Gradient field analysis

The localization functions described previously are scalar functions the gradient field analysis of which allows to locate attractors and basins with a clear chemical signification[17]. Usually, the attractors of a gradient field are single points as it is the case for the gradient field of the density. However, for the ELF function, they can also be circles and spheres if the system belongs to a continuous symmetry group (here, cylindrical and spherical symmetry respectively). 

Cell-Based Analysis of Drug Response Using Moving Optical Gradient Fields... 

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

M 72] [M 73] [P 65] The analysis of cross-sectional velocity profiles (water as fluid Re =12) shows that the intersecting structures have intricate gradient fields near the bars of the internals, while the helical device displays entrance and exit effects over more than one-quarter of the flow field (see [155] e.g. for fluid flow through macroscopic helical static elements) [2],... 

Brusseau ML, Srivastava,R (1999) Nonideal transport of reactive solutes in heterogeneous porous media. 4. Analysis of the Cape Cod natural-gradient field experiment. Water Resour Res 35 1113-1125... 

To verify correct jumps, jumping end points should be checked by hybridization with somatic cell hybrid panels or pulsed field gradient gel analysis. PPG results have to be interpreted with care, since jumps to very partially cleaved sites internal to well visible fragments, as well as jumps beyond well cleaved sites, have been observed (9). If the source of the DNA used in library construction differs from the DNA used in analysis, the possibility of site or methylation polymorphisms has to be considered in the analysis. 

In Section 5.2, phenomenological models of the first intermediate phase nucle-ation at reactive diffusion in a binary diffusion couple are presented, and methods of thermodynamic analysis of the process, based on the theory of nucleation in a concentration gradient field, are given. We have pioneered the explanation of experimental results using thermodynamic suppression of nucleation rather than kinetic factors [1]. 

Leermakers, F. A. M., BaUauff, M., Borisov, O. V. (2007). On the mechanism of uptake of globular proteins hy polyelectrolyte brushes a two-gradient self-consistent field analysis. Langmuir, 23, 3937-3946. http //dx.doi.org/10.1021/la0632777. 

Vector quantities, such as a magnetic field or the gradient of electron density, can be plotted as a series of arrows. Another technique is to create an animation showing how the path is followed by a hypothetical test particle. A third technique is to show flow lines, which are the path of steepest descent starting from one point. The flow lines from the bond critical points are used to partition regions of the molecule in the AIM population analysis scheme. 

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