לוח שנה משולב

Thirty-eight yield/plant-population-density (Y-PPD) data sets were collected from the literature and analyzed statistically to yield, inter alia, a single "universal" relationship that realistically describes the Y-PPD data obtained with various plants in various agricultural and environmental conditions. The present study aims to facilitate evaluation of the dependence of water availability to plant-root systems on plant-population density, plant-arrangement geometry, active-root-system size, and soil texture. The outlined evaluation of the relative water uptake rate/plant-population-density (RWUR-PPD) relationship can quantify the roles of water availability and competition among neighboring root systems in determining the Y-PPD relationship. In particular, this methodology quantifies the effects of root system size, soil capillary length and planting rectangularity, on the Y-PPD relationship. Overall, the proposed RWUR evaluation shows, in reasonable qualitative agreement with experimental findings, that the Y-PPD relationship increases with increasing root system radius and soil capillary length, and with decreasing rectangularity. RWUR evaluation shows that interplant competition for water increases approximately linearly with the product of (root-system radius) × (soil capillary length). The water-competition factor is approximately equal to 4 r01-1, i.e. to the surface area of a sphere with a radius equal to the geometric mean of the radius of root system (r0) and the soil capillary length (-1). Plant roots and shoots compete also for resources other than water, e.g., soil nutrients and oxygen and solar radiation. Thus, the agronomically important Y-PPD relationship depends on genetic, agricultural, and environmental factors that affect availability of other resources differently from their effects on water availability; and these differences render it virtually impossible to define and quantify the roles of the various essential resources and the effects of diverse factors in determining the Y-PPD relationship. This is why practical agronomists use empirical mathematical expressions to describe Y-PPD.

When time-narrow wave-packets scatter by complex target, the field is trapped for some time, and emerges as a time broadened pulse, whose shape reflects the distribution of the delay (trapping) -times. I shall present a comprehensive framework for the computation of the delay-time distribution, and its dependence on the scattering dynamics, the wave-packet envelope (profile) and the dispersion relation. I shall then show how the well-known Wigner-Smith mean delay time and the semi-classical approximation emerge as limiting cases, valid only under special circumstances. For scattering on random media, localization has a drastic effect on the delay-time distribution. I shall demonstrate it for a particular one-dimensional system which can be analytically solved.