Topic
Half-space
About: Half-space is a research topic. Over the lifetime, 2264 publications have been published within this topic receiving 33563 citations.
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143 citations
TL;DR: In this paper, the freeness of cones over truncated affine Weyl arrangements was shown to be characterized by properties around a fixed hyperplane, which was conjectured by Edelman and Reiner.
Abstract: We consider a hyperplane arrangement in a vector space of dimension four or higher. In this case, the freeness of the arrangement is characterized by properties around a fixed hyperplane. As an application, we prove the freeness of cones over certain truncated affine Weyl arrangements which was conjectured by Edelman and Reiner.
140 citations
TL;DR: In this paper, Biot's field equations were used to study dispersion and dissipation of Rayleigh-type surface waves in a porous, elastic half-space filled with a viscous liquid.
Abstract: Dispersion and dissipation of Rayleigh-type surface waves in a porous, elastic half-space filled with a viscous liquid are studied within the framework of Biot's field equations. The algebraic secular equation turns out to be of the seventh degree, its (complex) coefficients being functions of a dimensionless frequency parameter. It is shown that for small and for large values of this parameter the wave is essentially non-dissipative.
A numerical analysis of the secular equation pertaining to a kerosene-saturated sandstone reveals the existence of several extremal values of the phase velocity, a skewed bell-shaped variation of the dissipation per cycle, and a high-frequency cutoff for the surface wave for certain values of the dynamical coefficients.
139 citations
TL;DR: In this article, the scattering and diffraction of plane SV waves underground, circular, cylindrical cavities at various depths in an elastic half space is studied, where the cavities, studied here, are at depths of two to five cavity radii measured from the surface to the center of the cavity.
136 citations
TL;DR: In this article, the steady-state displacements and stresses within a multi-layered viscoelastic half-space generated by a buried or surface point load moving with constant speed parallel to the surface of the half space are obtained by an integral representation of the complete response in terms of wavenumbers.
134 citations