Application of a line implicit method to fully coupled system of equations for turbulent flow problems

For unstructured finite volume methods, we present a line implicit Runge–Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier–Stokes equations. To describe turbulence, we consider a one-equation Spalart–Allmaras turbulence model. The line implicit Runge–Kutta method extends a basic explicit Runge–Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge–Kutta when compared with explicit Runge–Kutta methods accelerated with local time stepping.     

Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

Zirconium oxide dielectric layer grown by a surface sol–gel method for low-voltage,hysteresis-free,and high-mobility polymer field effect transistors

A simple, facile surface sol–gel method is introduced for the fabrication of zirconium oxide films for use as a dielectric layer of a solution-processed polymer field effect transistor (PFET). High dielectric strength is demonstrated for a zirconium oxide layer under room-temperature fabrication conditions using a surface sol–gel method without any post-treatments, which are typically needed in general sol–gel methods. X-ray photoemission spectroscopy showed that the fabricated zirconium oxide layer consists of inorganic ZrO₂ and organic alkoxide groups, which can explain its marginal dielectric constant (∼9) and continuous film properties. In addition, by finishing the surface sol–gel synthesis at the stage of chemisorption, the hydrophobic nature of the final surface was retained, leading to a trap-free semiconductor/dielectric interface. As a result, the PFET made with a conventional polymeric semiconductor rendered nearly hysteresis-free and high mobility (0.3 cm²/V) characteristics at low voltage (<2 V).     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

Site-selective C–H nitration of N-aryl-7-azaindoles under palladium(II) catalysis

The site-selective C–H nitration reaction of 7-azaindoles with t-butyl nitrite under palladium catalysis is described. This protocol provides an efficient method for the construction of ortho-nitrated N-aryl-7-azaindoles with excellent site-selectivity and functional group compatibility. The formed 7-azaindole derivatives can be readily transformed into 7-azaindoles containing an aniline functional group under palladium-catalyzed hydrogenation conditions.     

Phragmen–lindelöf principle for weak subsolutions and cooperative reaction–diffusion systems

One of the principal techniques for treating sustems of reaction–diffusion equations is based on a comparison method using sub and super–solutions. In practice this method is much more effective if non–smooth subsolutions are allowed. In this note we extend the analysis in [2,3] for cooperative systems and prove a comparison principle for a natural and rather general class of weak subsolutions satisfying a Phragmen–Lindelöf condition. An application is then given to a biological model in involving a pair of mutualists.     

Designed Construction of SrTiO3/SrSO4/Pt Heterojunctions with Boosted Photocatalytic H2 Evolution Activity

Efficient separation of photogenerated electron–hole pairs is a crucial factor for high-performance photocatalysts. Effective electron–hole separation and migration could be achieved by heterojunctions with suitable band structures. Herein, a porous SrTiO₃/SrSO₄ heterojunction is prepared by a sol-gel method at room temperature followed by an annealing process. XRD characterization suggests high crystallinity of the heterostructure. A well-defined interface between the two phases is confirmed by high-resolution (HR)TEM. The photocatalytic H₂ evolution productivity of the SrTiO₃/SrSO₄ heterojunction with Pt as co-catalyst reaches 396.82 μmol g⁻¹ h⁻¹, which is 16 times higher than that of SrTiO₃/Pt. The boosted photocatalytic activity of SrTiO₃/SrSO₄/Pt can be ascribed to the presence of SrSO₄, which promotes the transfer and migration of photogenerated carriers by forming the heterojunction and porous structure, which provides a large amount of active sites. This novel porous heterostructure brings new ideas for the development of high-efficiency photocatalysts for H₂ release.     

Application of a Laplace Transform Method to the Study of Binary Mixtures of Spherical and Rod-Like Particles for Low Intensity Levels.

A Laplace Transform (LT) method is used to improve the results obtained in a quasi-elastic scattering (QELS) experiment. This is designed to determine the characteristic parameters of a bimodal solution of spherical and rod-like macromolecules. The theoretical study and the experimental simulation are carried out for low light levels and the results show that the LT technique provides a real alternative to the second order correlation function, g⁽²⁾(τ), in QELS measurements for these particularly difficult experimental conditions.     

Necessary and sufficient conditions for Hölder continuity of Gaussian processes

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition.