Trivially parallel

The multiple-instruction, multiple-data (MIMD) architecture permits multiple instruction streams to simultaneously interact with their own data stream. While MIMD machines composed of completely independent pairs of instruction and data streams may be of use for trivially parallel applications, it is generally necessary to use a network to connect the processors together in a way that allows a given processor s data stream to be supplemented by... 

All the system, however, is not a trivial parallel structure, because if the system is to work properly, always more than one subsystem should operate and the subsystems can operate only in configurations set in advance. 

The numerical solution of these equations is not trivial, since for reasonably low viscosities the flow becomes turbulent. A popular method of treating these equations (together with the equations of energy and mass conservation) is the MAC method [156,157]. For the case of immiscible fluids or moving internal interface a phase-field-type approach seems to be successful [78,158,159]. Because of the enormous requirements of computing ressources the development in this field is still relatively slow. We expect, however, an impact from the more widespread availability of massively parallel computers in the near future. 

As mentioned in the start of Chapter 4, the correlation between electrons of parallel spin is different from that between electrons of opposite spin. The exchange energy is by definition given as a sum of contributions from the a and /3 spin densities, as exchange energy only involves electrons of the same spin. The kinetic energy, the nuclear-electron attraction and Coulomb terms are trivially separable. 

One of the most useful applications of chiral derivatization chromatography is the quantification of free amino acid enantiomers. Using this indirect method, it is possible to quantify very small amounts of enantiomeric amino acids in parallel and in highly complex natural matrices. While direct determination of free amino acids is in itself not trivial, direct methods often fail completely when the enantiomeric ratio of amino acid from protein hydrolysis must be monitored in complex matrices. 

The solution of these problems is based on a simple idea the developed laboratory-scale process is used for manufacturing of a chemical product by parallelization of many small units. Although promising great advantages over scale-up, this procedure, denoted numbering-up , is not trivial by far. It cannot be carried out in a simple way due to the tremendous technological effort necessary a chemical plant with hundreds or even thousands of small-scaled vessels, stirrers, heaters, pumps. 

For the synthetic chemistry part, this is accomplished by using parallel reactors (a chemical reaction takes time, say 30 min), involving automated injection of all components. Such equipment had already been developed for pharma R D and is therefore, widely available. For an overview see, e.g., Tuchbreiter et al. [4] and Schmatloch et al. [8]. Producing materials, e.g., compounds, is less trivial. To produce a series of different polymer samples, e.g., blends, an approach using a mask, see, e.g., Figure 1, is often applied. 

A mathematically trivial, but experimentally important case is that of parallel-mode EPR, in which Bt IIB and, therefore, k = / . Substituting the expressions for the direction cosines of Equation 5.3 into Equation 8.17 gives the parallel-mode relative intensity... 

Notice that, with the current data, one cannot draw immediate parallels with the spectrochemical series (nor with the nephelauxetic series). At any rate, these comparisons are not trivial depending on the symmetry, CF parameters of orders 4 and 6 are more or less important compared with those of order 2. Thus, the ratio charge/distance cannot generally quantify the strength of the LF exerted by a kind of ligand, or at least not in a way that is totally independent of the geometry of the complex. 

The total computational cost is proportional to the number of notional particles (iVp), and the algorithm is trivial to parallelize. 

Another result of considerable interest is the fact that the total single ion hydration enthalpies AH% are nicely paralleled by the values for individual clustering steps in the gas phase, and hence even more markedly by the AH%t n values (Figs. 7 and 8). It is not at all trivial that properties brought about by an infinite number of solvent molecules should be displayed already by such small complexes. Nevertheless, the shapes of the plots for AH% and AHo,n are quite similar. 

The lUPAC names for polymers are often very complicated and lengthy. Therefore, parallel to the systematic names, some semi-systematic or trivial names are allowed. Here, in most cases, the name of the basic monomer is used in combination with the prefix poly . Polystyrene may serve as an example. Brackets are used for the name of the monomer when it contains more than one word such as poly(vinyl chloride) ... 

The split-and-pool synthesis not only simplifies the complexity of the combinatorial synthetic process, but also offers additional important benefits. To undertake a full range of solid-phase chemical reactions, elaborate reaction conditions are needed for some chemical transformations. These include, but are not limited to, low temperature and inert atmosphere conditions. Parallel synthesis of a thousand compounds requires handling of a thousand reaction vessels. The timely addition of sensitive reagents (e.g., butyl lithium) at low temperature (—78°) under inert atmosphere during parallel synthesis is not a trivial task. It can be done if sophisticated automated synthesizer equipment is designed to handle and tolerate such reaction conditions. Such a synthesis can alternatively be performed easily in a manual fashion using a split-and-pool method that requires only a limited number of reaction vessels. Examples from Nicolaou s17 and Schrei-ber s18,19 laboratories have shown that the split-and-pool method is the methodology of choice for the synthesis of complex and diversity-oriented combinatorial libraries. 

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