Exponential down model

The most common form for P(EIE ) is the exponential down model,... 

Numerous energy transfer models for P(E, E) are discussed in the literature [17] the most widely known and used one is the exponential down model. It assumes that the probability to transfer energy in a single collision event depends exponentially on the energy amount that is transferred. Small amounts of energy are more likely transferred than... 

Fig. 5. Comparison of predicted fall-off curves for the thermal dissociation of C2H5O radicals forming CH3 + CH2O at 406 K with experimental data. All calculations use the exponential down model with < down ) = 200 cm. (a) Unimol, (b) ChemRate (steady-state and time-dependent calculations yield similar results), (c) MultiWell, and (d)...

Even if we restrict ourselves to a ME analysis, we still have the choice of many different collision models. In the review section we only discussed the exponential down model (60),... 

Hydrodynamics Well-stirred model, i.e. uniform concentration inside intestine Parallel tube model, i.e. concentration decrease exponentially down the length of the intestine... 

King and King extend the method of by using a more complicated elution model. All parameters are determined with LSO, which implies that no standards have to be determined. Assumed is a pre-knowledge of the number of components (Bj), an exponential down scan correction (B ), a background subtraction (Bj), and a saturation correction (Bj). 

In order to compare the calculation of the disadvantage factor based on a Gaussian slowing down model (section 5) with its calculation based on an exponential model (section 4) we shall recalculate the neutron distributions of section 4 by expanding them in terms of the characteristic functions of section 5. 

In summary, the Samuel-Magee model of low-LET tracks consists of isolated spherical spurs distributed exponentially in energy. No distinction is made between primary and secondary tracks inherent slowing down of the particle is also ignored. 

The change of electronic conductivity G(r) over diameter of such two-sphere model composition as element in a system of contacting particles is shown in a Figure 10.6b. The transfer of electron across this composition consists of three stages electron tunneling over the interspace — Rq is replaced by the M/SC conductivity across a particle with subsequent electron tunneling over the further interspace R — Rq. The probability of electron tunneling falls down exponentially with increase in distance from the surface of particle. 

A radiochemical study [104] of the element distribution in the 238U+238U reaction at the unilac revealed the expected broad distribution of reaction products. Below uranium, where losses by sequential fission of transfer products are not significant, the observed yields decreased exponentially from Z=92 down to Z= 73. This trend was well reproduced [105] by a theoretical model treating nucleon transfer in the intermediate collision complex as a diffusion process. By extrapolation of the model to Z=70 nuclei about 100 microbam total production cross section resulted, associated with broad distributions of neutron numbers and excitation energies. 

Figure 7.3 Time courses of V (t) /Vo (up) and of k (t) /f (down) associated with the exponential, power-law, and gamma empirical models (solid, dashed, and dotted lines, respectively).

Pure rotary diffusion of rigid dipoles in two or three dimensions, then, gives exponential decay of polarization with a single relaxation time, provided the sites are uniformly distributed and D is constant. The description of the motion in terms of D alone breaks down, as we shall see, for very short times. A three-dimensional rigid body in any case executes a more complex motion. Even an internally uniform model of rectilinear charge-carrier difiurion automatically shows multiple relaxation. More realistic models must take account of the dynamic s of molecular motion. 

Despite these complications, there are now numerous evidences that the tube model is basically con-ect. The signatory mark that the chain is trapped in a tube is that the chain ends relax first, and the center of the chain remains unrelaxed until relaxation is almost over. Evidence that this occurs has been obtained in experiments with chains whose ends are labeled, either chemically or isotopically (Ylitalo et al. 1990 Russell et al. 1993). These studies show that the rate of relaxation of the chain ends is distinctively faster than the middle of the chain, in quantitative agreement with reptation theory. The special role of chain ends is also shown indirectly in studies of the relaxation of star polymers. Stars are polymers in which several branches radiate from a single branch point. The arms of the star cannot reptate because they are anchored at the branch point (de Gennes 1975). Relaxation must thus occur by the slower process of primitive-path fluctuations, which is found to slow down exponentially with increasing arm molecular weight, in agreement with predictions (Pearson and Helfand 1984). 

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