Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.     

Graph-Theoretical Method to the Existence of Stationary Distribution of Stochastic Coupled Systems

In this paper, by linking Fokker–Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker–Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator–prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results.     

Another refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for convex functions of several variables defined on simplices.     

Efficient synthesis of 3,4-dihydropyrano[3,2-c]chromenes catalyzed by Ni(II)-functionalized Li<Superscript>+</Superscript>-Montmorillonite in a one-pot fashion under solvent-free conditions

A family of 3,4-dihydropyrano[3,2-c]chromenes were synthesized from 4-hydroxycoumarin and malononitrile via a one-pot reaction under solvent-free conditions at 100 °C catalyzed by Ni@Imine-Li⁺-MMT. This methodology tolerates most of the substrates and has the merits of lower loading of the catalyst, absence of solvents, excellent yields and reusability of the catalyst. A reasonable mechanism is also proposed. This catalytic system can be reused for at least five times with a negligible loss of activity. The prepared catalyst was characterized by using FTIR, TGA, SEM, TEM, uv-DRS, EDX and XRD.     

Evolving groups

The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups are characterized as semidirect products of two nilpotent groups of coprime orders where the action of one on the other is via automorphisms that map each subgroup to a conjugate.     

The Polymer Physics of Multiscale Charge Transport in Conjugated Systems

Conjugated polymers are promising candidates for next‐generation low‐cost flexible electronics. Field‐effect transistors comprising conjugated polymers have witnessed significant improvements in device performance, notably the field‐effect mobility, in the last three decades. However, to truly make these materials commercially competitive, a better understanding of charge‐transport mechanisms in these structurally heterogeneous systems is needed for providing systematic guides for further improvements. This review assesses the key microstructural features of conjugated polymers across multiple length scales that can influence charge transport, with special attention given to the underlying polymer physics. The mechanistic understanding from collective experimental and theoretical studies point to the importance of interconnected ordered domains given the macromolecular nature of the polymeric semiconductors. Based on the criterion, optimization to improve charge transport can be broadly characterized by efforts to (a) promote intrachain transport, (b) establish intercrystallite connectivity, and (c) enhance interchain coupling. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1559–1571     

A conjugated alkyne functional bicyclic polybenzoxazine with superior heat resistance

A difunctional benzoxazine (coPh‐apa) with a conjugated alkyne group is synthesized by the oxidative coupling reaction from a monocycle‐benzoxazine (Ph‐apa) containing an alkyne group. A model compound, 1,4‐diphenylbutadiyne (coPa), is used to study the curing reaction process of coPh‐apa by DSC, Fourier transform infrared spectroscopy, and ¹³C NMR, and the results suggest that the conjugated alkyne groups are involved in the crosslinking reaction via the trimerization reaction of the conjugated alkynyl groups and the Diels–Alder reaction. Furthermore, thermal properties of the polybenzoxazine are studied by dynamic thermomechanical analysis and thermogravimetric analysis. A glass‐transition temperature (T_gs) of as high as 412 °C and a char yield of 75.6% at 800 °C under nitrogen are obtained with the aid of the conjugated alkyne groups. Its excellent heat resistance dominates most thermosetting resins and will serve for heat shields. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1587–1592     

Star-Shaped Ruthenium Complexes as Prototypes of Molecular Gears

The design and synthesis of two families of molecular-gear prototypes is reported, with the aim of assembling them into trains of gears on a surface and ultimately achieving controlled intermolecular gearing motion. These piano-stool ruthenium complexes incorporate a hydrotris(indazolyl)borate moiety as tripodal rotation axle and a pentaarylcyclopentadienyl ligand as star-shaped cogwheel, equipped with five teeth ranging from pseudo-1D aryl groups to large planar 2D paddles. A divergent synthetic approach was followed, starting from a pentakis(p-bromophenyl)cyclopentadienyl ruthenium(II) complex as key precursor or from its iodinated counterpart, obtained by copper-catalyzed aromatic Br/I exchange. Subsequent fivefold cross-coupling reactions with various partners allowed high structural diversity to be reached and yielded molecular-gear prototypes with aryl-, carbazole-, BODIPY- and porphyrin-derived teeth of increasing size and length.