Local source function

Bader and Gatti [38] suggested a decomposition scheme that divides the total ED into atomic sources on the basis of the local source function (LS)... 

In other parts of the world, plywood adhesive fillers are obtained from local sources and may be quite different than those used in North America. In Southeast Asia, banana flour is quite important. In Europe, calcium carbonate (chalk) is often used. Nearly any fibrous material or fine particulate material capable of forming a functionally stable suspension can be made to work if the formulator is sufficiently skillful. However, the mix formulator will be very specific about the type and grade of filler to be used in a particular mix. Substitutions may lead to serious gluing problems. 

FIG. 11.3 Comparison of the ab-initio local density functional deformation density for Si with the experimental static model deformation density. Contour interval is 0.025 e A-3. Negative contours are dashed lines. Source Lu and Zunger (1992), Lu et al. (1993). 

Superposition of two displaced step-function initial conditions permits solutions that describe diffusion from an initially localized source into an infinite domain. The two step-function initial conditions in Fig. 4.4 have error-function solutions (Eq. 4.31), and their superposition is a localized source of width Ax. The two step functions are... 

Section 4.2.2 shows how to use the scaling method to obtain the error function solution for the one-dimensional diffusion of a step function in an infinite medium given by Eq. 4.31. The same solution can be obtained by superposing the onedimensional diffusion from a distribution of instantaneous local sources arrayed to simulate the initial step function. The boundary and initial conditions are... 

ORM assumes that the atmosphere is in local thermodynamic equilibrium this means that the temperature of the Boltzmann distribution is equal to the kinetic temperature and that the source function in Eq. (4) is equal to the Planck function at the local kinetic temperature. This LTE model is expected to be valid at the lower altitudes where kinetic collisions are frequent. In the stratosphere and mesosphere excitation mechanisms such as photochemical processes and solar pumping, combined with the lower collision relaxation rates make possible that many of the vibrational levels of atmospheric constituents responsible for infrared emissions have excitation temperatures which differ from the local kinetic temperature. It has been found [18] that many C02 bands are strongly affected by non-LTE. However, since the handling of Non-LTE would severely increase the retrieval computing time, it was decided to select only microwindows that are in thermodynamic equilibrium to avoid Non-LTE calculations in the forward model. 

Recently, the therapeutic potential of stem cells engineered to release adenosine as a local source to augment endogenous adenosinergic functions was assayed in two cell transplantation experiments (Li et al. 2007, 2008 Boison 2008). Most of the studies about the role of adenosine as an anticonvulsant emphasize the preeminent involvement of A1 adenosine receptors. However, several studies using different experimental models of epilepsy have investigated the role of adenosine A2a and A3 receptors in this condition. 

Scattered quantum states SQs,(R), i = 1,2, have localized sources (origin) in real space. The principle of linear superposition works for these states. These functions carry information on interactions of the internal ingoing state I (x) with the slits V(x R0i) I/(x)) see Scully et al. case, Section 5.1. In what follows, both elastic and inelastic scattering situations are examined. Here, we hint at general cases emphasizing what differs from the standard models. 

ADAS seeks to provide integrating modeling. This is based on a number of strategic objectives which have become points of principle. These are to separate local atomic tasks from non-local issues, to provide derived atomic data close-linked to experimental spectroscopic data reduction, to provide consistent source function inputs to theoretical plasma modeling and to provide central management of atomic data. 

As in our simple treatment of solvation dynamics in Chapter 15, the solvent in Marcus theory is taken as a dielectric continuum characterized by a local dielectric function ( )). Thus, the relation between the source, D (electrostatic displacement) and the response, (electric field) is (cf. Eqs (15.1) and (15.2))... 

C. Gatti and L. Bertini, The local form of the source function as a fingerprint of strong and weak intra- and intermolecular interactions, Acta Cryst. A60, 438-449 (2004). 

Here X = E,M denotes the type of radiation, either electric or magnetic, index j takes the values 1, 2,..., and index m = —j,..., j. The complex field amplitudes are defined in terms of the source functions, describing the local distribution of current and intrinsic magnetization [25], The mode functions in (17) can be represented in the following form [2,26,27] ... 

