Teorells model ODEs

Teorell s yields model (ODEs). Substitution of (6.1.1) into (6.1.2) 

With a natural scaling (a detailed dimension analysis is deferred to subsequent sections), we get 

Ro is some typical value of the filter resistance. Equations (6.2.2), (6.2.3) are reduced to the dimensionless form 

Here i = ujR0I/V0 is the dimensionless current —the control parameter of this model. Furthermore, f(pt) is the dimensionless stationary resistance function of a general shape sketched in Fig. 6.1.3 and k = k/sv 1 is the dimensionless relaxation parameter, assumed large in accordance with Teorell s intuitive ideas. 

By expressing R(t) through p(t) from (6.2.4) and substituting the result into (6.2.5) we arrive at a single equation for p(t) of the form 

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Teorell studied the system (6.1-1)—(6.1.5) graphically, by the isocline method, and also numerically. He recovered most of the features observed experimentally. This study was further elaborated by several investigators. Thus, Kobatake and Fujita [5], [6] criticized the original model for invoking the ad hoc equation (6.1.5). These authors assumed instead instantaneous relaxation of the resistance to its stationary value while preserving the overall order of the relevant ordinary differential equation (ODE) system by including consideration of the mechanical inertia of the liquid column in the manometer tube. 

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