Local convergence of an algorithm for solving optimal control problems

In this paper, a method is proposed for the numerical solution of optimal control problems with terminal equality constraints. The multiplier method is employed to deal with the terminal equality constraints. It is shown that a sequence of control functions, which converges to the optimal control, is obtained by the alternate update of control functions and multipliers.The authors wish to thank Dr. N. Fujii for his most valuable comments and suggestions.     

Study of the pseudo-steady-state kinetics of CO2 hydrate formation and stability

This article describes a dynamic model for formation and stability of CO₂-hydrate on the interface of liquid CO₂(LCO₂) and ocean water at large depths. Experimental results indicate that a thin film of hydrate naturally forms on the interfaces between LCO₂ and water, and inhibits diffusion between the two phases. Experiments further shows that the flux of CO₂ through the hydrate film is dependent of the CO₂-concentration in the ambient sea water. The model proposed here explains these phenomena by introducing four major mechanisms; diffusion of water to the LCO₂-phase, formation of hydrate in the LCO₂-hydrate interface, decay of hydrate in the water-hydrate interface, and diffusion of CO₂ through the water phase. The model explains the CO₂ flux not by diffusion through the hydrate film, but suggest a mechanism of continuous hydrate formation and decay. The overall effect is a “moving,” pseudo-steady-state hydrate film due to transport of CO₂ through the film. The film velocity is dependent of liquid-liquid diffusivity parameters and reaction constant, and lacking experimental values of these parameters, an order–of-magnitude analysis is done by fitting the model to experimentally obtained data for the overall film velocity. The motivation for this work is to elucidate options for CO₂ depositions in deep oceans, of which liquid CO2 sequestration is believed to be one of the most feasible. Spreading of CO₂ from a liquid CO₂-lake and associated lowering of pH in the ecosystem surrounding the lake is of large concern. The work presented here concludes that diffusion of CO₂ in the ocean is largely reduced by the hydrate film and suggests that hydrate formation may alleviate some of the environmental concerns regarding deep ocean sequestration of liquid CO₂. © 1994 John Wiley & Sons, Inc.     

Relationships between oxygen diffusion characteristics of polycrystalline and single crystal 2MgO · TiO2

Self-diffusion coefficients of oxygen in both polycrystalline and single crystal 2MgO·TiO₂ have been measured at an ambient oxygen pressure of about 40 mm Hg over the temperature range 1080–1450°C. A convenient method to estimate the volume diffusion coefficient, D₁, of this polycrystal in which the relative magnitude in D_g (grain boundary diffusion coefficient) with respect to D₁ falls between two extremes, i.e., D_g = D₁ and D_g D₁, is newly proposed, and its plausibility is examined by comparing the resultant D₁ with that of single crystal 2MgO·TiO₂. Not only the magnitude but also the temperature dependence of the “apparent” diffusivity of these polycrystalline particles considerably varied with their particle size. The reason for this semiquantitatively interpreted in terms of the relative magnitude of D_g with respect to D₁.     

Structural and Morphological Changes Associated with Charge Ordering in La0.2Ca0.8MnO3

Both structural and morphological changes associated with charge ordering in perovskite manganese oxide, La_0.2Ca_0.8MnO₃, were studied by electron microscopic observations with imaging plates. Two types of long-period structures were observed at around 107 K, i.e., the structure with about 4-fold periodicity to the unit lattice distance of the room-temperature phase and the structure with much larger periodicity such as 23-fold. These long-period structures were suggested to be formed by a similar mechanism due to charge ordering of manganese ions, since they showed some crystallographic and morphological similarities. Superlattice reflections of a near 4-fold structure were observed as a function of temperature. They were found to become weak diffuse scattering just before the disappearance, and the peak positions moved slightly with heating. Considering those features, the kinetics of the charge ordering in this oxide was discussed.     

Electrophilic aromatic substitution by pummerer reaction of α-sulfinylacetate

Treatment of a mixture of aromatic compound and ethyl α-(methylsulfinyl)acetate (5) with p-toluenesulfonic acid under continuous removal of separated water brought about an intermolecular aromatic substitution to give ethyl α-(methylthio)arylacetate (6). Similar treatment of acylmethyl phenethyl sulfoxide (8) led to cyclization into 1-acylisothiochroman (9).     

Synthesis of 9-(trifluoromethyl)pyrido[1′,2′:1,2]-imidazo[4,5-b]quinoxalines

9-(Trifluoromethyl)pyrido[1′,2′:1,2]imidazo[4,5-b]quinoxalines (9-CF₃-PIQs) were obtained from the cyclization of 2-amino-3-chloro-6-(trifluoromethyl)quinoxaline ( 1a ) with some substituted pyridines. 3-[2-(4-Pyridyl)ethenyl]-9-CF₃-PIQ, one of thus obtained 9-CF₃-PIQs, cyclized with another molecule of 1a to produce the dihydro bis-PIQ-ethene derivative.     

Electromagnetic twisting of a penny-shaped crack in an elastic conducting cylinder

This paper deals with the electromagnetoelastic problem of an elastic, conducting circular cylinder with a penny-shaped crack under a uniform axial current flow and a constant axial magnetic field. The current flow is disturbed by the presence of the crack and the torsional stresses are caused by the interactions between the magnetic field and the disturbed current. Two problems concerning the electric current density field and the electromagnetoelastic field are formulated by means of integral transform techniques and reduced to two Fredholm integral equations of the second kind. Numerical calculations are carried out and stress intensity factors are obtained for several values of the geometric parameters.     

Mechanism for enhancing dispersion of Co3O4 nanoparticles in Co/SiO2 Fischer–Tropsch synthesis catalyst by adding glycol to impregnating solution: a quick‐XAFS study

In situ Co K‐edge quick‐EXAFS (QEXAFS) coupled with temperature‐programmed oxidation as well as ex situ XAFS was applied to investigating the mechanism for enhancing the dispersion of Co₃O₄ nanoparticles in a calcined Co/SiO₂ Fischer–Tropsch synthesis catalyst prepared by adding triethylene glycol (TEG) to a Co(NO₃)₂.6H₂O impregnating solution. Ex situ Co K‐edge XAFS indicated that, regardless of whether the catalysts were prepared with or without using TEG, the hexaaqua Co (II) complex was formed in impregnated samples which then underwent the dehydration process to some extent during the subsequent drying step at 393 K. In situ QEXAFS and ex situ EXAFS results also indicated that small oxide clusters were formed in the TEG‐modified catalyst calcined at ～400–470 K which interacted with polymer species derived from TEG. Since the Fischer–Tropsch synthesis activity of the TEG‐modified catalyst increased with an increase in the calcination temperature in a similar temperature range [Koizumi et al. (2011), Appl. Catal. A, 395 , 138–145], it was suggested that such an interaction enables the clusters to be distributed over the support surface uniformly, resulting in enhancing their dispersion. After combustion of polymer species, Co₃O₄‐like species were formed, and agglomeration of the Co₃O₄‐like species at high calcination temperatures was suppressed by the addition of TEG to the impregnating solution. It was speculated that the addition of TEG induced the formation of some surface silicate which worked as an anchoring site for Co₃O₄ and Co⁰ nanoparticles during calcination and H₂ reduction, respectively.