The lift velocity has the same dependence on parameters as the previous results derived for slow laminar flow (Cox and Brenner, 1968; Ho and Leal, 1974).
The cellular materials under investigation (polyurethane, melamine) are shown to behave as isotropic, (equivalent) homogeneous elastic solids with Rayleigh damping (equivalent to a rheological model having the same dependence of attenuation on frequency) in the frequency band of interest.
This implies that the steady state rate has the same dependence on the ligand concentration as observed in conventional mass action kinetics for any arbitrary enzyme catalyzed reaction network.
In this quasi-equilibrium limit, for an arbitrary reaction scheme we show that the catalytic rate has the same dependence on ligand concentrations as obtained from mass-action kinetics even in the presence of slow conformational fluctuations.
In the Results and Discussion section we analyze the kinetic laws resulting in the quasi-equilibrium limit and show that despite slow conformational fluctuations, the catalytic rate has the same dependence on substrate/modulator concentration as obtained from conventional mass action kinetics.
As discussed in the introduction, intronic miRNAs (same-strand with the host) are expected to be co-transcribed with their host gene, therefore their production rate k r (q) has the same dependence on the input TF level.
In this work, we show that global folding and compaction of the molecule have the same magnesium dependence as the local folding previously observed.
The vibration mode shapes are assumed to have the same spatial dependence as used in past investigations to study the room-temperature configurations of these laminates, and are thus assumed to be perturbations on the static equilibrium configurations.
One can show that, at least in the case of dilute gases, the Boltzmann entropy coincides with the thermodynamic entropy (in the sense that both have the same functional dependence on the basic state variables), and so it is plausible to say that the equilibrium state is the macro-state for which the Boltzmann entropy is maximal (since TD posits that entropy be maximal for equilibrium states).
