A Consolidation Problem and its Solution

As we know in civil engineering, it is the first task for constructing banks or building structures to predict the subsidence of the underlying ground. When ground of clay saturated with pore water is compressed, the water flows out and the total volume decreases. Consequently, the ground subsides and the strength of the clay increases. We call this phenomena consolidation. For the simplicity of analysis, we usually assume that the thickness of the clay stratum will not vary during consolidation and neglect the effect by its decrease. Alternatively in this paper, we formulate a mathematical model of one dimensional consolidation problem, taking the decrease of the thickness of the clay stratum into consideration. And we show the existence and uniqueness of the exact solution of the problem under the assumption of small initial data

First-principles calculation of field emission from metal surfaces

The field-emission current from realistic metal surfaces is evaluated within the density-functional theory using the Landauer-Buttiker approach. The electronic density in the surface region and the potential barrier induced by the finite electric field are calculated self-consistently using a Green's-function embedding scheme and the full-potential linearized-augmented plane-wave method. Application of this formalism to the (100) and (111) faces of Au and Cu demonstrates the sensitivity of the field-emission current to the surface electronic structure close to the Fermi energy