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. In the long run, this positive feedback is overridden by two long-term negative feedback loops which drastically reduces the nitrate uptake capacity. These two negative feedbacks are due to the generation of ammonium and amino acids, respectively, and inhibit the synthesis and the activity of high-affinity nitrate transporters. This model faithfully predicts the typical spiking behavior of the nitrate uptake, in which an initial strong increase of nitrate absorption capacity is followed by a drop, which regulates the absorption down to the initial value. The model outcome was compared with experimental data and they fit quite nicely. The model predicts that after the initial exposure of the roots with nitrate, the absorption of the anion strongly increases and that, on the contrary, the intensity of the absorption is limited in presence of ammonium around the roots.

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. Firstly, and among all the possible variations of stiffness, the linear one is indeed the simplest inhomogeneity distribution. Surprisingly however, according to our knowledge extent, the associated elastic fields were not yet addressed in the literature. Secondly, a linearly varying stiffness could reasonably imply a remarkable advantage from a technological point of view. In fact, unlike nonlinearly varying stiffness plates, manufacturing routes are only required to handle constant variations throughout the radial domain. After recalling the basic equations for plane stress elasticity, the displacement, strain, and stress fields around the hole were numerically tackled and discussed for different stiffness ratios. A comparison was also carried out with other Young's modulus distributions that have been commonly employed in the literature.

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. We also propose a dynamic model that explains and qualitatively reproduces the lightning transient behavior: initial generation of several plasma branches and subsequent dismissal of all branches but the one reaching the ground first, which is the optimal one.

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. Optimal Young's modulus distribution is found to be piecewise linear along the radial domain. A brief digression on the possible existence of switching points is addressed. Finally, a numerical example is performed within a special class of derived optimal solutions, showing promising results in terms of equivalent stress reduction with respect to the most used variations in literature.