Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory

We study the general asymptotic behavior of critical points, including those of non-minimal energy type, of the functional for the van der Waals-Cahn-Hilliard theory of phase transitions. We prove that the interface is close to a hypersurface with mean curvature zero when no Lagrange multiplier is present, and with locally constant mean curvature in general. The energy density of the limiting measure has integer multiplicity almost everywhere modulo division by a surface energy constant. Received March 16, 1999 / Accepted June 11, 1999     

High-Pressure Synthesis of Fully Occupied Tetragonal and Cubic Tungsten Bronze Oxides

A high-pressure reaction yielded the fully occupied tetragonal tungsten bronze K₃W₅O₁₅ (K_0.6WO₃). The terminal phase shows an unusual transport property featuring slightly negative temperature-dependence in resistivity (dρ/dT<0) and a large Wilson ratio of R_W=3.2. Such anomalous metallic behavior possibly arises from the low-dimensional electronic structure with a van Hove singularity at the Fermi level and/or from enhanced magnetic fluctuations by geometrical frustration of the tungsten sublattice. The asymmetric nature of the tetragonal tungsten bronze K_xWO₃-K_0.6−yBa_yWO₃ phase diagram implies that superconductivity for x≤0.45 originates from the lattice instability because of potassium deficiency. A cubic perovskite KWO₃ phase was also identified as a line phase—in marked contrast to Na_xWO₃ and Li_xWO₃ with varying quantities of x (<1). This study presents a versatile method by which the solubility limit of tungsten bronze oxides can be extended.     

Two-dimensional thermoelastic analysis of a functionally graded cylindrical panel due to nonuniform heat supply

This paper is concerned with the theoretical treatment of the steady-state thermoelastic problem of a functionally graded cylindrical panel due to nonuniform heat supply in the circumferential direction. The thermal and thermoelastic constants of the cylindrical panel are expressed as power functions of the radial coordinate. We obtain the exact solution for the two-dimensional temperature change in a steady state, and thermal stresses of a simple supported cylindrical panel under the state of plane strain. Some numerical results are shown in figures and tables. Furthermore, the influence of the nonhomogeneity of the material, the radius ratio and the span angle upon the temperature change, displacements and stresses is investigated.     

m × n] metal ion arrays templated by coordination cages

Three-dimensional m × n arrays of metal ion clusters can be assembled as aromatic stacks of planar polynuclear metal complexes within columnar coordination cages. The polynuclear complexes and cage height program the final array structures of the metal ion clusters. Cyclic trinuclear Au(I) complexes (m = 3) assembled into trigonal prismatic arrays (n = 1-3) within the cages and the array structures were clearly shown by X-ray crystallographic analysis. A silver-sandwiched hetero-Au(3)-Ag-Au(3) cluster was also prepared by treating a hexanuclear Au(3)-Au(3) cluster with Ag(I) ion.     

Shape‐Selective Alkylation of Naphthalene over Zeolites: Steric Interaction of Reagents with Zeolites

Steric interaction of reagents with zeolites was studied in isopropylation, sec‐butylation, and tert‐butylation of naphthalene (NP) over several large‐pore zeolites to elucidate the mechanism of selective catalysis. Selectivities for dialkylnaphthalene (DAN) isomers were influenced by the type of zeolite and bulkiness of alkylating agent. Selective formation of β,β‐ and 2,6‐diisopropylnaphthalene (DIPN) occurred only over H‐mordenite (MOR) in the isopropylation of NP using propene; bulky transition states of α,α‐ and α,β‐DIPN are excluded because of steric restriction by the channels, resulting in selective formation of β,β‐ and 2,6‐DIPN. However, low selectivities for β,β‐ and 2,6‐DIPN were observed over the zeolites, SSZ‐24 (AFI), SSZ‐55 (ATS), and SSZ‐42 (IFR) with 12‐membered‐ring (12‐MR) pore entrances of one‐dimensional channels, CIT‐5 (CFI), UTD‐1 (DON), and SSZ‐53 (SFH) with 14‐membered‐ring (14‐MR) pore entrances of one‐dimensional channels, and Y‐zeolite (FAU), zeolite β (BEA), and CIT‐1 (CON) with 12‐MR pore entrances of three‐dimensional channels, because their channels are too large for the exclusion of bulky isomers. Catalysis over these zeolites occurs under kinetic and/or thermodynamic control, resulting in predominant formation of α,α‐ and α,β‐DIPN at lower temperatures and an increase of the stable isomer β,β‐DIPN at higher temperatures. The selectivities for β,β‐ and 2,6‐DAN were enhanced with the increase in bulkiness of alkylating agents: 1‐butene for sec‐butylation and 2‐methylpropene for tert‐butylation. In particular, β,β‐di‐tert‐butylnaphthalene (DTBN) was selectively formed in the tert‐butylation. The selectivities for β,β‐ and 2,6‐DAN were enhanced even in large channels: the transition states of the least bulky isomers only fit the channels because other bulky isomers are excluded by steric restriction of the channels. However, tert‐butylation over FAU, BEA, and CON had selectivities for 2,6‐DTBN of around 50–60%, although selectivities for β,β‐DTBN were almost 100% selectivity; these zeolites can hardly recognize the differences between 2,6‐ and 2,7‐DTBN. The results indicate that the fitting of the least bulky isomers to zeolite channels, leading to the exclusion of other bulky isomers, is essential for highly shape‐selective catalysis.     

