Collision calculation

Temkin S. I., Thuet J. M., Bonamy L., Bonamy J., Robert D. Angular momentum and rotational energy relaxation in N2-N2 collisions calculated from coherent and stimulated Raman spectroscopy data,... 

Dickinson, A.S. (1979). Non-reactive heavy particle collision calculations, Computer Physics Communications 17, 51-80. 

Fig. 1. Resonant molecular formation rate in /it + Do collisions calculated for a 3 K target [7,8,9]. The rates are normalized to the liquid hydrogen density and averaged over fit hyperfine states. Also shown is the /it elastic scattering rate on the d nucleus [12]...

The boundary condition that Cp is zero cannot be strictly valid, as shown by Noyes [18] using as an example the recombination of iodine atoms in carbon tetrachloride solution, a quintessential diffusion-controlled reaction. The rate coefficient for collisions calculated from the simple kinetic theory of gases, 9.15 x 10-11 cm3 molecule-1 sec-1, is equated to k, which gives a value of 1.35 for the term (1 + 4irpDk l). More elaborate treatments of the rate of a diffusion-controlled reaction, as reviewed by Noyes [18], use more realistic boundary conditions, but this simple treatment gives answers certainly correct to within an order of magnitude. 

Obstacles to modelling the evolution of quantum state populations under multiple collisions primarily arise from the complexity of standard collision theory. An accurate PES is needed for all potential collision partners in a gas mixture and some species will be in highly excited states. State-to-state collision calculations are highly computer intensive for even the simplest of processes and, without a major increase in computational speed, are not suited to multiple, successive calculations. By contrast, the AM method is fast, accurate and calculations for atoms and/or diatomic molecules require only readily available data such as molecular bond length, atomic mass, spectroscopic constants and collision energy. 

Fig. 23. Example of a differential cross section for K+ production in K + Br2 collisions, calculated by the trajectory method. In contrast with experiment, the covalent and ionic contributions are completely separated. (Duren, 1973.)...

The integration of this set of coupled first-order differential equation can be done in a number of ways. Care must be taken since there are basically rather two different time scales involved, i.e. that of the nuclear dynamics and that of the normally considerably faster electron dynamics. It should be observed that this END takes place in a Cartesian laboratory reference frame, which means that the overall translation as well as overall rotation of the molecular system is included. This offers no complications since the equations of motion satisfy basic conservation laws and, thus, total momentum and angular momentum are conserved. At any time in the evolution of the molecular system can the overall translation be isolated and eliminated if so should be deemed necessary. This level of theory [16,19] is implemented in the program system ENDyne [20], and has been applied to atomic and molecular reactive collisions. Calculations of cross sections, differential as well as integral, yield results in excellent agreement with the best experiments. 

Krasnogorskaja N. V, Collision Calculations for Particles of comparable Sizes, Papers Acad. Sci. USSR, 1964, Vol. 154, No. 12 (in Russian). 

For the recoiling target atom final energy 2 is found from the binary collision calculation ... 

J.N.L. Connor. Reactive molecular collision calculations. Comput. Phys. Commun. 17, 117-43 (1979). 

The half-pressuFes quoted here for both reactions are for the strong collision calculation as explained in Chapter 7, the methyl isocyanide reaction does not conform exactly to the strong collision properties and the observed values of the half-pressure are actually some 20 Torr higher, see Figure 7.3. 

C If RANDKsO, only strong collision calculation is executed ... 

In our situation, we manage to define the critical time, which tells us, that the process of collision calculation lasts too long - the application is stuck without any response to the operator. This critical time is set to the Torit = 5 sec. 

We can see that the method based on the RBF2 neural network has the best quality of the time response. User will wait for collision calculation to finish shorter time with comparison to the presently used algorithm. 

The usual derivation recomputes Z as the sum of a collision part and an external force part, but here there is no external force. The collision calculation is nonetheless of interest, for writing... 

Fig. 5. Collision calculation in the plane of and for two initial (relative) phases. In both cases, particles i and / are approaching, but for A the collision coordinate bif>cr, while for B, by < a. For the latter case, v y indicates the postcollision velocity for an elastic collision.

Further workbench in the CATIA world is DMU Space Analysis that offers functionalities of collision calculation (called clash analysis), cutting and clipping, comparison of 3D geometry. Combined with the Object Manager Workbench the calculation of measurements, gravity center and center of inertia are possible. 

Collision calculations are almost always carried out in the center of mass frame, which moves with the center of mass. The relative motion of the two particles is described as that of a single particle of mass x subject to an interaction potential V (which is not the same as V in Equation 1.3). For structureless particles V depends only on the interparticle distance r, but more generally it also depends on internal degrees of freedom such as spins and rotations. Once the equations have been solved for the relative motion, they can, if desired, be transformed back into laboratory coordinates. 

Quantitative calculations of the rate constants ky y for vibrational transitions are relatively easy if the diatomic molecules are simulated by a harmonic oscillator interacting isotropically with the impinging atom (the so-called breathing sphere or the SSH (Schwartz-Slawsky-Herzfeld) model [3, 192, 339, 395] based on the one-dimensional Landau-Teller model [261]). Then the mean transition probability Py y per one gas-kinetic collision calculated to the first order of the semiclassical perturbation treatment is... 

Mies FH. (1973) Molecular theory of atomic collisions Calculated cross section for H+- -F( P). Phys. Rev. A 7 957-967. 

Net source term denoting the loss of the property caused by inelastic collisions Calculation domain... 

Wang F, Xu XC, Hong XH, Wang J, Gou BC (2011) A theoretical model for electron transfer in ion-atom collisions calculations for the collision of a proton with an argon atom. Phys Lett A 375 3290. doi 10.1016/j.physleta.2011.07.032... 

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