Prompt trajectories

Rasanz, /. flatness (as of a trajectory), rasch, a. quick, brisk, swift, rapid, prompt. — rascher SatZ Pyro.) meal-powder composition. 

The detection probability for a given trajectory depends on the fragment orientation (its Mj value) and the nature of the probe transition. All of these images were obtained via the two-photon Ilg XAS) transition. Five rotational branches are thus possible O, P, Q, R and S. The amplitudes for each of these two-photon transitions can be obtained from a sum of paired, Mj-dependent, one-photon amplitudes.37 The O branch, for example, consists of a contribution from a parallel P-type transition to a 7A virtual state, followed by a perpendicular P-type transition to the final 1ffs Rydberg (which is assumed to be ionized promptly). The product of those two transition amplitudes must be summed with another product in which the first transition is perpendicular and the second is parallel. The P and R branches consist of four contributions each and the Q branch has six such terms in its transition amplitude. The required one-photon amplitudes are taken from Ref. 37. 

Odelius and co-workers reported some time ago an important study involving a combined quantum chemistry and molecular dynamics (MD) simulation of the ZFS fluctuations in aqueous Ni(II) (128). The ab initio calculations for hexa-aquo Ni(II) complex were used to generate an expression for the ZFS as a function of the distortions of the idealized 7), symmetry of the complex along the normal modes of Eg and T2s symmetries. An MD simulation provided a 200 ps trajectory of motion of a system consisting of a Ni(II) ion and 255 water molecules, which was analyzed in terms of the structure and dynamics of the first solvation shell of the ion. The fluctuations of the structure could be converted in the time variation of the ZFS. The distribution of eigenvalues of ZFS tensor was found to be consistent with the rhombic, rather than axial, symmetry of the tensor, which prompted the development of the analytical theory mentioned above (89). The time-correlation... 

The ability of currently used aircraft probes to accurately sample aerosols has been questioned. Huebert et al. (8) conducted a comparative study of several different types of aerosol probes, all mounted on the same aircraft. The results suggested that substantial losses of particles occurred in all of the inlet systems. Because of the limited nature of the study, however, the causes of the aerosol losses could not be identified. The results of the Huebert study prompted a workshop to reexamine the entire issue of aerosol sampling from aircraft (9). An important conclusion of the workshop was that currently there is insufficient knowledge to adequately describe important characteristics of airflow and particle trajectories at flight speeds of aerosol sampling probes used on aircraft. 

In conclusion, we note that the pausing" of the -trajectory indicating an optimum scale factor prompts the statement of a generalized virial theorem. Since general techniques to ascertain resonances in the non-selfadjoint case are so much more difficult in comparison to the usual (Hermitean) case it is obvious that every bit of complementary information counts. This statement becomes no less important when realizing that the complex part of a resonance eigenvalue in many situations is order of magnitudes smaller in size compared to the real part. 

Fig. 9. Radial trajectories of several mass elements of the core of a 15 M star versus time after bounce. The trajectories are plotted for each 0.02 M up to 1 M , and for each 0.01 M outside this mass. The thick dashed line indicates the location of the shock wave. The prompt shock stalls within 100 ms after reaching 150 km, and recedes down to below 100 km. No sign of a revival of the shock that possibly leads to a successful D(elayed-)CCSN is seen either, even after 300 ms. Instead, a stationary accretion shock forms at several tens of km. A PNS is seen to form, reaching 1.6 M around 1 s after bounce (from [19])...

The different picture is observed for the PF(CH3>2-H2 complex where the trajectory of the P...dihydrogen bond path prompts the Lewis acid properties of H2 and Lewis base properties of the phosphorus species since the bond path crosses the... 

At first sight, it may appear strange that the equilibrium constant expression only depends on the stoichiometry of a reaction when it stems from equating the rate laws for the forward and reverse reactions, where these reactions have an empirical character and, except for the case of elementary reactions, the rate expressions cannot be obtained from the overall equation for the chemical reaction. However, this observation has its basis on an important physical principle, the principle of microscopic reversibility. This can be stated in the form that in the state of macroscopic equilibrium each elementary process is in equilibrium, and is reversible at the microscopic level. In other words, the mechanism of a reversible reaction is the same in the forward and reverse directions. The mathematical basis of this principle comes from the fact that the equations of motion are symmetrical relative to time inversion, from which a particle which follows a given trajectory in the time from 0 to f will follow the identical reverse trajectory in the time from f to 0. We can see, in fact, that at equilibrium, the concentrations of reactants and products are constant and do not oscillate about a mean value. Thus, mechanism (2.IX) represents a possible chemical system, which is in agreement with the principle of microscopic reversibility and which will respond promptly to any perturbation from the equilibrium state. The same is not true for mechanism (2.X), where the step for formation of A from B implies an intermediate which is not involved in the formation of B from A, i.e. the mechanism of formation of B from A is different from that for the formation of A from B. 

The calculation of the particle trajectories and collisions is usually done on the different grid than the CFD of the carrier phase— necessitating specific mapping and filtering techniques as well as closure models and prompting many numerical issues. Recent examples of such filtering studies are due to Radi and Sundaresan (2014) and Peng et al (2014). The study by Kriebitzsch et al (2013) shows that, compared to a DNS which resolves the gas flow field in a fluidized bed completely, an unresolved DEM simulation underpredicts the fluid—particle interaction force substantially. 

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