Grids direct product

We choose to use the primitive coupled basis, rather than the 712 coupled basis that is often employed, primarily because the primitive coupled basis has a direct product form. This form makes it easy to accomplish the transformation from ji, j2, fci to 0i, 02, - The potential matrix, V, may be written as a numerical quadrature over the angular grid points in the following matrix form ... 

If the functional base is already correlated, i.e., not a direct product type, a more complicated grid construction results. An important example is the Y/m(d, ) functional... 

For more general problems, it has been observed that the direct product representation, which for the Fourier method implies a representation by an equally spaced Cartesian grid, is not optimal. A careful analysis of the Fourier method leads to the observation that this direct product grid is not isotropic in momentum space, so that different directions have different sampling intervals. A faithful representation of a multidimensional... 

A nondirect product basis expansion method described in the previous section on gas-phase reaction, similar to the spirit of L-shaped grid method proposed by Mowrey (91), is also used in gas-surface reactions. This method is actually ideal for gas-surface reaction because the skewing angle of the PES is strictly 90° (see Fig. 14). A collinear model study showed explicitly that the required number of quasiadiabatic diatomic vibrational function is only larger near the potential saddle point region (92). Based on the treatment of non-direct product basis described in the previous section (Eq. 89), the translation basis function is given by... 

Perhaps surprisingly, even if the potential is not factorizable it is still possible to do matrix-vector products at a cost that scales as, if a direct product quadrature grid is used. For example, the quadrature approximation for the integral... 

Fig. 21. The product D-atom velocity-flux contour map, d

The inlet air duct, starting at the roof level of the cubicle, leads to the inlet air flap, inlet air filters, and steam heated heat exchanger coils to heat the inlet air. This heated air is directed through a 1/2 supporting grid and 100 mesh screen on the bottom of the product container. 

In Norway and Romania, hydrogen production and export is in direct competition with electricity transmission via high-voltage direct-current lines (HVDC). This solution is particularly attractive because hydropower is a non-fluctuating renewable energy source and does not destabilise the grid, as, for example, wind or solar power do. 

Wire mini-grid OTEs. A mini-grid" is constructed with an array (or mesh ) of microscopically thin wires criss-crossing the face of a sheet of glass, silica or quartz. The wires are themselves too thin to see, but as soon as product is formed, it diffuses away from the wire. Since diffusion is entropy-driven (i.e. random), electrogenerated material does not diffuse in straight lines, but moves in all directions at once. In practice, as soon as material is formed, it is seen between the wires, and hence can be detected by the light beam of a spectrometer. 

Initial attempts to prepare Cf metal using metallothermic reduction methods (Section II,A) were less than successful due to the high vapor pressure of Cf metal 28, 46). Reduction of californium oxide with La metal (Section II,B) and collection of the product Cf metal on a fused silica fiber (in the apparatus shown schematically in Fig. 15), were found to give metal with usable X-ray diffraction patterns (5). Later, the same method was used to collect Cf metal both on a fused silica fiber for X-ray diffraction analysis and on an electron microscopy grid for electron diffraction analysis 56). As more Cf became available, preparations via this method were carried out on 0.4-1.0-mg samples of californium oxide (55), using fibers of quartz. Be, or C (suitable for direct X-ray diffraction analysis) to collect the product Cf metal. 

For our part we have observed the production of Mo-nanoparticles starting from [Mo(CO)i5] directly on a carbon film deposited on a TEM grid at various sublimation temperatures and thus at various partial pressures of [Mo(CO)6] in the carrier... 

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