The critical rheology of sheared frictional granular materials near jamming transition is numerically investigated. It is confirmed that there exists a true critical density which characterizes the onset of the yield stress and two fictitious critical densities which characterize the scaling laws of rheological properties. We find the existence of a hysteresis loop between two of the critical densities for each friction coefficient. It is noteworthy that the critical scaling law for frictionless jamming transition seems to be still valid even for frictional jamming despite using fictitious critical density values.

Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa (Prog. Theor. Phys., 121, 647 (2009)). We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a mean field theory and the simulation.

The mineral assemblages of hematite-bearing basic schists in intermediate high-pressure metamorphism are temperature dependent. For assemblages with excess hematite. albite, muscovite and quartz, the paragenetic relations can be dealt with in terms of a fourcomponent system, without omitting or grouping major components.In the Sanbagawa belt in central Shikoku, the dominant amphibole in the hematite-bearing basic schists changes from winchite, via crossite and barroisite to hornblende. The stability of amphibole is described chemographically within a pseudoternary system with another excess phase, epidote. Many amphiboles are chemically heterogeneous owing to retrograde reactions which produced low-TIP amphibole around the prograde amphibole. The examination of amphibole zoning makes it possible to draw a retrograde P-T trajectory which passes on the lower pressure side of the prograde one.