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.     

Magnetic behavior of the bond random mixed compound FE(BR x I1−x )2(x = 0.9) with Mössbauer spectroscopy

The bond random mixed compound Fe(Br_0.9I_0.1)₂ has been studied by magnetization and Mössbauer measurements. Although the zero-field cooled and field-cooled magnetization variations are not like a typical spin glass one, the Mössbauer spectrum below Néel temperature shows a hyperfine field distribution. It implies that the 10% FeI₂ mixed in FeBr₂ can be induced by the bond random effect which causes the sample to exhibit a spin glass-like behavior.     

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.     

Microchannel-assisted thermal-lens spectrometry for microchip analysis

We present a new method for homocysteine quantitation in human plasma based on in-capillary reaction of homocysteine with 2,2′-dipyridyl disulfide. Homocysteine is in this so-called thiol-exchange reaction quantitatively transformed in mixed disulfide concomitantly with formation of an equimolar amount of 2-thiopyridone that is further separated by micellar electrokinetic chromatography and determined specifically at 343 nm. The concentration of homocysteine is thus estimated indirectly from the result of 2-thiopyridone determination. The linear detection range for concentration versus peak area for the assay was from 0.03–3 mM (correlation coefficient 0.994) with a detection limit of 6 μM and a limit of quantitation 20 μM. The inter-day reproducibility of the peak area and the migration time were 1.37% and 0.05%, respectively. The method is simple, relatively rapid and can be easily automated. Moreover the common capillary electrophoresis apparatus with a UV detector can be used to distinguish between normal and pathological hyperhomocysteinemia plasma samples.