Numerical method, desired properties

We focus on so-called symplectic methods [18] for the following reason It has been shown that the preservation of the symplectic structure of phase space under a numerical integration scheme implies a number of very desirable properties. Namely,... 

Measurements of the desired property or properties (usually grouped together under the general title specifications) are expressed as numerical values therefore, the accuracy of these measurements is of the utmost importance. The measurements need to be sufficiently accurate so as to preclude negative scientific or economic consequences. In other words, the data resulting from the test methods used must fall within the recognized limits of error of the experimental procedure so that the numerical data can be taken as fixed absolute values and... 

Before discussing the finite volume method, it is worthwhile to examine the desired properties of the numerical solution method, which are summarized below ... 

When deriving these expressions, it was assumed that velocity at all the cell faces is positive. In other cases, suitable modifications to include appropriate upstream nodes (in place of 0ww and 0ss) should be made. It can be seen that the continuity equation indicates that the last term inside the bracket of Eq. (6.19) will always be zero for constant density flows. The behavior of numerical methods depends on the source term linearization employed and interpolation practices. Before these practices are discussed, a brief discussion of the desired characteristics of discretization methods will be useful. The most important properties of the discretization method are ... 

For most multiphase reactive flow problems, it is not possible to analyze all the operators in the complete solution method simultaneously. Instead the different operators of the method are analyzed separately one by one. The working hypothesis is that if the operators do not possess the desired properties solely, neither will the complete method. Unfortunately, the reverse is not necessarily true. In practical calculation we can only use a finite grid resolution, and the numerical results will only be physically realistic when the discretization schemes have certain fundamental properties. The usual numerical terminology employed in the CFD literature is outlined in this section [141, 202, 49]. 

The molecular structure of any chemical will determine all of its physical, chemical and biological properties. Discovery chemists will therefore seek correlations between molecular structure and a desired property and the search for novel materials is therefore often guided by structure/ activity relationships (SARs). These can also be referred to as structure/ property relationships (SPRs) and when carried out with data inputs in a numerical form and using statistical methods for their analysis, the adjective quantitative is added giving quantitative structure/activity... 

The dendritic polymer literature reviewed herein provides compelling evidence that these materials are a unique and versatile class of branched polymers. The synthesis of dendritic macromolecules can be accomplished by numerous methods allowing for specific tailoring of the characteristics of the polymer, to yield desired properties or functionality. While some of the procedures reported are quite intricate, requiring multiple cycles of synthetic steps and work-up, one-pot syntheses have also been developed for hyperbranched and dendrigraft polymers, making these materials more viable for (large-scale) commercial production and industrial applications. 

Paints are made of numerous components, depending on the method of application, the desired properties, the substrate to be coated, and ecological and economic constraints. Paint components can be classified as volatile or nonvolatile. 

Although generalized coordinates are often useful for understanding molecular systems, as we shall learn in later chapters, it is desirable to avoid the use of formulations with a configmation-dependent mass matrix since it complicates the design of numerical methods with good conservation properties. This is one reason that molecular simulation methods are typically described in a Cartesian coordinate framework. 

The measurement of diffusion coefficients is particularly important in polymer electrolyte research. One of the desired properties of a potential electrolyte material is the selective mobility of the LE cation. Numerous strategies have been implemented to attain this property [1, 44, 45]. One method of quantifying the selective mobility is the calculation of transference numbers, which is the fraction of the total electric current that the anions and cations carry while passing through an electrolyte. Using the notation of Kalita et al. [46], the transference number for lithium, f, could be expressed as. 

The means available to operationalize the strategic properties of CE are numerous. With respect to integration, complexity and resilience, methods and tools for interoperabihty and SaaS can be used to achieve the desired properties. 

Abstract The polymer electrolyte fuel cell (PEFC) consists of disparate porous media microstructures, e.g. catalyst layer, microporous layer, gas diffusion layer, as the key components for achieving the desired performance attributes. The microstmcture-transport interactions are of paramount importance to the performance and durability of the PEFC. In this chapter, a systematic description of the stochastic micro structure reconstmction techniques along with the numerical methods to estimate effective transport properties and to study the influence of the porous structures on the underlying transport behavior is presented. 

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