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A potentiometric surface is the imaginary plane where a given reservoir of fluid will "equalize out to" if allowed to flow. A potentiometric surface is based on hydraulic principles. For example, two connected storage tanks with one full and one empty will gradually fill/drain to the same level.
In fact, since the potentiometric measurement is a non-destructive measurement, assuming that the electrode is in equilibrium with the solution, we are measuring the solution's potential. Potentiometry usually uses indicator electrodes made selectively sensitive to the ion of interest, such as fluoride in fluoride selective electrodes , so that ...
This is a simple form of inverse modeling, since the result (s) is measured in the well, r, t, and Q are observed, and values of T and S which best reproduce the measured data are put into the equation until a best fit between the observed data and the analytic solution is found. The Theis solution is based on the following assumptions:
The extension of the problem to higher dimensions (that is, for -dimensional surfaces in -dimensional space) turns out to be much more difficult to study.Moreover, while the solutions to the original problem are always regular, it turns out that the solutions to the extended problem may have singularities if .
The obvious solution is then to split that surface into several pieces, calculate the surface integral on each piece, and then add them all up. This is indeed how things work, but when integrating vector fields, one needs to again be careful how to choose the normal-pointing vector for each piece of the surface, so that when the pieces are put ...
An example of a solenoidal vector field, (,) = (,) In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: =
Surface reconstruction is an inverse problem. The goal is to digitally reconstruct a smooth surface based on a large number of points p i (a point cloud) where each point also carries an estimate of the local surface normal n i. [7] Poisson's equation can be utilized to solve this problem with a technique called Poisson surface reconstruction. [8]
Figure 2 gives an example; in this example, the two x-intercepts differ by about 0.2 mL but this is a small discrepancy, given the large equivalence volume (0.5% error). Similar equations can be written for the titration of a weak base by strong acid (Gran, 1952; Harris, 1998).