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To solve an urgent problem in the coal industry - forecasting emergency hazardous phenomena in mine workings, taking into account the geodynamic activity of the coal seam, it is advisable to represent such a coal seam in the form of some energy-saturated medium, capable of collapsing under certain conditions and releasing a significant amount of kinetic energy into the array. Based on the results of computer calculations for a particular scheme of drilling and blasting operations, it is possible to identify the moment and place of the outburst origin and evaluate the consequences of filling the working space with crushed coal masses and methane. The paper proposes a new model for modeling the entire ejection process. The model integrates well-developed numerical approaches: the finite element method and Euler solver and the Smoothed Particle Hydrodynamics (SPH) method. The first explicitly simulates the deformation, destruction and destruction of a solid, and the second simulates the flows of an ejected mixture of coal, rock and gases, the third is convenient for simulating explosive charges. The interaction and behavior of geomaterials with different physical and mechanical properties in a coupled model under dynamic loading are illustrated. A simple example is presented to simulate a coal and gas outburst process to demonstrate the potential of a coupled model. The results obtained for various parameters of energy saturation can be applied to the study of the regularities of the occurrence and course of the outburst phenomena. At the same time, the capabilities of the SPH method were tested as part of a combined computational approach for computer calculation of the stress-strain state of a coal-bearing rock mass, taking into account the possibility of an outburst. The main task was to obtain adequate results of the consequences of drilling and blasting operations in a rock mass near an outburst-hazardous coal seam. [ABSTRACT FROM AUTHOR]

The capture of a compact object in a galactic nucleus by a massive black hole (MBH) is the best way to map space and time around it. Compact objects such as stellar black holes on a capture orbit with a very high eccentricity have been wrongly assumed to be lost for the system after an intense burst of radiation, which has been described as a "direct plunge". We prove that these very eccentric capture orbits spend actually a similar number of cycles in a LISA-like detector as those with lower eccentricities if the central MBH is spinning. Although the rates are higher for high-eccentricity EMRIs, the spin also enhances the rates of lower-eccentricity EMRIs. This last kind have received more attention because of the fact that high-eccentricity EMRIs were thought to be direct plunges and thus negligible. On the other hand, recent work on stellar dynamics has demonstrated that there seems to be a complot in phase space acting on these lower-eccentricity captures, since their rates decrease significantly by the presence of a blockade in the rate at which orbital angular momenta change takes place. This so-called "Schwarzschild barrier" is a result of the impact of relativistic precession on to the stellar potential torques, and thus it affects the enhancement on lower-eccentricity EMRIs that one would expect from resonant relaxation. We confirm and quantify the existence of this barrier using a statitical sample of 2,500 direct-summation N-body simulations using both a post-Newtonian but also, and for the first time, a geodesic approximation for the relativistic orbits. The existence of the barrier prevents "traditional EMRIs" from approaching the central MBH, but if the central MBH is spinning the rate will be anyway dominated by highly-eccentric extreme-mass ratio inspirals, which insolently ignore the presence of the barrier, because they are driven by two-body relaxation. [ABSTRACT FROM AUTHOR]