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Gaussian approximation calculations

Having determined the effect of the diffusive interfaces on the structure parameters, we now turn to the calculation of H and K in microemulsions. In the case of oil-water symmetry three-point correlation functions vanish and = 0. In order to calculate K from (77) and (83) we need the exphcit expressions for the four-point correlation functions. In the Gaussian approximation... [Pg.734]

An interesting result occurs when instead of using the Gaussian approximation the Airy disk is used directly in the calculations. In this case the variance goes to infinity,... [Pg.388]

To calculate the partition function in post Gaussian approximation,by isolating cactus-type diagrams we use the method introduced in refs. (Rakhimov 2004,Leel997) and introduce the so called primed derivatives ... [Pg.303]

All the above numerical calculations were made in D=3 dimension. On the other hand it is widely known that, most of high Tc cuprates have layered structures with 2D CuO2 planes which play an essential role in the high Tc superconductivity.Therefore, it is nessesary to consider the dimensional contribution in the calculation.For this purpose,we consider the case of D = 2 + 2e (e / 0) in the post Gaussian approximation.In this case the optimal values of m and A also depend on e. Using Eq.(25) and the procedure outlined above one finds the e dependence of m2 presented in Fig.3 (solid line). [Pg.308]

Norisuye and Teramoto (47) have extended a similar approximate calculation to under the same restrictions as imposed above. Their expression, though not shown here, reduces to = (5/3) 2 for infinite N, which also confirms the conclusion that any interrupted helix behaves like a Gaussian chain when the chain is infinitely long. [Pg.98]

On Laplace inversion and then inserting the rate kernel into the Noyes expression for the rate coefficient [eqn. (191)], the rate coefficient is seen to be exactly that of the Collins and Kimball [4] analysis [eqn. (25)]. It is a considerable achievement. What is apparent is the relative ease of incorporating the dynamics of the hard sphere motion. The competitive effect comes through naturally and only the detailed static structure of the solvent is more difficult to incorporate. Using the more sophisticated Gaussian approximation to the reactant propagators, eqn. (304), Pagistas and Kapral calculated the rate kernel for the reversible reaction [37]. These have already been shown in Fig. 40 (p. 219) and are discussed in the next section. [Pg.353]

The results of these computations are presented in Figures 14, 15, 16, 17, and 18. These first few calculated moments indicate that the Gaussian transition probabilities for the linear and angular momentum may represent the dynamics fairly well, However, it may not yet be concluded that the Gaussian approximation is actually correct, since this same test must... [Pg.97]

From the above expressions it is evident that for the calculations of the vertex function and the propagator the knowledge of four-particle correlation functions are required. For simplification, Gaussian approximation has been assumed and the four-particle correlation function is written as the product of two two-particle correlation functions. [Pg.122]

Similar results were calculated for the corresponding carbon compounds by the SCF molecular orbital method in the Gaussian approximation. It was found that the electron density on the carbon atom in CH and F CH" is by 0.32 and 0.12 e lower than that in CH and FCH, K... [Pg.119]

This is a continuous function for the experimental variables, which is used as a convenient mathematical idealisation to describe the distribution of finite numbers of results. The factor 1 /(ay/lji) is a constant such that the total area under the probability distribution curve is unity. The mean value is given by p and the variance by a2. The variance in the Gaussian distribution corresponds to the standard deviation s in Eqn. 8.3. Figure 8-3 illustrates the Gaussian distribution calculated with the same parameters used to obtain the Poisson distribution in Figure 8-2, i.e. a mean of 40 and a standard deviation of V40. It can be seen that the two distributions are similar, and that the Poisson distribution is very dosely approximated by the continuous Gaussian curve. [Pg.303]

In ref 189 a potential of mean force is calculated and used to determine diffusion of ubiquinone through a light-harvesting complex determined using MD simulations. The complete JE and JE with a Gaussian approximation are used and compared. ... [Pg.198]

Here we list the two sets of initial conditions used for the parameter equations of motion in calculating the interference signal (3.12) in the Gaussian approximation. One Gaussian has initial conditions corresponding directly to the t = 0 values of the parameters of the ground state wave packet ... [Pg.38]

Because the IV bands are slightly distorted from Gaussian, we have also examined calculating Vab using the transition dipole moment (pi12) instead of the Gaussian approximation. Liptay pointed out that the proper equation for calculating /t12 is 48... [Pg.197]

The second approximation involving the ionic size can be improved upon even within the Gaussian approximation by including the structure of the ion in a self-consistent way [43], It would be worthwhile to extend our calculations to include this approach. [Pg.168]

Finally, we note that the model itself is not accurate in the ionic crystal phase. The condensed counterions sit on the rods in our model, whereas they really should sit in between the rods. In other words, the structure of the ionic crystal is not captured correctly by the model. Recent calculations argue that multiple moments perpendicular to the rod axis that arise when counterions lie between rods are important to the low-temperature behavior [23], This is probably a source of greater quantitative error at low temperatures than is the Gaussian approximation. [Pg.169]

Values of Au qQ 3 calculated from stress relaxation of the swollen networks agreed fairly well with those derived from swelling of polyurethane networks. The anomalous behavior of polyurethanes has been reported (12). Swelling at different solvent activity and stress relaxation of swollen networks are valuable techniques for network characterization. Other networks such as crosslinked polystyrene will be examined by these methods. The role of the Gaussian approximation in rubber elasticity will be evaluated in calculating Mc for highly swollen networks. [Pg.380]


See other pages where Gaussian approximation calculations is mentioned: [Pg.125]    [Pg.89]    [Pg.240]    [Pg.219]    [Pg.117]    [Pg.118]    [Pg.261]    [Pg.229]    [Pg.70]    [Pg.309]    [Pg.310]    [Pg.72]    [Pg.32]    [Pg.45]    [Pg.28]    [Pg.142]    [Pg.551]    [Pg.106]    [Pg.72]    [Pg.85]    [Pg.248]    [Pg.128]    [Pg.104]    [Pg.303]    [Pg.585]    [Pg.293]    [Pg.381]    [Pg.67]    [Pg.289]   
See also in sourсe #XX -- [ Pg.137 ]




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Approximate calculations

Gaussian approximation

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