Collision probability

Atoms and ions are excited via collisions, probably mainly with electrons, and then emit light. Most elements with ionization energies less than 8 eV exist mainly as singly charged ions in the plasma. Therefore, spectral lines from ions are most intense for these elements, whereas elements with high ionization energies (such as B, Si, Se and As), as well as the easily ionized alkalis (Li, Na, K, Rb, and Cs), emit most strongly as atoms. 

Although this collision rule conserves momentum and energy, in contrast to the original version of MPC dynamics, phase space volumes are not preserved. This feature arises from the fact that the collision probability depends on AV so that different system states are mapped onto the same state. Consequently, it is important to check the consistency of the results in numerical simulations to ensure that this does not lead to artifacts. 

Enhanced particle aggregation by tiny bubble bridging, giving rise to increased collision probability of the enlarged particle aggregates with flotation-sized bubbles... 

Fig. 2.27. Total collision probability and fractions of single, double, triple and quadruple collisions versus collision gas pressure. The transmission of the main beam /(is given on the right ordinate. Values are for an ion of collision cross section 5 x 10 cm and 1 cm collision path 10 Torr= 1.33 Pa. Reproduced from Ref. [9] with permission. John Wiley Sons, 1985.

Figure 1 Electron energy dependence of the inelastic collision probability, o ineiastic/Co meiastic + Inelastic), in liquid water (A) and the probability of an inelastic collision causing ionization,...

The ratio of the probability of a collision induced by a fluid velocity gradient (dv/dx) (i.e., orthokinetic coagulation) to the collision probability under the influence of Brownian motion (perikinetic coagulation—what we have considered so far) has been shown to be (Probstein 1994)... 

For polyatomic molecules equation (18) is employed with the vibrational matrix elements modified as described above. For vibrational exchange, in equation (18) the single vibrational matrix element is replaced by the product of the squares of the matrix elements for each molecule. In general, the theory leads to collision probabilities which are in good agreement with experiment. 

The hydrodynamic model is based on a sufficiently high collision probability under thermodynamic equilibrium. This condition is fulfilled only at p > 1 mbar, i.e., at high pressures above the typical PLD film deposition conditions, or at the beginning of plasma expansion, at high plasma density (small target to substrate distance). 

Vibrational and Rotational Excitation in Gaseous Collisions probability of excitation or deexcitation is determined from... 

Particle-Bubble Attacbment. In the above, principles leading to creation of desired hydrophobicity/hydrophihcity of the particles has been discussed. The next step is to create conditions for particle-bubble contact, attachment, and their removal, which is simply described as a combination of three stochastic events with which are associated the probability of particle-bubble collision, probability of attachment, and probability of retention of attachment. The first term is controlled by the hydrodynamic conditions prevailing in the flotation unit. The second is determined by the surface forces. The third is dependent on the survival of the laden bubble by liquid turbulence and impacts by the other suspended particles. A detailed description of the hydrodynamic and other physical aspects of flotation is found in the monograph by Schulze (1984). 

Where n is the charge-carrier concentration and e the elementary charge. The electrons do not move undisturbed, but are scattered by collision with other carriers and thermal lattice vibrations, so-called phonons, and structural defects. Upon lowering the temperature, collision probability and thermal lattice vibrations are reduced, and the mobility of the electron increases, while n is constant. This leads to a large increase of conductivity with decreasing temperature. 

Orogen have a continental affinity and could not have been produced from a subducted Tethyan oceanic slab. The very low 8Nd(0 values further require the protoliths of these eclogites to have formed long before the Triassic collision, probably in mid-Proterozoic times. It appears that, in... 

In the recollision method the probability of multiple collisions with the reaction site are considered. The reaction probability (]3 ) is expressed in terms of the recollision probability ), which is the probability that a molecule starting at r = f collides with the reaction surface rather than escaping to r=b, and the first collision probability (1 ), which is the probability that a molecule starting at the initiation surface collides with the reaction surface rather than escaping to r = oo. Both these probabilities are obtained from Brownian dynamics. In addition, the surface reaction probability ([Pg.812]

Neuhauser, D., Baer, M., Judson, R.S. and Kotiri, D.J. (1990) A time-dependent wave packet approach to atom diatom reactive collision probabilities - theory and application to H -P H2 (J=0) system,, 7. Chem. Phys. 93, 312-322. 

In contrast to the situation in real systems, the collision probability on lattices between two units is always fixed to unity because of the structural specificity of lattices [19,58-61]. Mathematically, this can be explained by the absence of the entropy term, v/V, in the intermolecular reaction on lattices. Consider an athermal reaction, and let Nbe the number of FUs. then the respective intermolecular reaction rates of Eqs. (38) and (69) can be simplified as follows... 

However, such processes occur relatively seldom, while E. Salpeter (Cornell University) showed that a two-step reaction should be more easily realisable (Kipper-hahn, 1980). A collision of two helium nuclei leads to the formation of a beryllium nucleus, which decomposes very rapidly to the starting materials unless it is hit by a further helium nucleus the newly-formed nucleus 12C is stabilized by radiation emission. The lifetime of the beryllium nucleus is only about 0.05 s (Hillebrand and Ober, 1982) thus, the density of the helium nuclei must be very high in order to give a high collision probability. 

A differential breakage density was then defined as a product of an eddy-bubble collision probability density di, A) and a breakage efficiency Psidi dj, A), which both depended on the eddy size (A). The total breakage rate source for a bubble of size di yields ... 

The eddy-bubble collision probability density uf di, A) has units (l/sm [mj). 

Luo and Svendsen [74] considered the collision of eddies with a given velocity v bombarding a number n of locally frozen bubbles, as illustrated in Fig 9.4. The eddy-bubble collision probability density was computed as ... 

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