Equivalent time constant

The fuel valve actuator and its mechanism may have sufficient inductance or inertia to introduce a perceptible lag in the valve stem response to its input signal. The equivalent time constant is Tfi. 

Objective Evaluation of Color. In recent years a method has been devised and internationally adopted (International Commission on Illumination, I.C.I.) that makes possible objective specification of color in terms of equivalent stimuli. It provides a common language for description of the color of an object illuminated by a standard illuminant and viewed by a standard observer (H). Reflectance spectro-photometric curves, such as those described above, provide the necessary data. The results are expressed in one of two systems the tristimulus system in which the equivalent stimulus is a mixture of three standard primaries, or the heterogeneous-homogeneous system in which the equivalent stimulus is a mixture of light from a standard heterogeneous illuminant and a pure spectrum color (dominant wave-length-purity system). These systems provide a means of expressing the objective time-constant spectrophotometric results in numerical form, more suitable for tabulation and correlation studies. In the application to food work, the necessary experimental data have been obtained with spectrophotometers or certain photoelectric colorimeters. 

An equivalency can be demonstrated between the concept of time constant ratios and the dimensionless parameters obtained from differential equations. The concept of time constants is discussed in Sec. 2.2. 

The term time constant is more or less equivalent to process time, characteristic time and relaxation time. Relaxation time is often used in physics, but is applied only to first-order processes and refers to the time for a process to reach a certain fraction of completion. This fraction is given by (1-1/e) = 0.63, which for a first-order process, as shown previously, is reached at a time t = X. Time constants also may be used to describe higher order processes and also non-linear processes. In these cases the time constant is defined as the time in which the process proceeds to a specified fraction of the resultant steady state. Higher order processes are often more elegantly described by a series of time constants. 

Some economies are possible if equilibrium is assumed between selected compartments, an equal fugacity being assignable. This is possible if the time for equilibration is short compared to the time constant for the dominant processes of reaction or advection. For example, the rate of chemical uptake by fish from water can often be ignored (and thus need not be measured or known within limits) if the chemical has a life time of hundreds of days since the uptake time is usually only a few days. This is equivalent to the frequently used "steady state" assumption in chemical kinetics in which the differential equation for a short lived intermediate species is set to zero, thus reducing the equation to algebraic form. When the compartment contains a small amount of chemical or adjusts quickly to its environment, it can be treated algebraically. 

This simplified equation is equivalent to Tian s equation [Eq. (16)], and it appears that n is indeed the time constant r of the calorimeter. Thence, the successive coefficients n in Eq. (29) may be called the calorimeter time constants of 1st, 2nd,. .., ith order. When the Tian equation applies correctly, all time constants r, except the first r may be neglected. Since the value of the coefficients n of successive order decreases sharply [the following values, for instance, have been reported (40) n = 144 sec, r2 = 38.5 sec, r3 = 8.6 sec, ri 1 sec], this approximation is often valid, and the linear transformation of many thermal phenomena produced by the thermal lag in the calorimeter may actually be represented correctly by Eqs. (16) or (30). It has already been shown (Section IV.A) that the total heat produced in the calorimeter cell is then proportional to the area limited by the thermogram. 

All three are completely equivalent. The time constant and the damping coeflicient for the system are... 

When a compound is administered by a route other than intravenously, the plasma level profile will be different, as there will be an absorption phase, and so the profile will be a composite picture of absorption in addition to distribution and elimination (Fig. 3.26). Just as first-order elimination is defined by a rate constant, so also is absorption kab. This can be determined from the profile by the method of residuals. Thus, the straight portion of the semilog plot of plasma level against time is extrapolated to the y axis. Then each of the actual plasma level points, which deviate from this during the absorptive phase, are subtracted from the equivalent time point on the extrapolated line. The differences are then plotted, and a straight line should result. The slope of this line can be used to calculate the absorption rate constant kab (Fig. 3.26). The volume of distribution should not really be determined from the plasma level after oral administration (or other routes except intravenous) as the administered dose may not be the same as the absorbed dose. This may be because of first-pass metabolism (see above), or incomplete absorption, and will be apparent from a comparison of the plasma... 

Fig. 2c. It can be seen that at 530 nm, the fluorescence decays mono-exponentially with the fluorescence lifetime of 3.24 ns. The rise of the emission seen below 50 ps in the corresponding FlUp data is obviously not resolved here. In contrast, the TCSP data at 450 nm is described by a triple-exponential decay whose dominant component has a correlation time well below the time resolution. This component is obviously equivalent to the fluorescence decay observed in the FlUp experiment. A minor contribution has a correlation time of about 3.2 ns and reflects again the fluorescence lifetime that was also detected at 530 nm. The most characteristic component at 450 nm however has a time constant of about 300 ps. It is important to emphasize that this 300 ps decay does not have a rising counterpart when emission near the maximum of the stationary fluorescence spectrum is recorded. In other words, the above mentioned mirror image correspondence of the fluorescence dynamics between 450 nm and 530 nm holds only on time scales shorter than 20 ps. Finally, in contrast to picosecond time scales, the anisotropy deduced from the TCSPC data displays a pronounced decay. This decay is reminiscent of the rotational diffusion of the entire protein indicating that the optical chromophore is rigidly embedded in the core of the 6-barrel protein.

Why are there two independent time constants corresponding to two successive proton transfer processes in such a system with an equivalent component of... 

Consideration of the equivalent circuit diagram of an electrochemical cell, such as that given in Figure 5.1, reveals the major limitation on the rate at which the potential of an electrode can be varied, namely, the time constant of the electrochemical cell, RuCd. When a potential sweep is applied across the cell, the nonfaradaic charging current that flows is described by [24]... 

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