Synthesis of three-dimensionally arranged porphyrin arrays via intramolecular meso-meso coupling

The synthesis and photophysical properties of three-dimensionally arranged porphyrin arrays with through-space electronic communication are reported. 1,3,5-Trioxamethylphenylene bridged Zn(II) porphyrin trimer 3 was coupled by Ag(I)-promoted oxidative coupling reaction to give porphyrin cage 5 comprising three meso-meso linked diporphyrins, which was then transformed by oxidation with DDQ and Sc(OTf)₃ into porphyrin cage 7 comprising three fused diporphyrins. Intramolecular meso-meso coupling reaction was applied to porphyrin pentamer 11 to provide porphyrin array 12 consisting of a porphyrin core flanked by two meso-meso linked diporphyrins. Further oxidation of 12 with DDQ and Sc(OTf)₃ afforded triply stacked porphyrin array 13 that is comprised of a porphyrin core flanked by two porphyrin tapes. UV-vis-NIR absorption and fluorescence spectra of 5, 7, 12, and 13 showed their distorted conformations and electronic interaction within the stacked porphyrin arrays.     

Optimization of double plasma jet torches in a scramjet combustor

Ignition tests by double plasma jet (PJ) torches in a supersonic flow were conducted. Two PJ torches with different feedstocks were arranged in a straight line in the direction of flow. The Mach number of the airflow was 2.3, and the total temperature and total pressure of the main flow were those of room conditions. A C₂H₄ fuel perpendicularly injected with its sonic speed into the main flow was tested. A combination of O₂–O₂ feedstocks for the two torches was more effective than other combinations such as H₂/N₂–O₂. Moreover, the effectiveness of the double PJs was found to be almost the same as that of a single PJ. These results indicate that combustion reactions of the main fuel injected upstream of the PJ were mostly completed in the vicinity of the upstream PJ. The upstream PJ was considered to be dominant for ignition and the combustion process, indicating that the influence of the downstream PJ was small. On the other hand, the advantage of the double PJs over the single PJ in reducing damage to the torch nozzle was confirmed.     

Periodic solutions for doubly nonlinear evolution equations

We discuss the existence of periodic solution for the doubly nonlinear evolution equation A(u^′(t))+∂?(u(t))∋f(t) governed by a maximal monotone operator A and a subdifferential operator ∂? in a Hilbert space H. As the corresponding Cauchy problem cannot be expected to be uniquely solvable, the standard approach based on the Poincaré map may genuinely fail. In order to overcome this difficulty, we firstly address some approximate problems relying on a specific approximate periodicity condition. Then, periodic solutions for the original problem are obtained by establishing energy estimates and by performing a limiting procedure. As a by-product, a structural stability analysis is presented for the periodic problem and an application to nonlinear PDEs is provided.     

Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations

Every solution u = u(x, t) of the Cauchy–Dirichlet problem for the fast diffusion equation, ? _t (|u| ^m-2 u) = Δu in Ω × (0, ∞) with a smooth bounded domain Ω of ${\mathbb{R}^N}$ and 2 < m < 2* : = 2N/(N ? 2)₊, vanishes in finite time at a power rate. This paper is concerned with asymptotic profiles of sign-changing solutions and a stability analysis of the profiles. Our method of proof relies on a detailed analysis of a dynamical system on some surface in the usual energy space as well as energy method and variational method.