Geometric coefficient

Here, dg is a spatial fractal dimension of the point set where relaxing units are interacting with the surroundings. R is the size of a sample volume section where movement of one relaxing unit occurs. Rq is the cutoff size of the scaling in the space or the size of the cooperative domain. G is a geometrical coefficient of order unity, which depends on the shape of the system heterogeneity. For example, the well-known two-dimensional recurrent fractal Sierpinski carpet has dG = ln(8)/ ln(3) 1.89, G = V3/4 0.43 [213],... 

If foam dispersity is expressed in terms of a sphere radius with volume equal to the volume of the dodecahedral cell then the geometric coefficients will be respectively C d =... 

It should be noted that in these calculations the geometric coefficient Q applies for the whole foam including that part which is not polyhedral and is in contact with the foaming solution. A detailed analysis performed by Krotov [2], of the various ways to calculate the maximum liquid volume in a foam that contacts the solution, shows that the maximum liquid volume per unit area A in the polyhedral part of the foam is expressed by... 

Sharovamikov and Tsap [66] have proposed another way to measure the liquid distribution in a foam based on the evaluation of the geometric coefficient B. The dependence of the film liquid volume fraction on the total foam liquid volume (ft = cp/( +(p) can be expressed by two almost equivalent formulae (see Section 8.3.)... 

For evaluating the geometric coefficient B it is necessary to determine foam expansion ratio and electrical expansion ratio , which is equal to k[/kF (where kL and kF are the specific electrical conductivities of the solution and the foam, respectively). 

Crystallographic studies provide two grades of intemuclear distances R, between nuclei at special positions (frequently with a precision 0.005 to 0.002 A) determined by geometric coefficients times the unit cell parameters, and between two nuclei which are both (or at least one) on general positions (typically 10 times less precise). It should be noted that R values with 4 or 5 decimals 48) usually are derived from micro-wave rotational spectra, especially of gaseous diatomic molecules, giving the time average of R 2. The thermal vibrations at room temperature frequently have an amplitude of 0.05 to 0.1 A which would only be decreased by a factor around 2 or 3 at the absolute zero. 

For arbitrary dimension d of Euclidean space in which the fractal set Qf is embedded and arbitrary form of the initial element, the mass (the number of bonds) can be defined by singling out the factorial geometric coefficient F ... 

The key point to note is that (10-143)-( 10-147) are completely independent of the geometric coefficients u, in, and so on. Similarly, if we continued the series to higher-order terms, the corresponding equations and boundary conditions would all be independent of the This means that the functions f (Y /iTj") are universal functions that apply to cylindrical bodies of arbitrary cross-sectional shape or to any boundary-layer problem for which the... 

Geometric coefficients a for the electrostatic energy of several structures. 

Performing the integration and assuming the logarithmic term can be represented by a geometric coefficient a, one obtains an energy per unit length of dislocation... 

Table 18.5 Geometrical coefficients monomer structure models are depicted r r and p r for various polymers whose united atom in Fig. 18.12 (Freed and Dudowicz 1998) ...

Emig and Klemm [19] also used the Einstein-Smoluchowski relation to estimate the diffusion time in microchannels. Nevertheless, for the basic considerations they set, in contrast to Pippel [20], the geometrical coefficient equal to 1. This causes a doubling of the estimated diffusion time ((d) ... 

The first term on the right-hand side of Equation (6-12) represents the energy decrease along the streamline in the manifold due to velocity loss the second term is the pressure drop due to friction with the walls,- and the last term is the pressure loss due to local disturbances described by the geometric coefficient. 

An assumption is made that the reactivity feedback for the reactor is divided evenly between the fuel Doppler effect and feedback from the core structural materials. Doppler temperature feedback is a function of the square root of the volume average temperature of the volume to which the feedback is being applied. The overall temperature feedback is divided between two heat structures the fuel pin structure for Doppler feedback and the core block structure for geometric feedback. Axial feedback coefficients are based on power squared weighting of the Doppler term calculated from the tabular input, and a geometric coefficient assumed to be half of the total temperature feedback. The... 

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