Straight path

Figure 6 shows a two-dimensional schematic view of an individual ion s path in the ion implantation process as it comes to rest in a material. The ion does not travel in a straight path to its final position due to elastic collisions with target atoms. The actual integrated distance traveled by the ion is called the range, R The ion s net penetration into the material, measured along the vector of the ion s incident trajectory, which is perpendicular to the... 

Figure 1 illustrates the specific ionization of an alpha particle, on the order of tens of thousands of ion pairs per centimeter in air. An alpha particle travels a relatively straight path over a short distance. 

The membranes in electrodialysis stacks are kept apart by spacers which define the flow channels for the process feed. There are two basic types(3), (a) tortuous path, causing the solution to flow in long narrow channels making several 180° bends between entrance and exit, and typically operating with a channel length-to-width ratio of 100 1 with a cross-flow velocity of 0.3-1.0 m/s (b) sheet flow, with a straight path from entrance to exit ports and a cross-flow velocity of 0.05-0.15 m/s. In both cases the spacer screens are... 

These arguments may be extended to an -compositional space the straight paths will be replaced by planes in a three-component system, by hyperplanes in a four-component system, and so on. Moreover, in an -component system at fixed P and T, no more than n phases may be stable at the same P-T-Xcondition, and their compositions are uniquely determined at any combination of P, T, and X. 

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. 

Model correlation functions. Certain model correlation functions have been found that model the intracollisional process fairly closely. These satisfy a number of physical and mathematical requirements and their Fourier transforms provide a simple analytical model of the spectral profile. The model functions depend on the choice of two or three parameters which may be related to the physics (i.e., the spectral moments) of the system. Sears [363, 362] expanded the classical correlation function as a series in powers of time squared, assuming an exponential overlap-induced dipole moment as in Eq. 4.1. The series was truncated at the second term and the parameters of the dipole model were related to the spectral moments [79]. The spectral model profile was obtained by Fourier transform. Levine and Birnbaum [232] developed a classical line shape, assuming straight trajectories and a Gaussian dipole function. The model was successful in reproducing measured He-Ar [232] and other [189, 245] spectra. Moreover, the quantum effect associated with the straight path approximation could also be estimated. We will be interested in such three-parameter model correlation functions below whose Fourier transforms fit measured spectra and the computed quantum profiles closely see Section 5.10. Intracollisional model correlation functions were discussed by Birnbaum et a/., (1982). 

The LB model. Levine and Birnbaum have developed a classical line shape theory, assuming straight paths for the molecular encounters and a dipole model of the form [232]... 

In Quercus alba the rays represent 28% of the wood volume and in other oak species 19-32% in most other hardwoods the rays occupy about 15% but only 8% of the wood volume in the conifer Sequoia sempervirens (13). The large rays of the oak are so spaced and numerous that a molecule of water diffusing through the side of a barrel must cross five or more large rays if it exits on a straight path or follow a much extended path if it is to go around the rays interposed. These large rays no doubt contribute to the strength and bendability of oak as well as to its dimensional stability and relative impermeability. 

The electron trajectories in a spectrometer are affected by magnetic fields. This is demonstrated with the help of Fig. 4.40 the formerly straight path of an electron with velocity v is deflected, under the action of the magnetic field B perpendicular to the trajectory, through a distance d given by... 

Mixer 28 [M 28] T-type Micro Mixer with Straight Path... 

Mixer type T-type micro mixer with straight path... 

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