Analysis of Stress Concentration in Functionally Graded Plates with Linearly Increasing Young's Modulus.

In this article, the strain and stress analyses of functionally graded plates with circular holes that are subject to a uniaxial far-field traction load are analytically considered. The Young's modulus is assumed to vary linearly along the radial direction around the hole. The adoption of such a type of inhomogeneity variation can be justified as follows.

A mechanistic mathematical model for describing and predicting the dynamics of high-affinity nitrate intake into roots of maize and other plant species.

A fully mechanistic dynamical model for plant nitrate uptake is presented. Based on physiological and regulatory pathways and based on physical laws, we form a dynamic system mathematically described by seven differential equations. The model evidences the presence of a short-term positive feedback on the high-affinity nitrate uptake, triggered by the presence of nitrate around the roots, which induces its intaking.

A threshold mechanism ensures minimum-path flow in lightning discharge.

A well-known property of linear resistive electrical networks is that the current distribution minimizes the total dissipated power. When the circuit includes resistors with nonlinear monotonic characteristic, the current distribution minimizes in general a different functional. We show that, if the nonlinear characteristic is a threshold-like function and the current generator is concentrated in a single point, as in the case of lightning or dielectric discharge, then the current flow is concentrated along a single path, which is a minimum path to the ground with respect to the threshold.

A Dynamic Programming Setting for Functionally Graded Thick-Walled Cylinders.

Material property variation in non-homogeneous internally pressurized thick-walled cylinders is investigated within the context of dynamic programming theory. The material is assumed to be linear, elastic, isotropic, and functionally graded in the radial direction. Based on the plane stress hypothesis, a state space formulation is given and the optimal control problem is stated and solved by means of Pontryagin's Principle for different objective functionals.