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.     

Synthesis of 5-heteroarylazulenes: first selective electrophilic substitution at the 5-position of azulene

1,3-Di-tert-butylazulene reacted with highly electrophilic trifluoromethanesulfonate of N-containing heterocycles to give 5-(dihydroheteroaryl)azulene derivatives in good yield and treatment of the 5-(dihydroheteroaryl)azulene derivatives with KOH afforded 5-(heteroaryl)azulenes in excellent yield.     

Characteristic curved structure derived from collagen-containing tubular giant vesicles under static magnetic field

Collagen-containing tubular giant vesicles (Col–tGVs) under a high static magnetic field were found to constitute characteristic curved structures (e.g. circular, 8-figure, and hairpin-loop), which were sustained by polymerization of collagen units inside the tGV. We ascribed the formation of these structures to the elasticity of the tGV and to the competing diamagnetic anisotropies between collagen and the tGV. These curved structures can be well expressed by the equation of elastica.     

A novel transformation of a 1 : 1 : 1 racemic complex of 2,2'-dihydroxy-1,1'-binaphthyl, Me4N+ Cl- and MeOH into a conglomerate in the solid state by heating or contact with MeOH vapour

The title racemate-to-conglomerate transformation which occurs in the solid state on heating or contact with MeOH vapour has been studied by IR and DTA spectral measurements, microscopic observation, and by X-ray structural and X-ray powder diffraction analysis.