Distribution function calculation

Fig. 5.1.7 (a) Propagators in both a clean square capillary (dotted) and for flow around a biofilm structure (dashed) for an observation time, A = 15 ms. (b) Residence time distribution functions calculated from the propagator data shown in (a). The induction of a high... 

By extension, the probability that a given number of actives or fewer should occur in a given distribution is described by the cumulative binomial distribution function, calculated as... 

Figure 7. Water oxygen-exocyclic methylene carbon pair distribution function, calculated from a molecular dynamics simulation of a-D-glucopyranose in aqueous solution, giving the normalized probability of finding a water oxygen atom a given distance r from the C6 carbon atom. (Reproduced from Ref. 32. Copyright 1989 American Chemical Society.)...

Here, p(r) is the average density of atoms found in a thin shell at a radius r from an arbitrary atom in the material, and p is the average density of the entire material. For very small values of r, g(r) —> 0, since atoms cannot overlap one another. For large values of r, on the other hand, g(r) —> 1, because atoms that are separated from one another by large distances in a disordered material are not influenced by one another. The distribution functions calculated by Lewis et al. for liquid and amorphous InP are shown in Fig. 9.4. As might be expected, the amorphous material has considerably more structure than the liquid. One important feature in the amorphous material is the peak in the P-P distribution near r 2.2 A. This peak shows the existence of P-P bonds in the amorphous material, a kind of bond that does not exist in the crystalline solid. 

Figure 2.9 Glucose-cation (solid line) and glucose-anion (dashed line) center-of-mass radial distribution functions calculated from molecular dynamics simulations of a single sugar molecule in [CjCjlm]Cl.

FIGURE 3.12 Methane-methane radial distribution functions calculated from successive 0.9 ns portions of the simulation, indicating ordering of the methane molecules during hydrate nucleation. (Reproduced from Moon, C., Taylor, P.C., Rodger, P.M., J. Am. Chem. Soc., 125, 4706 (2003). With permission from the American Chemical Society.)... 

Figure 6.3 Quantal effects. Typical set of data after administration of increasing doses of drug to a group of subjects and observation of minimum dose at which each subject responds. Data shown are for 100 subjects dose increased in 0.2 mg/kg of body weight increments. Mean (ji) (and median) dose is 3.0 mg/kg standard deviation (v) is 0.8 mg/kg. Results plotted as histogram (bar graph) showing number responding at each dose smooth curve is normal distribution function calculated for ji of 3.0 and v of 0.8.

An example of an Li-0 radial distribution function (calculated by MD) is shown in Fig. 2.56. From such calculations one can obtain relaxation features of the rotational and translational motion of the neighboring waters and find the effect of Li or F , for example. 

Figure 21. Radial distribution functions calculated using a Fourier transform of scattering patterns produced with a Debye equation. Top Cuboctahedron (cluster with both octahedral 111 and cnbe 100 faces) and icosahedron (multiply twinned hep structure) clusters of the same size. Center Cuboctahedra of different sizes. Bottom Experimental and simulated cluster RDF of a Pt colloid. The fit is a 90 10 mixture of 55 and 147 cuboctahedral clusters, respectively. After Casanove et al. (1997).

Figure 1. Radial distribution functions calculated for a Lennard-Jones KrAr binary mixture (left) and molten LiF alloy (right).

Since 2 = i + A B ln(ln2) and A 2 = d i the distribution function calculated in the hypothesis of first order kinetics coincides with that calculated in the assumption of second order kinetics provided that the energy axis is shifted by an amount —fcB7 ln(ln2) = OMlksT... 

Figure 2 shows the distribution functions calculated for second-order kinetics in the frame of the condensation approximation for Elovich equations with different values of l — it is immediately seen that the larger is the ratio (i.e., the more accurate is the... 

Figure 36. distribution functions (calculated using only intact bonds) for the... 

Figure 65. distribution function (calculated using only intact bonds) for the DRP system. The dashed curve shows the distribution calculated using randomly chosen bond angles and the same coordination number statistics 0 as the WCA system. The inset shows an expanded view. 

Figure 4.5 From the result of a molecular dynamics simulation, the x-ray scattering intensity was calculated, and from it (r), given in the broken curve, was derived, by using exactly the same procedure as was used to treat experimental x-ray scattering intensities. The solid curve is the C-C atom pair distribution function calculated directly from the simulation result. (From Mondello et al.13)...

The radial distribution function of a liquid is intermediate between the solid and the gas, with a small number of peaks as short distances, superimposed on a steady decay to a constant value at longer distances. The radial distribution function calculated from a molecular dynamics simulation of liquid argon (shown in Figure 6.2) is typical. For short distances (less... 

Figure 1.11 Comparison between the radial distribution function, calculated with HS.EXE, for the Li-2s orbital and from the simple Slater function.

Druyvesteyn Electron Energy Distribution Function. Calculate the average electron energy for the Druyvesteyn distribution. Define the effective electron temperature of the distribution and compare it with that of the Maxwellian distribution frmction. 

In the liquid, a first view of the structure was given by the radial distribution functions calculated from the centers of the ions. The simulations revealed a first... 

Figure 21 presents the graphs of mercury-penetrated volume versus pressure in the pores of Na- and La-montmorimllonitamples. Figure 22 shows the pore-size distribution functions calculated from the porosimetry data. 

Fig. 1.9 Relaxation time distribution functions calculated on the basis of Debye law (D), Cole-Cole law (CC), Davidson-Cole law (DC) and...

Comparison of the radial distribution function calculated tor the 5.1-residue helical configuration, with inclusion of a jS carbon atom per residue, and the experimental radial distribution function for carbonmonoxyhemo-globin, as calculated from the three-dimensional Patterson function given by Perutz. 

Fig. 5.22 Qualitative picture of the orientational distribution function calculated from the angular dependence of the diffracted intensity along the arc depicted in Fig. 5.22b...

Potential of mean-force (PMF) calculations have been frequently used in the study of solvation at ambient and supercritical conditions [168,226-232], especially when researchers are interested in the behavior of solutes at high dilution, conditions at which solute-solute interactions become rare events and, consequently, cannot be accounted for by conventional distribution function calculations. The resulting PMF are in fact free energy profiles which can be used to determine the corresponding association constants, as well as the (transition state theory) kinetic rate constants for the conversion governing different solute-pair configurations separated by energy barriers. 

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