Statistical mechanics of random paths on disordered lattices

The dependence of the universality class on the statistical weight of unrestricted random paths is explicitly shown both for deterministic and statistical fractals such as the incipient infinite percolation cluster. Equally weighted paths (ideal chain) and kinetically generated paths (random walks) belong, in general, to different universality classes. For deterministic fractals exact renormalization group techniques are used. Asymptotic behaviors for the end-to-end distance ranging from power to logarithmic (localization) laws are observed for the ideal chain. In all these cases, random walks in the presence of nonperfect traps are shown to be in the same universality class of the ideal chain. Logarithmic behavior is reflected insingular renormalization group recursions. For the disordered case, numerical transfer matrix techniques are exploited on percolation clusters in two and three dimensions. The two-point correlation function scales with critical exponents not obeying standard scaling relations. The distribution of the number of chains and the number of chains returning to the starting point are found to be well approximated by a log-normal distribution. The logmoment of the number of chains is found to have an essential type of singularity consistent with the log-normal distribution. A non-self-averaging behavior is argued to occur on the basis of the results.     

Circles and spheres in pseudo-Riemannian geometry

Summary A totally umbilical pseudo-Riemannian submanifold with the parallel mean curvature vector field is said to be an extrinsic sphere. A regular curve in a pseudo-Riemannian manifold is called a circle if it is an extrinsic sphere. LetM be ann-dimensional pseudo-Riemannian submanifold of index (0n) in a pseudo-Riemannian manifold with the metricg and the second fundamental formB. The following theorems are proved. For ₀ = +1 or –1, ₁ = +1, –1 or 0 (2–2 ₀+ ₁2n–2–2) and a positive constantk, every circlec inM withg(c, c) = ₀ andg( _c c, _c c) = ₁ k ² is a circle in iffM is an extrinsic sphere. For ₀ = +1 or –1 (–₀n–), every geodesicc inM withg(c, c) = ₀ is a circle in iffM is constant isotropic and B(x,x,x) = 0 for anyx T(M). In this theorem, assume, moreover, that 1n–1 and the first normal space is definite or zero at every point. Then we can prove thatM is an extrinsic sphere. When = 0 orn, this fact does not hold in general.     

Study of open-tubular micro-capillary liquid chromatography

Capillary columns in gas chromatography, first proposed by Golay [1,2], have become well established [3] which have extremely high column efficiencies and separabilities. Everyone could imagine it to be a great tool if such a kind of high efficiency column could be established in liquid chromatography (LC). Microcapillary liquid chromatography (MCLC) may be one way of achieving high-efficiency in terms of theoretical plates. Few papers were published in this field before 1976 [4–6], but more recently, after 1977 [7–15], this field has become one of topical interest in liquid chromatography. Temporarily there are two microcapillary liquid chromatography, that is: ?open-tubular”? [7,8,10–15] and ?packed”? [9] MCLC. In this presentation we focus on open-tubular microcapillary liquid chromatography and a review contemporary developments of ours and others.     

Variety of the molecular conformation in Peptide nanorings and nanotubes

Possible molecular conformations in peptide nanorings and nanotubes were theoretically investigated by a mathematical conformation analysis as well as ab initio Hartree-Fock calculations. The mathematical analysis predicts not only the conventional nanorings having an extended-type (E-type) backbone (trans zigzag) but also the novel ones having bound-type (B-type) backbones with a smaller internal diameter. Ab initio calculations for the amino acid substitution reveal that all 20 encoded residues can form both types of the above nanorings as a local minimum. However, the energetically stable type is determined in accordance with the kind of the replaced side chains. Moreover, the present work theoretically reveals that both types of nanorings stack to form nanotubes through inter-ring hydrogen bonds, i.e., larger E-type nanotubes and smaller B-type nanotubes. Electronically, the HOMO and LUMO states of the nanoring and nanotube backbones are formed by the in-plane pi state. The replacement by the appropriate residues is furthermore predicted to intrude additional levels in the energy gap and to form the frontier states localized at the side chains.     

Detection of wood discoloration in a canker fungus-inoculated Japanese cedar by neutron radiography

Summary Neutron radiography (NRG) was applied to trace the development of discolored tissue in the wood of Japanese cedar (<Emphasis Type=Italic>Cryptomeria japonica</Emphasis>) after being infected with a canker fungus. Japanese cedar seedlings were wound inoculated with a virulent and avirulent isolate of a canker fungus, <Emphasis Type=Italic>Guignardia cryptomeriae</Emphasis>. Three, 7, 13 and 22 days after the inoculation, the seedlings were irradiated with thermal neutrons. The image on the X-ray film showed that the whiteness in the image corresponded to the water content in the sample. Discolored tissue and surrounding dry zones induced by the fungal inoculation were detected as dark areas, indicating water deficiency with a high resolution. Through image analysis, the dry zones were detected as early as 3 days after inoculation. Neutron images also showed the difference in the size of water deficient parts due to the tissue damage among the treatments. The neutron beam dose used in this experiment had no effect on the growth rate of the fungus on a medium, showing that NRG is an effective method for pathological research of trees.