In Kohn-Sham (KS) density functional theory (DFT), the occupied orbital functions of a model state are derived by minimizing the ground-state energy functionals of Hohenberg and Kohn. It has been assumed for some time that effective potentials in the orbital KS equations are always equivalent to local potential functions. When tested by accurate model calculations, this locality assumption is found to fail for more than two electrons. Here this failure is explored in detail. The sources of the locality hypothesis in current DFT thinking are examined, and it is shown how the theory can be extended to an orbital functional theory (OFT) that removes the inconsistencies and paradoxes. 

Releases of radionuclides from the nuclear fuel-re-processing plants at Sellafield and Cap de la Hague have provided tracers for detailed studies of the circulations of the local environment into which they are released, namely the Irish Sea, English Channel, and North Sea, and for the larger-scale circulation processes of the North Atlantic and Arctic Oceans. These tracers have very different source functions for their introduction into the oceans compared to other widely used anthropogenic tracers, and in some cases compared to each other. The fact that they are released at point sources makes them highly specific tracers of several interesting processes in ocean circulation, but the nature of the releases has complicated their quantitative interpretation to some extent. 

In the final version of the Paris potential, also known as the parametrized Paris potential [14], each component (there is a total of 14 components, 7 for each isospin) is parametrized in terms of 12 local Yukawa functions of multiples of the pion mass. This introduces a very large number of parameters, namely 14 x 12 = 168. Not all 168 parameters are free. The various components of the potential are required to vanish at r = 0 (implying 22 constraints [14]). One parameter in each component is the nNN coupling constant, which may be taken from other sources (e.g., nN scattering). The 2n-exchange contribution is derived from dispersion theory. The range of this... 

The number of participant nucleons and the energy-density of this localized source increase with decreasing impact parameter. The spectators are the target and projectile remnants outside the overlap volume and they decouple from the participant source on a time scale that decreases with increasing projectile energy and then decay statistically. The excitation energy of these spectators is a function of the overlap region. 

The exact source of somatostatin acting on the oxyntic mucosa has been a matter of some debate, because cells containing somatostatin-D cells-are present both in the antrum and in the oxyntic mucosa. Additionally, postganglionic nerve fibers in the submucosa contain somatostatin, which may act as a neural transmitter. Because mucosal D cells, both in the antrum and in the fundus, possess elongated basal processes, somatostatin released locally may function as a paracrine regulator. 

The model (2)-(4) is referred to as the quenched solid non-local density functional theory (QSNLDFT). There are several advantages in considering the solid as a quenched component of the system rather than a source of the external field. On the one hand, this approach offers flexibility in the description of the fluid-solid boundary by varying the solid density and the thickness of the diffuse solid surface layer. On the other hand, it retains the main advantage of NLDFT computational efficiency because even a one-dimensional solid density distribution ceui include the effects of surface roughness and heterogeneity. For example, the solid density distribution can be taken from simulations of amorphous silica surfaces [29,30]. 

We presented a novel quenched solid non-local density functional (QSNLDFT) model, which provides a r istic description of adsorption on amorphous surfaces without resorting to computationally expensive two- or three-dimensional DFT formulations. The main idea is to consider solid as a quenched component of the solid-fluid mixture rather than a source of the external potential. The QSNLDFT extends the quenched-annealed DFT proposed recently by M. Schmidt and cowoikers [23,24] for systems with hard core interactions to porous solids with attractive interactions. We presented several examples of calculated adsorption isotherms on amorphous and microporous solids, which are in qualitative agreement with experimental measurements on typical polymer-templated silica materials like SBA-15, FDU-1 and oftiers. Introduction of the solid density distribution in QSNLDFT eliminates strong layering of the fluid near the walls that was a characteristic feature of NLDFT models with smoodi pore walls. As the result, QSNLDFT predicts smooth isotherms in the region of polymolecular adsorption. The main advantage of the proposed approach is that QSNLDFT retains one-dimensional solid and fluid density distributions, and thus, provides computational efficiency and accuracy similar to conventional NLDFT models. 

SFLAI Source Function Local Aromaticity Index... 

Eventually, we proposed an our own index based on the SF descriptor (SFLAI, Source Function Local Aromaticity Index) for quantifying the degree of aromaticity of 6-membered rings (6MRs) in polycyclic systems. Analogously to the SF analysis of electron delocalization, such an index might prove to be particularly useful for application to experimentally-derived ED s, as, at variance with other commonly employed quantum-mechanical (local) aromaticity descriptors, it does not require the knowledge of the pair density. 

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