Exact and analytic-numerical solutions of lagging models of heat transfer in a semi-infinite medium

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Community attributes determine facilitation potential in a semi-arid steppe

Studies on positive plant–plant relations have traditionally focused on pair-wise interactions. Conversely, the interaction with other co-occurring species has scarcely been addressed, despite the fact that the entire community may affect plant performance. We used woody vegetation patches as models to evaluate community facilitation in semi-arid steppes. We characterized biotic and physical attributes of 53 woody patches (patch size, litter accumulation, canopy density, vegetation cover, species number and identity, and phylogenetic distance), and soil fertility (organic C and total N), and evaluated their relative importance for the performance of seedlings of Pistacia lentiscus, a keystone woody species in western Mediterranean steppes. Seedlings were planted underneath the patches, and on their northern and southern edges. Woody patches positively affected seedling survival but not seedling growth. Soil fertility was higher underneath the patches than elsewhere. Physical and biotic attributes of woody patches affected seedling survival, but these effects depended on microsite conditions. The composition of the community of small shrubs and perennial grasses growing underneath the patches controlled seedling performance. An increase in Stipa tenacissima and a decrease in Brachypodium retusum increased the probability of survival. The cover of these species and other small shrubs, litter depth and community phylogenetic distance, were also related to seedling survival. Seedlings planted on the northern edge of the patches were mostly affected by attributes of the biotic community. These traits were of lesser importance in seedlings planted underneath and in the southern edge of patches, suggesting that constraints to seedling establishment differed within the patches. Our study highlights the importance of taking into consideration community attributes over pair-wise interactions when evaluating the outcome of ecological interactions in multi-specific communities, as they have profound implications in the composition, function and management of semi-arid steppes.