Fractional diffusion

Calcium Adequate intake (Table 3-1) in divided doses Absorption-predominantly active transport with some passive diffusion, fractional absorption 10-60%, fecal elimination for the unabsorbed and renal elimination for the absorbed calcium... 

Special attention should be paid to polypeptides isolated from a non-diffusible fraction of normal human urine by Boulanger et al. (BIO). By means of paper chromatography they isolated from this mixture seven single polypeptides and determined their amino acid composition. The results of the analyses are given in Table 3. 

Van Orman J. A., Grove T. L., and Shimizu N. (2002b) Diffusive fractionation of trace elements during production and transport of melt in Earth s upper mantle. Earth Planet. Sci. Lett. 198, 93-112. 

Representing the two components of the soil-atmosphere flux, respiration and atmospheric invasion, the associated CO2 in equilibrium with soil water, 5s, and the effective diffusion fractionation in going from the soil into the atmosphere, 8eff. These components, and what influence them is briefly discussed below. 

Fraction By reduction By diffusion Fraction By reduction By dif-f usion... 

The model from R.E. Bird and R.L. Hulstrom [5.42], see also [5.34], is once again mentioned for the calculation of the diffuse fraction of radiation in (5.126). The source of the scattered radiation is the non-absorbed direct solar radiation with the irradiance... 

The best physical model is the simplest one that can explain all the available experimental time series, with the fewest number of assumptions. Alternative models are those that make predictions and which can assist in formulating new experiments that can discriminate between different hypotheses. We start our discussion of models with a simple random walk, which in its simplest form provides a physical picture of diffusion—that is, a dynamic variable with Gaussian statistics in time. Diffusive phenomena are shown to scale linearly in time and generalized random walks including long-term memory also scale, but they do so nonlinearly in time, as in the case of anomalous diffusion. Fractional diffusion operators are used to incorporate memory into the dynamics of a diffusive process and leads to fractional Brownian motion, among other things. The continuum form of these fractional operators is discussed in Section IV. 

Figure 4. Examples of direct and diffuse solar irradiance and a correction factor for diffuse path length in measurements (Hargreaves, unpublished). (A) Diffuse fraction of irradiance as a function of solar zenith angle during summer, 1996, L. Lacawac, Pennsylvania (41.3°N) and August 2001, Crater Lake, Oregon (42.9°N). (B) Calculated correction [17] to remove effects of irradiance field from near-surface diffuse attenuation (K ) measurements, based on data in part (A).

The linear relations depicted in Figs. 16-3a and 16-3b may be forced. The data from which these plots were constructed have some deficiencies in precision and self-consistency. Data of good precision are available from the work of Melpolder ei a .[10] on thermally diffused fractions of a petroleum oil, as listed in Tables 16-6 and 16-7 ... 

Molecular Composition of Thermal Diffusion Fractions of Saturates from a Midcontinent Lubricating Oil... 

Composition of Saturates from Thermal Diffusion Fractions of Solvent Extracted U.S. Midcontinent 150N Base Stock... 

Prinzhofer A, Pematon E (1997) Isotopically light methane in natural gas bacterial imprint or diffusive fractionation Chem Geol 142 193-200... 

Sulfonamides are widely distributed. The diffusible fraction of sulfadiazine is distributed uniformly throughout the total-body water, whereas sulfisoxazole is confined largely to the extracellular space. The sulfonamides readily enter body fluids and may reach concentrations therein that are... 

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