Function profile

Similarity solutions of the velocity profile functions for the Von Karman problem. (From Von Karman, Th, Z., Angew. Math. Mech., 1,231,1921.)... 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

The used S5mbols are K, scale factor n, number of Bragg peaks A, correction factor for absorption P, polarization factor Jk, multiplicity factor Lk, Lorentz factor Ok, preferred orientation correction Fk squared structure factor for the kth reflection, including the Debye-Waller factor [Pg.136]

Equation (31) shows an instanee of a temperature profile function which incorporates the thickness of a speeifie polymer tpoiy, the width of the heater eleetrode Wheat, and the heat generation rate as parameter, and constants c and Cl are fitted from caleulated temperature profiles,... 

As has already been emphasised, it is very difficult to approach a plane wave with the laboratory sources, which are properly described as spherical-wave sources. A single-crystal reflectivity profile from such a source will be dominated by the source profile rather than by the above formulae the integrated intensity expressions will be multiplied by the source profile function. 

Develop a system of equations in nondimensional form that can be solved to determine nondimensional velocity and temperature profiles function nondimensional length (z = z/D) along the channel. Define Reynolds and Prandtl numbers in the ordinary way as... 

In the following, we will present some cases of complex compounds the spectra of which exhibit vibrational progressions of a quality that can be used for carrying out a band analysis. These data then are worthwhile to be compared with the theoretical band profile functions as derived before. 

From a fit to the theoretical band profile function Eqs. (29,36,37) to the triple progressional series one obtains for the spectroscopic parameters... 

Peak Breadths And Reflection Profile Function. As has been mentioned, the individual reflection profiles tend to be broad for polymers. With both x-ray and neutron radiation the peaks exhibit large peak-widths. In a neutron diffraction pattern of isotactic polypropylene (A. Immirzi, work in progress) the peak width at half maximum, K j, had values ranging from 0.60° at 20= 14° to 1.00° at 26= 43° (X= 1.542 A), whilst, with the same... 

The whole-pattern-fitting structure-refinement method, which was first introduced by Rietveld and used for neutron diffraction powder patterns, does yield from x-ray diffraction patterns correct, refined structural information for linear polymers. Remarkably precise lattice parameters are obtained incidentally in the use of the method. The method lends itself to improved estimations of the fraction of amorphous and crystalline materials, or of two polymorphic forms, present. As improved profile functions come in to use, the method promises to provide crystallite size information, almost as a spin-off benefit. 

The peaks are defined by the parameters A the peak height, W- the width of the peak at half height, and P-t the peak position f- is the profile function parameter,which can vary between -0.5 and 1.0 for sensible profiles and effectively describes the tail region of the profile (j). The scatter from disordered molecules in the fibre is considered to have the polynomial form... 

Needs factors Target profile Functional specification Class comparators Market size/ growth Benefits... 

---