Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Application of total reflection X-ray fluorescence spectrometry to small glass fragments.

Total reflection X-ray fluorescence spectrometry (TXRF) has been applied for trace elemental analysis of small glass fragments. A small glass sample (a fragment with weight less than 0.5 mg) was decomposed by 100 microg of HF/HNO3 acid; the material was condensed to 10 microl and was dried on a Si wafer. Since the size of the dried residue on the Si wafer was less than 1 cm in diameter, an incident X-ray beam with about 1 cm in width could effectively excite elemental components in such a small glass fragment. The precision of the present technique was checked by analyzing the glass fragments (<0.5 mg) from NIST SRM612; the relative standard deviations (RSD) of less than 8.1% were achieved for elemental ratios that were normalized by Sr. Fragments (<0.5 mg) obtained from 23 figured sheet glasses were used as samples for estimating the utility of this technique to forensic discrimination. Comparison of five elemental ratios of Ti/Sr, Mn/Sr, Zn/Sr, Rb/Sr, and Pb/Sr calculated from X-ray fluorescence spectra was effective in distinguishing glass fragments that could not be differentiated by their refractive indexes (RI).     

A Genus-3 Topological Recursion Relation

In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof of this formula is a new relation in the tautological ring of the moduli space of 1-pointed genus-3 stable curves. Research of the first author was partially supported by NSF grant DMS-0204824 Research of the second author was partially supported by NSF grant DMS-0505835     

A fast atom bombardment mass spectrometric analysis of crown ether complexes [1]

Analyses of crown ether complexes of alkali metal ions and characterization of the complexes formed inm-nitrobenzyl alcohol have been carried out by fast atom bombardment (FAB) mass spectrometry. By using m-nitrobenzyl alcohol as a matrix for measurements, the stoichiometry of the complexes was assessed on the basis of the observed FAB peaks. In addition, the formation of crown ether-alkali metal complexes at a 2 : 1 molar ratio was enhanced by increasing the ionic radius of the metal ion in agreement with previous observations. On these grounds, FAB mass spectrometry may provide a rapid means for investigation of the complexation behavior of crown ethers and the stoichiometry of the complexes.     

Keratinized epithelial transport of beta-blocking agents. I. Relationship between physicochemical properties of drugs and the flux across rat skin and hamster cheek pouch.

The maximum fluxes (Jmax) of beta-blockers through keratinized membranes were determined in vitro and compared with their physiochemical parameters such as lipophilicity (log k'0) and melting point (mp). Rat abdominal skin and hamster cheek pouch mucosa were used as the model membranes. Propranolol, metoprolol, timolol, pindolol, nadolol and agenolol were used as beta-blockers with a variety of physicochemical characters. Linear relations of Jmax with either log k'0 or mp were observed both in intact rat skin and in intact hamster cheek pouch, suggesting that the lipophilicity and thermodynamic activity of a drug in the crystal state primarily affect the drug's permeation through these membranes. However, the slope, dJmax/d(log k'0), for cheek pouch mucosa was greater than that for rat skin, corresponding to the lack of appendigeal shunt pathways in cheek pouch. Penetration studies using the delipidized membranes and the isolated stratum corneum sheet of hamster cheek pouch mucosa clarified that the primary rate-limiting barrier function might exist in the lipid layer of the stratum corneum. Jmax values for the tape-stripped and delipidized skins correlated with both the solubilities of drugs in the vehicle and with the mp, suggesting the polar porous characteristics of both model membranes. However, a theoretical approach confirmed that the contribution of an intracellular or aqueous pore route in the intact membrane to the permeation of drugs with positive lipophilic indexes is negligible.     

Synthesis and orientation study of a magnetically aligned liquid‐crystalline chitin/poly(acrylic acid) composite

A high magnetic field of 5 T was used to fabricate a magnetically aligned, optically anisotropic, liquid‐crystalline chitin/poly(acrylic acid) composite. The aligned mesophase was fixed by photoinitiated free‐radical polymerization. From an examination of polarized optical micrographs and an X‐ray diffraction study, a high degree of orientation of 0.70 was observed for the composite with a higher liquid‐crystalline chitin concentration (10.70 wt %); the orientation was reduced with a decreased chitin concentration at a given acrylic acid concentration. The X‐ray data for the developed composite showed a uniplanar orientation for the chitin crystallites, with its molecular long axes perpendicular to the direction of the magnetic field. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 711–714, 2003     

Average heat transfer rates measured and numerically analyzed for combined convection of air in an inclined cylindrical enclosure due to both magnetic and gravitational fields

The average heat transfer rates were measured for natural convection of air in a shallow cylindrical enclosure heated from below and cooled from above in a bore space of an inclined super-conducting magnet. Depending on the location of the enclosure in the bore space, the angle of inclination and the strength of magnetic field, the net acceleration force could be arbitrarily varied and in this report, two locations where mostly axial magnetizing force prevails were selected. The average heat transfer rates varied with the angle of inclination due to the change in the total net acceleration of gravitational and magnetizing forces. Numerical computations were also carried out for the similar system under the combined magnetizing and gravitational forces and the computed average Nusselt numbers agreed mostly with the measured results. Detailed flow modes were graphically presented for the computed cases.     

Growth process of TiC clusters from Ti nanoparticles with evaporated carbon layer

Titanium carbide formation by the solid–solid reaction on the surface of Ti nanoparticles was studied in situ using a high-resolution transmission electron microscope with a heating stage. The cross-sectional image of the Ti surface was clearly observed. Vacuum-deposited carbon covered the whole the surface of Ti nanoparticles in spite of the partly evaporation on the nanoparticle surface. The diffusion of the carbon atoms inside the Ti nanoparticles depended on the size of the nanoparticles. When the Ti nanoparticle diameter was less than 30 nm, carbon atoms diffused into the Ti nanoparticle and formed TiC. The superstructure of the Ti nanoparticles was observed, which revealed the growth process of TiC to be the diffusion of carbon atoms. For Ti nanoparticles with diameter larger than 30 nm it was observed that diffusion of Ti atoms into the carbon layer was dominant, which resulted in formation of TiC in the carbon layer at the surface of Ti nanoparticles.