Investigation on strength and stability of jointed rock mass using three‐dimensional numerical manifold method

This paper proposes a numerical model for jointed rock masses within the 3‐D numerical manifold method (NMM) framework equipped with a customized contact algorithm. The strength of rock sample containing a few sets of discontinuities is first investigated. The results of models with simple geometries are compared with the available analytical solutions to verify the developed computer code, whereas models with complex geometries are simulated to better understand the fundamental behavior and failure mechanism of jointed rock mass. Furthermore, the stability of jointed rock mass in an underground excavation is studied, where rock failure process is determined by the 3‐D NMM simulation. The simulation results provide valuable guidance on excavation process design and stabilization design in rock engineering practice. Copyright © 2012 John Wiley & Sons, Ltd.     

Electromagnetic inertio-gravity waves in the Earth's ionosphere

Propagation of electromagnetic inertio-gravity (IG) waves in the partially ionized ionospheric E- and F-layers is considered in the shallow water approximation. Accounting of the field-aligned current is the main novelty of the investigation. Existence of two new eigen-frequencies for fast and slow electromagnetic waves is revealed in the ionospheric E-layer. It is shown that in F-layer slowly damping new type of inertial-fast magnetosonic waves can propagate. Slowly damping low-frequency oscillations connected with the field-aligned conductivity are found. Broad spectrum of oscillations is investigated.     

Symplectic adaptive algorithm for solving nonlinear two-point boundary value problems in Astrodynamics

In this paper, from a Hamiltonian point of view, the nonlinear optimal control problems are transformed into nonlinear two-point boundary value problems, and a symplectic adaptive algorithm based on the dual variational principle is proposed for solving the nonlinear two-point boundary value problem. The state and the costate variables within a time interval are approximated by using the Lagrange polynomial and the costate variables at two ends of the time interval are taken as independent variables. Then, based on the dual variational principle, the nonlinear two-point boundary value problems are replaced by a system of nonlinear equations which can preserve the symplectic structure of the nonlinear optimal control problem. Furthermore, the computational efficiency of the proposed symplectic algorithm is improved by using the adaptive multi-level iteration idea. The performance of the proposed algorithm is tested by the problems of Astrodynamics, such as the optimal orbital rendezvous problem and the optimal orbit transfer between halo orbits.     

Radio Observations at 232 MHz and Multifrequency Spectral Studies of SNR HB21

Radio observational results at 232 MHz and multifrequency studies of supernova remnant (SNR) HB21 are presented. Its integrated flux density at 232 MHz is about 390 ± 30 Jy. Both the integrated spectral index and the spatial variations of spectral index of the remnant were calculated by combining the new map at 232 MHz with previously published maps made at 408, 1420, 2695, and 4750 MHz. The SNR has an integrated spectral index of about α = -0.43(S _ν ∝ ν^α) between 232 and 4750 MHz. In general the spectral index varies from –0.5 in southeast and west regions of the remnant to –0.3 in the central region and near the northwest edge. The new data of 232 MHz reveals that there is interaction between the remnant and the surrounding gas along the east edge of the remnant which causes the spectrum flattening at low frequency, while the very good agreement between the structure of X-ray emission and the central flat spectrum area suggests that the existence of thermal emission is the reason of spectrum flattening in the area. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observations of active galactic nuclei with the GT-48 CrAO gamma-ray telescope in 2004

Observations of several active galactic nuclei were performed with the GT-48 gamma-ray telescope at CrAO in 2004: 3C 66A, Mk 421, Mk 501, 1H 1426, 1ES 1959, and BL Lac. Very-high-energy (E ≥ 10¹² eV) gamma-ray fluxes were recorded from 3C 66A, Mk 421, Mk 501, and 1H 1426 at a confidence level of more than 4σ. Upper limits for the flux of very-high-energy gamma rays are presented for 1ES 1959 and BL Lac. The 2004 observational data for 3C 66A (z = 0.44) confirm the results obtained previously at CrAO.     

Accretion onto neutron star: The X-ray spectra and luminosity

The equations of stationary fluid motion are solved for the case of spherical accretion onto non-magnetic, non-rotating neutron star. The X-ray radiation flux is calculated in two different ways: An approximate solution of the moment equations coupled to the gas fluid equations and numerical Monte-Carlo simulation of the photon random walk. We show that the spectrum of the X-ray radiation in the outer parts of the inflowing envelope has a characteristic power-law behaviour. We suggest that some of the properties of the X-ray sources in the globular clusters can be explained with this model.     

Electromagnetic waves and electrostatic oscillations in an inhomogeneous plasma structure at the geomagnetic equator

The measurements of the broadband wave radiation in the region of the geomagnetic equator in the topside ionosphere are presented (the APEX satellite experiment). It has been indicated that the electromagnetic radiation, observed in a plasma density pit, could be related to the formation of a large-scale plasma cavern in the vicinity of the geomagnetic equatorial surface. A large-scale plasma density pit could be formed in the region of heating during damping of plasma vortical structures and electrostatic oscillations, propagating across geomagnetic field lines and crossing the geomagnetic equatorial surface. Brightness of the electromagnetic radiation, observed at frequencies higher than the plasma eigenfrequencies and local plasma and/or upper hybrid frequencies, decreases with increasing eigenfrequencies.     

Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.