In this paper we advocate for the idea that two seemingly unrelated mysteries with almost 90 year history-the nature of dark matter and the million-degree solar corona-may be but two sides of the same coin-the axions of dark matter born in the core of the Sun and photons of axion origin in the million-degree solar corona, whose modulations are controlled by the anticorrelated modulation of the asymmetric dark matter (ADM) density in the solar interior.

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.

On the basis of the condition for nuclear burning wave existence in the neutron-multiplicating media (U-Pu and Th-U cycles) we show the possibility of surmounting the so-called dpaparameter problem, and suggest an algorithm of the optimal nuclear burning wave mode adjustment, which is supposed to yield the wave parameters (fluence/neutron flux, width and speed of nuclear burning wave) that satisfy the dpa-condition associated with the tolerable level of the reactor materials radioactive stability, in particular that of the cladding materials.It is shown for the first time that the capture and fission cross-sections of 238 U and 239 Pu increase with temperature within 1000-3000 K range, which under certain conditions may lead to a global loss of the nuclear burning wave stability. Some variants of the possible stability loss due to the so-called blow-up modes (anomalous nuclear fuel temperature and neutron flow evolution) are discussed and are found to possibly become a reason for a trivial violation of the traveling wave reactor internal safety.

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 core. Analyzing the uncertainty of antineutrino spectrum of georeactor origin, we show that the theoretical (which takes into account the soliton-like nuclear georeactor) total reactor antineutrino spectra describe with good accuracy the experimental KamLAND-data over the years of 2002-2007 and 2002-2009, respectively. At the same time, the parameters of mixing (△m²₂₁=2.5×10^-5 eV², tan²θ₁₂=0.437) calculated within the framework of georeactor hypothesis substantially differ from the parameters of mixing ((△m²₂₁=7.49×10^-5 eV², tan

The solution of energy-balance model of the Earth global climate and the EPICA Dome C and Vostok experimental data of the Earth surface palaeotemperature evolution over past 420 and 740 kyr are compared.In the framework of proposed bifurcation model (i) the possible sharp warmings of the Dansgaard-Oeschger type during the last glacial period due to stochastic resonance is theoretically argued; (ii) the concept of climatic sensitivity of water in the atmosphere, whose temperature instability has the form of so-called hysteresis loop, is proposed, and based of this concept the time series of global ice volume over the past 1000 kyr, which is in good agreement with the time series of δ 18 O concentration in the sea sediments, is obtained; (iii) the so-called "CO 2 doubling" problem is discussed.