Mathematical models predictions

Filing of applicants plans, specifications, air quality monitoring data, and mathematical model predictions. 

Neely, W. B., G. E. Blau, and J. Alfrey Jr., Mathematical models predict concentration-time profiles resulting from chemical spill in a river , Environ. Sci. Technol., 10, 72-76 (1976). 

Existing mathematical models predicting cognitive readiness/performance from sleep/wake history are based on the interaction of three factors. These factors are sleep homeostasis, circadian rhythm, and sleep inertia (12). Three-factor models successfully predict performance effects of acute, total sleep deprivation and... 

In order to extrapolate the laboratory results to the field and to make semiquantitative predictions, an in-house computer model was used. Chemical reaction rate constants were derived by matching the data from the Controlled Mixing History Furnace to the model predictions. The devolatilization phase was not modeled since volatile matter release and subsequent combustion occurs very rapidly and would not significantly impact the accuracy of the mathematical model predictions. The "overall" solid conversion efficiency at a given residence time was obtained by adding both the simulated char combustion efficiency and the average pyrolysis efficiency (found in the primary stage of the CMHF). 

TCE is extensively metabolized (40-75% of the retained dose) in humans to trichloroethanol, glucuronides, and trichloroacetic acid (TCA). Saturation of metabolism has not been demonstrated in humans up to an exposure concentration of 300 ppm. Mathematical models predict, however, that saturation of metabolism is possible at TCE concentrations previously used for anesthesia (i.e., 2000 ppm). Although the liver is the primary site of TCE metabolism in animals, there is evidence for extrahepatic metabolism of trichloroethylene in the kidneys and lungs. 

All four mathematical models predict well the steady-state concentration profiles and the performance parameters of the experimental SMB system. The two transient models predict the time evolution of the internal concentration profiles of each component and the number of cycles that is required to reach steady-state. 

Fig. 48. Atomic oxygen concentration, measured by optical emission actinometry, as a function of radius in a 13.56 MHz oxygen discharge sustained in a diode reactor. The electrode is covered with a reactive film up to a radius of 3.75 cm. This film acts as a sink for atomic oxygen (loading) resulting in significant radial concentration gradients. Such gradients are responsible for etch non-uniformity. Solid lines show the result of mathematical model predictions. After [231]. Pressure 2 torr, gas flow 100 seem.

Fractional uptake Figure 9.5-1 shows the fractional uptake of ethane and propane, and we observe the overshoot of ethane. Ethane, being a weaker adsorbing species, will penetrate the particle faster and hence adsorb more than its share of equilibrium capacity under the condition of ethane and propane presence in the system. Propane, on the other hand, is a stronger adsorbing species than ethane, and therefore it penetrates slower into the particle. When it moves into the particle interior, it displaces some of the previously adsorbed ethane molecules from the surface, resulting an overshoot in the fractional uptake of ethane. Experimental data are also shown in the same figure, and we see that the mathematical model predicts very well the fractional uptakes of all species. The model also predicts the correct time when the maximum overshoot occurs. 

Mathematical models predicting the performance of a fuel cell can assist system development. Seeking for the optimal operating conditions, these mathematical models can effectively substitute expensive experimental runs. Many questions of practical importance such as the excess air requirement and fuel flow rates can be answered using state of the art numerical models. Moreover, simple mathematical models such as a zero dimensional polarization models help to understand the influence of various electrochemical parameters on fuel cell performance [76,78,83]. 

To enhance our understanding of spinal loads, mathematical models are helpful. These models require the concepts of equilibrium and mechanical stability to be addressed. An early equilibrium model to predict the loading in the spine was developed by Schultz et al. (1982). These investigators used an indeterminate analysis with optimization to predict the loading in the spine in a variety of muscle groups at the L3 level of the lumbar spine. The concept of mechanical stability has been adopted in more recent mathematical models since it was realized that the osteoligamentous spine is inherently unstable (Lucas 1961 Crisco 1992). These mathematical models predict co-activation of the spinal musculature which increases compressive forces and anterior shear forces in the lumbar spine (Mirka 1993 Mar-ras 1997). 

Good fits to the experimental data were obtained for different inlet methane fractions (see curves in Fig. 1). The curves in Fig. 2 represent the calculated conversions for different flowrates. Although the predicted values can follow the general trend, higher deviations than those of Fig. 1 can be observed. In fact for variations in the inlet flowrate, the mathematical model predicts a higher sensitivity than that observed during the experimentation. 

The experimental concentrations are about the same as the mathematical models predict, and the curves are consistent with the above discussion. Despite the small distance from the outlet, the values close to the wall are very much less than the values predicted by the no-radial-diffusion model, indicating an appreciable radial diffusion effect. The experimental curves represent the com-bined effect of back-diffusion and upstream bulk flow of carbon dioxide, because of the manner in which carbon dioxide was injected the bulk flow effect would be greater close to the wall where the local nitrogen velocity is lower. Diffusion alone would result in lower local concentrations and flatter curves. The lack of symmetry is due to imperfect positioning of the injection tubes. It was found, after the equipment was dismantled, that the center of the tube pattern corresponded to die minimum in the curves. 

What is the significance of the mathematical model predictions of negative pressure ... 

The oil-based and synthetic-based muds (Fig. 25) showed remarkable stability, both experimentally and mathematically. Both the weighted and unweighted OBM and SBM exhibited high yield stress, and all fiber-fluid combinations tested showed stable behavior. This was reinforced with the mathematical model predictions of similar results. 

One of the main attractions of the IR technique is that the dichroism of the absorption bands assigned to different groups, and orientation of the different groups of the monomer can be determined (Gedde, 2001). Herman s mathematical model predicts... 

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