Gaussian shaped mass distribution

For a stationary spray without scanning, a Gaussian shaped mass distribution typically develops with an annular-jet or discrete-jet atomizer. The radial mass distribution in the spray can be formulated in terms of mass flux)632]... 

The mass flux in the spray scales with liquid metal flow rate. Gas pressure tends to narrow the spray whereas melt superheat tends to flatten the spray)3] By changing the process parameters and/or manipulating the configuration and/or motion of the spray, the mass distribution profile can be tailored to the desired shape. For example, a linear atomizer produces a relatively uniform mass distribution in the spray. The mass flux distribution in the spray generated with a linear atomizer has been proposed to follow the elliptical form of the Gaussian distribution)178]... 

Fig. 8. Normalized residence time curves for ions of different mass accelerated to a fixed ion exit energy of 6.8 eV under conditions of a dc repeller field. Plotted is the relative ion intensity having a relative residence time greater than r/t, where t is the average residence time. Theory predicts that the shape of the curve is not mass-dependent, and experiment confirms this. The theoretical curve is computed for a Gaussian electron-beam distribution, with a full-width at half-maximum equal to the dimension of the slit through which the electron beam enters the source. Corrections resulting from the initial Maxwellian velocity distribution of the ions are ignored since they are negligible.

Real chromatograms (Fig. 2.6-3) take into account the thermodynamic influences as well as the kinetics of mass transfer and fluid distribution. A rectangular concentration profile of the solute at the entrance of the column soon changes into a bell-shape Gaussian distribution, if the isotherm is linear. Figure 2.7a shows this distribution and some characteristic values, which will be referred to in subsequent chapters. With mass transfer resistance or nonlinear isotherms the peaks become asym-... 

In this simulated-data example, a twelve-story shear building is considered. It is assumed that this building has uniformly distributed floor mass and uniform stiffness across the height. The mass per floor is taken to be 100 metric tons, while the interstory stiffness is chosen to be k = 202.767 MN/m so that the first five modal frequencies are 0.900,2.686,4.429,6.103 and 7.680 Hz. The covariance matrix is diagonal with the variances corresponding to a 1.0% coefficient of variation of the measurement error of the squared modal frequencies and mode shapes for all modes, a reasonable value based on typical modal test results. For the simulated modal data, a sample of zero-mean Gaussian noise with covariance matrix was added to the exact modal frequencies and mode shapes. 

Apart from the use of uniform (or almost uniform) standards, other methods for determining the BB function have been developed. For example, by assuming a uniform and Gaussian BB function with a linear molar mass calibration, it is possible to use the mass and molar mass chromatograms for simultaneously estimating the standard deviation of the BB function and the calibration coefficients.Alternatively, if the shape of the MMD is known (e.g., it is a Poisson distribution on a linear molar mass axis), then the BB function can be estimated from the difference between the (mass or molar mass) chromatogram and its theoretical prediction in the absence of BB. Finally, the BB function can be theoretically predicted from a representative fractionation model. " Unfortunately, however, this approach is so far unfeasible due to the difficulty in determining the associated physicochemical parameters. 

Figure 8 Trajectory of a trapped ion of m/z 105. The initial position was selected randomly from a population with an initial gaussian distribution (FWHM of 1 mm) = 0.3 zero initial velocity. The projection onto the xy plane illustrates planar motion in three-dimensional space. The trajectory develops a shape that resembles a flattened boomerang. Reproduced from Nappi etal (1997) International Journal of Mass Spectrometry and Ion Processes 161 77-85.

---