Nonlinear interaction between Alfvén and acoustic-gravity waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere permeated by a uniform magnetic field directed against the action of gravity, we considered the nonlinear interaction between vertically propagating Alfvén and acoustic-gravity waves. We established that Alfvén waves are efficiently generated at the difference and sum frequencies. We ascertained that no acoustic-gravity waves are formed at the corresponding combination frequencies. A horizontal magnetohydrodynamic wind whose direction changes with height was found to be formed in the solar atmosphere at zero difference frequency.     

Diffusive propagation of fast particles in the presence of a moving shock wave

Based on an analytical model, we determined the temporal dynamics of the spectral shape and spatial distribution of the particles that were impulsively (in time) injected with a specified spectrum in the vicinity of a moving plane shock front. We obtained a condition to determine the influence of the shock front on the particle propagation, where the spatial diffusion coefficient of the particles plays a major role. Diffusive shock acceleration is shown to strongly affect low-energy particles (the intensity maximum coincides spatially with the shock front; hard and soft spectral regions are formed in the spectrum) and weakly affect high-energy particles (the time at which the intensity reaches its maximum is well ahead of the shock arrival time; the spectral shape does not change). In events accompanied by a significant increase in the turbulence level, the influence of the shock front on high-energy particles can change from weak to strong. This change shows up in the spatial distribution and spectral shape of the particles. The dynamics of the particle intensity, calculated with the diffusion coefficients that were determined in accordance with the quasi-linear theory for measured turbulence levels, qualitatively corresponds to the observed solar energetic-particle intensity.     

Primary and remote fracture around underground cavities

The development of fractures around cavities in rock is examined using physical and numerical models. In uniaxial compression, fracture proceeds from primary through remote to compressional (slabbing) fracture. There is a wide stress interval where the only event is the stable propagation of the primary fracture. When the crack length becomes equal to about the size of the diameter of the cavity, the critical stress condition shifts to either side of the primary fracture, leading to the nucleation of remote fractures. Almost simultaneously, failure at the compressive stress concentration follows. With increasing stress, fracture in the remote region is seen to extend away from and towards the compressive region, eventually merging with the slabbing fractures. Increasing the confining pressure shortens the stress interval during which primary fracture is the only process and shifts failure to the remote and the compressional fracture zone.     

Cutoff frequency and the reflection of vertically propagating magnetoacoustic gravity waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere stratified in the field of gravity, we investigate the main patterns of vertical propagation of magnetoacoustic gravity waves (MAGWs) in the approximation of a horizontal potential magnetic field. We have established that the cutoff frequency for MAGWs below which they cannot propagate does not depend on the magnetic field strength and is equal to that for acoustic gravity waves, the Lamb frequency. The cutoff frequency is shown to be unaffected by the linear interaction between counterpropagating MAGWs that results from a nonuniform height distribution of the Alfvén velocity and that causes the reflection of propagating waves at relatively large heights.     

Effects of cosmic rays and density inhomogeneity of the circumstellar medium on the formation of a supernova shell

We consider the self-similar problem of a supernova explosion in a radially inhomogeneous medium by taking into account the generation of accelerated relativistic particles. The initial density of the medium is assumed to decrease with distance from the explosion center as a power law, ρ ₀ = A/r ^θ. We use a two-fluid approach in which the total pressure in the medium is the sum of the circumstellar gas pressure and the relativistic particle pressure. The relativistic particle pressure at the shock front is specified as an external parameter. This approach is applicable in the case where the diffusion coefficient of accelerated particles is small and the thickness of the shock front is much smaller than its radius. We have numerically solved a system of ordinary differential equations for the dimensionless quantities that describe the velocity and density behind the shock front as well as the nonrelativistic gas and relativistic particle pressures for various parameters of the inhomogeneity of the medium and various compression ratios of the medium at the shock front. We have established that the shock acceleration of cosmic rays affects most strongly the formation of a supernova shell (making it thinner) in a homogeneous circumstellar medium. A decrease in the circumstellar matter density with distance from the explosion center causes the effect of shock-accelerated relativistic particles on the supernova shell formation to weaken considerably. Inhomogeneity of the medium makes the shell thicker and less dense, while an increase in the compression ratio of the medium at the shock front causes the shell to become thinner and denser. As the relativistic particle density increases, the effect of circumstellar matter inhomogeneity on the shell formation becomes weaker.     

Jusa and Barsuchi Log Volcanogenic Massive Sulfide Deposits from the Southern Urals of Russia: Devonian Analogs of the Kuroko Deposits of NE Honshu, Japan

Chemical analysis of 60 samples from the Jusa and Barsuchi Log volcanogenic massive sulfide (VMS) deposits by inductively coupled plasma–mass spectrometry shows that, on average, the Jusa deposit is more enriched in the chalcophilic elements than the Barsuchi Log deposit, whereas the Barsuchi Log deposit is more enriched in the lithogenous elements and Te. In addition, the yellow ores in these deposits are more enriched on average in Cu, As and Mo and the black ores more enriched in Zn, Ga, Cd, Sb, Ba , Hg and Pb relative to each other. Both these deposits are similar in composition to the Kuroko deposits of NE Honshu and may be considered to be analogs of these deposits. The Kuroko deposits, however, contain much higher concentrations of As, Ag, Sb, Ba, Hg and lower contents of Te on average than the Jusa and Barsuchi Log deposits. Based on the higher contents of Te in the Barsuchi Log deposit compared to the Jusa deposit, as well as on textural considerations, it is concluded that the Barsuchi Log deposit is intermediate between the Urals- and Kuroko-type deposits, whereas the Jusa deposit is more analogous to the Kuroko-type deposits. Based on the compositional data presented here, the Jusa and Barsuchi Log deposits may be described as Zn-Pb-Cu-Ba deposits rather than as Zn-Cu-Ba deposits, as the Baimak-type deposits of the west Magnitogrosk zone have previously been described.     

Parametric generation of magnetoacoustic-gravity waves in the solar atmosphere

Based on a plane-parallel isothermal solar model atmosphere permeated by a horizontal magnetic field whose strength is proportional to the square root of the plasma density and in the approximation of a specified field for vertically propagating and nonpropagating magnetoacoustic-gravity waves, we consider the nonlinear interaction between the corresponding disturbances, to within quantities of the second order of smallness. We investigate the efficiency of the nonlinear generation of waves at difference and sum frequencies and of an acoustic flow (wind) as a function of the magnetic-field strength and the excitation frequency of the initial disturbances at the lower atmospheric boundary.     

Effects of nonlinear Alfvén wave interaction on particle diffusive shock acceleration. The Earth’s bow shock

We investigate the role of nonlinear Alfvén-wave interaction in the diffusive shock acceleration of solar-wind ions at the Earth’s bow shock. Allowance for the nonlinear wave interaction through induced scattering and two-quanta absorption at plasma parameters β≲0.1 is shown to limit the Alfvén-wave amplitude δB to δB≲B, whereas the quasi-linear approach predicts the generation of waves with amplitudes much larger than the diffusive shock magnetic field strength B. The nonlinear interaction results in spectral wave energy transfer to lower frequencies, which yields a significant increase in the particle acceleration rate.