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Two-phase, miscible, incompressible flow in porous media is governed by a system of nonlinear partial differential equations. Many numerical methods have been given by different authors to this system, but these methods need very high regularity conditions. Actually, in most practical applications these regularity conditions couldn’t be satisfied. In this paper, the problem of discontinuous coefficients with lower regularity conditions is considered and the error estimates are demonstrated.

A highly sensitive all-optical atomic magnetometer based on the magnetooptical effect which uses the advanced technique of single laser beam detection is reported and demonstrated experimentally. A sensitivity of 0.5 pT/Hz1/2 is obtained by analyzing the magnetic noise spectrum, which exceeds that of most traditional magnetometers. This kind of atomic magnetometer is very compact, has a low power consumption, and has a high theoretical sensitivity limit, which make it suitable for many applications.