Spatial range

Scheringer M. 1997. Characterization of the environmental distribution behavior of organic chemicals by means of persistence and spatial range. Environ Sci Tech 31(10) 2891-2897. 

Table 4.16 displays the energies and occupancies of the five bond and corresponding antibond NBOs of HW=WH. Successive metal-metal bonds would be expected to be formed in the order shown in Table 4.16 (i.e., cr before n before 5), on the basis of the spatial range and energy of each overlap type. 

Packing efficiency can also be described by the extent of short-range order in the amorphous state. Mitchell has shown through X-ray scattering studies that, while the local molecular organization of noncrystalline polymers is random, in many cases, there are additional correlations that do not perturb the chain trajectory but will impact polymer properties.15 These correlations have a limited spatial range (<50A) but will have a particular impact on bulk properties... 

GfSOj) for Hq/Bp (50) PSF is intermediate between G(S02> for the homopolymers. Thus, there is no additional protective effect analogous to the non-linear response of G(H.) as the mole fraction of benzene in cyclohexane is increased (3.47. This indicates that the spatial range of enhanced radiation protection afforded by the biphenyl group is limited. 

But even a small-scale trial-and-error strategy has to be organised within society. As discussed in the previous section, iimovations are rather improbable and disadvantaged by stractural frameworks. Iimovations depend upon freedom for them to be developed. At the same time safety barriers have to be formulated within which the search process can move freely. For example, possible environmental effects must be anticipated, necessitating controlled release in small increments and retrievability must be ensured. (Quantitative and qualitative restrictions must be imposed so that retrieval and repair options can still be effective if a trial is aborted. This approach is more successful if the persistence and spatial range of a chemical is low than for persistent chemicals like CFCs and PCBs. This requires that limited Teaming spaces or experimentation spaces have to be created intentionally under technical and economic risk considerations. Small increments and a steady increase are to be preferred, accompanied by intensive monitoring of detectable consequences. 

Innovation is also driven by state-promoted R D programmes. An emphatic reorientation of research support in accordance with guiding principles such as intrinsic safety of products , chemicals of low spatial range or sustainable chemistry may create an impetus for innovation efforts in the industry. 

Scheringer, M. Persistence and Spatial Range of Environmental Chemicals New Ethical and Scientific Concepts for Risk Assessment (Wiley-VCH) Weinheim i.a. 2002... 

Fig. 4 Schematic layout of the optical setup for holographic lithography using diffractive DOE, and phase control of the interfering beams. The callouts illustrate the selection of the beams using transmission mask, their incidence directions (top), and extended transverse spatial range of the interference region using tilted pulses produced by DOE (bottom)...

In contrast, if C is considered as a function ofx, our choice is greater. Imagine that we are looking for the solution of Eq. 22-7 within a given spatial range along the x-axis, say between x = 0 and x = L. Then we have six choices to specify the boundary conditions we can either prescribe the two boundary values,... 

Spatial range in Marsh 1989 Spatial average in July 1993 Spatial range in July 1995... 

Another physical consideration is the spatial range of the interactions If a large number of distinct solution elements make small contributions to it is reasonable to hope that fluctuations in the net result would be less for that statistical reason. In typical physical cases, this statistical point is insufficient as a sole argument, but it is typically a helpful additional point. 

The scale parameter A in (10.4.7) is used to adjust the spatial range of the basis functions to the spatial extension of the wave functions of the model atom. 

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