Self-consistent approach

To. solve the Kohn-Sham equations a self-consistent approach is taken. An initial guess of the density is fed into Equation (3.47) from which a set of orbitals can be derived, leading to an improved value for the density, which is then used in the second iteration, and so on until convergence is achieved. 

Ke S-H, Baranger HU, Yang W (2004) Electron transport through molecules self-consistent and non-self-consistent approaches. Phys Rev B 70(8) 085410... 

If we understand FM or magnetic properties of quark matter more deeply, we must proceeds to a self-consistent approach, like Hartree-Fock theory, beyond the previous perturbative argument. In ref. [11] we have described how the axial-vector mean field (AV) and the tensor one appear as a consequence of the Fierz transformation within the relativistic mean-field theory for nuclear matter, which is one of the nonperturbative frameworks in many-body theories and corresponds to the Hatree-Fock approximation. We also demonstrated... 

Self-consistent approaches in molecular modeling have to strike a balance of appropriate representation of the primary polymer chemistry, adequate treatment of molecular interactions, sufficient system size, and sufficient statistical sampling of structural configurations or elementary transport processes. They should account for nanoscale confinement and random network morphology and they should allow calculating thermodynamic properties and transport parameters. 

The most reliable and self-consistent approach for passive remote sensing of the troposphere is, therefore, the simultaneous use of limb and nadir sounding of the atmosphere (as pioneered by SCIAMACHY and related instruments). 

The A-self-consistent approach Absorption, emission and Stokes shift... 

The theory of Chaban (16) involves a self-consistent field technique for randomly distributed inclusions at low concentrations. The field at each inclusion is equal to the sum of the incident field and the fields scattered by all other inclusions minus its own self field. Thus, the self consistent approach attempts to improve... 

Powell, D.H., Dhubhghaill, O.M.N., Pubanz, D., et al. (1996) Structural and dynamic parameters obtained from O NMR, EPR, and NMRD studies of monomeric and dimeric Gd complexes of interest in magnetic resonance imaging an integrated and theoretically self-consistent approach. Journal of the American Chemical Society, 118, 9333-9346. 

Another important point is that, when approaching Me, the tube consistency becomes weaker or in other words, the constraint release scaling law is modified and the rubbery plateau disappears whereas the steady-state compliance J decreEises. A self-consistent approach should predict that aroimd Me, the reptation modes would be gradually replaced by Rouse modes in order to describe the non entangled - entangled transition. 

The Unperturbed Real Chain The Self-Consistent Approach... 

Stroud, D., Pan, F.P. Self-consistent approach to electromagnetic wave propagation in composite media Application to model granular metals. Phys. Rev. B 17. 1602-1610 (1978)... 

Explicit account of the electron interaction within a self-consistent approach modifies the interpretation of the parameters. Slater s notion of the average of configurations and fractional occupation will be consistently applied in the grand canonical ensemble form. The one-particle reduced density matrix retains the symmetry of the crystal field and spin-orbit matrices, thus... 

In the self-consistent approach of McRae (54, 55, 58, 59,177) and others (43, 68) the complete multiple diffraction problem, with attenuation of the wave by elastic backscattering alone, has been solved in self-consistent fashion for certain idealized cases. Inelastic losses were not included in the theory at all. However, in the recent work of Duke and Tucker (179) and of Jones and Strozier (66) inelastic absorption is treated as the dominant effect, and this is nearer reality when considering the LEED problem at all but the lowest energies. 

Using this self-consistent approach, the variation of the Lagrangian with respect to a gives the by-now familiar result... 

The SC solutions appear to run into difficulties when there is a large elastic mismatch between the constituent phases, for example, at high concentrations of a rigid phase in a compliant matrix or of a porous phase in a stiff matrix. The latter situation will be discussed in Section 3.6. One approach to this problem is known as the Generalized Self-Consistent Approach, the concept behind which is illustrated in Fig. 3.14. Instead of a single inclusion in an effective medium, a composite sphere is introduced into the medium. As in the composite sphere assemblage discussed in the last section, the relative size of the spheres reflects the volume fraction, i.e., V = a bf as before. Interestingly, this approach leads to the HS bounds for the bulk modulus. The solution for the shear modulus is complex but can be written in a closed form. 

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