Core field

G.-Q. Lu, and A. Wieckowski, Heterogeneous Electrocatalysis A Core field of Interfacial Science, Current opinion in Colloid and Interface Science 5, 95 (2000). 

With regard to your second remark I would like to say this The calculations I showed for CaF and BaF Rydberg states are examples where the core field is a Coulomb field but where a very strong dipole field is superimposed. Here we have used the generalized version of quantum defect theory, which takes account of this modified long-range field. 

In a molecule, the one-electron eigenfunctions (Mulliken and Hund s molecular orbitals, M. 0.) are determined by a core field U(x,y,z) and have well-defined symmetry type yn. However, the actual calculation of such M. 0. is very difficult in polyatomic molecules, whereas the Hartree-Fock method can be applied to monatomic entities when large electronic computers are available (13,14). I have written a book about several of the principal problems regarding the concept of one-electron functions... 

Rather than to consider the ligand field as an external electrostatic field, we may profitably define a ligand field V(x,y,z) as the difference between the core field of the polyatomic entity U(x,y,z) (in the following, we are concentrating our attention on an octahedral complex MXe) and the central field of the central ion U(r) ... 

Hartree-Fock M.O. previous models, eigenfunction of the with Watson s correlation effects1 -25 already core-field (Ux,y,z). found in gaseous monatomic ions. ... 

The total core field U(x,y,z) of a molecular system [14) containing a central ion forming essentially heteropolar bonds to the surrounding ligands can be written [Ref. [8) p. 370] as... 

The purpose of the calibration exercise was to determine appropriate parameters which would result in a best-fit match between model simulations and the soil core field observations. The first step in the procedure was to assign values to field-measured, physically-based, parameters which include all parameters for the water balance and crop development portions of the model. The second step was to calibrate chemically and biologically based parameters which are not easily measured in the field. These include the adsorption partition coefficient, K, and the first-order rate of decay, k, of aldicarb. Using reasonable ranges of and k as defined by the literature, a trial-and-error method was used until model predictions matched field observations. 

Facility planning can be divided into seven planning fields and concentrates on four core fields, which are each directed to a characteristic term, Fig. 1 (Wiendahl 2010). 

CAUSED BY SPIN-ORBIT COUPLING OR LOW SYMMETRY COMPONENTS OF THE CORE FIELD, C. Schaffer... 

In the field, the cores should be recorded by the geologist directly after their removal from the core barrel. Such records can most suitably be supplemented by colour photographs of each core. Fields records should be as comprehensive as possible so as to enable the samples also to be correlated with any supplementary borings that may be made later or with the actual conditions encountered on... 

The Mellon Mays Undergradnate Fellowship Program (MMUF), http //www.mmuf.org/ (accessed December 15,2010). Funded by the Andrew W. Mellon Foundation, the MMUF objective is to increase the nnmber minority students, and others with a demonstrated commitment to eradicating racial disparities, who will pursne PhDs in core fields in the arts and sciences in core fields within the arts and sciences, and to diversify the faculties at colleges and universities by providing support for qualified minority scholars (from Web page). 

The core fields of each mode on a step-profile planar waveguide can be decomposed exactly into just two families of plane waves, as we show in... 

The normalized distance (rp /p) — l from the interface is a measure of the effective depth of penetration of the core field into the cladding. We plot this quantity as a function of Kin Fig. 14-3(a), taking g = e for the lower curve and 0 = 0.1 for the upper curve. For example, when V = 2.5 we deduce from the rj curve that about 84 % of total fundamental-mode power flows within the... 

The trigonometrical dependence of the core fields for the modes of the step-profile planar waveguide in Table 12-1, page 242, can be decomposed into two components. For example, the electric field for the even TE modes is expressible as... 

In contrast to the planar waveguide, the core fields of the circular fiber, which are given in terms of Bessel functions in Table 12-3, page 250, do not represent a single family of rays [1]. However, the fields of higher-order modes, which have C/ > 1, are asymptotically equivalent to a single family. To demonstrate this, we first use the recurrence relations of Eq. (37-72) to express i in Table 12-3 in terms of J, and its derivative. Then, provided 1/ > 1 and 1/ — v s> we can substitute the far Debye approximations of Eq. (37-89). The azimuthal dependence on sin(v ) or cos(v ) is... 

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