A Frequency-Domain Approach to Watermarking 3D Shapes by Ohbuchi, Mukaiyama, Takahashi

By Ohbuchi, Mukaiyama, Takahashi

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Indeed, if one phase is immobile, then these vectors are collinear). From a physical viewpoint, there is a natural tendency for vapom to rise relative to liquid, which may impose a vertical ordering on the system. GRAHAM J. WEIR 512 From (31), (32) and (36), volumetric flux (for water-steam phases) never points below the corresponding energy flux, since ( 42) and so the mass, energy and volumetric fluxes are ordered vertically, with volumetric fluxes directed above the others; energy flux is directed above mass flux.

Equation (8) may be considered a saturation (or concentration) equation because it is usu::llly a convection-dominated parabolic equation for saturation (or concentration) with coefficients depending on pressure through the total Darcy velocity. In the case of immiscible displacement, the diffusion term R in the saturation equation vanishes at some points (S = 0 or S = 1). The equation degenerates at these points. NUMERICAL SIMULATION AND HOMOGENIZATION OF TWO-PHASE FLOW 523 Reservoir y scale xjma~~oscopic FIG.

E. coefficients depending on both the period

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