Collision model elastic

Billiard-ball model, see also Elastic-collision model... 

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... 

Summarizing the observations on the ionic crystals it may be said that there is abundant evidence that reactions in the hot zone play an important part. Thus, any theory, such as the elastic-collision model which neglects specific chemical effects, e.g., reduction by NH4+ and H2O, or oxidation by C104, under the influence of the high local temperature," cannot ve a complete explanation of the data. In none of the studies of the hot-atom chemistry of a series of oxyanion salts, e.g., the permanganates, have correlations been established between the retention and... 

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. 

In this section we will briefly review the collision model for binary hard-sphere collisions using the notation in Fox Vedula (2010). The change in the number-density function due to elastic hard-sphere collisions (Boltzmann, 1872 Cercignani, 1988 Chapman Cowling, 1961 Enksog, 1921) obeys an (unclosed) integral expression of the form ... 

The elastic Boltzmann collision model has a unique equilibrium solution defined by C = 0. This Maxwellian distribution is given by... 

In this case we do not rely on facts observed directly but begin by designing on the basis of reasonable assumptions a model of the perfect gas on the proper choice of this model depends the success of the whole undertaking. Wc assume that both the gases enclosed in volumes V and V2 consist respectively of n and ri2 spherical atoms or molecules, of very small total volume as compared with Vi and V2 (e.g. roVir) which exert no forces on one another and behave on collision as elastic rigid spheres following the laws of classic mechanics. In each of the partial volumes these particles should execute entirely random motions at velocities w characterized by MaxwelPs law of distribution, the average value w of which can be calculated simply from the Boyle-Charles equation... 

A FIGURE 5.15 A Model for Gas Behavior In the kinetic molecular theory of gases, a gas sample is modeled as a collection of particles in constant straight-line motion. The size of each particle is negligibly small, and the particles collisions are elastic. 

The first molecular dynamics simulation of a condensed phase system was performed by Alder and Wainwright in 1957 using a hard-sphere model [Alder and Wainwright 1957]. In this model, the spheres move at constant velocity in straight lines between collisions. All collisions are perfectly elastic and occur when the separation between the centres of... 

RBS is based on collisions between atomic nuclei and derives its name from Lord Ernest Rutherford who first presented the concept of atoms having nuclei. When a sample is bombarded with a beam of high-energy particles, the vast majority of particles are implanted into the material and do not escape. This is because the diameter of an atomic nucleus is on the order of 10 A while the spacing between nuclei is on the order of 1 A. A small fraction of the incident particles do undergo a direct collision with a nucleus of one of the atoms in the upper few pm of the sample. This collision actually is due to the Coulombic force present between two nuclei in close proximity to each other, but can be modeled as an elastic collision using classical physics. 

When the product ion moved with a higher kinetic energy than predicted by the stripping model, the collision apparently was more elastic— i.e., less kinetic energy of the incident ion was used for internal excitation of the products. In an ideal elastic collision with H transfer the products carry no internal energy at all. If the secondary ion moves forward and the H atom moves backwards, conservation of momentum requires that the primary ion has a velocity ... 

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