P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

Relativist ic Corrections to the Thermal Sunyaev-Zel''''dovich Power Spectrum

We present a quantitative estimate of the relativistic corrections to the thermal SZ power spectrum produced by the energetic electrons in massive clusters. The corrections are well within 10% for current experiments with working frequencies below v < 100 GHz, but become non-negligible at high frequencies v > 350 GHz. Moreover, the corrections appear to be slightly smaller at higher l or smaller angular scales. We conclude that there is no need to include the relativistic corrections in the theoretical study of the SZ power spectrum especially at low frequencies unless the SZ power spectrum is used for precision cosmology.     

Galaxy formation: Warm dark matter, missing satellites, and the angular momentum problem

We present warm dark matter (WDM) as a possible solution to the missing satellites and angular momentum problem in galaxy formation and introduce improved initial conditions for numerical simulations of WDM models, which avoid the formation of unphysical haloes found in earlier simulations. There is a hint, that because of that the mass function of satellite haloes has been overestimated so far, pointing to higher values for the WDM particle mass. This revised version was published online in August 2006 with corrections to the Cover Date.     

The response of an elastic half‐space under a momentary shear line impulse

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.