Statistics bimodal distribution

As a consequence of exclusion, the coordination number shows very peculiar behavior (Fig. 7). For example, six percent relative quadratic fluctuation yields to a bimodal distribution (Fig. 8). This indicates that every statistical homogeneous coordination needs larger distance fluctuations of segments lying in the... 

Another common symptom of reactions that display nonstatistical behavior is a bimodal distribution of trajectory lifetimes. The nonstatistical trajectories have much shorter lifetimes than predicted by TST or RRKM. Trajectories will then cluster in two (or more) groups, the very short lifetime group and those with a much longer lifetime, consistent with statistical dynamics. Both direct trajectories that seemingly avoid local minima and bimodal lifetime distributions will be seen in many of the examples to follow. 

Advanced off-fine analysis software can help to access the statistical and the lateral distribution of the pull-off forces (panels c and d, respectively). The corresponding data, e.g., magnitude of the pull-off force, displayed in a 2D adhesion map (Fig. 4.4d) show that the border region is indeed characterized by a gradually changing, mixed chemical composition. The corresponding composition gradient can thus be mapped. Similarly, the statistically treated data yield a bimodal distribution of the pull-off forces (Fig. 4.4c). 

Mills and Mabbutt have pointed out that accurate determination of Rn requires that the statistical distribution of the intensity of the fluctuations should have a Gaussian distribution about the mean intensity [130]. These authors observed that in situations of competition between passivity and inhibition, a non-Gaussian, bimodal distribution could occur, and suggested that a second parameter in addition to Rn might be appropriate. 

Simultaneously, Delmas et al. suggested that the Mossbauer spectra were fitted by considering a distribution of quadrupole splitting values. They also found that a statistical distribution did not fit to the experimental values, and a bimodal distribution emerged [7]. A combined Ni and Fe Mossbauer spectroscopy study by Giitlich and coworkers [8] unfolded the cationic site assignment in Li, ferromagnetic properties of this material... 

T-Ben l-I glutamate (PBLG), 106, 200 Bernoulli statistics, 184 Bifunctional monomers, 130 Bimodal distributions, 39 Biopolymers, 112-16, 146-70,213 Birefringence measurement, 399-401... 

Particle size distribution is usually plotted on a log-probabiHty scale, which allows for quick evaluation of statistical parameters. Many naturally occurring and synthetic powders foUow a normal distribution, which gives a straight line when the log of the diameter is plotted against the percent occurrence. However, bimodal or other nonnormal distributions are also encountered in practice. 

Even though the lifetime distributions appear to be quite different, the recreated data are almost identical except for a small deviation near 200 ns and less obvious ones at shorter times. If the relative differences are plotted, systematic differences beyond the statistical noise are noticeable up to 200 ns, particularly when several channels are binned together. Given sufficient statistics, in principle, one can tell the difference between a bimodal and a monomodal distribution. The shown simulated spectra are based on 108 counts, five to 10 times the amount collected for the data discussed here. 

Pore diameters and their distribution. Small pores himt accessibility of internal surface because of increased resistance to diffusion of reactants inwards. Diffusion of products outward also is slowed down and may result in degradation of those products. When the catalyst is expensive, the inaccessible internal surface is a liability. A more or less uniform pore diameter is desirable, but the distribution usually is statistical and only molecular sieves have nearly uniform pores. Those catalyst granules that are extrudates of compacted masses of smaller particles have bimodal pore size distribution, between the particles and within them. Clearly a compromise between large specific surface and its accessibility as measured by pore diameter is required in some situations. 

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