Exact non-Hookean scaling of cylindrically bent elastic sheets and the large-amplitude pendulum

A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence on the interplate distance [Siber and Buljan, arXiv:1007.4699 (2010)]. The phenomenon has been used as a basis for an experimental problem at the 41st International Physics Olympiad. We show that the corresponding variational problem for the equilibrium energy of the deformed cylinder is equivalent to a minimum action description of a simple gravitational pendulum with an amplitude of 90 degrees. We use this analogy to show that the power-law of the force is exact for distances less than a critical value. An analytical solution for the elastic force is found and confirmed by measurements over a range of deformations covering both linear and non-Hookean behavior.Comment: 5 pages, extra figures and stability proof, accepted by American Journal of Physic

Diversity between and within farmers’ varieties of tomato from Eritrea

Tomato yields in Eritrea are low (15 Mg/ha) compared with 19 Mg/ha in Africa and 27 Mg/ha worldwide. This is partly caused by poor quality of varieties used. This study analysed the diversity among and heterogeneity within farmers’ varieties of tomato from Eritrea and compared these varieties with other African and Italian varieties. Fifteen simple sequence repeat (SSR) markers were used for the genetic analysis. Genetic similarities among the varieties were calculated and an Unweighted Pair Group Method with Arithmetic Mean analysis was performed. Furthermore, individual plants of varieties were genotyped to evaluate uniformity within varieties. A high degree of diversity was observed among the Eritrean varieties. Thirteen out of the 15 SSRs were polymorphic, with 2 to 5 alleles per marker. The dendrogram showed two major types of varieties: San-Marzano and Marglob. Eritrean varieties were closely related to old Italian varieties in both types. Analysis of the within-variety variation showed that the Eritrean tomato genotypes were less uniform than the other varieties, probably because of deliberate mixing. A survey among farmers showed that some of them purposely mixed seeds to prolong the harvesting period, for yield stability and stress tolerance. Farmers value ‘new material’ as a source of influ

Crescent Singularities in Crumpled Sheets

We examine the crescent singularity of a developable cone in a setting similar to that studied by Cerda et al [Nature 401, 46 (1999)]. Stretching is localized in a core region near the pushing tip and bending dominates the outer region. Two types of stresses in the outer region are identified and shown to scale differently with the distance to the tip. Energies of the d-cone are estimated and the conditions for the scaling of core region size R_c are discussed. Tests of the pushing force equation and direct geometrical measurements provide numerical evidence that core size scales as R_c ~ h^{1/3} R^{2/3}, where h is the thickness of sheet and R is the supporting container radius, in agreement with the proposition of Cerda et al. We give arguments that this observed scaling law should not represent the asymptotic behavior. Other properties are also studied and tested numerically, consistent with our analysis.Comment: 13 pages with 8 figures, revtex. To appear in PR

Wrapping an adhesive sphere with a sheet

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss'Theorema Egregium shows that this operation necessarily generates metric distortions (i.e. stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two non-dimensional parameters comparing respectively bending and stretching energies to adhesion. A complete configuration diagram is finally proposed

Seed potato quality improvement through positive selection by smallholder farmers in Kenya

In Kenya, seed potato quality is often a major yield constraint in potato production as smallholder farmers use farm-saved seed without proper management of seed-borne pests and diseases. Farm-saved seed is therefore often highly degenerated. We carried out on-farm research to assess whether farmer-managed positive seed selection could improve yield. Positive selection gave an average yield increase in farmer-managed trials of 34%, corresponding to a 284-€ increase in profit per hectare at an additional production cost of only 6€/ha. Positive selection can be an important alternative and complementary technology to regular seed replacement, especially in the context of imperfect rural economies characterized by high risks of production and insecure markets. It does not require cash investments and is thus accessible for all potato producers. It can also be applied where access to highquality seed is not guaranteed. The technology is also suitable for landraces and not recognized cultivars that cannot be multiplied formally. Finally, the technology fits seamlessly within the seed systems of Sub-Saharan Africa, which are dominated by self-supply and neighbour supply of seed potatoes

Spontaneous curvature cancellation in forced thin sheets

In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container. We show that this feature is independent of thickness of the sheet, the supporting radius and the amount of deflection. Several variants of developable cone are studied to examine the necessary conditions that lead to the vanishing of mean curvature. It is found that the presence of appropriate amount of radial stress is necessary. The developable cone geometry somehow produces the right amount of radial stress to induce just enough radial curvature to cancel the conical azimuthal curvature. In addition, the circular symmetry of supporting container edge plays an important role. With an elliptical supporting edge, the radial curvature overcompensates the azimuthal curvature near the minor axis and undercompensates near the major axis. Our numerical finding is verified by a crude experiment using a reflective plastic sheet. We expect this finding to have broad importance in describing the general geometrical properties of forced crumpling of thin sheets.Comment: 13 pages, 12 figures, revtex

Prediction of long and short time rheological behavior in soft glassy materials

We present an effective time approach to predict long and short time rheological behavior of soft glassy materials from experiments carried out over practical time scales. Effective time approach takes advantage of relaxation time dependence on aging time that allows time-aging time superposition even when aging occurs over the experimental timescales. Interestingly experiments on variety of soft materials demonstrate that the effective time approach successfully predicts superposition for diverse aging regimes ranging from sub-aging to hyper-aging behaviors. This approach can also be used to predict behavior of any response function in molecular as well as spin glasses.Comment: 13 pages, 4 figure

Helical structures from an isotropic homopolymer model

We present Monte Carlo simulation results for square-well homopolymers at a series of bond lengths. Although the model contains only isotropic pairwise interactions, under appropriate conditions this system shows spontaneous chiral symmetry breaking, where the chain exists in either a left- or a right-handed helical structure. We investigate how this behavior depends upon the ratio between bond length and monomer radius.Comment: 10 pages, 3 figures, accepted for publication by Physical Review Letter

Boost invariant marginally trapped surfaces in Minkowski 4-space

The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing two marginally trapped surfaces which are invariant under the group of boost isometries. As an application, a proper star-surface is constructed.Comment: 13 pages, comment added in section