Quantum Mechanics for the Swimming of Micro-Organism in Two Dimensions

In two dimensional fluid, there are only two classes of swimming ways of micro-organisms, {\it i.e.}, ciliated and flagellated motions. Towards understanding of this fact, we analyze the swimming problem by using $w_{1+\infty}$ and/or $W_{1+\infty}$ algebras. In the study of the relationship between these two algebras, there appear the wave functions expressing the shape of micro-organisms. In order to construct the well-defined quantum mechanics based on $W_{1+\infty}$ algebra and the wave functions, essentially only two different kinds of the definitions are allowed on the hermitian conjugate and the inner products of the wave functions. These two definitions are related with the shapes of ciliates and flagellates. The formulation proposed in this paper using $W_{1+\infty}$ algebra and the wave functions is the quantum mechanics of the fluid dynamics where the stream function plays the role of the Hamiltonian. We also consider the area-preserving algebras which arise in the swimming problem of micro-organisms in the two dimensional fluid. These algebras are larger than the usual $w_{1+\infty}$ and $W_{1+\infty}$ algebras. We give a free field representation of this extended $W_{1+\infty}$ algebra.Comment: OCHA-PP-48, NDA-FP-16, Latex file, 15p

Design Concept of Pile Foundation to Lateral Load Considering Soil-Pile-Structure Interaction

To rationalize the aseismic design of pile foundations it is essential to make clear the load conditions applied to piles. This paper describes 1) the results of earthquake motion measurement carried out in and around a pile-supported building, 2) the simulation using soil-pile structure lumped mass interaction model and 3) case study of typical combination models of structure and soil. Fundamentally both the seismic loads of super-structure and the forced deformation by surrounding soil should be applied to piles as external loads. In the coupling and evaluation of these loads the dynamic interaction among soil, pile and structure plays a very important role