Level as a function of time

Fig. 23. Population ratios in the Fe(.a Dj) levels, as a function of time, illustrating the quasiequilibrium in the upper levels. (-----------------------) theory (- —) experiment.

Until now only time-frequency smearing of the audio signal by the ear, which leads to an excitation representation, has been described. This excitation representation is generally measured in dB SPL (Sound Pressure Level) as a function of time and frequency. For the frequency scale one does, in most cases, not use the linear Hz scale but the non-linear Bark scale. This Bark scale is a pitch scale representing the... 

The same characteristic shape of curve was found with the absolute viscosity levels as a function of time depending on fat content. Obviously, the fat droplets in the system have an impact on the reaction, although the source of the structure build up is thought to be protein-based. Therefore, the effect of the protein content was assessed. As expected, a higher level of the protein content in the continuous phase increases the probability of networking and gel formation as also shown in Figure... 

S - threshold level as a function of time A adaptation constant... 

The curves in Fig. 6 represent the kynurenine levels as a function of time and demonstrate that blood levels of kynurenine are higher and... 

If a process settles at a new steady state after an input change, the process is referred to as self-regulating. Levels in tanks, accumulators, and reboilers, and many pressure systems, behave as integrating processes. Consider the level in a tank for which both the flow in and the flow out are set independently. Initially, the flow out, is equal to the flow in, and the level is constant. Figure 15.8 shows the level as a function of time for a step change in the flow out at time equal to 10 s. Note that the level in the tank begins to decrease at a constant rate. This is an example of a non-self-regulating process, since the process does not move to a new steady state. 

It was mentioned in Section III that cools vibrationally in storage rings on time scales much shorter than the radiative vibrational lifetimes. The effect was shown to be correlated with the interaction of the stored ion beam with the electron beam, and it was concluded that since higher vibrational levels recombine faster than lower levels, there will be an increase of the relative population of lower vibrational levels as a function of time. More recent work has shown that superelastic collisions... 

Typical overall sound level as a function of time. (From Hong, J., Baukal, C., Schwartz, R., and Fleifil, M., Chemical Engineering Progress, 102, no. 5,35-39, 2006.)... 

To handle this we can physically reason that the density of the bed must be a function of the level of filling of the bed. We need to bring this idea into the analysis quantitatively so that we might better predict the level as a function of time in the reactor. We begin with the statement of conservation of mass in the reactor ... 

Now we test this expression for its appearance of fit against the data set. We do so by creating the function lev [t] with it, computing the level as a function of time, and then plotting this with the actual data in order to visualize the fit. 

The dimensions of the constants a and /3 are of interest. The constant /3 is an element of the argument of the sine, which is a transcendental function. As such its argument must be dimensionless, and therefore /3 is an inverse time constant. On the other hand, the product of a and qfo must have dimensions of volumetric flow rate and so a must be dimensionless. From basic physics we also know that a is the amplitude of the wave while is the peak-to-peak time or the period of the wave. Now if this is the input to our tank how will the level as a function of time behave ... 

For a tank of the same dimensions as the previous one and with the same flow rate the level as a function of time is shown here along with a comparison ... 

Figure 7 shows a simple case of filling a spherical tank. The liquid flow into the tank is again a constant and we wish to be able to predict the level as a function of time. 

When the plug is pulled out of the orifice, the liquid flows out. One can measure the flow rate or the level as a function of time to learn how the system behaves. If we did this, then we would notice from these experiments that the flow rate out is not constant, but seems to drop with time. As the level drops, so does the rate at which mass leaves the tank. Before we... 

The mass flow in is zero, so we are left with just one term on the right-hand side. The density is a constant inside and outside of the vessel and the cross section of the liquid is just that of the tank A, and it too remains constant as the level drops. This leads us to the following equation for the change in level as a function of time ... 

For reference the dashed line across the data is set at the 10-cm level. With this we can see that once this level is reached, then independent of the starting point, it takes 50 sec to finish the process. The fluid moving out of the vessel then has no "memory" of the level at which the process was initiated. What we seek now is the relationship between the rate of change in level and the level in the tank, since both the material balance and the experimental data drive in this direction. We can get to this by computing the rate of change in level as a function of time for each experiment and then plotting this for comparison. 

In this expression Aoo is the nominal aperture size to deliver at the design flow rate based on the constant set input flow rate. The second term in the parenthetical expression is the product of a proportionality constant K and the difference between the set point level and the actual level as a function of time. We substitute this for Ao in Torricelli s Law and also in the equation describing a system with sinusoidally fluctuating input flow ... 

Male Fischer 344 rats received various doses of DEN and/or 600 mg kg body wt. of ABA prior to measurement of NAD. DEN was dissolved in saline (4 mg ml ) and ABA in DMSO (300 mg ml ) and given intraperitoneally. The dose-response effect of DEN on NAD levels 12 h after administration is shown in Fig. la. DEN depleted dose-dependently the NAD level. Figure lb represents the NAD level as a function of time after a 200 mg kg body wt. injection of DEN. The depletion of NAD reached a maximum at 12 h and returned to the control level 48 h after DEN administration. The effect of 600 mg kg body wt. ABA on NAD level as a function of time after the administration is shown in Fig. 2a. The NAD level was increased after 4 h... 

Fig. 1. A Dose-response effect of DEN on NAD level 12 h after the administration in rat liver. B NAD level as a function of time after administration of 200 mg kg body wt. DEN in rat liver...

Fig. 7. Study of the unimolecular dissociation of ethoxy to CH3 + CH2O at 900 K and 1 atm with Multi Well. (Top) Change of the distribution and population of vibrational energy levels as a function of time. (Bottom) Integrated C2H5O profiles versus time (inset) ln(C2H50) versus time. Notice the statistical noise inherent to all stochastic calculations.

Fig. 2.18. (a) Normalized transition probability as a function of the detuning cj — coba) in the rotating-wave approximation (b) probability of a transition to the upper level as a function of time for different detuning (c) h t) under broadband excitation and weak fields... 

One of the main drawbacks of corona treatment, as well as plasma and flame treatments, is the decay of treatment level as a function of time, also known as the aging phenomenon or hydrophobic recovery. The possible explanations include the thermodynamically driven reorientation (rotation) of the polar groups from the surface into the bulk, the migration... 

C. Supercritical Operation After attaining criticality at as low a power level as possible, remove one of the control rods to a position which will yield about a 60-sec period. Then plot power level as a function of time for about 5 min. How long does it take after the rod movement for the period to become asymptotic ... 

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