la première année avec 244.81±12.15 mm, ce qui augure de très bonnes performances aquacoles.Mots clés: Clarias anguillaris, squelettochronologie, marques de croissance, longévité, Delta Central du Niger, Mal

Impact on floating thin elastic sheets: A mathematical model

We investigate impact of a sphere onto a floating elastic sheet and the resulting formation and evolution of wrinkles in the sheet. Following impact, we observe a radially propagating wave, beyond which the sheet remains approximately planar but is decorated by a series of radial wrinkles whose wavelength grows in time. We develop a mathematical model to describe these phenomena by exploiting the asymptotic limit in which the bending stiffness is small compared to stresses in the sheet. The results of this analysis show that, at a time $t$ after impact, the transverse wave is located at a radial distance $r\sim t^{1/2}$ from the impactor, in contrast to the classic $r\sim t^{2/3}$ scaling observed for capillary--inertia ripples produced by dropping a stone into a pond. We describe the shape of this wave, starting from the simplest case of a point impactor, but subsequently addressing a finite-radius spherical impactor, contrasting this case with the classic Wagner theory of impact. We show also that the coarsening of wrinkles in the flat portion of the sheet is controlled by the inertia of the underlying liquid: short-wavelength, small-amplitude wrinkles form at early times since they accommodate the geometrically-imposed compression without significantly displacing the underlying liquid. As time progresses, the liquid accelerates and the wrinkles grow larger and coarsen. We explain this coarsening quantitatively using numerical simulations and scaling arguments, and we compare our predictions with experimental data.Comment: 30 pages, 9 figures. Small edits toaccepted versio

Wrinkling and developable cones in centrally confined sheets

Thin sheets respond to confinement by smoothly wrinkling, or by focusing stress into small, sharp regions. From engineering to biology, geology, textiles, and art, thin sheets are packed and confined in a wide variety of ways, and yet fundamental questions remain about how stresses focus and patterns form in these structures. Using experiments and molecular dynamics (MD) simulations, we probe the confinement response of circular sheets, flattened in their central region and quasi-statically drawn through a ring. Wrinkles develop in the outer, free region, then are replaced by a truncated cone, which forms in an abrupt transition to stress focusing. We explore how the force associated with this event, and the number of wrinkles, depend on geometry. Additional cones sequentially pattern the sheet, until axisymmetry is recovered in most geometries. The cone size is sensitive to in-plane geometry. We uncover a coarse-grained description of this geometric dependence, which diverges depending on the proximity to the asymptotic d-cone limit, where the clamp size approaches zero. This work contributes to the characterization of general confinement of thin sheets, while broadening the understanding of the d-cone, a fundamental element of stress focusing, as it appears in realistic settings.Comment: 11 pages, 9 figure