Diffusion data analysis

The search for Turing patterns led to the introduction of several new types of chemical reactor for studying reaction-diffusion events in feedback systems. Coupled with huge advances in imaging and data analysis capabilities, it is now possible to make detailed quantitative measurements on complex spatiotemporal behaviour. A few of the reactor configurations of interest will be mentioned here. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Shen Q, Ren H, Fisher M, Bouley J, Duong TQ. Dynamic tracking of acute ischemic tissue fates using improved unsupervised isodata analysis of high-resolution quantitative perfusion and diffusion data. J Cereb Blood Flow Metab. 2004 24 887-897. 

A quantitative analysis of these self-diffusion data according to the two-state model of Eq. (1) to generate the order parameter of Eq. (2) is straightforward. was found to be... 

This measurement methodology and data analysis is general and can be extended to other porous media. The results from MRI moisture profiles can also be used to measure moisture diffusivity that enable moisture transport models to be developed for a wide range of materials. 

Table 1 summarizes several of the experimental methods discussed in this chapter. A need exists for new or revised methods for transport experimentation, particularly for therapeutic proteins or peptides in polymeric systems. An important criterion for the new or revised methods includes in situ sampling using micro techniques which simultaneously sample, separate, and analyze the sample. For example, capillary zone electrophoresis provides a micro technique with high separation resolution and the potential to measure the mobilities and diffusion coefficients of the diffusant in the presence of a polymer. Combining the separation and analytical components adds considerable power and versatility to the method. In addition, up-to-date separation instrumentation is computer-driven, so that methods development is optimized, data are acquired according to a predetermined program, and data analysis is facilitated. 

Barnes, R. J., Dhanoa, M. S., Lister, S. J. Appl. Spectrosc. 43,1989, 772-777. Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra. Barnes, R. J., Dhanoa, M. S., Lister, S. J. J. Near Infrared Spectrosc. 1, 1993, 185-186. Correction of the description of standard normal variate (SNV) and De-Trend transformations in practical spectroscopy with applications in food and beverage analysis. Brereton, R. G. Chemometrics—Data Analysis for the Laboratory and Chemical Plant. Wiley, Chichester, United Kingdom, 2006. 

The root time method of data analysis for diffusion coefficient determination was developed by Mohamed and Yong [142] and Mohamed et al. [153]. The procedure used for computing the diffusion coefficient utilizes the analytical solution of the differential equation of solute transport in soil-solids (i.e., the diffusion-dispersion equation) ... 

DAF-1, butene diffusion in, 42 36 Dangling bonds, 34 138 Data analysis, in extended X-ray absorption fine structure studies, 35 31-33 Dawson structure... 

In conclusion, if temperature can be chosen freely, the best one is around the high-temperature maximum of a". Then, the NOESY spectrum has the highest possible sensitivity but is still free of spin diffusion. Low-temperature spectroscopy can increase sensitivity immensely, but quantitative data analysis requires either the full matrix or the buildup curve analysis. 

Figure 3-37 Compositional dependence of diffusivities. (a) Fe-Mg interdiffusivity along the c-axis in olivine as a hinction of fayalite content at P — O.l MPa and log /b2 =-6.9 0.1. Diffusion data are extracted using Boltzmann analysis. Some of the nonsmoothness is likely due to uncertainty in extracting interdiffusivity using the Boltzmann method. Data are from Chakraborty (1997). (b) Ar and CO2 diffusivity in melt as a function of H2O content. Data are from Watson (1991b) and Behrens and Zhang (2001).

The following diffusion data are adapted from experimental diffusion data for water diffusion in a basaltic melt (Zhang and Stolper, 1991). The experiment was carried out at 1 300°C and the duration of the experiment is 10 minutes. Using Boltzmann analysis to obtain diffusion coefficients or water as a function of water concentration. Hint You will probably need to use a spreadsheet program to do simple integration and differentiation. You may also try to write a simple program. You may fix the concentration at one end to be 0.410 and the other end to be 0.100.)... 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

This work presented here covers the basic experimental techniques and data analysis procedures together with the analysis of the contribution of intracrystalline diffusion to the performance of AP catalysts. 

Application of the dual mode concept to gas diffusion in glassy polymers was originally subject to the limitation that DT2 = OinEq. (6) ( total immobilization model )6-Later this simplifying assumption was shown to be unnecessary, provided that suitable methods of data analysis were used 52). Physically, the assumption DX2 = 0 is unrealistic, although it is expected that DT2 < DX1 52). Hence, this more general approach is often referred to as the partial immobilization model . 

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