Number of k-fold Precursor Particles. Dynamic differential equations were written for the concentration of the k-fold precursors to account for birth and death by coagulation, growth by propagation, and the formation of primary precursors by homogeneous nucleation. There [Pg.365]

In a second step d5mamical effects must be taken into account. For dynamical refinement we used a multi-slice least squares (MSLS) procedure [21], where the centre of laue circle, crystal thickness and scaling factor were refined for each zone separately with fixed atom positions. In the case of non-centrosymmetric space groups the enantiomorph used for refinement can be chosen for each zone, additionally. After the basic parameters have been derived satisfactorily, the atom positions can be refined. The R-values (see Eq. 2) refined by MSLS usually dropped down to 6-13%. [Pg.418]

In contrast to the pseudo 3-D models, tmly multi-dimensional models use, in general, finite element or finite volume CFD (Computational Fluid Dynamics) techniques to solve full 3-D Navier-Stokes equations with appropriate modifications to account for electrochemistry and current distribution. The details of electrochemistry may vary from code to code, but the current density is calculated almost exclusively from Laplace equation for the electric potential (see Equation (5.24)). Inside the electrolyte, the same equation represents the migration of ions (e g. 0= in SOFC), elsewhere it represents the electron/charge transfer. In what follows, we briefly summarize a commonly used multi-dimensional model for PEM fuel cells because of its completeness and of the fact that it also addresses most essential features of SOFC modeling. [Pg.140]

The complementarity of variational- and perturbative-type approaches, specifically of Cl and CC methods, should now be obvious While the former ones can simultaneously handle a multitude of states of an arbitrary spin multiplicity, accounting well for nondynamic correlation in cases of quasidegeneracy, they are not size-extensive and are unable to properly describe dynamic correlation effects unless excessively large dimensions can be handled or afforded. On the other hand, CC approaches are size-extensive at any level of truncation and very efficiently account for dynamic correlation, yet encounter serious difficulties in the presence of significant nondynamic correlation effects. In view of this complementarity, a conjoint treatment, if at all feasible, would be highly desirable. [Pg.5]

Considerations regarding the effect that the operators have, with respect to the response in the environment, are analogous to the linear and quadratic response, that is, zeroth-order terms correspond to a static environment, whereas higher-order terms account for dynamic response in the environment. [Pg.130]

Let us now turn to the results obtained in the simulation of various typical secondary structures found in peptides and proteins, using equation (2). We shall focus on the importance of allowing flexibility of the molecular geometry and the necessity for accounting for dynamic effects, especially low frequency deformation modes, in order to describe conformational equilibrium in [Pg.170]

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