Logarithmic grid

It is a function of the translational energy, Ej, or alternatively, of the relative speed vn of the encounter. At the smallest speeds, the attractive intermolecular forces dominate and the cross section is large. In a double logarithmic grid, logQ versus logf, at low speeds we generally find... 

Fig. 3.2. The (smoothed) spectral functions derived from the measurements, Fig. 3.1, of the normalized binary absorption coefficients of helium-argon, neon-argon and argon-krypton mixtures at room temperature in a semi-logarithmic grid, Eq. 3.2.

One can think of an infinite number of transformation functions which could be used in atomic structure calculations, but two of them have been used widely in atomic structure calculations. These are the rational and the logarithmic grid ... 

Figure 17 VEDs in the (100) plane for TiC (left) and TiN (light). For the contour lines a logarithmic grid has been used. = 0.2 e/A. (From Ref. 58.)...

D. THE EXPONENTIAL FUNCTION WITH A LOGARITHMICALLY EQUIDISTANT GRID... 

E. A GAUSSIAN WITH A LOGARITHMICALLY EQUIDISTANT GRID We consider now (C.l) but with the transformation... 

We create a range of temperatures and volumes. The command logspace (-1.2,0,50) creates a vector of 50 logarithmically spaced values between 10 12 and 10°=1 the command meshgrid produces the matrices V and T that contain all the pressures and temperatures required for the grid of values needed for the plot. 

Logarithmic scales are often labeled only at intervals differing by factors of ten with no intermediate grid lines. If x is plotted on a logarithmic scale, the distance between two values x and X2 depends on the ratio of X2/X1. The distance on the paper between 1 and 2 is the same as the distance between 2 and 4 and between 5 and 10. In reading values between 1 and 10 it is well to remember that 2 is at a point about 0.3 times the distance between 1 and 10, so 5 is represented by a point about 0.7 times of the distance between 1 and 10 (Figure 21.9). 

Plot the summation curve of the data given in Problem 1 on log-probability grid and obtain the logarithmic standard deviation. What is the value of the uniformity modulus ... 

Asymmetrical Distributions—These are included in our binomial expansion Eq (23-1). However, it is more convenient to use another equation similar to Eq (23-8) for such distributions by merely changing variables. Many frequency distribution data which plot asymmetrically on arithmetic grid become symmetric if the independent variable is plotted logarithmically. When a normal distribution results by this method we may apply Eqs (23-5) and (23-6) by taking the logarithms of the variables, thus ... 

The grid in the r coordinate has a maximum of 300 points, which are distributed according to a logarithmic scale, such that their density is higher near the nucleus. 

The values of the Betti numbers at the grid points (a,b), or at the points [log(u), log 6 ] of the logarithmic map, form a matrix, M1" 1 1. In either of the direct or the logarithmic representations, this matrix is a numerical shape code for the fuzzy electronic density cloud of the molecule, representing the actual molecular shape. 

If, for the ranges [0.001,0.1 a.u.] for the density threshold values a and [—1.0,1.0] for the reference curvature b, a rather natural 41 x 21 grid is used, justified by the logarithmic scales, then the elements of the 41x21 matrix can also be stored as an integer vector C of 861 components. Using this alternative, the shape similarity measure x(A,B) can also be expressed as... 

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