A model for water uptake by plant roots.

We present a model for water uptake by plant roots from unsaturated soil. The model includes the simultaneous flow of water inside the root network and in the soil. It is constructed by considering first the water uptake by a single root, and then using the parameterized results thereby obtained to build a model for water uptake by the developing root network. We focus our model on annual plants, in particular the model will be applicable to commercial monocultures like maize, wheat, etc. The model is solved numerically, and the results are compared with approximate analytic solutions. The model predicts that as a result of water uptake by plant roots, dry and wet zones will develop in the soil. The wet zone is located near the surface of the soil and the depth of it is determined by a balance between rainfall and the rate of water uptake. The dry zone develops directly beneath the wet zone because the influence of the rainfall at the soil surface does not reach this region, due to the nonlinear nature of the water flow in the partially saturated soil. We develop approximate analytic expressions for the depth of the wet zone and discuss briefly its ecological significance for the plant. Using this model we also address the question of where water uptake sites are concentrated in the root system. The model indicates that the regions near the base of the root system (i.e. close to the ground surface) and near the root tips will take up more water than the middle region of the root system, again due to the highly nonlinear nature of water flow in the soil

Parasitic suppressing circuit

A circuit for suppressing parasitic oscillations across an inductor operating in a resonant mode is described. The circuit includes a switch means and resistive means connected serially across the inductor. A unidirectional resistive-capacitive network is also connected across the inductor and to the switch means to automatically render the switch means conducting when inductive current through the inductor ceases to flow

Differences between stellar and laboratory reaction cross sections

Nuclear reactions proceed differently in stellar plasmas than in the laboratory due to the thermal effects in the plasma. On one hand, a target nucleus is bombarded by projectiles distributed in energy with a distribution defined by the plasma temperature. The most relevant energies are low by nuclear physics standards and thus require an improved description of low-energy properties, such as optical potentials, required for the calculation of reaction cross sections. Recent studies of low-energy cross sections suggest the necessity of a modification of the proton optical potential. On the other hand, target nuclei are in thermal equilibrium with the plasma and this modifies their reaction cross sections. It is generally expected that this modification is larger for endothermic reactions. We show that there are many exceptions to this rule.Comment: 4 pages, Proceedings of Nuclear Physics in Astrophysics 4, Frascati, Italy; to appear in J. Phys. Conf. Serie

Electrostatic Analyzer for 1.5-Mev Protons

A system for analyzing the ion beam of an electrostatic generator is described. A weak magnetic field separates protons from heavier components and a 90° electrostatic deflection gives the required energy resolution. With the analyzer controlling the generator voltage, a proton beam of one microampere with an energy spread of the order of 300 volts in one million is obtained

Guidance methods for low-thrust space vehicles Cumulative progress report, 1 Jan. 1969 - 31 Jan. 1970

Guidance and control schemes for optimal low-thrust Earth-Mars transfer mission

A mathematical model of plant nutrient uptake

The classical model of plant root nutrient uptake due to Nye. Tinker and Barber is developed and extended. We provide an explicit closed formula for the uptake by a single cylindrical root for all cases of practical interest by solving the absorption-diffusion equation for the soil nutrient concentration asymptotically in the limit of large time. We then use this single root model as a building block to construct a model which allows for root size distribution in a more realistic plant root system, and we include the effects of root branching and growth. The results are compared with previous theoretical and experimental studies