Limiting constant

Figure 3-50 Methods of constant current limiting (a) discrete overcurrent limiting (constant-current limiting) (b) precision resistive current-sensing overcurrent protection (constant-current limiting) (c) use of a current transformer to sense ac current.

So, for catalytic cycles with the limiting constant fc in, the relaxation time is also determined by one constant, but another one. This is K, the second in order rate constant. It should be stressed that the only smallness condition is required, fcmin should be much smaller than other constants. The second constant, k should be just smaller than others (and bigger than fc in), but there is no condition for k required. 

The steady-state approximation on the base of the rule (13) is a linear function of the restored-and-cut cycles rate-limiting constants. It is the first-order approximation. 

Let us find the first-order (in rate limiting constants) approximation to the steady states. If 21 12 en fc 2 the rate-limiting constant for the... 

If, inverse, k fcjj then k is the rate-limiting constant for the cycle A <->-A and almost all concentration in the steady state is accumulated inside A c 1 — and For distributions of concentra-... 

Figure 5.38. The adsorbed amount 6 of a polyelectrolyte on a surface of opposite charge sign, as a function of the fractional charge a per segment, for various salt concentrations (indicated). The dashed curve represents the charge compensation limit = constant.

K., but approaches a limiting constant value at 1 5°K. On the Unear part of the curve the constant is approximately 1, the lowest value known, and for a substance with the lowest critical temperature. ... 

Equation (2.a) presents the objective function, equation (2.b) corresponds to the underlying model structure, equations (2.c) formalize the assignment of the points to segments, where is a magnitude limit (constant), here set to = max(Y] ) -I-... 

In some cases an adjustment of both constants (k] 2 and k A) must be performed in Eq. (3.12) in order to impart a physical sense upon them. A substantial simplification of this procedure is taking place if direct data about deactivation and/or about the pressure dependence of the apparent high limit constant are available. 

Note that the ionic equivalent conductivities A, and Ap represent free ion conductivities, unperturbed by interionic interactions. The counterion conductivity Ai may therefore in dilute solutions be approximated by its limiting constant value A°, since it only depends on the hydrodynamic solvent friction coefficient/, which for small ions is fairly constant in dilute solutions. 

Table 1-5. Integration limits, constants, and variables used in the hydraulic conductivity calculations (Eq. [56]). 

Freund6 found the Eotvos constant abnormally high for high molecular weight oils it increased regularly with the mol. wt. and could be calculated from this. For liquid helium7 the constant is abnormally small, 1 464 the value of o M Iq)213 for liquid helium is a linear function of temperature down to 2-4° K., but approaches a limiting constant value at 1 5°K. On the linear part of the curve the constant is approximately 1, the lowest value known, and for a substance with the lowest critical temperature.8... 

Fig. 9.3. Example of current-limited constant-voltage (CV or lU) charging for a 200-Ah VRLA battery at 2.23 VPC (solid line) and 2.40 VPC (dotted line). Larger Ah charge returns are for 2.40 VPC charge. (From Ref. [3], p. 84.)...

Fig 42. Comparison of the predicted low- pressure limit constant (in N2) with experimental values in the temperature range of 200 - 400 K. The meanings of thick lines are the same as those in Fig. 41. The dash-dotted line is taken from the equation given in Ref 131. , Ref 131 T, Ref 141 the error bar represents the range of results based AH%= 14.8 2.9 kcal/mol (Ref 130). 

The autocorrelation function picture of a frequency domain spectrum (Heller, 1981) is derived as follows. Consider the e,v e <— g, t>" electronic absorption spectrum. In the Franck-Condon limit (constant transition moment) and neglecting rotation, the eigenstate spectrum observed from the v" vibrational level... 

At longer times, the cumulative filtrate volume Vflinear dependence on time, indicating that the filter cake has reached a constant thickness. The limiting (constant) dynamic filtration rate is a marked function of 7C and rc. The limiting dynamic filtration rate Qm (= dVfa/ Adt as t - oo) has been scaled by 7C and rc by (135)... 

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