Triple crossing numbers of graphs

We introduce the triple crossing number, a variation of crossing number, of a graph, which is the minimal number of crossing points in all drawings with only triple crossings of the graph. It is defined to be zero for a planar graph, and to be infinite unless a graph admits a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs including all complete graphs.Comment: 34 pages, 53 figures: We reorganized the article and revised some argument

Box-counting dimension of solution curves for a class of two-dimensional nonautonomous linear differential systems

A class of two-dimensional linear differential systems is considered. The box-counting dimension of the graphs of solution curves is calculated. Criteria to obtain the box-counting dimension of spirals are also established.Comment: 20 pages, 6 figure

Flankside plasma sheet isolation in the ionosphere for northward interplanetary magnetic field

The Tenth Symposium on Polar Science/Ordinary sessions: [OS] Space and upper atmospheric sciences, Wed. 4 Dec. / Institute of Statistics and Mathematics (ISM) Seminar room 2 (D304) (3rd floor

Chiral Ordering in Supercooled Liquid Water and Amorphous Ice

The emergence of homochiral domains in supercooled liquid water is presented using molecular dynamics simulations. An individual water molecule possesses neither a chiral center nor a twisted conformation that can cause spontaneous chiral resolution. However, an aggregation of water molecules will naturally give rise to a collective chirality. Such homochiral domains possess obvious topological and geometrical orders and are energetically more stable than the average. However, homochiral domains cannot grow into macroscopic homogeneous structures due to geometrical frustrations arising from their icosahedral local order. Homochiral domains are the major constituent of supercooled liquid water and the origin of heterogeneity in that substance, and are expected to be enhanced in low-density amorphous ice at lower temperatures

On the Occurrence of Clathrate Hydrates in Extreme Conditions: Dissociation Pressures and Occupancies at Cryogenic Temperatures with Application to Planetary Systems

We investigate the thermodynamic stability of clathrate hydrates at cryogenic temperatures from the 0 K limit to 200 K in a wide range of pressures, covering the thermodynamic conditions of interstellar space and the surface of the hydrosphere in satellites. Our evaluation of the phase behaviors is performed by setting up quantum partition functions with variable pressures on the basis of a rigorous statistical mechanics theory that requires only the intermolecular interactions as input. Noble gases, hydrocarbons, nitrogen, and oxygen are chosen as the guest species, which are key components of the volatiles in such satellites. We explore the hydrate/water two-phase boundary of those clathrate hydrates in water-rich conditions and the hydrate/guest two-phase boundary in guest-rich conditions, either of which occurs on the surface or subsurface of icy satellites. The obtained phase diagrams indicate that clathrate hydrates can be in equilibrium with either water or the guest species over a wide range far distant from the three-phase coexistence condition and that the stable pressure zone of each clathrate hydrate expands significantly on intense cooling. The implication of our findings for the stable form of water in Titan is that water on the surface exists only as clathrate hydrate with the atmosphere down to a shallow region of the crust, but clathrate hydrate in the remaining part of the crust can coexist with water ice. This is in sharp contrast to the surfaces of Europa and Ganymede, where the thin oxygen air coexists exclusively with pure ice

Lennard-Jones Parameters Determined to Reproduce the Solubility of NaCl and KCl in SPC/E, TIP3P, and TIP4P/2005 Water

Most classical nonpolarizable ion potential models underestimate the solubility values of NaCl and KCl in water significantly. We determine Lennard-Jones parameters of Na+, K+, and Cl– that reproduce the solubility as well as the hydration free energy in dilute aqueous solutions for three water potential models, SPC/E, TIP3P, and TIP4P/2005. The ion–oxygen distance in the solution and the cation–anion distance in salt are also considered in the parametrization. In addition to the target properties, the hydration enthalpy, hydration entropy, self-diffusion coefficient, coordination number, lattice energy, enthalpy of solution, density, viscosity, and number of contact ion pairs are calculated for comparison with 17 frequently used or recently developed ion potential models. The overall performance of each ion model is represented by a global score using a scheme that was originally developed for comparison of water potential models. The global score is better for our models than for the other 17 models not only because of the quite good prediction for the solubility but also because of the relatively small deviation from the experimental value for many of the other properties

Yttrium phosphate microspheres with enriched phosphorus content prepared for radiotherapy of deep-seated cancer

Ceramic microspheres composed of β-emitters are useful for in situ radiotherapy of deep-seated cancer by implantation around the tumor. In addition, microspheres 20–30 µm in diameter can combine β-emission with the embolization effect. Yttrium phosphate is an attractive candidate material for such microspheres, because both Y and P play roles as β-emitters. The half-life of 31P is known to be much larger than that of 90Y. Therefore, it is expected that yttrium phosphate microspheres with high P content can maintain a longer radiotherapy effect. In the present study, preparation of microspheres with enriched P content has been attempted by water-in-oil emulsions using polyphosphate as a starting material. Yttrium phosphate microspheres with a higher P/Y molar ratio (2.5) than in previously reported YPO4 microspheres were obtained. It was found that emulsification for sufficient time (more than 10 min) is necessary to obtain microspheres that are 20–30 µm in size. Although the microspheres released Y sparingly, they released larger amounts of P than previously reported YPO4 microspheres in a simulated body environment. Heat treatment at moderate temperature can suppress P release to some extent. Further improvement in chemical durability through surface modification is essential for long-term clinical use

The behavior of the cusp in various solar wind conditions

The Tenth Symposium on Polar Science/Ordinary sessions: [OS] Space and upper atmospheric sciences, Wed. 4 Dec. /Entrance Hall (1st floor) at National Institute of Polar Research (NIPR