An ALE mesh movement scheme for long‐term in‐flight ice accretion

The rather irregular shapes that glaze ice may grow into while accreting over the surface of an aircraft represent a major difficulty in the numerical simulation of long periods of in‐flight icing. There is a constant need for remeshing: a wasteful procedure. In the framework of ALE formulations, a mesh movement scheme is presented, in which frame and elasticity analogies are loosely coupled. The resulting deformed mesh preserves the quality of elements, especially in the near‐wall region, where accurate prediction of heat flux and shear stresses is required. The proposed scheme handles mesh deformation in a computationally efficient manner by localizing the mesh deformation. The 2D problem of ice accretion over single and multi‐element airfoils is considered here as a numerical experiment. Experimentally measured glaze ice shapes were used to evaluate the performance of the present approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Enhanced Entanglement and Controlling Quantum Steering in a Laguerre–Gaussian Cavity Optomechanical System with Two Rotating Mirrors

Gaussian quantum steering is a type of quantum correlation in which two entangled states exhibit asymmetry. An efficient theoretical proposal is presented for the control of quantum steering and enhancement of entanglement in a Laguerre–Gaussian (LG) cavity optomechanical system. The system contains two rotating mirrors and a coherently driven optical parametric amplifier (OPA). The numerical results show significantly improved mirror-mirror and mirror-cavity entanglements by controlling the system parameters such as parametric gain, parametric phase, and the frequency of the two rotating mirrors. In addition to bipartite entanglement, our system also exhibits mirror-cavity-mirror tripartite entanglement as well. Another intriguing finding is the control of quantum steering, for which several results were obtained by investigating it for various system parameters. It is shown that the steering directivity is primarily determined by the frequency of two rotating mirrors. Furthermore, for two rotating mirrors, quantum steering is found to be asymmetric both one-way and two-way. Therefore, it can be asserted that the current proposal may help in the understanding of non-local correlations and entanglement verification tasks.     

Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions

Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of Kuhn-Tucker points of a general Hilbertian composite monotone inclusion problem. Applications to systems of coupled monotone inclusions are presented. Our framework does not impose additional assumptions on the operators present in the formulation, and it does not require knowledge of the norm of the linear operators involved in the compositions or the inversion of linear operators.     

Parallel sheet structure in cyclopropane gamma-peptides stabilized by C-H...O hydrogen bonds

A three-residue trans-cyclopropane gamma-peptide adopts an infinite parallel sheet structure in the solid state stabilized by intermolecular C-H...O hydrogen bonds, as demonstrated by single crystal X-ray diffraction.     

An application of a fixed point theorem to best simultaneous approximation

Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.     

Free-Standing CoO-POM Janus-like Ultrathin Nanosheets

A single-step solution-based strategy is used to obtain 2D Janus-like free-standing ultrathin nanosheets build from two structurally unrelated species, that is, polyoxomolybdate (POM) and CoO. A controlled 2D-to-1D morphological transition was achieved by judiciously adjusting the solvent choice. These POM-CoO heterostructures can behave as an ideal catalyst for the epoxidation of styrene. Benefiting from their amphiphilic nature, these 2D POM-CoO nanosheets have also been used as surfactant to emulsify immiscible solvents. It is anticipated that structurally diverse polyoxometalates will offer promise as design elements for variety of structurally and compositionally tunable van der Waals integrated heteromaterials having a broad range applications.     

Convergence of an iterative scheme for multifunctions

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, we generalize some of their results to Suzuki-type multifunctions.     

Fixed point theorems for mappings with convex diminishing diameters on cone metric spaces

In this work, Cantor’s intersection theorem is extended to cone metric spaces and as an application, a fixed point theorem is derived for mappings with locally power diminishing diameters.