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.     

Nanostructured Crystals of Fluorite Phases Sr1 – xRxF2 + x (R Are Rare-Earth Elements) and Their Ordering. 13: Crystal Structure of SrF2 and Concentration Dependence of the Defect Structure of Nonstoichiometric Phase Sr1 – xLaxF2 + x As Grown (x = 0.11, 0.20, 0.32, 0.37, 0.47)

Crystallography Reports - The defect structure of as-grown SrF2 and nonstoichiometric phases Sr1 – xLaxF2 + x (x = 0.11, 0.20, 0.32, 0.37, 0.47) single...     

Growth of $${\text{N}}{{{\text{d}}}_{{{\text{1}}\; - \;y}}}{\text{Eu}}_{y}^{{{\text{2}} + }}{{{\text{F}}}_{{{\text{3}}\; - \;y}}}$$ Single Crystals with Tysonite-Type (LaF3) Structure and Investigation of the Concentration Dependence of Some Their Properties

Crystallography Reports - Nd1 – yEuyF3 – y crystals (y is the molar fraction of EuF2; 0 ≤ y ≤ 0.15) with a tysonite (LaF3) structure have...     

Collective Tunnelling of Strongly Interacting Cold Atoms in a Double-Well Potential

It is known that under resonance conditions, a group of strongly interacting bosonic atoms, trapped in a double-well potential, mimics a single particle, performing Rabi oscillations between the wells. By implication, all atoms need to tunnel at roughly the same time, even though the Bose–Hubbard Hamiltonian accounts only for one-atom-at-a-time transfers. The mechanism of this collective behavior is analyzed, the Rabi frequencies in the process are evaluated, and the limitation of this simple picture is discussed. In particular, it is shown that the small rapid oscillations superimposed on the slow Rabi cycle result from splitting the transferred cluster at the sudden onset of tunnelling, and disappear if tunnelling is turned on gradually.