The two-dimensional series and parallel models provide upper and lower bounds of the effective diffusion coefficient, respectively, whereas the three-dimensional model provides the accurate effective diffusion coefficient.
However, in simulations, where the user activity is determined a-priory, the model provides an upper bound on the solution quality of the three simple schemes that do not require exact information about the future.
This is motivated by the assumption that the theoretical model provides an (estimated) upper bound on prediction accuracy, so the empirical accuracy estimates should not exceed the theoretical accuracy estimates.
Many models tend to provide upper-end or worst-case outcrossing predictions and management recommendations, either because of experimental design underlying datasets, biological and environmental stochasticity, or chosen statistical analysis.
This provides upper limits for real performances.
Ureteral stents are used to provide upper urinary-tract drainage.
Since the model does not account for convective heat dissipation out of the sides and top of the tumor or of conduction though the animal itself, it is conservative and provides upper limits of the temperature increase in the tissue.
We can be certain, however, that search cannot succeed without contrast detection; thus our model provides a lower bound on the contrast required, or an upper bound on the distance at which detection is possible.
It is also found that the strain gradient model provides the lower bound and the stress gradient model provides the upper bound for the critical buckling load of nanotubes.
Furthermore, this predictive model provides a new idea for the design of high-efficient photocatalysts and may upper limits of SPR-mediated enhancement of photocatalytic performance for plasmonic nanostructure-involved photocatalysts.
