Collision model inelastic

Rahn L. A., Palmer R. E., Koszykowski M. L., Greenhalgh D. A. Comparison of rotationally inelastic collision models for Q-branch Raman spectra of N2, Chem. Phys. Lett. 133, 513-6 (1987). 

Bulgakov Yu. I., Storozhev A. V., Strekalov M. L. Comparison and analysis of rotationally inelastic collision models describing the Q-branch collapse at high density, Chem. Phys. 177, 145-55 (1993). 

Elastic-inelastic collision model, Szilard-Chalmers reaction and, 1 269 Electrical conduction, in organic superconductors, 29 278-286 Electrical conductivity of chalcogenide halide compounds, 23 331 of Group IB, 23 337-339, 342, 346-349 photoelectric effects, 23 368, 410 semiconductors, 23 368, 390, 395-396, 400-402, 410-412 superconductors, 23 375-377 of graphite intercalation compounds, 23 290, 294, 309-310, 312, 317-318 Electric discharges arc type, 6 146-147 chemical reactions in, 6 189-191 chemical reactions in, 6 143-206... 

Elastic-collision model, Szilard-Chalmers reaction and, 268-269 Elastic-inelastic collision model, Szilard-Chalmers reaction and, 269 Electrolytes, sulfuric acid solutions, acids and, 400-403 acid-base reactions and, 403-405 anhydride formation and, 399 metal hydrogen sulfates and, 395-397 simple conjugate acid formation and, 397... 

The rest of this chapter is organized as follows. First, in Section 6.1, we consider the collision term for monodisperse hard-sphere collisions both for elastic and for inelastic particles. We introduce the kinetic closures due to Boltzmann (1872) and Enksog (1921) for the pair correlation function, and then derive the exact source terms for the velocity moments of arbitrary order and then for integer moments. Second, in Section 6.2, we consider the exact source terms for polydisperse hard-sphere collisions, deriving exact expressions for arbitrary and integer-order moments. Next, in Section 6.3, we consider simplified kinetic models for monodisperse and polydisperse systems that are derived from the exact collision source terms, and discuss their properties vis-d-vis the hard-sphere collision models. In Section 6.4, we discuss properties of the moment-transport equations derived from Eq. (6.1) with the hard-sphere collision models. Finally, in Section 6.5 we briefly describe how quadrature-based moment methods are applied to close the collision source terms for the velocity moments. 

For inelastic collisions, the hard-sphere collision model is given by (Fox Vedula, 2010 Jenkins Mancini, 1989 Jenkins Richman, 1985)... 

At equilibrium, where the yelocity distribution is Maxwellian, it is straightforward to show that < > = 4 J p/7T, where 0p is the granular temperature. We should note that Eq. (6.109) corresponds to an inelastic Maxwell particle (Maxwell, 1879), and, most importantly, it still contains the exact dependence on tu = (1 + e)/2. We will therefore refer to this kinetic model as the inelastic Maxwell collision model. 

Chapter 6 is devoted to the topic of hard-sphere collision models (and related simpler kinetic models) in the context of QBMM. In particular, the exact source terms for integer moments due to collisions are derived in the case of inelastic binary collisions between two particles with different diameters/masses, and the use of QBMM to overcome the closure problem is illustrated. 

The preceding discussion has shown that both elastic and inelastic collisions cause spectral line broadening. The elastic collisions may additionally cause a line shift which depends on the potential curves E. (R) and E (R). This can be quantitatively seen from a model introduced by LINDHOLM [3.6], which treats the excited atom A as a damped oscillator which suffers collisions with particles B (atoms or molecules). In this model inelastic collisions damp the amplitude of the oscillation. This is described by introducing a damping constant such that the sum of radiative and col-lisional damping is represented by y = y + y qi From the derivation in Sect.3.1 one obtains for the line broadened by inelastic collisions a Lorentzian profile with halfwidth (3.38)... 

Here 0(a) is the density of distribution over a after collision and tc is the average collision time. The popular Keilson-Storer model, presented in Eq. (1.6) and Fig. 1.2, uses the single numerical parameter y to characterize the strength of inelastic collisions. It will be discussed in Section 1.3. 

In conclusion, we were able to reproduce the optical response of GFP with a novel photodynamical model which includes VER, an energy-dependent ESPT, and an additional decay pathway leading to internal conversion of the protonated chromophore. In particular, the non-exponentiality of the kinetics is traced back to VER dynamics which are slower than the primary ESPT. This might be attributed to the highly rigid tertiary structure of the protein which protects its chromophore from inelastic collisions with the aqueous surroundings. 

The oscillatory structure just mentioned has been clearly demonstrated to result from quantum-mechanical phase-interference phenomena. The necessary condition264,265 for the occurrence of oscillatory structure in the total cross section is the existence in the internuclear potentials of an inner pseudocrossing, at short internuclear distance, as well as an outer pseudo-crossing, at long internuclear distance. A schematic illustration of this dual-interaction model, proposed by Rosenthal and Foley,264 is shown in Fig. 37. The interaction can be considered to involve three separate phases, as discussed by Tolk and et al. 279 (1) the primary excitation mechanism, in which, as the collision partners approach, a transition is made from the ground UQ state to at least two inelastic channels U, and U2 (the transition occurs at the internuclear separation 7 , the inner pseudocrossing, in Fig. 37), (2) development of a phase difference between the inelastic channels,... 

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