The operation of an indirectly cooled semibatch reactor in which an exothermic reaction occurs is usually considered safe if the characteristic time of the coreactant dosing is much higher than the characteristic times of all the other phenomena involved (chemical reaction and mass transfer), so that the conversion rate is controlled by the coreactant supply itself.
The amplitude of the inlet pressure variations is assumed to be significantly higher than that characteristic for acoustic oscillations.
Owing to these effects, at frequencies higher than the characteristic sound frequncy, the usual Alfvén dispersion relation is modified into the Alfvén ballooning mode relation (e.g., Denton, 1998; Klimushkin et al., 2004).
In the case of the relaxation time related to conductive processes, it has been observed that Maxwell time is higher than the characteristic time associated with the crossover frequency which determines the transition from dc to ac regime.
However, the frequency of the elastic wave (2 MHz) is much higher than the characteristic frequency for the flow between cracks, f=frac{1}{2pi}frac{K}{eta }{alpha}^3sim 1kern0.5em left(mathrm{kHz}right), where K, η, and α are the bulk modulus of the solid phase, the viscosity of the fluid, and the aspect ratio of a crack, respectively (O'Connell and Budiansky 1977).
Upon calcination they evolved towards well ordered, slightly oxygen-rich Mn3O4 nanocrystals, while in Na-L derived catalysts the MnOx grains were structurally less ordered and size-wise more diversified, of average oxidation state significantly higher than that characteristic of Mn3O4.
The rates corresponding to α growth are significantly higher than those characteristics of γ growth.
Compositional convection, however, can be very different from the scenario described above in smaller planetary bodies or for higher sulfur contents than characteristic of the eutectic composition.
Levels of bilirubin higher than normal are characteristic in Gilbert's disease; middle-aged people with this genetic condition have rates of heart disease sixfold lower than those with normal bilirubin levels (Vitek et al. 2002).
Whenever the external driving frequency is much higher than the inverse characteristic response time τc 1, the molecules cannot fully respond, decreasing the fluorescence enhancement or modulation depth at these high frequencies.
