Branch tracks

Bartczak et al. s entire track calculation is contingent on the specific detail of track structure. They argue that branch tracks of energy <50 or 100 KeV should be treated as a single entity whereas those of higher energy could be broken into their constituent spurs and tracks. In this manner, Bartczak and Hummel (1993) found that... 

A more refined model was then presented by Mozumder and Magee [11]. It takes into account glancing and knock-on collisions and gives a complete picture of the track. Many new entitites called blobs, short tracks and branch tracks were defined in order to obtain this picture. 

Magee does not regard the branch tracks as particular entities but he develops them in the same way as the track of the primary fast electron. To compare his results with the theory of PRCY it is, however, necessary (20) to develop even the blobs and the short tracks into their constituting spurs. For the corresponding partition of the total yield of spurs we then obtain... 

Fromm and Hill s paper, while a sophistieated and almost miraculous application of complex variable theory, produced a formula that exhibited two problems from a practical viewpoint. It contained the dilogarithm function, Li2, and squares of logarithmic functions, in combinations that were multiple-valued with respect to both their real and imaginary parts, and no simple recipe was provided to indicate which branches of these functions should be used. Fromm and Hill s provisional solution was to start from a point in the parameter space where the proper branch was known from asymptotic considerations, and then move in steps to the required parameter values. This procedure was referred to as branch tracking . 

The most extensive use of the analytical formulas for four-hody wavefunctions has been by Rebane and associates in 1992 Rebane and Yusupov [27] presented a preliminary study on model problems there followed a detailed study of the positronium molecule Ps2 (e e e e ) hy Rebane et al. [28] and an application to a number of four-particle mesomolecules by Zotev and Rebane [29]. These authors then refined the branch-tracking procedure so as to make it applicable to complex parameter sets [30,31]. At this point, the use of multiconfiguration exponential wavefunctions has produced results of a quality similar to that from more extensive Gaussian expansions, hut with what appears to be a comparable amount of effort. There are at present insufficient data to indicate whether the exponential wavefunctions have significant superiority over the Gaussian functions for short-range (e.g., delta-function) properties. 

The initial result of the interaction of a gamma photon or an electron with a material is the formation of ionized and excited species via Compton scattering and the photo-electron effect.For each initial 1 MeV electron or photon entering a material there may be around lO particles formed, distributed in the main track of the particle, branch tracks formed by the passage of Compton electrons, and blobs of particles formed as the electron energy drops towards thermal levels. It is the reaction of these particles which leads to dramatic changes in the material properties of polymers. 

In condensed phases there are two to four activated molecules in one spur corresponding to 100 eV energy loss. 5 electrons in the 100-500 eV range produce larger spurs that may be called blobs. 8 electrons in the 500 eV-5 keV range can generate short tracks, or above 5 keV branch tracks. 

The core of the network is the region of the rail network in which the branch line of two transformer substations or of any other branch line is less than 2 km distant in a direct line. All branch lines outside the core of the network are termed outlying lines. In a branched rail network, not only the stretches of line within a circle with a radius of 2 km from the most negative return current point of a transformer substation belong to the core of the network, but also connecting branch lines that are less than 2 km from each other [1]. The area of a network core can be simply determined on a track plan with the help of a circular template as in Fig. 15-1. 

Fig. 4.6(a) Migration of LHRH neurocrine cells prenatal transportation along the track of extra-bulbar VN axons (caudal branch). CB, cribriform plate FB, forebrain cell types, TAG-1, transient axonal surface glycoprotein and N-CAM, neural cell adhesion molecule (from Yoshida et al, 1995). 

For acute releases, the fault tree analysis is a convenient tool for organizing the quantitative data needed for model selection and implementation. The fault tree represents a heirarchy of events that precede the release of concern. This heirarchy grows like the branches of a tree as we track back through one cause built upon another (hence the name, "fault tree"). Each level of the tree identifies each antecedent event, and the branches are characterized by probabilities attached to each causal link in the sequence. The model appiications are needed to describe the environmental consequences of each type of impulsive release of pollutants. Thus, combining the probability of each event with its quantitative consequences supplied by the model, one is led to the expected value of ambient concentrations in the environment. This distribution, in turn, can be used to generate a profile of exposure and risk. 

PN nucleus, horizontal-branch and white-dwarf regions. The dotted line shows a schematic main sequence and evolutionary track for Population II, while various dashed lines show roughly the Cepheid instability strip, the transition to surface convection zones and the helium-shell flashing locus for Population I. After Pagel (1977). Copyright by the IAU. Reproduced with kind permission from Kluwer Academic Publishers. 

Using this scheme, we can track the original alkyl radical through the most likely mechanisms for oxidation at low temperatures that lead to chain-branching. Once formed from the parent molecule (R—H), an alkyl radical (R ) can react with molecular oxygen to form an alkene and hydroperoxyl (HO2 ) radical [Equation (2)], via... 

---