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** Atomic multipole moments, higher-order **

** Dipole and Higher Multipole Moments **

** Electric moment effect of higher terms **

Higher moments of the distribution are often of interest too, especially when noniso-tropic or anhannonic processes are being studied. The third moment of the distribution reflects the skewness defined as [Pg.54]

Higher moments are usually taken about the mean to characterize the shape of the distribution about this centroid. [Pg.323]

Accurate values of the higher moments are not. easy to obtain. The substantial sensitivity of an RTD curve to small differences in a third moment is brought out in problem P5.02.07A. [Pg.509]

TABLE Illb Evaluation of Higher Moments Property Exact Quantum Variable Quadratic [Pg.97]

You must use rather than T in order for quadrupole and higher moments to be included in the output. [Pg.21]

More terms of the series are usually not justifiable because the higher moments cannot be evaluated with sufficient accuracy from e)meri-mental data. A comparison of the fourth-order GC with other distributions is shown in Fig. 23-12, along with calculated segregated conversions of a first-order reaction. In this case, the GC is the best fit to the original. At large variances the finite value of the ordinate at [Pg.2086]

One problem with this treatment is that it neglects higher-order terms depending on higher moments of i/au that become undefined for slowly decaying interaction potentials (see Problem III-9). [Pg.62]

Instead of analyzing the structure and the properties of the second and higher moments, in the next section, we will perform analysis of temporal evolution of the survival probability. [Pg.412]

Having determined b by the above method, the true number average molecular weight and higher moments for the whole polymer can be calculated as follows [Pg.133]

In other words, to calculate G we must be able to determine a converged value of

Roughly speaking, the first moment, t, measures the size of a residence time distribution, while higher moments measure its shape. The ability to characterize shape is enhanced by using moments about the mean [Pg.544]

For certain values of q and a harmonic potential, the distribution pq (F) can have infinite variance and higher moments. This fact has motivated the use of the g-expectation value to compute the average of an observable A [Pg.201]

For polarizable charge distributions, additional classical-type interactions arise from the induced dipole, quadrupole, and higher moments on each monomer, which are proportional to the fields created by the asymmetric charge distribution on the other monomer. The proportionality constants for each multipole field are the monomer polarizabilities aa and ah (a111 for dipole fields, a(Q) for quadrupole fields, etc.). The leading two induction interactions are [Pg.589]

Hitherto it has been generally assumed that the repulsive forces between atoms arise from the interaction of the quadrupole (and higher) moments of the atoms, that is, from their departure from spherical symmetry.7 [Pg.258]

The Erlang number /leriang. nd the variances O (t ) and 0 (t) are single parameter characterizations of RTD curves. The skewness y (t), and higher moments can be used to represent RTD curves more closely if the data are accurate enough. [Pg.2083]

In this section we restrict our consideration by potentials of type II only (in this case moments of transition time are moments of decay time). The approach, considered above for derivation of the mean transition time may also be used to obtain higher moments, given by Eq. (5.1). [Pg.411]

Here the lattice positions i and j should be adjacent and the -function assures that one of the two lattice positions is occupied and the other one is free, r/j is a characteristic time scale for a diffusion jump. The time-dependence of the average si) is calculated by approximating the higher moments (siSj) [49]. In practice the analysis is rather involved, so we do not give further details here. An important result, for example, is the correction to the Wilson-Frenkel rate (33) at high temperatures [Pg.882]

** Atomic multipole moments, higher-order **

** Dipole and Higher Multipole Moments **

** Electric moment effect of higher terms **

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