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.     

Affine scaling algorithm fails for semidefinite programming

In this paper, we introduce an affine scaling algorithm for semidefinite programming (SDP), and give an example of a semidefinite program such that the affine scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and they are non-degenerate everywhere.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

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.     

Adsorption Isotherm of Water Vapor and Its Large Hysteresis on Highly Ordered Mesoporous Silica

The first and second adsorption–desorption isotherms of water vapor on a new mesoporous material derived from kanemite have been measured. The isotherms show unusual type V isotherms and large hysteresis. The type V isotherms, which have never been observed for the other adsorbates, suggest that the mesoporous material has a hydrophobic surface, although the hydrophobicity decreased after treatment with water vapor because of rehydration of the surface. The significantly large hysteresis could be explained by the difference in contact angle between adsorption and desorption.     

Stability of porphyrin-calix[4]arene complexes analyzed by electrospray ionization mass spectrometry

The stability of some porphyrin-calix[4]arene sodium-ion complexes were determined by a collision-activated decomposition (CAD) method utilizing electrospray ionization mass spectrometry (ESI-MS). Comparing the values of E(1/2), the collision energy at which the relative intensity of the complex ion is 0.5, we found that the porphyrin-calix[4]arene complex with the higher value of E(1/2) corresponded to that with the larger association constant (Kass), as measured by 1H-NMR in CDCl3. Both our ESI-MS and NMR studies proved that the number of hydrogen bonds and the rigidity of the calix[4]arene stabilized the complex. The ESI-MS technique could be successful in screening the binding affinity in host-guest systems with a small amount of sample.     

The study of electron beam flue gas treatment for coal-fired thermal plant in Japan

The fundamental research work with simulated coal-fired flue gas was performed in JAERI to get basic data for electron beam treatment of flue gas from thermal power plants in Japan. The standard condition of the experiments was set to be the same as that of next large scale pilot test in Nagoya. The concentrations of NO_x and SO_x were 225 ppm and 800 ppm, respectively. The temperature of the system was 65°C. The effect of multiple irradiation was observed for NO_x removal. The target SO_x and NO_x removals (94% and 80%, respectively) with low NH₃ leakage (less than 10 ppm) were achieved at 9 kGy irradiation with 0.9 NH₃ stoichiometry during 7 hours continuous operation. The facility for the pilot plant (12,000 Nm³/hr) has just built at the site of Shin-Nagoya power plant of Chubu Electric Power Company and will be started in full operation in November 1992.