Plasticity of stomatal distribution pattern and stem tracheid dimensions in Podocarpus lambertii: an ecological study

Leaf and wood plasticity are key elements in the survival of widely distributed plant species. Little is known, however, about variation in stomatal distribution in the leaf epidermis and its correlation with the dimensions of conducting cells in wood. This study aimed at testing the hypothesis that Podocarpus lambertii, a conifer tree, possesses a well-defined pattern of stomatal distribution, and that this pattern can vary together with the dimensions of stem tracheids as a possible strategy to survive in climatically different sites. Leaves and wood were sampled from trees growing in a cold, wet site in south-eastern Brazil and in a warm, dry site in north-eastern Brazil. Stomata were thoroughly mapped in leaves from each study site to determine a spatial sampling strategy. Stomatal density, stomatal index and guard cell length were then sampled in three regions of the leaf: near the midrib, near the leaf margin and in between the two. This sampling strategy was used to test for a pattern and its possible variation between study sites. Wood and stomata data were analysed together via principal component analysis. The following distribution pattern was found in the south-eastern leaves: the stomatal index was up to 25 higher in the central leaf region, between the midrib and the leaf margin, than in the adjacent regions. The inverse pattern was found in the north-eastern leaves, in which the stomatal index was 10 higher near the midrib and the leaf margin. This change in pattern was accompanied by smaller tracheid lumen diameter and length. Podocarpus lambertii individuals in sites with higher temperature and lower water availability jointly regulate stomatal distribution in leaves and tracheid dimensions in wood. The observed stomatal distribution pattern and variation appear to be closely related to the placement of conducting tissue in the mesophyll.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.