Diffusion coefficient histograms

A radial distribution function can be determined by setting up a histogram for various distances and then looking at all pairs of molecules to construct the diagram. Diffusion coefficients can be obtained by measuring the net distances... 

Fig. 7.2. GFP PAR-2 (a) and NMY-2 GFP (b) imaged before the first cell division. Histograms of measured diffusion coefficients of (c) GFP PAR-2 and (d) NMY-2 GFP with PCS in the cytoplasm of C. elegans embryos. Scale bar represents 10 pm. a anterior, p posterior...

We can deduce the linewidth (and therefore the diffusion coefficient) as well as the amplitude of each step in the histogram. 

Figure 7. Histograms of diffusion coefficients of Sample C(II) in KCl buffer at different temperatures. Diffusion coefficients corrected to the viscosity of water at 30°C D c,3o = Duci.t X t)Kci/Ti X 303/ qxo.SO.

Figure 8. Histograms of diffusion coefficients of Sample C(H) at t = 30°C in water solutions adjusted to the indicated pH with HCl or NaOH. The natural pH is 4.1 at a concentration of about 1 mg/mL.

To compare the predictions from (7.43) with the observed values, we need to estimate the parameters T, D, and r. As in previous sections, T is the mean time elapsed between two successive migrations, i.e., the generation time. It can be estimated as the time needed for a newborn individual to grow into an adult and reproduce. When the adult age is reached, individuals leave the paternal territory and fly to new places. Since the available data for the dispersal process correspond to a histogram of frequencies of jump distances, the diffusion coefficient can be calculated from the discrete version of (7.4) ... 

Fig. 2. The normalized histogram distribution functions of the diffusion coefficients for samples 1 --------------, 2 and...

Carlos and Latif both fluidised glass particles in dimethyl phthalate. Data on the movement of the tracer particle, in the form of spatial co-ordinates as a function of time, were used as direct input to a computer programmed to calculate vertical, radial, tangential and radial velocities of the particle as a function of location. When plotted as a histogram, the total velocity distribution was found to be of the same form as that predicted by the kinetic theory for the molecules in a gas. A typical result is shown in Figure 6.11(41 Effective diffusion or mixing coefficients for the particles were then calculated from the product of the mean velocity and mean free path of the particles, using the simple kinetic theory. 

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