Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

Free radical-mediated vinyl amination: a mild, general pyrrolidinyl enamine synthesis

The complete scope of free radical-mediated vinyl amination is described, using 5-exo-trig cyclizations of vinyl radicals to the nitrogen of azomethines. The focus is primarily on N,N-dialkyl enamines since their nucleophilicity renders them the most challenging enamines to synthesize using redox conditions. These studies establish several encouraging precedents for the broader application of this strategy.     

Cyclo[(6-amino-6-deoxy-d-galactonic acid)4]: a new class of carbopeptoid-cyclodextrin

The formation of the 28-membered ring cyclo[(6-amino-6-deoxy-d-galactonic acid)₄] by cyclisation of a protected open chain fully hydroxylated nylon 6 linear tetramer in modest yield provides the first example of a new class of carbopeptoid-cyclodextrin.     

An efficient synthesis of 5-aminoimidazol-2-ones via cyclization reactions of 2-aminoacetonitriles and isocyanates

The scope of a cyclization reaction between amino-acetonitriles and isocyanates was investigated. The study revealed that this reaction tolerates various functional groups leading to highly functionalized 5-amino-imidazole-2-ones, which are useful intermediates for purine synthesis.     

Ideals and Subalgebras in BCI-Algebras

We prove that there exists a maximal ideal of a BCI-algebra X in which each subalgebra is an ideal.AMS Subject Classification (1991): 06F35, 03G25.The second author was supported by the LG Yonam Foundation (1995).     

Codes Over the p-adic Integers

We study codes over the p-adic integers and correct errors in the existing literature. We show that MDS codes exist over the p-adics for all lengths, ranks and p. We show that self-dual codes exist over the 2-adics if and only if the length is a multiple of 8 and that self-dual codes exist over the p-adics with p odd if and only if the length is 0 (mod 4) for p ≡ 3 (mod 4) and 0 (mod 2) for p ≡ 1 (mod 4).     

In‐line monitoring of UV photopolymerization with a quartz crystal resonator

An in‐line monitoring device using a quartz crystal resonator for thin film polymerization was proposed, and its performance has been evaluated by implementing in the UV polymerization of 2‐hydroxyethyl methacrylate with a photoinitiator of 1‐chloroanthraquinone. Because the variation of resonant resistance of the resonator is proportional to the square root of viscosity change that is closely related to the polymerization degree, the resistance can be used as a measure of the polymerization degree. The resistance measurements were compared with the outcome of instrumental analyses of polymerization degree using an FTIR spectrometer and a gel permeation chromatograph. The experimental results showed that the resistance measurements were consistent with the experimental outcome of the instrumental analyses, and this indicates the effectiveness of the proposed device. Owing to the simplicity and availability of the resonator system, its wide utilization in the monitoring of a variety of film polymerization processes, including photoresistor application, is expected. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2428–2439, 2006     

Synthesis and luminescence characteristics of conjugated dendrimers with 2,4,6‐triaryl‐1,3,5‐triazine periphery

We have synthesized conjugated dendrimer with triazine peripheries, and their luminescence properties were investigated. The dendrimers consist of dendritic triazine wedges for electron transport, distyrylbenzene core as an emitting moiety, and t‐butyl peripheral groups for good processing properties. The dendrimers have LUMO values of about ?2.7 eV possibly because of the triazine moiety with high electron affinity. Photoluminescence study indicates that energy transfer occurs from the triazine wedges to the stilbene bridge, and finally to the core chromophore units due to a cascade decrease of bandgap from the peripheral wedge to core moiety. Therefore, the emission wavelength was determined by the structure of the core unit. The energy transfer efficiency of distyrylbenzene‐cored dendrimers was about 75 and 55% for Trz‐1GD‐DSB and Trz‐2GD‐DSB, respectively. A preliminary electroluminescence property also was investigated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 254–263, 2006     

Thermal stability of shear-induced precursor structures in isotactic polypropylene by rheo-X-ray techniques with couette flow geometry

Combined in situ rheo-SAXS (small-angle X-ray scattering) and -WAXD (wide-angle X-ray diffraction) studies using couette flow geometry were carried out to probe thermal stabilty of shear-induced oriented precursor structure in isotactic polypropylene (iPP) at around its normal melting point (162 °C). Although SAXS results corroborated the emerging consensus about the formation of “long-living” metastable mesomorphic precursor structures in sheared iPP melts, these are the first quantitative measures of the limiting temperature at which no oriented structures survive. At the applied shear, rate = 60 s⁻¹ and duration t_s = 5 s, the oriented iPP structures survived a temperature of 185 °C for 1 h after shear, while no stable structures were detected at and above 195 °C. Following Keller's concepts of chain orientation in flow, it is proposed that the chains with highly oriented high molecular weight fraction are primarily responsible for their stability at high temperatures. Furthermore, the effects of flow condition, specifically the shear temperature, on the distributions of oriented and unoriented crystals were determined from rheo-WAXD results. As expected, at a constant flow intensity (i.e., rate = 30 s⁻¹ and duration, t_s = 5 s), the oriented crystal fraction decreased with the increase in temperature above 155 °C, below which the oriented fraction decreased with the decrease in temperature. As a result, a crystallinty “phase” diagram, i.e., temperature versus crystal fraction ratio, exhibited a peculiar “hourglass” shape, similar to that found in many two-phase polymer–polymer blends. This can be explained by the competition between the oriented and unoriented crystals in the available crystallizable species. Below the shear temperature (155 °C), the unoriented crystals crystallized so rapidly that they overwhelmed the crystallization of the oriented crystals, thus depleting a major portion of the crystallizable species and increasing their contribution in the final total crystalline phase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3553–3570, 2006