Influence of head shape of solid body plunging into water on splash formation

Abstract  

We experimentally investigated the influence of a head shape of a solid body plunging into water on splash formation. Three different head shapes were tested: a hemisphere, cone, and circular cylinder. A hemisphere as a tail shape is common to all three head shapes. We captured images of splash formation using a high-speed CMOS camera. We found that a film flow generated at an early stage when a body impacts the water surface influences subsequent events until the splash sequence is completed. We explain the origin of the film flow according to the principle of conservation of momentum. The film flow as the primary splash originates from water displaced by the head. The meridian line, which connects the head to the tail of the body, affects separation of the film flow and causes the secondary splash. The air cavity generated when the body plunges into the water is also influenced by the head shape. The tertiary splash is formed by a reaction of the air cavity, which is detached from the body. We found that the secondary dome-type splash obstructs growth of the tertiary splash. Thus, we conclude that the head shape affects all events of the splash.     

White light emission of Mn-doped SnO-ZnO-P2O5 glass containing no rare earth cation

The authors have demonstrated white light emission of rare earth (RE)-free Mn-doped SnO-ZnO-P(2)O(5) glass. The RE-free glass shows white light emission with a high value of quantum efficiency (QE) comparable to conventional crystalline phosphor. It is notable that the high QE value is attained for RE-free transparent glass, and the broad emission can be continuously tuned by both the amount of activator and the composition of the glass. Since this glass possesses low-melting property, we emphasize that the glass phosphor will lead to the development of a novel inorganic white-light-emitting device in combination with a solid state UV light-emitting source.     

A new Brézis‐Gallouët‐Wainger inequality from the viewpoint of the real interpolation functors

The Brézis‐Gallouët‐Wainger inequality describes a subtle embedding property into . The relation between the Brézis‐Gallouët‐Wainger inequality and the real interpolation functor together with the sharpness of the results is discussed in the present paper. As our first main results shows, it turns out that there are two intermediate terms between and the logarithmic boundedness, which is supposed to be the right‐hand side of the Brézis‐Gallouët‐Wainger inequality. As the second result, the first result is extended to inequalities which reflect the meaning of the second index of Besov spaces and the interpolation theorem.     

A general regularity theory for weak mean curvature flow

We give a new proof of Brakke’s partial regularity theorem up to $C^{1,\varsigma }$ for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The new proof extends to a general flow whose velocity is the sum of the mean curvature and any given background flow field in a dimensionally sharp integrability class. It is a natural parabolic generalization of Allard’s regularity theorem in the sense that the special time-independent case reduces to Allard’s theorem.     

Synthesis of chiral 3,3′-disubstituted 1,1′-binaphthyl-2,2′-disulfonic acids

A convenient synthesis of chiral 3,3′-disubstituted 1,1′-binaphthyl-2,2′-disulfonic acids (BINSA, 1) was developed. The key was directed ortho-lithiation of BINSA methyl ester 2 with n-BuLi and subsequent reaction with an electrophile. Electrophiles such as Br₂, I₂, Me₃SiOTf, and i-PrOB(Pin) reacted smoothly with 3,3′-dilithiated BINSA methyl ester, and the corresponding 3,3′-dihalo-, 3,3′-bis(trimethylsilyl)-, and 3,3′-diboryl-BINSA derivatives were obtained in yields of 21–78%. This simple synthetic method is highly attractive since the ability to prepare 3,3′-disubstituted BINOLs in advance can be useful.