This value tells a random number generator to use a certain sequence of random numbers. Use the Mathcad default for this variable. Solve Blocks were discussed in Chapter 10. This variable controls how closely a constraint in a Solve Block must be met for a solution to be acceptable. It also controls the precision to which integrals and derivatives are evaluated. This value was discussed in detail in Chapter 10. This variable controls the length of the iteration in Solve Blocks and in the root function. The Mathcad default for this variable is 0, but earlier in the book we changed this value to 1. This option controls the value for the built-in variable “ORIGIN.” This variable represents the starting index of all arrays in your worksheet. If large-diameter roots are more likely to suffer root–soil gaps, then the advantages of small-diameter roots in nutrient uptake would include the benefit of more continuous nutrient uptake.įigure 14.7. To the degree that the formation of root–soil gaps increases with root age, this factor is represented in our analysis of root uptake rate decreasing with longevity, and would contribute to the benefits of rapid root replacement. Alternatively, the principal role of root hairs might be to prevent the development of root–soil gaps and the resulting resistance to solute transport to the root surface ( Caldwell, 1979), rather than to enhance the absorbing area of roots. The effect of root hairs on nutrient uptake can be simulated by increasing the effective radius of the root by the average length of the root hairs it would be misleading to consider them independently of the roots because root hairs, to a greater extent than hyphae, operate within the depletion zone of roots. In addition, root hairs might be considered a plant adaptation in the direction of finer absorbing organs. The mycorrhizal symbiosis provides absorbing surfaces of much smaller diameters than roots, with consequent advantages, as we have illustrated. In pines, only diarch and tetrarch roots (i.e., those of relatively large diameter) appear to be morphogenetically capable of becoming mother roots ( Wilcox, 1968), and hence of long-distance, exploratory growth, illustrating a trade-off necessitated by existing root system design. Glass and Siddiqi (1984) observed that under K limitation, shoot K remained constant while root concentration declined markedly, indicating that K stored in the root cortex had been transported to maintain shoot K concentrations. The root cortex may serve as a short-term reservoir for nutrient storage. For example, larger diameter roots may be able to withstand greater soil impedence before buckling ( Whitely et al., 1982).
Most likely, other root functions or anatomical constraints limit the minimum diameter of roots. The results of our simulations indicated that, unless root longevity is strongly tied to root diameter, average lifetime root efficiency increases continuously with decreasing diameter. Miller, in Resource Physiology of Conifers, 1995 B Discussion Provided several engineering examples to illustrate the use of the solve features. Told how the Minerr function can be used in place of the Find function if Mathcad is not finding a solution.
▪ĭiscussed the built-in variables TOL and CTOL. ▪Įmphasized the rules of using Given, Find, Maximize, and Minimize. Introduced Solve Blocks and showed how they can be used to find solutions to multiple unknowns using multiple equations. ▪īriefly introduced the two solution methods used by the polyroots function (LaGuerre and Companion Matrix Methods). Introduced the polyroots function and showed how it can be used to solve for all the roots of a polynomial equation. ▪Įncouraged the use of a plot to help define the initial guess values for the root function.
Showed how the root function can be used with an initial guess prior to using root, or how two guesses can be included as arguments in the root function. Introduced the root function and showed how it can be used to solve for a single variable with a single function.
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