Self-correction, phenomenon

While the LSD exchange-correlation hole is accurate for small interelec-tronic separations (Sect. 2.3), it is less satisfactory at large separations, as discussed in Sect. 2.5. For example, consider the hole for an electron which has wandered out into the classically-forbidden tail region around an atom (or molecule). The exact hole remains localized around the nucleus, and in Sect. 2.5 we give explicit results for its limiting form as the electron moves far away [19]. The LSD hole, however, becomes more and more diffuse as the density at the electron s position gets smaller, and so is quite incorrect. The weighted density approximation (WDA) and the self-interaction correction (SIC) both yield more accurate (but not exact) descriptions of this phenomenon. 

Figure 2.2 presents the results obtained with our mechanism-based model of the ultradian insulin-glucose oscillations [9], Although clearly only a preliminary model of the phenomenon, the applied model passes all of the above tests. The model produces self-sustained oscillations of the correct period and proper amplitudes, and the model also responds correctly both to a meal and to changes in the rate of glucose infusion. The next step is to use the model to predict the outcome of experiments that have not previously been performed. To the extent that the model is successful in such predictions, the hypothesis underlying the model structure gains additional support. 

Different aspects of synchronization theory can be found in a number of monographs [1, 11, 28, 30, 34, 38, 47]. It is important to emphasize that synchronization is an essentially nonlinear effect. In contrast to many classical physical problems, where consideration of nonlinearity gives a correction to a linear theory, here the account of nonlinearity is crucial the phenomenon occurs only in intrinsically nonlinear, so-called self-sustained systems. 

One peculiar feature in the calculations of Masarik and Reedy (1995) is the disturbance of the neutron flux near the air-surface interface. Figure 9 shows that in contrast to the exponential decrease on either side of the boundary, the pattern is flat to about 10-20 g/cm above and below the rock surface. That disturbance is caused by different neutron production and transport mechanisms in air and rock and the loss of neutrons from the rock to the atmosphere (O Brien et al. 1978). There is a welcome side effect to this phenomenon in exposure age studies in that there is no need to correct for self-shielding in surface samples of less than a few centimeters size. Likewise, erosional loss by a few centimeters will not affect the cosmogenic nuclide production in the surface layer. On the other hand, the escape of neutrons from the outermost rock layers may reduce production rates in boulder samples relative to those in a flat surface (Masarik et al. 2000), by as much as 12% for the surface of a hemisphere with Im radius. It must be cautioned that these results have so far not been tested experimentally. If the flat profile down to 10 g/cm is correct, production rates at depth would be some 6% higher than for an exponential decrease starting at the very surface. 

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