In this paper, we are concerned with the multi-disc data allocation problem. We shall show that the symbolic Gray code can be used as a data allocation scheme for two-disc systems. We then show that this allocation method is a strictly optimal one for all possible partial match queries. There are many other interesting properties of this allocation method. For example, there is a disc-to-record transformation which can be used to determine the records stored on certain disc. In addition, all records are uniformly stored on discs if this allocation method is used. At the end of this paper, we shall point out that the resulting allocation is good for nearest neighbour searching.

This study investigated the flow bifurcations of flows driven by a pressure gradient in a rectangular curved tube. When fluid flows within a curved tube, due to the centrifugal effect, secondary vortices can be induced in the cross section of the tube. The secondary flow states are dependent on the magnitude of the pressure gradient (q) and the aspect ratio (γ). In this study, the continuation method was applied to investigate the flow bifurcations in a curved tube with increasing pressure gradient (1 < q < 6000) and aspect ratio (0.9 < γ < 1.4).The bifurcation diagrams are composed of solution branches, which are linked by limiting points or bifurcation points. The flow states in a solution branch belong to the same group. The ranges of the flow states and the relationship between the states can also be derived from the bifurcation diagrams. In this study, two types of bifurcation were found, one in the range of 0.9 < γ < 1.17, and another in the range of 1.18 < γ < 1.4. The ranges of stable flow solutions and the distributions of limit and bifurcation points in both pressure gradient and aspect ratio are derived in this study.