Rational Points on Diagonal Cubic Surfaces

We show under the assumption that the Tate-Shafarevich group of any elliptic curve over the rational numbers is finite that the cubic surface $x_1^3 + p_1p_2x_2^3 + p_2p_3x_3^3 + p_3p_1x_4^3 = 0$ has a rational point, where $p_1, p_2$ and $p_3$ are rational primes congruent to $2$ or $5$ modulo $9$

Truncation Error Analysis of Approximate Operators for a Moving Particle Semi-Implicit Method

This paper considers several approximate operators used in a particle method based on a Voronoi diagram. Under some assumptions on a weight function, we derive truncation error estimates for our approximate gradient and Laplace operators. Our results show that our approximate gradient and Laplace operators tend to the usual gradient and Laplace operators when the ratio (the radius of the interaction area/the radius of a Voronoi cell) is sufficiently large. The key idea of our approach is to divide the integration region into two ring-shaped areas.Comment: 2 figure

Effect of Powder Compaction in Plastic Laser Sintering Fabrication

Powder compaction is introduced into plastic laser sintering fabrication. Compaction was carried out by using a roller of which rotation speed is independently controlled of its traversing speed. This additional process improved packing density of powder bed by a factor of 20% and reduced residual porosity of obtained parts by a factor of 30%. As an advantage, powder compaction can improve mechanical strength of parts of semi-crystalline powder, but increases excessive sinter to reduce fabrication accuracy especially in fabrication of amorphous plastic. This paper presents characteristics of the powder compaction process itself and its effects on performance of obtained parts.Mechanical Engineerin

Process Resolution of Laser Sintering Process Using Plastic Powder Containing Inorganic Filler at a High Rate

Research is being performed on a laser sintering process in which inorganic filler is employed as porogen at a high content to fabricate highly porous three dimensional tissue engineering scaffold. Previously, the scaffold, which included capillary like flow channel network, was used in cell culture test, but obtained cell density was limited due to insufficient fineness of the network structure. In the scaffold fabrication the author experienced degradation of process resolution when inorganic filler was introduced at a high content, but reasons for the low resolution has not been cleared. This paper investigates the dominating cause of the low resolution. Discussion is focused on effect of optical and thermal properties of filler. Experiments using transparent and opaque fillers are performed, and existence of dominating effect of difference in the optical property is denied. Experiments using thermally conductive solid filler and insulating hollow filler is performed, and it is concluded that temperature conductivity is dominating on process resolution.Mechanical Engineerin

対角的三次曲面の有理点

Tohoku University花村 昌樹課

Neutron scattering study on spin correlations and fluctuations in the transition-metal-based magnetic quasicrystal Zn-Fe-Sc

Spin correlations and fluctuations in the 3d-transition-metal-based icosahedral quasicrystal Zn-Fe-Sc have been investigated by neutron scattering using polycrystalline samples. Magnetic diffuse scattering has been observed in the elastic experiment at low temperatures, indicating development of static short-range-spin correlations. In addition, the inelastic scattering experiment detects a $Q$-independent quasielastic signal ascribed to single-site relaxational spin fluctuations. Above the macroscopic freezing temperature $T_{\rm f} \simeq 7$ K, the spin relaxation rate shows Arrhenius-type behavior, indicating thermally activated relaxation process. In contrast, the relaxation rate remains finite even at the lowest temperature, suggesting a certain quantum origin for the spin fluctuations below $T_{\rm f}$.Comment: To be published in Phys. Rev.