[1] We give an alternative description of the data produced in the KamLAND experiment. Assuming the existence of a natural nuclear reactor on the boundary of the liquid and solid phases of the Earth's core, a geoantineutrino spectrum is obtained. This assumption is based on the experimental results of V. Anisichkin and his collaborators on the interaction of uranium dioxide and uranium carbide with iron-nickel and silica-alumina melts at high pressure (5-10 GPa) and temperature (1600-2200°C), which led to the proposal of the existence of an actinide shell in the Earth's core. We describe the operating mechanism of this reactor as solitary waves of nuclear burning in 238 U and/or 232 Th medium, in particular, as neutron fission progressive waves of Feoktistov and/or Teller et al. type. Next, we propose a simplified model for the accumulation and burn-up kinetics in Feoktistov's U-Pu fuel cycle. We also apply this model for numerical simulations of neutron fission wave in a two-phase UO 2 /Fe medium on the surface of the Earth's solid core. The proposed georeactor model offers a mechanism for the generation of

Physical fundamentals of traveling wave reactor are considered. We show that the condition of existence of nuclear burning soliton-like wave in a neutron-multiplying medium is determined in general by two conditions. The first condition (necessary) is determined by relationship between the equilibrium concentration and critical concentration of active (fissionable) isotope that is a consequence of the Bohr-Sommerfeld quantization condition. The second condition (sufficient) is set by the so-called Wigner quantum statistics, or more accurately, by a statistics of the Gaussian simplectic ensembles with respect to the parameter that describes the squared width of burning wave front of nuclear fuel active component.

a b s t r a c tBased on theoretical and experimental consideration of the first (the Twomey effect) and second indirect aerosol effects the quasianalytic description of physical connection between the galactic cosmic rays intensity and the Earth's cloud cover is obtained.It is shown that the basic equation of the Earth's climate energy-balance model is described by the bifurcation equation (with respect to the temperature of the Earth's surface) in the form of assemblytype catastrophe with the two governing parameters defining the variations of insolation and Earth's magnetic field (or the galactic cosmic rays intensity in the atmosphere), respectively.The principle of hierarchical climatic models construction, which consists in the structural invariance of balance equations of these models evolving on different time scales, is described.

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