Full-model for $\gamma(\omega)$

The high- and low-frequency limits of $\gamma$ are then connected by a simple frequency function to obtain the final model  

$$\gamma(\omega) = \gamma_p \sqrt{1- i \omega/\omega_p}$$ (79)

where the transition frequency $\omega_p$ is defined

$$\omega_p = \frac{B_1 K }{\eta_1 \alpha}\frac{k (v_1 V/S)^2}{L_1^4} \left(1 + \sqrt{\frac{\eta_2 B_2}{\eta_1 B_1}}\right)^2$$ (80)

and where $\gamma_p = v_1 k /(\eta_1 L_1^2)$. Equation (79) has a single singularity (a branch point) at $\omega = - i \omega_p$. Causality requires that with an $e^{-i\omega t}$ time dependence, all singularities and zeroes of a transport coefficient like $\gamma(\omega)$ must reside in the lower-half complex $\omega$ plane. Equation (79) satisfies this physically important constraint.