Background function diffuse

Diffuse background function to account for a peculiar scattering from amorphous phases (e.g. see Figure 4.2, specimen C) or from a noncrystalline sample holder ... 

Figure 7.10 A Series of Nested Background-Subtracted Diffuse Reflectance Spectra for the O-H Stretching Region for TJ-AljOj as a Function of Increasing Coverage of Pyridine.

The autocorrelation function G(t) corresponds to the correlation of a time-shifted replica of itself at various time-shifts (t) (Equation (7)).58,65 This autocorrelation defines the probability of the detection of a photon from the same molecule at time zero and at time x. Loss of this correlation indicates that this one molecule is not available for excitation, either because it diffused out of the detection volume or it is in a dark state different from its ground state. Two photons originating from uncorrelated background emission, such as Raman scattering, or emission from two different molecules do not have a time correlation and for this reason appear as a time-independent constant offset for G(r).58... 

Figure 3.16 The pair potential for rutile in ethylene glycol at infinite dilution as a function of diffuse layer potential. Background concentration 1 x 10 4 Ml ] electrolyte...

Figure 16. Schematic illustration of envelopes of gas species i, in this case Mg, surrounding a volatilizing molten chondrule in space. The size of the gas envelope is a function of ambient background pressure P by virtue of the effect that pressure has on the gas molecule diffusivity D,. The diffusion coefficient can be calculated from the kinetic theory of gases, as shown. The level of isotopic fractionation associated with volatilization of the molten chondrule depends upon the balance between the evaporative flux J vap and the condensation flux Tom When the fluxes are equal (i.e., when = 0), there is no mass-dependent isotope fractionation associated with volatilization. This will be the case when the local partial pressure P, approaches the saturation partial pressure P,...

The presence of the central spot (the primary beam) and diffuse rings Idiff from the film support brings significant errors into estimated intensities. The shape of the primary beam feam can be approximated by one of several peak-shape functions such as pseudo-Voigt, Gaussian or Lorentzian [16], The diffuse background can be described by a polynomial function of order 12. Then equation (1) becomes... 

The method of Simpson and Steinfink (4, 5) which uses liquid scattering functions was employed to take into account the unlocated atoms, assuming that they are uniformly distributed throughout a sphere. Atomic parameters were refined with 235 structure factors corresponding to all reflections with h2 + k2 + l2 <396 except the 111 line. A Guinier-type camera with monochromatized Cu K i radiation was used because of its low background diffusion, to detect the broad diffraction fines of external... 

So much for the background. The question now is whether we can visualize the solution before going to the computer. This is particularly necessary as we have a delta function as initial condition. However, the equation looks rather like the equation for diffusion and flow in a straight tube, which, if to were the concentration of a solute, D( ) its spatially varying diffusion coefficient, and V(x) its spatially varying convective velocity, would be... 

---