Size optimization

The advantage of a conjugate gradient minimizer is that it uses the minimization history to calculate the search direction, and converges faster than the steepest descent technique. It also contains a scaling factor, b, for determining step size. This makes the step sizes optimal when compared to the steepest descent technique. 

The resulting numerical prediction for the size-optimal cooling curve is shown in Figure 7.3. It predicts that in order to maximize the final sizes of the S-crystals, the temperature should be held constant for a period at both the start and end of the operation with a convex curve in between. This has the result of reducing both the early and terminal supersaturation levels and so maximizes solute deposition on the S-crystals and their growth rather than that of the A -crystals. Thus, programmed cooling is strictly sub-optimal , but nevertheless remarkably close to the optimum result in this case to be a practical alternative (Jones, 1974). 

Pore size optimization is one area where developmental efforts have been focused. Unimodal pore (NiMo) catalysts were found highly active for asphaltene conversion from resids but a large formation of coke-like sediments. Meanwhile, a macroporous catalyst showed lower activity but almost no sediments. The decrease of pore size increases the molecular weight of the asphaltenes in the hydrocracked product. An effective catalyst for VR is that for which average pores size and pore size distribution, and active phase distribution have been optimized. Therefore, the pore size distribution must be wide and contain predominantly meso-pores, but along with some micro- and macro-pores. However, the asphaltene conversion phase has to be localized in the larger pores to avoid sediment formation [134],... 

The objective of programmed cooling is to control the rate at which the magma temperature is reduced so that supersaturation remains constant at some prescribed value, usually below the metastable limit associated with primary nucleation. Typically the batch is cooled slowly at the beginning of the cycle and more rapidly at the end. An analysis that supports this approach is presented later. In size-optimal cooling, the objective is to vary the cooling rate so that the supersaturation in the crystallizer is adjusted to produce an optimal crystal size distribution. 

So Get the stationary phase particle size as small as possible, get the pore size optimized and you re sailing. Slow down - it s not quite so simple. There are other major effects that have to be considered when scaling a preparative separation. The friction caused by the eluent passing over stationary phase particles generates heat, which in turn reduces the viscosity of the solvent. Cooling by conduction in the vicinity of the column walls reduces the viscosity of the solvent close to the wall in comparison to that at the centre of the column. Consequently, the solvent at the centre of the column is now travelling at a... 

As the pore diameter increases in size (s decreases) relative to molecular or colloidal dimensions, less restrictions are imposed on the motions of contained species. Thus the exclusion effect gradually subsides as the pore size increases and consequently K-+1. For the separation of two molecules of different size, it is important to pick a pore diameter that will substantially exclude one species but not another. Pore size selection is thus of utmost importance in membrane science and in choosing a support for size exclusion chromatography (SEC). Aspects of pore size optimization in SEC based on the above partitioning theory have been developed [28]. 

Kozlowski, J. and Weiner, J. (1997). Interspecific allometries are by-products of body size optimization. American Naturalist, 149, 352-80. 

Target Library size Optimization Hits/tested compounds Reference... 

D. Manry, D. Gyawali, J. Yang, Size optimization of biodegradable fluorescent nanogels for cell imaging, J. High Sch. Res. (2011), In press. 

Figure 9.12. Natural, controlled constant nucleation) and size-optimal cooling modes in a batch crystallizer a) temperature profiles, b) supersaturation profiles...

Catalyst Particle Size Optimization and Dispersion Uniformity 87... 

Tersine, R. and S. Barman. 1991. Lot size optimization with quantity and freight rate discounts. Logistics and Transportation Review. 27(4) 319-332. 

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