Simulations bilinear model

The bilinear model is confirmed by simulations, using experimental rate constants of drug transport, which were determined from the time dependence of substance concentrations in the different phases of a three-compartment system water/n-octanol/water (Figure 15) [443]. 

An alternative to the parabolic model is the bilinear model (equation 6) which was derived from computer simulations, using experimental rate constants of drug transport in simple in vitro systems. " In most cases it describes nonlinear lipophilicity-activity relationships more accurately than the parabolic model. 

In the present simulation we apply a simple model consisting of two vibrational modes in the relevant system. The first one will contribute to the Stokes shift as well as to the Herzberg-Teller correction, while the second one only to the Stokes shift. Next, we will assume a mutual coupling of the modes in the bilinear form Q Qi for the excited state. This type of coupling is usually omitted in literature. The Hamiltonian 77s is written as... 

Equation (13,35) is the exact golden-rule rate expression for the bilinear coupling model. For more realistic interaction models such analytical results cannot be obtained and we often resort to numerical simulations (see Section 13.6). Because classical correlation functions are much easier to calculate than their quantum counterparts, it is of interest to compare the approximate rate ks sc, Eq. (13.27), with the exact result kg. To this end it is useful to define the quantum correction factor... 

Model simulations (see chapter 4.4) substantiate that the lipophilicity dependence of the rate constants of drug transport should follow bilinear relationships [41,156, 175,345,440,442]. Indeed, bilinear equations have been derived for the rate constants of drug transport in n-octanol/water (eqs. 95 — 98, chapter 4.4) [444 —447] and for the rate constants of the transfer of various barbiturates (38) in a Sartorius absorption simulator from an aqueous phase (pH = 3) through an organic membrane to another aqueous phase (pH = 7.5), modeling the gastric absorption of these compounds (Figure 41) (eq. 162 recalculated optimum log P value) [442]. 

Idealize the pushover curve F — u, using a bilinear or multi-linear shape or the shape of any other curve which can be used to simulate theF — M force-displacement relationship of the SDOF model. 

A method of predicting failure based on the concepts of stress and fracture mechanics is the cohesive zone method. The cohesive zone model has been used increasingly in recent years to simulate crack initiation, propagation, and failure. The cohesive zone model allows multiple cracks to be modelled and the direction of crack propagation need not be known in advance however, cohesive zone elements need to be present at all possible crack paths. Cohesive zone models follow a traction-separation constitutive law to predict failure initiation, damage, and failure. Several shapes for the traction-separation law have been presented in the literature, with the bilinear, exponential, and trapezoidal shapes, as shown in Fig. 25.14, being the most commonly used for strength prediction. 

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