From nonlocal Eringen's model to fractional elasticity

Eringen's model is one of the most popular theories in nonlocal elasticity. It has been applied to many practical situations with the objective of removing the anomalous stress concentrations around geometric shape singularities, which appear when the local modelling is used. Despite the great popularity of Eringen's model in mechanical engineering community, even the most basic questions such as the existence and uniqueness of solutions have been rarely considered in the research literature for this model. In this work we focus on precisely these questions, proving that the model is in general ill-posed in the case of smooth kernels, the case which appears rather often in numerical studies. We also consider the case of singular, non-smooth kernels, and for the paradigmatic case of the Riesz potential we establish the well-posedness of the model in fractional Sobolev spaces. For such a kernel, in dimension one the model reduces to the well-known fractional Laplacian. Finally, we discuss possible extensions of Eringen's model to spatially heterogeneous material distributions

Lower semicontinuity and relaxation via young measures for nonlocal variational problems and applications to peridynamics

“First Published in SIAM Journal of Mathematical Analysis in [50, 1, 2018], published by the Society for Industrial and Applied Mathematics (SIAM)” and the copyright notice as stated in the article itself (e.g., “Copyright © SIAM. Unauthorized reproduction of this article is prohibited"We study nonlocal variational problems in Lp, like those that appear in peridynamics. The functional object of our study is given by a double integral. We establish characterizations of weak lower semicontinuity of the functional in terms of nonlocal versions of either a convexity notion of the integrand or a Jensen inequality for Young measures. Existence results, obtained through the direct method of the calculus of variations, are also established. We cover different boundary conditions, for which the coercivity is obtained from nonlocal Poincaré inequalities. Finally, we analyze the relaxation (that is, the computation of the lower semicontinuous envelope) for this problem when the lower semicontinuity fails. We state a general relaxation result in terms of Young measures and show, by means of two examples, the difficulty of having a relaxation in Lp in an integral form. At the root of this difficulty lies the fact that, contrary to what happens for local functionals, nonpositive integrands may give rise to positive nonlocal functionals.Supported by the Spanish Ministerio de Economía y Competitividad through grants MTM2011-28198 and RYC-2010-06125 (Ramón y Cajal programme), and the ERC Starting Grant 30717

Minimizers of Nonlocal Polyconvex Energies in Nonlocal Hyperelasticity

We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable to nonlocal solid mechanics, especially nonlinear elasticity. This nonlocal gradient was introduced in an earlier work, inspired by Riesz' fractional gradient, but suitable for bounded domains. The main assumption on the integrand of the energy is polyconvexity. Thus, we adapt the corresponding results of the classical case to this nonlocal context, notably, Piola's identity, the integration by parts of the determinant and the weak continuity of the determinant. The proof exploits the fact that every nonlocal gradient is a classical gradient. Contrary to classical elasticity, this existence result is compatible with cavitation and fracture

Evaluación de la proximidad de sistemas ovinos de la raza Segureña a un modelo de producción agroecológico

La sociedad europea demanda cada vez más que la producción de alimentos sea respetuosa con el medio ambiente, cuidando además su calidad nutritiva. Muchos de los sistemas pastorales de pequeños rumiantes presentes en España cumplen con la mayoría de los criterios de sostenibilidad. Los sistemas de la raza Segureña se basan en un modelo pastoral en una de las zonas más desfavorecidas del territorio español. Con el presente trabajo se pretende valorar la cercanía que dichos sistemas tienen a un modelo agroecológico optimizado. Los resultados muestran un valor de cercanía o proximidad del 64,4%, pudiendo este valor aumentar realizando algunas modificaciones funcionales o de manejo. El manejo alimentario es el aspecto que tiene una mayor proximidad, en cambio los factores relacionados con la sanidad son los que presentan menores valores de proximidad. Potenciar los aspectos agroecológicos que favorezcan la sostenibilidad a través de criterios que sean fácilmente comprensibles por los consumidores, mejora las posibilidades de comercialización de los productos de estos sistemas en nichos de mercado especializados

Long term oscillations of Mediterranean sardine and anchovy explained by the combined effect of multiple regional and global climatic indices

This study is a contribution to the PELWEB project (“Winners, losers and shifts of PELagic food WEB changes in the western Mediterranean Sea: from ecosystem consequences to future projections”, CTM2017-88939-R,2018–2020), and to “Fostering the capacity of marine ecosystem models to PROject the cumulative effects of global change and plausible future OCEANS” (PROOCEANS): Funding by Ministerio de Ciencia e Innovación, Proyectos de I+D+I (RETOS-PID2020-118097RB-I00).It is widely known that the abundance and distribution dynamics of populations of small pelagic clupeid fish, such as sardines and anchovies, are affected by large-scale climate variability, which may lead to changeovers to new regimes of small pelagics. However, long-distance climatic oscillations, such as El Niño/La Niña and the Pacific Decadal Oscillation, have been little explored in the Western Mediterranean Sea. We investigated the possible effects of the South Oscillation Index (i.e. the atmospheric oscillation coupled with the El Niño/La Niña) and Pacific Decadal Oscillation on fluctuations in catches of European anchovy (Engraulis encrasicolus) and sardine (Sardina pilchardus) in the Western Mediterranean Sea, and their association with regional climate oscillations (i.e. the Atlantic Multidecadal Oscillation, the North Atlantic Oscillation, the Western Mediterranean Oscillation index, and the Arctic Oscillation)

La Oscilación del Atlántico Norte y la temperatura superficial del mar afectan la abundancia de la tortuga boba alrededor del estrecho de Gibraltar

The aim of this study was to explore the possible link between variations in the North Atlantic Oscillation (NAO) and sea surface temperature (SST) and the abundance of loggerhead turtles around the Strait of Gibraltar, using stranding data for the Andalusian coastal area as a proxy for abundance. The annual average SST (from November to October) in the Gulf of Cadiz was negatively associated with the total number of loggerhead strandings each year from November 1997 to October 2006 in the Gulf of Cadiz and the Alboran Sea. The average NAO index was positively associated with the number of strandings in the Gulf of Cadiz in the following year. Prevailing westerly winds during positive NAO phases and the subsequent delayed decrease in SST may lead to turtles from the west Atlantic accumulating in the Gulf of Cadiz and unsuccessfully attempting to return. Secondary causes, such as buoyancy, cold stunning, longline fisheries, net fisheries, debilitated turtle syndrome, and trauma may also increase the number of turtle strandings.El objetivo de este estudio fue explorar la posible relación entre las variaciones de la Oscilación del Atlántico Norte (NAO) y la temperatura superficial del mar (SST), y la abundancia de tortugas bobas alrededor del Estrecho de Gibraltar, utilizando los datos de varamientos como sustituto de la abundancia. La SST promedio en el Golfo de Cádiz se relacionó negativamente con el número total de tortugas bobas varadas durante cada año (de noviembre a octubre) desde 1997 hasta 2006 en el Golfo de Cádiz y en el Mar de Alborán, mientras que el promedio del índice NAO se relacionó positivamente con el número de varamientos en el Golfo de Cádiz durante el año siguiente. Vientos predominantes del oeste durante las fases de la NAO positiva, y su posterior retraso en la reducción de la SST, pueden provocar la acumulación en el Golfo de Cádiz de las tortugas que entran desde el Atlántico occidental y, las que sin éxito, tratan de regresar a sus playas de origen. Debido a causas secundarias (como problemas de flotabilitdad, enfriamiento, la pesca con palangre, la pesca con redes, DTS, y traumatismos) aumenta el número de tortugas varadas