Isometric bending requires local constraints on free edges

While the shape equations describing the equilibrium of an unstretchable thin sheet that is free to bend are known, the boundary conditions that supplement these equations on free edges have remained elusive. Intuitively, unstretchability is captured by a constraint on the metric within the bulk. Naively one would then guess that this constraint is enough to ensure that the deformations determining the boundary conditions on these edges respect the isometry constraint. If matters were this simple, unfortunately, it would imply unbalanced torques (as well as forces) along the edge unless manifestly unphysical constraints are met by the boundary geometry. In this paper we identify the source of the problem: not only the local arc-length but also the geodesic curvature need to be constrained explicitly on all free edges. We derive the boundary conditions which follow. Contrary to conventional wisdom, there is no need to introduce boundary layers. This framework is applied to isolated conical defects, both with deficit as well, but more briefly, as surplus angles. Using these boundary conditions, we show that the lateral tension within a circular cone of fixed radius is equal but opposite to the radial compression, and independent of the deficit angle itself. We proceed to examine the effect of an oblique outer edge on this cone perturbatively demonstrating that both the correction to the geometry as well as the stress distribution in the cone kicks in at second order in the eccentricity of the edge.Comment: 25 pages, 3 figure

Force dipoles and stable local defects on fluid vesicles

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area and volume preserving conformal transformations, which breaks the symmetry between the two points. The volume constraint fixes the distance $S$, measured along the surface, between the two points; if it is relaxed, a second zero mode appears, reflecting the independence of the energy on $S$; in the absence of this constraint a pathway opens for the membrane to slip out of the defect. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. The magnitude of these forces varies inversely with $S$ and so diverges as the points merge; the corresponding torques vanish in these defects. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and in distant regions as a biharmonic quadrupole. Comparison of the distribution of stress with the quadratic approximation in the height functions points to shortcomings of the latter representation. Radial tension is accompanied by lateral compression, both near the singularities and far away, with a crossover from tension to compression occurring in the region between them.Comment: 26 pages, 10 figure

Aborto epidémico y endémico asociado a la infección por Neospora caninum en el ganado bovino: relación entre la respuesta inmune y las consecuencias de la infección a lo largo de la gestación

Neospora caninum es un protozoo intracelular obligado perteneciente al Phylum Apicomplexa. La neosporosis bovina se considera una de las principales causas de fallo reproductivo en el ganado bovino. La transmisión transplacentaria del parásito puede originar aborto ó el nacimiento de terneros congénitamente infectados. La transmisión transplacentaria endógena ocurre tras la recrudescencia de una infección crónica en la hembra durante la gestación, mientras que la exógena se da tras una primoinfección adquirida de forma postnatal. Un mayor conocimiento de la epidemiología, integrado con el empleo de adecuadas técnicas de diagnóstico serológico son la base del control. El objetivo del presente estudio fue determinar mediante diferentes pruebas diagnósticas la relación existente entre la respuesta serológica desarrollada por reproductoras bovinas infectadas a lo largo de una gestación, el origen de la infección y sus repercusiones reproductivas.Neospora caninum is an apicomplexan protozoan parasite. At present bovine neosporosis is one of the main causes of reproductive failure in cattle worldwide. Transplacental transmission of the parasite can lead to abortion or birth of congenitally infected calves. Endogenous transplacental transmission occurs as a consequence of the recrudescence of a previous chronic infection in the cow during gestation. On the other hand, exogenous transplacental transmission occurs after an acquired postnatal primo infection. Control programmes are based on updated knowledge about the epidemiology together with the employment of appropriate diagnostic serological tests. The aim of the present study was to determine the relationship between the serologic response developed by infected breeding cattle along gestation, the mode of transmission and the future consequences in reproduction