Entire Solutions with Merging Fronts to Reaction–Diffusion Equations

We deal with a reaction–diffusion equation u _t = u _xx + f(u) which has two stable constant equilibria, u = 0, 1 and a monotone increasing traveling front solution u = φ(x + ct) (c > 0) connecting those equilibria. Suppose that u = a (0 < a < 1) is an unstable equilibrium and that the equation allows monotone increasing traveling front solutions u = ψ₁(x + c ₁ t) (c ₁ < 0) and ψ₂(x + c ₂ t) (c ₂ > 0) connecting u = 0 with u = a and u = a with u = 1, respectively. We call by an entire solution a classical solution which is defined for all . We prove that there exists an entire solution such that for t≈ − ∞ it behaves as two fronts ψ₁(x + c ₁ t) and ψ₂(x + c ₂ t) on the left and right x-axes, respectively, while it converges to φ(x + ct) as t→∞. In addition, if c > − c ₁, we show the existence of an entire solution which behaves as ψ₁( − x + c ₁ t) in and φ(x + ct) in for t≈ − ∞.     

Synthesis of an Alternated Heterobimetallic Supramolecular Polymer Based on Ru(II) and Fe(II)

A heterobimetallic supramolecular polymer (polyRuFe) with alternately complexed Ru(II) and Fe(II) is prepared following a stepwise synthetic route through harnessing first the strongly binding metal ion Ru(II) and then the weakly binding metal ion Fe(II). A high yield of product is achieved in each step. The heterometal ions are incorporated into the polymer chain in identical coordination environments formed by two 2,2′:6′,2″-terpyridine moieties. Characterization is accomplished by NMR spectroscopy, MALDI–TOF mass spectrometry, UV–Vis spectroscopy, and cyclic voltammetry. PolyRuFe shows a wide optical window (λ = 311–577 nm) and a broad distinct reversible redox nature of two types, originated from the coupling of the two heterometallic segments into the polymer chain. Such characteristics of polyRuFe suggest its potential for various electrochemical and electro-optical applications.     

Ta2O5 thin-films deposited by off-axis and on-axis pulsed laser deposition techniques

The crystalline properties of Ta₂O₅ thin films deposited by an off-axis aperture-installation-type pulsed laser deposition technique are investigated and the results are compared with the results for films deposited by the conventional on-axis technique. No significant difference in the substrate temperature dependence is seen between films deposited on-axis or off-axis at a pulse repetition frequency of 30 Hz. When the repetition frequency is lowered, the degree of c-axis orientation is increased in both films. This tendency is more pronounced in the off-axis films. Therefore it is found that the off-axis aperture-installation-type pulsed laser deposition technique is effective not only for decreasing the density of droplets, but also for obtaining more highly c-axis-oriented crystalline films.     

Visco-elastic properties of reentrant nematic liquid crystalline mixtures

The visco-elastic properties for binary mixtures of 4-n -hexyloxy-4′-cyanobiphenyl (6OCB) and 4-n-octyloxy-4′-cyanobiphenyl (8OCB) are investigated in detail by a light scattering technique. The mixtures exhibit a reentrant nematic (RN) phase between the smectic A (SmA) and crystal phases in the range 22.0–29.5 wt % of 6OCB. The viscosity and the elastic constant increase with cooling in both the nematic and reentrant nematic phases. It is also found that the mixtures exhibit anomalously large values of viscosity and elastic constant near the phase transition, i.e. a pretransitional phenomenon can be observed. The activation energy for viscosity is smaller in the RN phase than in the ordinary nematic phase appearing at higher temperatures, while the normalized elastic constant (defined as the ratio of the elastic constant to the square of the dielectric anisotropy) is larger. Moreover, the visco-elastic behaviour depends on the specific time during which the sample has been kept in the SmA phase. These results confirm that the SmA phase has a strong influence on the formation of molecular aggregates, which plays an important role in the reentrant phenomenon of these systems.