Space-time minimality

Following Cappello [6], we have the following two definitions for space-time minimality ... 

Definition 3.2 A systolic array is space-time-minimal when it is scheduled in minimal time and when it uses the minimal number of processors among all possible minimal-time solutions. 

A. Benaini and Y. Robert. Space-time-minimal systolic arrays for gaussian elimination and the algebraic path problem. Parallel Computing, 15, pages 211-225, 1990. 

P. R. Cappello. A space-time-minimal systolic array for matrix product. In J. McCanny et al., editors, Systolic array processors, pages 347-356. Prentice Hall, 1989. 

Recently, the miniaturization procedures of bioanalytical studies have become an important research area with particular focus on modem concept of lab-on-a-chip technology [48], with a reduction in manufacturing costs, easy transport, minimal space and minimal maintenance requirements (and costs) in the laboratory and in the fields, even if this progress require a long design and implementation time, non-stable robotic operation, and limited error recovery abilities. 

Principal component analysis is a simple vector space transform, allowing the dimensionality of a data set to be reduced, while at the same time minimizing... 

Optimum Recycle Operations. When material is to be processed to some fixed final conversion Xp f in a recycle reactor, reflection suggests that there must be a particular recycle ratio which is optimum in that it minimizes the reactor volume or space-time. Let us determine this value of R. 

For laboratory cells, minimizing the energy consumption and optimizing the space-time yield are not as important. It is more important that the different reaction parameters like electrode materials, diaphragms, and the working potentials can be varied easily. For electrolyses under potential control, a three-electrode construction has to be used, which is schematically shown in Figure 22.8. 

Fig. 6 Climatic fields of the minimal water temperature (degrees Celsius) in the Black Sea a in February and b in August and the space-time diagrams of its climatic annual cycle along c line 1 and d line 2. Dashed lines in b locations of the space-time diagrams. Dashed lines in c,d phase shift of the temperature minimum...

In Section 6.1 we saw. that the undesired product could be minimized by adjusting the reaction conditions (e.g., concentration) and by choosing the proper reactor. For series of consecutive reactions, the most important variable is time space-time for a flow reactor and real-timE for a batch reactor. To illustrate the importance of the time factor, we consider the sequence... 

Centrifugal extractors Allow short contact time for unstable solutes, minimal space requirements (minimal footprint and height), can handle s) tems with low density difference or tendency to easily emulsify Petrochemical Chemical Pharmaceutical Nuclear... 

Productivity during scale-up is therefore a major concern for efficiently getting an active compound to market. In scale-up operations, productivity is related to throughput, the amount of product that can be made per reactor volume per day. Sometimes this is referred to as space-time yield or volume efficiency [15],To increase productivity, conditions are developed to minimize reaction times, streamline operations, and simplify processing. 

The study by Hitzler et al. has illustrated the broad scope of potential hydrogenation reactions in SC-Some of the substrates investigated included m-cresol, benzaldehyde, acetophenone, 1-octene, and cyclohexene. Reactions were performed in 5 and 10 ml packed bed reactors and space times of up to 300 hr were achieved. Residence times of this magnitude render the issue of scale-up largely irrelevant for small (kilogram) quantities of product in a continuous process. This is advantageous for the commercialization of SCF reaction processes because it minimizes development and capital costs. 

Mitra et al. (1998) employed NSGA (Srinivas and Deb, 1994) to optimize the operation of an industrial nylon 6 semibatch reactor. The two objectives considered in this study were the minimization of the total reaction time and the concentration of the undesirable cyclic dimer in the polymer produced. The problem involves two equality constraints one to ensure a desired degree of polymerization in the product and the other, to ensure a desired value of the monomer conversion. The former was handled using a penalty function approach whereas the latter was used as a stopping criterion for the integration of the model equations. The decision variables were the vapor release rate history from the semibatch reactor and the jacket fluid temperature. It is important to note that the former variable is a function of time. Therefore, to encode it properly as a sequence of variables, the continuous rate history was discretized into several equally-spaced time points, with the first of these selected randomly between the two (original) bounds, and the rest selected randomly over smaller bounds around the previous generated value (so as... 

What if the first-order reaction were carried out in tubular reactors of different diameters, but with the space time, t, remaining constant The diameters would range from a diameter of 0.1 dm to a diameter of 1 m for V = p/p = 0.01 cm-/s, i/ = 0,1 ctn/s, and = ICF cmVs. How would your conversion change Is there a diameter that would maximize or minimize conversion in this range ... 

The main attraction of using the integral approach in conventional studies is that it avoids the need to measure rates of reaction. Instead, the output conversions from several isothermal runs at different space times are plugged into the integrated rate expression and the rate parameters are optimized as simple constants for a given temperature. Since there usually are few parameters in a rate expression, a few runs will suffice to define all the constants at one temperature certainly, fewer runs than would be necessary to make valid estimates of rates from a plot of X vs. x. Repeating this procedure at several temperatures yields a set of constants suitable for plotting on an Arrhenius plot. This procedure minimizes the number of isothermal runs necessary to obtain the rate parameters. 

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