Average collision length

For a step train, two neighboring steps collide when the fluctuation Wgq determined in (35) becomes the average step separation i. Therefore, the collision takes place for each step length Lcow 7 /T. To realize a large fluctuation, all the steps meander simultaneously. The step fluctuation for a long step (L > F gon) is reduced to the logarithmic form [3]... 

As described above, the magnitude of Knudsen number, Kn, or inverse Knudsen number, D, is of great significance for gas lubrication. From the definition of Kn in Eq (2), the local Knudsen number depends on the local mean free path of gas molecules,, and the local characteristic length, L, which is usually taken as the local gap width, h, in analysis of gas lubrication problems. From basic kinetic theory we know that the mean free path represents the average travel distance of a particle between two successive collisions, and if the gas is assumed to be consisted of hard sphere particles, the mean free path can be expressed as... 

In the description of MPC dynamics, the size of the collision cell was not specified. Given the number density h = N/V of the system, the cell size will control how many particles, on average, participate in the multiparticle collision event. This, in turn, controls the level of coarse graining of the system. As originally formulated, it was assumed that on average particles should free stream a distance comparable to or somewhat greater than the cell length in the... 

Thus, the average stopping power is proportional to the initial energy except for corrections due to atomic collisions (electronic excitation) near 108 eV. For a medium of nuclear charge Ze and mass number A, the radiation length is given by (Bethe and Ashkin, 1953)... 

Table I lists some characteristic wave lengths from the work of Gregory (9). The calculations of f shown in Figure 2 are taken from the work of Clayfield and Lumb.(lO) By using these calculations one can determine the attractive energy per pair of particles at various separation distances, and determine for any particular value gf Aj2i> Xj, and radius (a) the critical value of H that makes U j 21= kT, where k is the Boltzmann constant and kT is the average vibrational energy of a pair of particles flocculated at separation distance H. If Uj2l is greater than -kT the particles will nearly always bounce apart on collision, but if it is less than -kT the particles tend to flocculate.

All of the molecules are in motion. Due to constant collisions, however, they do not advance in a straight path but move in zigzags. Due to their large mass, proteins are particularly slow. However, they do cover an average of 5 nm in 1 ms—a distance approximately equal to their own length. Statistically, a protein is capable of reaching any point in a bacterial cell in less than a second. 

The gas molecules fly about and among each other, at every possible velocity, and bombard both the vessel walls and collide (elastically) with each other. This motion of the gas molecules is described numerically with the assistance of the kinetic theory of gases. A molecule s average number of collisions over a given period of time, the so-called collision index z, and the mean path distance which each gas molecuie covers between two collisions with other molecules, the so-called mean free path length X, are described as shown below as a function of the mean molecule velocity c the molecule diameter 2r and the particle number density molecules n - as a very good approximation ... 

The average energy loss per unit track length of a 1-MeV electron is about 0.2 eV/nm [64]. With an average energy loss per collision event of 60 eV the mean separation of spurs is 300 nm, which is much too far apart for interspur reactions. (It is assumed throughout... 

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