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

Anisotropic colloids through non-trivial buckling

We present a study on buckling of colloidal particles, including experimental, theoretical and numerical developments. Oil-filled thin shells prepared by emulsion templating show buckling in mixtures of water and ethanol, due to dissolution of the core in the external medium. This leads to conformations with a single depression, either axisymmetric or polygonal depending on the geometrical features of the shells. These conformations could be theoretically and/or numerically reproduced in a model of homogeneous spherical thin shells with bending and stretching elasticity, submitted to an isotropic external pressure.Comment: submitted to EPJ

Decoupling of soil nutrient cycles as a function of aridity in global drylands

18 páginas.- 10 figuras.- 72 referencias.- Online Content Any additional Methods, Extended Data display items and Source Data are available in the online version of the paper; references unique to these sections appear only in the online paper..- Puede conseguir el texto completo en el Portal de la producción científica de la Universidad Complutense de Madrid https://produccioncientifica.ucm.es/documentos/5ec78dc52999520a1d557660 .- o en lel respositorio institucional CONICET digital https://ri.conicet.gov.ar/bitstream/handle/11336/29204/CONICET_Digital_Nro.ead4e2ed-0da6-4041-814b-259e8f27bbf6_D.pdf?sequence=5&isAllowed=yThe biogeochemical cycles of carbon (C), nitrogen (N) and phosphorus (P) are interlinked by primary production, respiration and decomposition in terrestrial ecosystems1. It has been suggested that the C, N and P cycles could become uncoupled under rapid climate change because of the different degrees of control exerted on the supply of these elements by biological and geochemical processes1,2,3,4,5. Climatic controls on biogeochemical cycles are particularly relevant in arid, semi-arid and dry sub-humid ecosystems (drylands) because their biological activity is mainly driven by water availability6,7,8. The increase in aridity predicted for the twenty-first century in many drylands worldwide9,10,11 may therefore threaten the balance between these cycles, differentially affecting the availability of essential nutrients12,13,14. Here we evaluate how aridity affects the balance between C, N and P in soils collected from 224 dryland sites from all continents except Antarctica. We find a negative effect of aridity on the concentration of soil organic C and total N, but a positive effect on the concentration of inorganic P. Aridity is negatively related to plant cover, which may favour the dominance of physical processes such as rock weathering, a major source of P to ecosystems, over biological processes that provide more C and N, such as litter decomposition12,13,14. Our findings suggest that any predicted increase in aridity with climate change will probably reduce the concentrations of N and C in global drylands, but increase that of P. These changes would uncouple the C, N and P cycles in drylands and could negatively affect the provision of key services provided by these ecosystems.This research is supported by the European Research Council (ERC) under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no. 242658 (BIOCOM), and by the Ministry of Science and Innovation of the Spanish Government, grant no. CGL2010-21381. CYTED funded networking activities (EPES, Acción 407AC0323). M.D.-B. was supported by a PhD fellowship from the Pablo de Olavide University.Peer reviewe