Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.

Small-scale variation of vegetation in a mixed forest understorey is partly controlled by the effect of overstory composition on litter accumulation

We investigated how richness and composition of vascular plant species in the understory of a mixed hardwood forest stand varied with respect to the abundance and composition of the overstory. The stand is in central Spain and represents the southernmost range of distribution of several tree and herbaceous species in Europe. Understory species were identified in 46 quadrats (0.25 m2) where variables litter depth and light availability were measured. In addition, we estimated tree density, basal area, and percent basal area by tree species within 6-m-radius areas around each plot. Species richness and composition were studied using path analysis and scale-dependent geostatistical methods, respectively. We found that the relative abundance of certain trees species in the overstory was more important than total overstory abundance in explaining understory species richness. Richness decreased as soil litter depth increased, and soil litter increased as the relative proportion of Fagus sylvatica in the overstory increased, which accounted for a negative, indirect effect of Fagus sylvatica on richness. Regarding understory species composition, we found that some species distributed preferentially below certain tree species. For example, Melica uniflora was most frequent below Fagus sylvatica and Quercus petraea while the increasing proportion of Q. pyrenaica in the overstory favored the presence of Cruciata glabra, Arenaria montana, Prunus avium, Conopodium bourgaei, Holcus mollis, Stellaria media and Galium aparine in the understory. Overall, these results emphasize the importance of individual tree species in controlling the assemblage and richness of understory species in mixed stands. We conclude that soil litter accumulation is one way through which overstory composition shapes the understory community.

Comparison of different pre-treatments to improve accuracy of total soluble solids.

The applicability of a portable NIR spectrometer for estimating the °Brix content of grapes by non-destructive measurement has been analysed in field. The NIR spectrometer AOTF-NIR Luminar 5030, from Brimrose, was used. The spectrometer worked with a spectral range from 1100 to 2300 nm. A total of 600 samples of Cabernet Sauvignon grapes, belonging to two vintages, were measured in a non-destructive way. The specific objective of this research is to analyse the influence of the statistical treatment of the spectra information in the development of °Brix estimation models. Different data pretreatments have been tested before applying multivariate analysis techniques to generate estimation models. The calibration using PLS regression applied to spectra data pretreated with the MSC method (multiplicative scatter correction) has been the procedure with better results. Considering the models developed with data corresponding to the first campaign, errors near to 1.35 °Brix for calibration (SEC = 1.36) and, about 1.50 °Brix for validation (SECV = 1.52) were obtained. The coefficients of determination were R2 = 0.78 for the calibration, and R2 = 0.77 for the validation. In addition, the great variability in the data of the °Brix content for the tested plots was analysed. The variation of °Brix on the plots was up to 4 °Brix, for all varieties. This deviation was always superior to the calculated errors in the generated models. Therefore, the generated models can be considered to be valid for its application in field. Models were validated with data corresponding to the second campaign. In this sense, the validation results were worse than those obtained in the first campaign. It is possible to conclude in the need to realize an adjustment of the spectrometer for each season, and to develop specific predictive models for every vineyard.

Structural efficiency variation with the problem size in some bending problems = Variación del rendimiento estructural con el tamaño del problema en algunos casos de flexión simple

