Multi geometry

Equilibrium terms, multi- Geometries QM, electron diffraction, mi-... 

Stephens MM, Moorhead ED (1987) A global finite element Galerkin/B-spline (GBS) numerical model of electrochemical kinetics, transport and mechanism for multi-geometry working electrodes. Part 1. Modeled Nernstian voltammetry. J Electroanal Chem 220 1. 

A resonance in the layered stracture occurs when echoes between two boundaries travel back and forth due to differences in acoustic impedances at the boundaries. For multi-layer structures a number of resonances can be observed depending on their geometry and condition. For each particular defect-free structure and given transducer we obtain a characteristic resonance pattern, an ultrasonic signature, which can be used as a reference. 

The Champ-Sons model is a most effieient tool allowing quantitative predictions of the field radiated by arbitrary transducers and possibly complex interfaces. It allows one to easily define the complete set of transducer characteristics (shape of the piezoelectric element, planar or focused lens, contact or immersion, single or multi-element), the excitation pulse (possibly an experimentally measured signal), to define the characteristics of the testing configuration (geometry of the piece, transducer position relatively to the piece, characteristics of both the coupling medium and the piece), and finally to define the calculation to run (field-points position, acoustical quantity considered). 

Such effects principally cannot be observed in multi band detectors such as a UV diode array detector or a Fourier transform infrared (FTIR) detector because all wavelengths are measured under the same geometry. For all other types of detectors, in principle, it is not possible to totally remove these effects of the laminar flow. Experiments and theoretical calculations show (8) that these disturbances can only be diminished by lowering the concentration gradient per volume unit in the effluent, which means that larger column diameters are essential for multiple detection or that narrow-bore columns are unsuitable for detector combinations. Disregarding these limitations can lead to serious misinterpretations of GPC results of multiple detector measurements. Such effects are a justification for thick columns of 8-10 mm diameter. 

In general it is found that GGA methods often give geometries and vibrational frequencies for stable molecules of the same or better quality than MP2, at a computational cost similar to HE For systems containing multi-reference character, where MP2 usually fails badly, DFT methods are often found to generate results of a... 

The coimter-current coupling of an endothermic reaction to a heating gas stream in a multi-layer architecture was studied by Hardt et al. [120], The 2-D geometry their model was based on is displayed in Figure 2.52. 

Figure 4.23 Near-ideal multi-lamination flow patterns in the second-generation caterpillar mini mixer as a result of introducing a splitting plate and improving micro structure geometry [50],...

This plate cuts the flow into pieces which are better defined than the poorly defined ones obtained by the first-generation caterpillar mini mixer. In addition, the micro structure geometry was improved by means of simulation. As a result, near-ideal multi-lamination flow patterns were yielded (Figure 4.23), which showed excellent correspondence with simulation [50]. 

Pore shape is a characteristic of pore geometry, which is important for fluid flow and especially multi-phase flow. It can be studied by analyzing three-dimensional images of the pore space [2, 3]. Also, long time diffusion coefficient measurements on rocks have been used to argue that the shapes of pores in many rocks are sheetlike and tube-like [16]. It has been shown in a recent study [57] that a combination of DDIF, mercury intrusion porosimetry and a simple analysis of two-dimensional thin-section images provides a characterization of pore shape (described below) from just the geometric properties. 

Normal geometry Term used to describe the construction of a conventional dual/multi channel probe. Since the X nucleus is a far less sensitive nucleus than 1H, a normal geometry probe has the X nucleus receiver coils as close to the sample as possible to minimise signal loss and the XH receiver coils outside the X nucleus coils (i.e., further from the sample). This design of probe is thus optimised for X nucleus sensitivity at the expense of some XH sensitivity. 

It is important to note that, even when the coordination geometry prescribed by the macrocyclic cavity is ideal for the metal ion involved, unusual kinetic and thermodynamic properties may also be observed (relative to the corresponding open-chain ligand complex). For example, very often the macrocyclic complex will exhibit both enhanced thermodynamic and kinetic stabilities (kinetic stability occurs when there is a reluctance for the ligand to dissociate from its metal ion). These increased stabilities are a manifestation of what has been termed the macrocyclic effect - the multi-faceted origins of which will be discussed in detail in subsequent chapters. 

The major problem with the application of the TNO multi-energy method is that the user must decide on the selection of a severity factor, based on the degree of confinement. Little guidance is provided for partial confinement geometries. Furthermore, it is not clear how the results from each blast strength should be combined. 

In this way, the geometry-dependent Casimir fluctuations can be extracted from the m//W/ /e-scattcri ng part of the scattering matrix. The determinant of the n-spherc/disk S-matrix can be separated into a product of the determinants of the 1-sphere/disk S-matrices S E, a,i), where a, are the radii of the single scatterers, and the ratio of the determinant of the multi-scattering matrix M(k) and its complex conjugate (A. Wirzba., 1999) ... 

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