Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Regiocontrol in the oxidative Heck reaction of indole by ligand-enabled switch of the regioselectivity-determining step

Efficient control of regioselectivity is a key concern in transition-metal-catalyzed direct C–H functionalization reactions. Various strategies for regiocontrol have been established by tuning the selectivity of the C–H activation step as a common mode. Herein, we present our study on an alternative mode of regiocontrol, in which the selectivity of the C–H activation step is no longer a key concern. We found that, in a reaction where the C–H activation step exhibits a different regio-preference from the subsequent functionalization step, a ligand-enabled switch of the regioselectivity-determining step could provide efficient regiocontrol. This mode has been exemplified by the Pd(ii)-catalyzed aerobic oxidative Heck reaction of indoles, in which a ligand-controlled C3-/C2-selectivity was achieved for the first time by the development of sulfoxide-2-hydroxypyridine (SOHP) ligands.

Ligand-enabled switch of the regioselectivity-determining step allowed for efficient regiocontrol in the aerobic oxidative Heck reaction of indole.     

Effects of Strain Rate,Temperature and Grain Size on the Mechanical Properties and Microstructure Evolutions of Polycrystalline Nickel Nanowires: A Molecular Dynamics Simulation

Through molecular dynamics(MD)simulation,the dependencies of temperature,grain size and strain rate on the mechanical properties were studied.The simulation results demonstrated that the strain rate from 0.05 to 2 ns~(–1 )affected the Young’s modulus of nickel nanowires slightly,whereas the yield stress increased.The Young’s modulus decreased approximately linearly;however,the yield stress firstly increased and subsequently dropped as the temperature increased.The Young’s modulus and yield stress increased as the mean grain size increased from 2.66 to6.72 nm.Moreover,certain efforts have been made in the microstructure evolution with mechanical properties association under uniaxial tension.Certain phenomena such as the formation of twin structures,which were found in nanowires with larger grain size at higher strain rate and lower temperature,as well as the movement of grain boundaries and dislocation,were detected and discussed in detail.The results demonstrated that the plastic deformation was mainly accommodated by the motion of grain boundaries for smaller grain size.However,for larger grain size,the formations of stacking faults and twins were the main mechanisms of plastic deformation in the polycrystalline nickel nanowire.     

Fatigue life enhancement by irradiation of 12Cr1MoV steel with a Zr<Superscript>+</Superscript> ion beam. Mesoscale deformation and fracture

The structure and properties of 12Cr1MoV steel irradiated with a zirconium ion beam were studied by optical microscopy, scanning electron microscopy, and micro- and nanoindentation. It is shown that the modification covers the entire cross-section of the irradiated specimens to a depth of 1 mm. The data on irradiation-induced structural changes are used to interpret the changes in mechanical properties of the irradiated specimens under static and cyclic loading. Particular attention is given to analysis of strain estimation by the digital image correlation method.