Interpretable Housing for Freedom of the Body: The Next Generation of Flexible Homes

If we have gone through the first generation of housing design that pursued functional optimization, ergonomics, and circulation efficiency during the last century, now we are living in the second generation where more advanced goals, such as universal design, ubiquitous design, sustainable design, and environment-friendly design, are emphasized. Al-though this second generation of design focuses upon the wellness of humans in accordance with environment, it still has the attitude that a more precisely designed home can guarantee a better life. What lacks in this approach is the free-dom of the body; it needs to make its own choice as to how to use a space. Thus, it is suggested in this paper that what is important in designing a home is to provide alternatives in daily lives so as to make a full exploration of a given space. These alternatives can be made by offering residents an interpretable space where they can figure out space usages and routs in a constantly changing context. Two spatial devices are discussed in depths as a way to realize this interpretable house: room-to-room enfilade and ring spatial structure. By investigating some existing house plans, it is illustrated how they can guarantee the freedom of the body, and thus alternatives for the flexible domestic life

Construction of class fields over cyclotomic fields

Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ let $k_\mu$ be the ray class field of $k=\mathbb{Q}(e^{2\pi i/\ell})$ modulo $2p^\mu$. We present certain class fields $K_\mu$ of $k$ such that $k_\mu\leq K_\mu\leq k_{\mu+1}$, and find the degree of $K_\mu/k_\mu$ explicitly. And we also construct, in the sense of Hilbert, primitive generators of the field $K_\mu$ over $k_\mu$ by using Shimura's reciprocity law and special values of theta constants

On equivalence of discrete-discrete and continuum-discrete design sensitivity analysis

Developments in design sensitivity analysis (DSA) method have been made using two fundamentally different approaches as shown. In the first approach, a discretized structural finite element model is used to carry out DSA. There are three different methods in the discrete DSA approach: finite difference, semi-analytical, and analytical methods. The finite difference method is a popular one due to its simplicity, but a serious shortcoming of the method is the uncertainty in the choice of a perturbation step size of design variables. In the semi-analytical method, the derivatives of stiffness matrix is computed by finite differences, whereas in the analytical method, the derivatives are obtained analytically. For the shape design variable, computation of analytical derivative of stiffness matrix is quite costly. Because of this, the semi-analytical method is a popular choice in discrete shape DSA approach. However, recently, Barthelemy and Haftka presented that the semi-analytical method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. They found that accuracy problems occur even for a simple cantilever beam. In the second approach, a continuum model of the structure is used to carry out DSA

Ray class fields generated by torsion points of certain elliptic curves

We first normalize the derivative Weierstrass $\wp'$-function appearing in Weierstrass equations which give rise to analytic parametrizations of elliptic curves by the Dedekind $\eta$-function. And, by making use of this normalization of $\wp'$ we associate certain elliptic curve to a given imaginary quadratic field $K$ and then generate an infinite family of ray class fields over $K$ by adjoining to $K$ torsion points of such elliptic curve. We further construct some ray class invariants of imaginary quadratic fields by utilizing singular values of the normalization of $\wp'$, as the $y$-coordinate in the Weierstrass equation of this elliptic curve, which would be a partial result for the Lang-Schertz conjecture of constructing ray class fields over $K$ by means of the Siegel-Ramachandra invariant

Simulation of Multi-Layer-Liquid Sloshing Effects on Vessel Motions by Using Moving Particle Simulation

The coupling and interactions between ship motions and inner-liquid tank sloshing have been investigated by a coupled program between ship motion and sloshing analysis programs. For the sloshing program, Moving Particle Simulation (MPS), which is based on the Lagrangian approach, is used. This sloshing program is validated through comparisons with corresponding experimental results both qualitatively and quantitatively. This validated MPS method has been extended to multi-liquid systems by adding newly adopted models which are buoyancy-correction, surface tension, and boundary conditions at interfaces. Each new model is validated either mathematically or theoretically for comparison. Moreover, a new tracing method of interface particles is suggested by modifying the conventional free-surface searching method in MPS for a single-liquid system. The newly developed MPS for multi-liquid system has been tested for three-liquid sloshing and the obtained results have been compared with the corresponding experimental results. The verified MPS system is coupled with a ship motion program to investigate the sloshing effects on vessel motions. The coupled program was applied to two sloshing tanks, partially filled with fresh water, on a barge-type FPSO. The simulation results were compared with experiments by MARIN and showed good agreement. The most noticeable coupling effects on vessel motions show that the peak frequencies are split and shifted, especially in roll motions. Furthermore, comparison between cases of liquid- and rigid-cargo showed the importance of sloshing effects more clearly. The developed program was also applied to the multi-liquid sloshing problem to consider the wash-tank. In the case of the multi-liquid-layer, there are more than one sloshing natural frequencies, so the relevant physics can be much more complicated compared to the case of a single-liquid-tank. The oscillations of the interfaces have different amplitudes and frequencies. Since the wash-tank contained multi-liquids, short waves at the interface were generated due to Kelvin-Helmholtz instability and the phenomenon was successfully reproduced by the developed MPS-simulation technique