[1] Lightning initiation and the associated in-cloud parts of lightning flashes have been studied by comparing thunderstorm data from two independent networks, LINET and SAFIRtype systems, operating in the VLF/LF and VHF regime, respectively. The two networks respond to radiation pulses with different length scales; an event detected by VLF/LF must be hundreds of meters long. In all 12 storms studied, up to half of the first in-cloud events detected with the VHF networks were found to be closely time-correlated with the first VLF/LF signal. Range-normalized VLF/LF signal amplitudes of the time-coincident events (TCEs) are comparable to amplitudes of weak cloud-to-ground strokes. Without measured preparatory VHF emission activity, initial breakdown in TCEs seems to start directly with a strong discharge step producing signatures in VLF/ LF records. The TCE data are consistent with lightning initiation via a runaway breakdown mechanism that extended over hundreds of meters. Citation:
The origin of the Gompertz function G(t)=G(0)e(b/a(1-e(-at))) widely applied to fit the biological and medical data, particularly growth of organisms, organs, and tumors is analyzed. It is shown that this function is a solution of a time-dependent counterpart of the Schrödinger equation for the Morse oscillator with anharmonicity constant equal to 1. The coherent states of the Gompertzian systems, which minimize the time-energy uncertainty relation, have been found. These are eigenstates of the annihilation operator identified with the operator of growth, whereas eigenstates of the creation operator represent the Gompertzian states of regression. The coherent formation of the specific growth patterns in the Gompertzian systems appears as a result of the nonlocal long-range cooperation between the microlevel (the individual cell) and the macrolevel (the system as a whole).
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