Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.     

Oxygen isotope effect of superconducting (Nd1−xCex)2CuO4−δ system

The effect of oxygen isotope substitution on the transition temperature T_c of a superconducting (Nd_1−xCe_x)₂CuO_4−δ system was studied, where the special synthetic method was taken to minimize ambiguous factors on the oxygen concentration and to guarantee the complete substitution of ¹⁶O by ¹⁸O. The isotope exponent in the relationship of T_c∝1/M was estimated to be less than 0.15 by magnetic susceptibility measurements.     

Design of a widely tunable laser with a chirped ladder filter

We theoretically investigated a digitally tunable laser with a chirped ladder filter and a ring resonator to obtain a wide wavelength tuning range covering the whole C- or L- band. The clear relation between the tuning range and laser structure, especially the ladder filter, is described analytically. The introduction of a chirped structure into a ladder filter is effective in achieving both wide tunability and a stable lasing mode. A numerical simulation based on multimode rate equations shows that a tuning range of over 40 nm and a mode suppression ratio over 40 dB can be achieved by introducing a chirped ladder filter.     

Exiguolide, a new macrolide from the marine sponge Geodia exigua

A new 20-membered macrolide designated exiguolide has been isolated from the marine sponge Geodia exigua, and its structure determined by interpretation of spectroscopic data. Exiguolide specifically inhibited fertilization of sea urchin (Hemicentrotus pulcherrimus) gametes but not embryogenesis of the fertilized egg.     

Crosslinked poly(N-isopropylacrylamide) gel for electrophoretic separation and recovery of substances

Crosslinked poly(N-isopropylacrylamide) gel was tested on the feasibility for a preparative electrophoretic matrix. Horse heart myoglobin and bovine hemoglobin were well separated on the gel matrix electrophoretically by molecular sieving effect of the gel network. Relative mobilities of those proteins in the gel were larger than those in a crosslinked polyacrylamide gel of the same polymer concentration. After the separation, the protein-containing portion of the gel underwent swelling at 4°C and deswelling at 37°C, alternatively. As a result of the deswelling, each protein was recovered in a discharged solution out of the gel at almost 100% yield.     

The preparation of nano‐scope chitosan‐oligomer copper complexes and their interaction with DNA

Water‐soluble low molecular weight chitosan of nanometer level and its copper complexes were prepared, and characterized by IR spectra, elemental analysis and gel permeation chromatography (GPC). The modes and mechanism of these copper complexes interaction with DNA were studied by a fluorescent probe method and electrophoresis analysis. It is suggested that there are electrostatic and intercalation modes of copper complexes interacting with DNA. At first, the cationic complex electrostaticly binds to the negatively charged phosphate backbone of DNA, and then a portion of the complex intercalates between the base pairs on the DNA duplex strand. Copyright © 2005 John Wiley & Sons, Ltd.     

Photografting of vinyl polymers onto ultrafine inorganic particles: Photopolymerization of vinyl monomers initiated by AZO groups introduced onto these surfaces

The photografting of polymers onto ultrafine inorganic particles, such as silica and titanium oxide, initiated by azo groups introduced onto these surfaces was investigated. The introduction of azo groups onto the particles was achieved by the reaction of 4,4′-azobis(4-cyanopentanoic acid) with surface isocyanate groups, which were introduced by the treatment with tolylene 2,4-diisocyanate. It was found that the photopolymerization of vinyl monomers, such as methyl methacrylate (MMA), styrene, and N-vinylcarbazole, is initiated by ultrafine particles having azo groups. The corresponding polymers were effectively grafted onto these surfaces through the propagation of the polymer from the surface radicals formed by the photodecomposition of the azo groups: e.g., the percentage of grafting of PMMA and polystyrene onto silica was reached to 112 and 176%, respectively. The percentage of grafting onto silica in the graft polymerization initiated by photodecomposition of surface azo groups was much larger than that initiated by thermal decomposition. Polymer-grafted ultrafine particles thus obtained gave a stable colloidal dispersion in good solvents for the grafted chain. © 1994 John Wiley & Sons, Inc.     

Thermolysis of reactive oligo(p-phenylene sulfide) containing disulfide bond

Oligo(phenylene sulfide) (OPS) containing one disulfide bond at the end of the chain, which was obtained by the oxidative polymerization of diphenyl disulfide, had a relatively low Td_10%(temperature for 10% weight loss) of 412 °C because of degradation of the disulfide bond. But this thermal cleavage of the disulfide bond promoted the curing reaction through thiophenoxy radical formation. OPS was allowed to react with diiodobenzene at 220 °C. The thermal stability of OPS was improved through the consumption of the disulfide bond and the coupling of the chain.     

Enhancement of electronic excitation energy transfer in the colloidal crystals of colloidal silica suspensions doped with fluorescent dyes

The efficiency of electronic excitation energy transfer from photo-excited rhodamine 110 (Rh110, energy donor) to rhodamine B (RhB, energy acceptor) in an exhaustively deionized colloidal silica suspension has been studied. This colloidal suspension shows Bragg reflection due to the formation of colloidal crystals and the Bragg-peak wavelength is controllable by the volume fraction of the silica spheres. When the Bragg-peak wavelength matches with the fluorescence band of Rh110, a depletion was observed in the Rh110 fluorescence spectrum. This means the fluorescence of Rh110 is partially trapped due to the Bragg reflection inside the crystal lattice. In the coexistence of RhB, the enhancement of RhB fluorescence intensity was observed. These facts clearly indicate the trapped photon energy of Rh110 is efficiently transferred to RhB within the colloidal crystals. The quantitative measurements showed that the enhancement of the transfer efficiency is 20% (or slightly more) in the present experimental conditions.