Diverge

In the highly nonlinear equilibrium situations characteristic of liquid separations, the use of priori initial estimates of phase compositions that are not very close to the true compositions of these phases can lead to divergence of iterative computations or to spurious convergence upon feed composition. 

Second card FORMAT(8F10.2), control variables for the regression. This program uses a Newton-Raphson type iteration which is susceptible to convergence problems with poor initial parameter estimates. Therefore, several features are implemented which help control oscillations, prevent divergence, and determine when convergence has been achieved. These features are controlled by the parameters on this card. The default values are the result of considerable experience and are adequate for the majority of situations. However, convergence may be enhanced in some cases with user supplied values. 

Often the divergence in costs shown in Figure 14.11 does occur, and must be managed. The objective is to maintain production in a safe and environmentally responsible manner, while trying to contain or reduce costs. The approach to managing this problem is through reviewing... 

In Dynamic Spatial Reconstructor at the expense of use 2D matrix of detectors there was the opportunity to use a divergent cone beam of source emission. This system had a number of lacks. In particular the number of projections is rigidly limited by the number of x-ray sources. The dispersion of source emission results in errors of data collected.. However the system confirmed basic advantages of application of conic beams and 2D matrices of detectors for collecting information about 3D object. 

The divergent shape of the beam provides facilities for magnification in the distances of the source to detector and of the sources to the axis of rotation, which used in conjunction with a microfocus x-ray source opens the way to high resolution. 

Grangeat P. Description of a 3-D reconstruction algorithm for diverging X-ray beam., Radiol. Soc. North. America Conf Proc., Nov.1985. 

In traditional Fan-Beam CT the radiation emitted from the X-ray tube is collimated to a planar fan, and so most of the intensity is wasted in the collimator blades (Fig. 2a). Cone-Beam CT, where the X-rays not only diverge in the horizontal, but also in the vertical direction, allows to use nearly the whole emitted beam-profile and so makes best use of the available LINAC photon flux (Fig. 2b). So fast scanning of the samples three-dimensional structure is possible. For Cone-Beam 3D-reconstruction special algorithms, taking in consideration the vertical beam divergence of the rays, were developed. 

The divergence factor (DF) introduced by the asymptotic expansion, accounts for the deformation of the refracted wavefront (initially spherical in the coupling medium). It ensures, under the GO approximation, the energy conservation of a ray-pencil propagating... 

The ability to image lateral heterogeneity in Langmuir monolayers dates back to Zocher and Stiebel s 1930 study with divergent light illumination [166]. More recently the focus shifted toward the use of fluorescence microscopy of mono-layers containing a small amount of fluorescent dye [167]. Even in single-corn-... 

The mathematics is completed by one additional theorem relating the divergence of the gradient of the electrical potential at a given point to the charge density at that point through Poisson s equation... 

The density of states for a one-dimensional system diverges as 0. This divergence of D E) is not a serious issue as the integral of the density of states remains finite. In tliree dimensions, it is straightforward to show that... 

Dalgarno A and Lewis J T 1956 The representation of long-range forces by series expansions. I. The divergence of the series Proc. Phys. Soc. A 69 57... 

This is known as the Stefan-Boltzmaim law of radiation. If in this calculation of total energy U one uses the classical equipartition result = k T, one encounters the integral f da 03 which is infinite. This divergence, which is the Rayleigh-Jeans result, was one of the historical results which collectively led to the inevitability of a quantum hypothesis. This divergence is also the cause of the infinite emissivity prediction for a black body according to classical mechanics. 

This leads to the third virial coefficient for hard spheres. In general, the nth virial coefficient of pairwise additive potentials is related to the coefficient7) in the expansion of g(r), except for Coulombic systems for which the virial coefficients diverge and special teclmiques are necessary to resiim the series. 

The divergence m the correlation length is characterized by the critical exponent v defined by... 

This equation is analogous to the compressibility equation for fluids and diverges with the same exponent y as the critical temperaUire is approached from above ... 

The correlation length C = T -T diverges with the exponent v. Assuming that when T>T the site... 

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