The present author proposed 'Origami Technology', and envisages the formation of a new discipline; mathematical analysis of Origami and its development in academic applications especially in engineering use. Origami structures consisting of zigzagged faces have foldable/deployable functions as well as solidification characters. Models presented in this paper include typical foldable/deployable thin cylinders, conical-shaped membranes, circular sheets which may be folded or wrapped. These shape-changeable origami models are analytically designed by folding or creasing a flat sheet or a thin plate into a 3-dimentional shape. New types of ultra-light 3-D honeycomb core models and a newly developed core panel named "dia-core" (consisting of 2 periodically dimpled panel pieces) are also presented for use in building such as aerospace structures. The former models are designed by analyzing the helical patterns or structures often found in living organisms, because such helical structures are easily deployed due to the presence of fewer dynamic restraints. The latter are developed on purely geometrical basis. As for academic applications of Origami modeling, two examples are shown; the phyllotaxis of leaves or flowers showing helical patterns, and axial buckling and torsional buckling of cylindrical tubes and conical shells are explained by using origami modeling.

View full abstract

Microorganism and insects move through fluid such as water and air by moving their (part of) body. The mechanisms of the locomotion and the flight depend on the flow characteristics. We discuss here the microorganism locomotion before butterfly's flight focusing on the difference. An analytical attempt for flapping flight is also discussed.

View full abstract

We study the scattering problem for the pseudo-conformally invariant nonlinear Schrodinger equation in space-time R^<n+1>. In Section 1, we give a brief survey on nonlinear Schrodinger equations with various critical powers. In Section 2, the scattering problem is formulated. In Section 3, we introduce a recent joint work with R. Carles on new identities of wave operators and associated Poisson formulas.

View full abstract

[in Japanese]

View full abstract