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.     

Can a Procedure for the Growth of Single-layer Graphene on Copper be used in Different Chemical Vapor Deposition Reactors?

In the last decade, catalytic chemical vapor deposition (CVD) has been intensively explored for the growth of single-layer graphene (SLG). Despite the scattering of guidelines and procedures, variables such as the surface texture/chemistry of catalyst metal foils, carbon feedstock, and growth process parameters have been well-scrutinized. Still, questions remain on how best to standardize the growth procedure. The possible correlation of procedures between different CVD setups is an example. Here, two thermal CVD reactors were explored to grow graphene on Cu foil. The design of these setups was entirely distinct, one being a “showerhead” cold-wall type, whereas the other represented the popular “tubular” hot-wall type. Upon standardizing the Cu foil surface, it was possible to develop a procedure for cm²-scale SLG growth that differed only by the carrier gas flow rate used in the two reactors.     

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.