We have revisited the problem of anomalously diffusing species, modelled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics.If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a non-standard diffusion term.Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term.We have also developed further extensions of the CTRW model to include more general reaction dynamics.
The gas phase vibrational overtone spectrum of propane is measured using conventional near infrared (NIR) spectroscopy for the ΔvCH=2–5 regions and intracavity dye laser photoacoustic spectroscopy (IDL-PAS) for the ΔvCH=5 and 6 regions. The peaks are assigned in terms of the local mode model. Experimental oscillator strengths are compared to values calculated for the CH-stretching components of the spectrum. The calculations use a harmonically coupled, anharmonic oscillator local mode model to obtain the vibrational wave functions, and ab initio MO calculations at the SCF level with a 6-31G* basis set to obtain the dipole moment function. The importance of intermanifold coupling is explored. The calculations can account for the fall-off in intensity with increasing v, and can give a reasonably quantitative account of the relative intensities of the individual peaks within a given vibrational manifold. The questions of the relative intensities of primary and secondary CH bonds, and of the relative intensities of different methyl CH bonds are also explored.
Vapor phase room temperature overtone spectra of cyclohexane are measured with conventional near infrared spectroscopy for the lower overtones, ΔvCH=2–4, and with intracavity dye laser photoacoustic spectroscopy for the higher overtones, ΔvCH=5–7. The relative intensity of the axial to equatorial peak is explained in terms of the local mode model of harmonically coupled anharmonic oscillators, where all modes but the two CH-stretching modes are neglected. The dipole moment function is expanded in the two CH-stretching coordinates, where the expansion coefficients are determined from ab initio molecular orbital calculations. This simple calculation, which contains no adjustable parameters, can account very well for the observed relative intensity of axial and equatorial pure local mode peaks in the overtone spectra from ΔvCH=3–7. We also investigate different ways of obtaining the dipole moment derivatives, and find that a fourth order series expansion around the equilibrium geometry is a good approximation when calculating the relevant matrix elements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.