Previous attempts to model steady state Munch pressure flow in phloem (Christy and Ferrier. [19731. Plant Physiol. 52: 531-538; and Ferrier et al. [19741. Plant Physiol. 54: 589-600) lack sufficient equations, and results were produced which do not represent correct mathematical solutions. Additional equations for the present closed form model were derived by assuming that unloading of a given solute is dependent upon the concentration of that solute in the sieve tube elements. Examples As no unique steady state mathematical solution could be found, the above models were used to approximate steady state sieve tube transport by a judicious choice of initial concentrations and convergence criteria, in a quasi-time-dependent iteration procedure. It is unlikely that such inconsistencies occur in real phloem, and thus, another equation must exist which would provide a unique, closed form solution at a given loading rate.The above problem did not arise in the mechanical analogue model of Eschrich et al. (4). In this system, a given, initial amount of sugar was placed within an open or closed tubular, semipermeable membrane. In the absence of continuous loading and/or unloading of solute, their mathematical model correctly predicted the velocity of the solute front, the lack of equilibrium in the open tube, and the equilibrium condition when the front reached the end of the closed tube. Therefore, the necessary additional equations for a closed form mathematical model of steady state phloem translocation may lie with the assumptions regarding the loading and/or unloading of solutes. These considerations can best be illustrated by examining the existing equations as they apply to all of the individual elements of a sieve tube.REVIEW OF GENERAL THEORY The standard water potential terminology (9,15,16) Water potentials of the xylem-apoplast continuum will be denoted by the subscript x, and those of the sieve tube elements as i. The flux of water through the peripheral membrane (J,i, see Table I for units) of the ith sieve element would be a function of the water potential difference, and the hydraulic conductivity (La) and reflection coefficient (c-) of membranes, i
The quantity of solar radiation penetrating a crop canopy and reaching the soil surface affects greatly the microenvironment beneath the canopy. The influence of this microenvironment upon soil radiation and evaporation as well as upon development and mortality rates of insect plant pests is well known. The development of adequate models of light penetration is an important problem associated with the characterization of the subcanopy microenvironment.
In this paper, an analytical model is proposed which estimates the sunlit soil area within a row crop where plants are randomly spaced along rows. Only direct beam, parallel light is considered. The model combines both individual plant geometry and row structure. for simplicity, plant canopies are assumed to be ellipsoidal in shape. The model incorporates plant sizes, row spacings and azimuthal orientation, foliage density, planting density, leaf orientation, and solar location. Available experimental data are inadequate for a complete validation of the model; however, a relative verification was made by comparing model output to real experimental measurements. Included in the paper is a critique of available data in light of the data requirements necessary for satisfactory model validation.
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