Existe normalmente el propósito de obtener la mejor solución posible cuando se plantea un problema estructural, entendiendo como mejor la solución que cumpliendo los requisitos estructurales, de uso, etc., tiene un coste físico menor. En una primera aproximación se puede representar el coste físico por medio del peso propio de la estructura, lo que permite plantear la búsqueda de la mejor solución como la de menor peso. Desde un punto de vista práctico, la obtención de buenas soluciones—es decir, soluciones cuyo coste sea solo ligeramente mayor que el de la mejor solución— es una tarea tan importante como la obtención de óptimos absolutos, algo en general difícilmente abordable. Para disponer de una medida de la eficiencia que haga posible la comparación entre soluciones se propone la siguiente definición de rendimiento estructural: la razón entre la carga útil que hay que soportar y la carga total que hay que contabilizar (la suma de la carga útil y el peso propio). La forma estructural puede considerarse compuesta por cuatro conceptos, que junto con el material, definen una estructura: tamaño, esquema, proporción, y grueso.Galileo (1638) propuso la existencia de un tamaño insuperable para cada problema estructural— el tamaño para el que el peso propio agota una estructura para un esquema y proporción dados—. Dicho tamaño, o alcance estructural, será distinto para cada material utilizado; la única información necesaria del material para su determinación es la razón entre su resistencia y su peso especifico, una magnitud a la que denominamos alcance del material. En estructuras de tamaño muy pequeño en relación con su alcance estructural la anterior definición de rendimiento es inútil. En este caso —estructuras de “talla nula” en las que el peso propio es despreciable frente a la carga útil— se propone como medida del coste la magnitud adimensional que denominamos número de Michell, que se deriva de la “cantidad” introducida por A. G. M. Michell en su artículo seminal de 1904, desarrollado a partir de un lema de J. C. Maxwell de 1870. A finales del siglo pasado, R. Aroca combino las teorías de Galileo y de Maxwell y Michell, proponiendo una regla de diseño de fácil aplicación (regla GA), que permite la estimación del alcance y del rendimiento de una forma estructural. En el presente trabajo se estudia la eficiencia de estructuras trianguladas en problemas estructurales de flexión, teniendo en cuenta la influencia del tamaño. Por un lado, en el caso de estructuras de tamaño nulo se exploran esquemas cercanos al optimo mediante diversos métodos de minoración, con el objetivo de obtener formas cuyo coste (medido con su numero deMichell) sea muy próximo al del optimo absoluto pero obteniendo una reducción importante de su complejidad. Por otro lado, se presenta un método para determinar el alcance estructural de estructuras trianguladas (teniendo en cuenta el efecto local de las flexiones en los elementos de dichas estructuras), comparando su resultado con el obtenido al aplicar la regla GA, mostrando las condiciones en las que es de aplicación. Por último se identifican las líneas de investigación futura: la medida de la complejidad; la contabilidad del coste de las cimentaciones y la extensión de los métodos de minoración cuando se tiene en cuenta el peso propio. ABSTRACT When a structural problem is posed, the intention is usually to obtain the best solution, understanding this as the solution that fulfilling the different requirements: structural, use, etc., has the lowest physical cost. In a first approximation, the physical cost can be represented by the self-weight of the structure; this allows to consider the search of the best solution as the one with the lowest self-weight. But, from a practical point of view, obtaining good solutions—i.e. solutions with higher although comparable physical cost than the optimum— can be as important as finding the optimal ones, because this is, generally, a not affordable task. In order to have a measure of the efficiency that allows the comparison between different solutions, a definition of structural efficiency is proposed: the ratio between the useful load and the total load —i.e. the useful load plus the self-weight resulting of the structural sizing—. The structural form can be considered to be formed by four concepts, which together with its material, completely define a particular structure. These are: Size, Schema, Slenderness or Proportion, and Thickness. Galileo (1638) postulated the existence of an insurmountable size for structural problems—the size for which a structure with a given schema and a given slenderness, is only able to resist its self-weight—. Such size, or structural scope will be different for every different used material; the only needed information about the material to determine such size is the ratio between its allowable stress and its specific weight: a characteristic length that we name material structural scope. The definition of efficiency given above is not useful for structures that have a small size in comparison with the insurmountable size. In this case—structures with null size, inwhich the self-weight is negligible in comparisonwith the useful load—we use as measure of the cost the dimensionless magnitude that we call Michell’s number, an amount derived from the “quantity” introduced by A. G. M. Michell in his seminal article published in 1904, developed out of a result from J. C.Maxwell of 1870. R. Aroca joined the theories of Galileo and the theories of Maxwell and Michell, obtaining some design rules of direct application (that we denominate “GA rule”), that allow the estimation of the structural scope and the efficiency of a structural schema. In this work the efficiency of truss-like structures resolving bending problems is studied, taking into consideration the influence of the size. On the one hand, in the case of structures with null size, near-optimal layouts are explored using several minimization methods, in order to obtain forms with cost near to the absolute optimum but with a significant reduction of the complexity. On the other hand, a method for the determination of the insurmountable size for truss-like structures is shown, having into account local bending effects. The results are checked with the GA rule, showing the conditions in which it is applicable. Finally, some directions for future research are proposed: the measure of the complexity, the cost of foundations and the extension of optimization methods having into account the self-weight.