Correlated distribution

We will now define this equation and discuss practical aspects of its implementation in computer simulators. Furthermore, in the next section we will develop a biomolecular interpretation of the fully correlated distributions of the p-tensor elements. For Ir J = 1 Equation 9.8 simplifies to (Hagen et al. 1985c)... 

FIGURE 12.4 S = 7/2 EPR of the [8Fe-7S] P-cluster in Azotobacter vinelandii nitrogenase. The experimental spectrum (trace A) has been simulated in the absence (trace B) and the presence (trace C) of D-strain modeled as a correlated distribution in the zero-field parameters D and E. 

Lastly, studies of the many-particle effects for reaction with correlated distributions of traps [65, 66] have shown that a trapping process could be accelerated or become slower depending on whether traps attract or repulse each other. 

After these transformations the model can be solved effectively by numerical methods. As the initial condition, we have to specify the concentration of adsorbed particles and the pair correlation function. For example, for non-correlated distributed pairs we set F Jr) = 1. 

Fig. 4.8. Electron momentum-correlation distributions (4.20) and their dependence on the initial bound state. The left-hand panels (a)-(c) are for the interaction (4.14d) and the right-hand panels (a)-(c) for the interaction (4.14a), for initial Is, 2p, and 3p states for both electrons. Panels (d) are for the three-body effective interactions (4.14b) (left) and (4.14c) (right) with the first electron in a Is state. In all situations (even for the 3p - state case), the atomic species was taken to be neon ( Eoi = 0.79 a.u. and E02 = 1.51 a.u.), in order to facilitate a clear assessment of the effects caused by the different initial states. From [27]...

Ditrbutbns of everpihg. The latter comment on distributions of x values brings us to our next topic, the fact that most samples containing nanoparticles contain many different nanoparticles, with entire distributions of particle sizes and shapes, particle compositions and structures, matrix media, etc. Natural and synthetic assemblies of nanoparticles are complex, mainly because there are correlated distributions of all the physico-chemical properties of the nanoparticles themselves, not to mention the supporting medium or matrix. As a result, most measured properties cannot be understood on the basis of the properties of individual nanoparticles alone. For example. Equation (2) leads to a predicted exponential time dependence of the sample magnetization, at constant temperature and applied field, of the form... 

The first branch has become somewhat stronger by the correlating distribution of another apomorphic character. Of the other throe species P. pilose and P. oleracea share spirally arranged leaves numerous stamens and stellate testa cells. If these character states can be considered apomorphic then the alternative states must be con-... 

Although difficulties in sample integrity would appear to be the most likely explanation for discrepancies in the measured size of mucins, problems associated with the methodology of the physical techniques employed may also have contributed to them. For example, the low values of molecular weight obtained previously could possibly be explained by some difficulties in the particular method employed, difficulties manifested by correlating distributions of sedimentation coefficient with distributions of molecular weight for flexible, linear polymers, M, is not a linear function of the sedimentation coefficient, s, but rather, so the mean value of... 

The FWHM of the D (Ga) line was found to be roughly proportional to the ratio Ni/Nq where N is 2[As] and No is [Ga] - [As], indicating the dominant contribution of a quadrupole interaction between the acceptor atoms and the electric field gradient. Estimations of the compensation dependence of the FWHM of D (Ga) for correlated and random distributions of ionized impurities showed that the experimental dependence could be explained by a correlated distribution (with the random model, the dependence of the FWHM on Nj was overestimated by a factor of 4-5). The comparison of the correlated distribution fit with the experimental dependence also showed that the domain of validity of the fit determined by Kogan and Lien [83] extended beyond the compensation limit where the fit was supposed to be valid. By... 

In preliminary design work, it is convenient to correlate distribution coefficients on a mass-fraction basis. An empirical correlation technique that is simple to use and often highly effective is... 

It should be noted that in the original work by Gross [57], where mathematical representation of the model is quite different from that given above, only the case g = 1 was originally considered. Here the term Gross collision model is ascribed to an arbitrary g-value, which is involved in Eq. (280). Note that previously (e.g., in GTI, VIG) the orientational distribution Fq due to the factor employed was termed the correlation-orientation or orientation-correlation distribution. 

Figure 2. Two examples of possible correlated product state distributions from a photodissociation reaction, (a) A completely statistical distribution is shown. (b) A highly correlated distribution is shown.

One of the most elaborate of these approaches is that developed by Denison and Webb [147-153]. Instead of fitting the parameters of the WSGG model to the total emissivity data (as done for all other models), they used the high resolution transmission molecular absorption database of Rothman et al. [156]. By doing so, they replaced the spectral integration over wavenumber by a quadrature over an absorption cross section. Their approach is also known as the correlated -distribution method. 

Conrad, P.A., Nederlof, M.A., Herman, l.M. et al. (1989). Correlated distribution of actin, myosin, and microtubules at the leading edge of migrating Swiss 3T3 fibroblasts. Cell Motil. Cytosheleton 14, 52T--543. 

Li G, Parr J, Fedorov I, Reisler H (2006) Imaging study of vibrational predissociation of the HCl-acetylene dimer pair-correlated distributions. Phys Chem Chem Phys 8 2915-2924... 

The previous expressious involve particle number (and energy) fluctuations. It is more conunon, and totally equivalent, to use correlation/distribution functions to replace the number fluctuations. In many cases this can help to clarify the significance of the number fluctuations (correlations) as we indicate in this section. However, in doing so one has to lemanber that these distributions correspond to a systan volume that is open to aU species. 

Distribution coefficient (a) is the ratio of the concentrations of a solute in two immiscible solvents in equilibrium with each other. As an equilibrium constant, it can be substituted for K in Equation (4) and is therefore logarithmically related to free energy. Most of the work on correlating distribution coefficients with biological activities has been based on the system 1-octanol water, and the distribution coefficients quoted in a dimensionless form n. it is defined by Equation (40), where the suffix H represents the unsubstituted parent compound and X the derivative in which hydrogen has been replaced by the group X. A review by Hansch [47 ] summarises much of this work. 

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