Maximum of the distribution

Figure 14 shows the displacement of the distribution function towards high / , i.e. the uncoiling of molecules under the influence of stretching for polyethylene (A = 3 x 10-9 m, N = 100 and T = 420 K). This displacement will be characterized by the position of the maximum of the distribution curve, the most probable value of / , i.e. j3m, as a function of x (Fig. 15). Figure 15 also shows the values of stresses a that should be applied to the melt to attain the corresponding values of x (o = xkT/SL, where S is the transverse cross-section of the molecule). 

The nitrogen adsorption isotherms for the onion-like Fe-modified MLV-0.75 materials are of type IV, although their hysteresis loops are of complex types, HI, H2, and H3. The H2-type hysteresis loop indicates the presence of bottle-shaped pores. The pore sizes obtained with the BJH method can be assigned to entry windows of mesopores. For pure MLV-0.75 and Fe-modified MLV-0.75 (x = 1.25), the pore size distributions exhibit two peaks (Fig. Id). The first peak appears at 9.0 and ca. 6 nm for MLV-0.75 and Fe-MLV-0.75, respectively. The shift of the broad peak maximum of the distribution curve... 

In order to define the statistical characteristics of a many particle system, for instance an ideal gas, their distribution function with some defined physical parameters (for example, velocity, momentum, energy, etc) should be fully determined. In particular it is physically important to define the velocity of particles corresponding to the most probable state, which is the maximum of the distribution function. 

The photodissociation of H2O2 is a generic example of modest rotational excitation. The maximum of the distribution corresponds to only... 

These results can be cross checked by performing a simulation where the director is constrained to lie in the vorticity plane but leaving it free to select the alignment angle. The angular distribution of the director is shown in Fig. 5 In these simulations only 256 particles were used. Therefore the distribution is fairly wide. As the system size increases the distribution becomes narrower and it is completely sharp in the thermodynamic limit. The maximum of the distribution appears ai 6 - 20° which is in agreement with the zero of the antisymmetric pressure tensor. A similar value of 6q was also found by using the equilibrium fluctuation relations (4.13) and (4.14). One can consequently conclude that the liquid crystal is flow stable. 

The differences in fatty acid distributions brought about by varying lithotype are rather more subtle than the differences brought about by varying the rank, since variation of rank brings about a change in the position of the maximum of the distribution. 

Here V% is the cumulative volume percent of particles below diameter a, file is a characteristic diameter related to the maximum of the distribution function, and fii a, is the largest drop diameter in the dispersion. Figure 6 illustrates experimental results described by a Schwarz-Bezemer distribution. Gal-Or and Hoelscher (G2) gave the following relation for drop size distribution ... 

Calculate the location of the maximum of the distribution of end-to-end distances (Fig. 2.12) of an ideal chain with N Kuhn monomers of length b. Calculate the average end-to-end distance of an ideal linear chain with N... 

Curve J of Fig. 28 represents the size distribution of atmospheric aerosol particles obtained by A. Meszaros and Vissy (1974) from samples collected on membrane filters over the oceans of the Southern Hemisphere. The samples were evaluated by optical and electron microscopy in the radius range of 0.03-64 /tm8. The total concentration of these particles is also shown. It can be seen that the maximum of the distribution occurs around 0.1 /Jir> radius, a value in the range of the... 

Furthermore, the most probable micelle size T is calculated from the maximum of the distribution function by taking logarithms of both sides of Eq. 10, rearranging, and differentiating ... 

Fig. 2.24. Distribution of protein adsorption in various states Fi with respect to the surface area tOi covered by the protein molecuie in the adsorption layer at n = 1.2 mN/m (1), and surface pressure as a function of area per protein molecule in the maximum of the distribution function (2) parameters used M = 24000 g/mol, tUmax 40 nmVmolecule, (Omi = 2 mnVmoIecule, Am = 1 nmVmolecule, 3,1= 100, a = 1.

Assuming that a polymer has a molar-mass distribution defined by (m) = ae ", where n m)Am represents the fraction of molecules with molar masses between m and m + Am, show that a = b and calculate (i) the number- and weight-average molar masses, and hence the polydispersity index and (ii) the molar mass at the mode (maximum) of the distribution function. 

From Eq. (65) one can calculate the portion of adsorbed molecules which exist in the state (o j. The dependencies of the distribution function T omega969j and the area per protein molecule in flie maximum of the distribution function are shown in Fig. 4. It is seen that the adsorption layer of proteins is characterized by an almost complete denaturation at low surface pressure while at large surface pressures the adsorption layer is composed of molecules in a state with a minimum molecular surface area demand. 

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