応用数理

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This paper presents a detailed comparison of CFD-EFD results for the supersonic flow around a next generation supersonic transport. The CFD results show fairly good agreement with each other as well as the experimental data except for following discrepancies : C_D, C_<Lα>, C_<Mα> and the pressure distributions at the leading edge on the upper surface as well as at the outer wing. Detailed studies on the above discrepancies were conducted as follows : sensitivity analysis for parameters of the experiments, repeatability check of the experimental data, geometry measurement of the wing tunnel model, aeroelasticity analysis of the wind tunnel model, and effects of transition. The results show that the discrepancies of C_<Lα> and C_<Mα> are caused by the aeroelastic deformation of the wind tunnel mode. Also the discrepancy of the pressure distributions are caused by the difference of the model geometry and the transition specification. The importance of mutual validation between CFD and EFD was shown through this study.

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A particle simulation method is proposed for computing the dynamics of fiber dispersed system. In this method, a particle is modeled by using arrays of spheres. Considering the deformation of the particle, each pair of adjacent spheres is connected with three types of springs; stretch, bend, and twist. The motion of the particles in flow is followed by solving the translational and rotational equations of motion for each constituent sphere. The hydrodynamic interaction among fibers is considered by the mobility matrix for each fiber and the lubrication force between fibers. The method was well validated for the well-known motion of rodlike particle and fracture theory. The method was applied to predicting the rheological properties of fiber dispersed systems, fiber fracture phenomenon of the fiber reinforced polypropylene, the motion of fillers during an injection molding process of thermoplastics, and the motion of fibers in mixing sections of a single screw extruder.

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A molecular-dynamics technique for determining the adhesion strength of the interfaces between different materials has been developed. This technique evaluates the adhesion strength by calculating the adhesive fracture energy defined as the difference between the total potential energy of the material-connected state and that of the material-separated state. The extended Tersoff-type potential is applied to calculate the adhesive fracture energy of metal/ceramics interfaces as well as metal/metal interfaces. We used the technique to determine the adhesion strength of the interfaces between ULSI-interconnect materials (Al and Cu)and diffusion-barrier materials (TiN and W). Because the adhesion strength determined by this technique agrees well with that measured by scratch testing, this technique is considered to be effective for determining the adhesion strength. It was found that Ru is an effective underlayer material for preventing adhesive fracture of Cu interconnection films.

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Following "Computer-Assisted Proofs I", we will continue to discuss the possibility to 'prove' mathematical theorems with the aid of digital computers and present different methods to approach this goal.

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