Analysis, computers dynamic range

Finite difference — Finite difference is an iterative numerical procedure that has been used to quantify current-voltage-time relationships for numerous electrochemical systems whose analyses have resisted analytic solution [i]. There are two generic classes of finite difference analysis 1. explicit finite difference (EFD), where a new set of parameters at t + At is computed based on the known values of the relevant parameters at t and 2. implicit finite difference (IFD), where a new set of parameters at t + At is computed based on the known values of the relevant parameters at t and on the yet-to-be-determined values at t + At. EFD is simple to encode and adequate for the solution of many problems of interest. IFD is somewhat more complicated to encode but the resulting codes are dramatically more efficient and more accurate - IFD is particularly applicable to the solution of stiff problems which involve a wide dynamic range of space scales and/or time scales. 

A digital tape data acquisition system and off-line computer analysis, in use for several years prior to the development of the on-line computer system, provides a backup for either GC-MS in the event of a computer system failure. The results produced by the minicomputer system are consistent with the earlier system, but with increased flexibility and dynamic range. The immediate availability of results is especially valuable for discovery of problems before excessive time and samples are wasted. The potentiometric recorder output of the sample runs provides continuous, direct backup by displaying the data, as collected, in a familiar and directly accessible form. The ion current signal is displayed throughout the computer controlled run on an oscilloscope to allow the operator to assess system performance instantly. 

These systems were effective and some are still in use. Their major drawbacks lay in some tedium in sample preparation, film development and spectral analysis. The recording film also limited the dynamic range of the system (the range of concentrations that could be detected in a single sample) and trace elemental analysis was difficult. These early systems have largely been replaced by a variety of more sensitive, wider range, computer-based equipment. All of the newer equipment is also much more expensive to purchase and operate and requires careful handling and preparation of samples to avoid contamination. 

Computational fluid dynamics (CFD) is the analysis of systems involving fluid flow, energy transfer, and associated phenomena such as combustion and chemical reactions by means of computer-based simulation. CFD codes numerically solve the mass-continuity equation over a specific domain set by the user. The technique is very powerful and covers a wide range of industrial applications. Examples in the field of chemical engineering are ... 

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