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## Equation Simulations (equation + simulation)
## Selected Abstracts## Energy transfer in master equation simulations: A new approach INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 12 2009John R. BarkerArticle first published online: 8 OCT 200Collisional energy transfer plays a key role in recombination, unimolecular, and chemical activation reactions. For master equation simulations of such reaction systems, it is conventionally assumed that the rate constant for inelastic energy transfer collisions is independent of the excitation energy. However, numerical instabilities and nonphysical results are encountered when normalizing the collision step-size distribution in the sparse density of states regime at low energies. It is argued here that the conventional assumption is not correct, and it is shown that the numerical problems and nonphysical results are eliminated by making a plausible assumption about the energy dependence of the rate coefficient for inelastic collisions. The new assumption produces a model that is more physically realistic for any reasonable choice of collision step-size distribution, but more work remains to be done. The resulting numerical algorithm is stable and noniterative. Testing shows that overall accuracy in master equation simulations is better with this new approach than with the conventional one. This new approach is appropriate for all energy-grained master equation formulations. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 748,763, 2009 [source] ## Multiple-Well, multiple-path unimolecular reaction systems. INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 4 2001Vibrationally excited 2-methylhexyl radicals formed by shock wave activation or by chemical activation can isomerize by multiple pathways to form any of six stable isomers, can fragment by multiple CH and CC bond fission pathways, and can be collisionally stabilized. Master equation simulations of chemical activation and of shock wave activation are used to explore the generic behavior of this complicated coupled system. Selecting the argon pressure in chemical activation systems that produce the 2-methyl-1-hexyl radical isomer (1) can control the yield of specific isomers. Shock heating of 1 also shows a highly regular sequence of isomer formation. This regular behavior is because the first isomerization steps are faster than subsequent steps. Other radical isomers, such as 2-methyl-3-hexyl (3), do not show such regular behavior, because the first isomerization step is slower than subsequent steps. Incubation and unimolecular rate-constant fall-off are observed in the shock wave simulations. The unimolecular rate-constant fall-off for the coupled system produces low-pressure limiting rate constants proportional to [M]n, where n can be greater than unity. The fact that n can be greater than unity is a natural feature of multichannel coupled unimolecular reaction systems, but detection of the effect in experiments may be very demanding. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 246,261, 2001 [source] ## Dependence of initial cluster aggregation kinetics on shear rate for particles of different sizes under turbulence AICHE JOURNAL, Issue 12 2009Lyonel EhrlAbstract Initial aggregation kinetics for three particle sizes and broad range of Péclet numbers were investigated under turbulent conditions in stirred tank. This allowed us to observe the transition from diffusion-controlled to purely shear-induced aggregation. The evolution of the root-mean-square radius of gyration, zero-angle intensity of scattered light, and obscuration was obtained by small-angle static light scattering. For a given particle size the measured evolution of all integral quantities obtained for various volume average shear rates ,G,, scales with a dimensionless time, ,exp = ,exp × ,G, × , × t. The experimentally obtained aggregation efficiency ,exp, follows the power law ,exp = Pe,n, where Pe is the primary particle Péclet number. With increasing particle size a decrease in n is observed in accordance with theory and literature data. As previously predicted by population balance equation simulations three aggregation regimes were observed experimentally. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] ## Additive angle method for fast large-tip-angle RF pulse design in parallel excitation MAGNETIC RESONANCE IN MEDICINE, Issue 4 2008William A. GrissomAbstract Current methods for parallel excitation RF pulse design are based on the small-tip-angle approximation, which provides a computationally efficient means of pulse calculation. In general, pulses designed with those methods are inaccurate when scaled to produce large-tip angles, and methods for large-tipangle pulse design are more computationally demanding. This paper introduces a fast iterative method for large-tip-angle parallel pulse design that is formulated as a small number of Bloch equation simulations and fast small-tip-angle pulse designs, the results of which add to produce large-tip-angle pulses. Simulations and a phantom experiment demonstrate that the method is effective in designingmultidimensional large-tip-angle pulses of high excitation accuracy, compared to pulses designed with small-tip-angle methods. Magn Reson Med 59:779,787, 2008. © 2008 Wiley-Liss, Inc. [source] |