Kono approach

The consumption coefficient (f) can be numerically estimated from experimental data on growth, as shown in Fig. 5.19. The concept of a critical cell mass concentration is used, and it is determined by numerical methods from the plot of Fig. 5.19. The basic concept of the Kono approach is that reaction order changes at x nt following the general growth equation... 

Figure 5.19. Representation of the numerical Kono approach in a. c/t diagram of growth (a) and a kinetic plot versus x (b). In agreement with different well-known growth phases I-IV, (cf. Fig. 5.23, lag phase, I transition, II exponential. III and S-limitation decline phase, IV), and incorporating a linear growth phase in case of transport limitations (V in case B instead of exponential case A), numerical values can be taken from the plots to quantify the growth behavior with concentrations at certain times Xq — inoculum at Iq, — lag-time, = critical concentration at critical time...

Figure 5.44. Schematic representation of the numerical Kono approach to microbial product formation expressed as the general formulas of the rates of growth and production rp, including different growth phases (1, induction 2, transient 3, exponential and 4, declining), according to Equ. 5.126 and Table 5.2. (Adapted from Kono and Asai, 1968a-c, 1969a-c) (a) both and kp2 have a positive value. The dotted lines take into account a linear growth phase, as shown in Fig. 5.19. (b) kp >0, kp2 = 0. (c) kpi = 0, kp2 > 0. (d) /cpi > 0, kp2 < 0.

Kato and Kono [4] were the first to develop an approximate method for computing the TDPES in an intense laser field. In their approach, the TDPES was defined in terms of instantaneous eigenvalues of the field-dressed electronic Hamiltonian. In other words, in the Kato-Kono approach, the TDPES is basically the adiabatic potential energy that is computed by including the instantaneous value of electron-field interactions in the Hamiltonian. This method has proved to be extremely helpful in understanding many intense field phenomena in realistic molecular systems. However, this method lacks the exact dynamical features of the intense laser-molecule interactions, and therefore, a need still exists for a method that is not computationally as expensive as the exact methods but captures the dynamical features of electrons/molecules in strong laser fields. 

The limitations that apply to this type of analysis do not necessarily diminish its value. Applications will remain limited to cases of very difficult to analyze processes and to the initial phases of process development (e.g., Grm, Mele, and Kremser, 1980). Sooner or later, when economic incentive is adequate, mathematical models with parameters interpretable in clear biological terms will be preferred. The well-known kinetic approach of Kono (see Chap. 5.3) is also a numerical fitting procedure of great engineering value. 

Kubota K, Kono I, Uno H (1976) Permeability - approach to design. Kajima Institute Publishing,... 

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