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.     

Isometric embeddings into Heisenberg groups

We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not necessarily sub-Riemannian. We show that if all infinite geodesics in the target are straight lines, then such an embedding must be a homogeneous homomorphism. We discuss a necessary and certain sufficient conditions for the target space to have this ‘geodesic linearity property’, and we provide various examples.     

On structure-preserving connections

In this paper we find the formula of connections under which an almost complex structure is covariantly constant. These types of connections on anti-Kähler–Codazzi manifolds are described. Also, twin metric-preserving connections are analyzed for quasi-Kähler manifolds. Finally, anti-Hermitian Chern connections are investigated.     

Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

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.     

On the New Shear Constraint for Plane-Stress Orthotropic Plasticity Modeling of Sheet Metals

Experimental Mechanics - A shear constraint was very recently proposed by Abedini et al. (Int. J. Solids and Structures 151: 118–134 2018) to evaluate and calibrate advanced non-quadratic...     

Theory and model implementation for analyzing line structures subject to dynamic motions of large deformation and elongation using the absolute nodal coordinate formulation (ANCF) approach

This paper presents the theory development and numerical implementation of a new gradient-deficient-based ANCF (Absolute Nodal Coordinate Formulation) model applied to perform the nonlinear dynamic analysis of elastic line structures subject to large stretching and deformation. The derivations of model equations, introduced numerical approaches, and result validations are the focuses of this study. Different from the traditional rod theory for small stretching consideration, the present model implements the line structures’ large elongation concepts into both the control mechanisms of constitutive formulations and equations of motion. The effect of external hydrodynamic forces on structures is also included in the model formulations. Based on the conservation of energy, the line model developed in this study covers the variation in strain and takes a full account of the bending effect with large stretching. A finite-element-based implicit scheme according to a modified Newmark-beta method is employed to solve the assembled system equations with unknown variables of nodal position vectors, their tangential derivatives, and strains. Selected cases with dynamic motions, such as nonlinear oscillation of a compound pendulum, free falling of a horizontal elastic beam in air with two different settings of gravity, free falling of a submerged horizontal tether with and without an attached concentrated mass, and a submerged vertical tether with a prescribed translational motion, are simulated to verify the developed model by comparing the results with analytical solutions and published experimental data and numerical results. It is found the present ANCF model, as noticed with good matched results with analytical solutions, measurements and other published solutions, is demonstrated to be able to provide converged and reasonably accurate predictions on the responses of line structures subject to large dynamic motions.

     

Bis-amino methylation for the synthesis of spiro-fused piperidines using iron(III) trifluroacetate in aqueous micellar medium

An environmentally benign, multicomponent integrated chemical process has been developed for the synthesis of 3,5-dispirosubstituted piperidines by cyclo-condensation reaction of amines, formaldehyde, and dimedone using iron(III) trifluroacetate [Fe(F₃CCO₂)₃] Lewis acid in aqueous micellar medium at ambient temperature (25–30 °C). The heterogeneous solid acid catalyst conveniently promotes this double amino methylation reaction in which six molecules condense in one pot to form six new covalent bonds. The synthesized 3,5-dispirosubstituted piperidines have been screened for their in vitro antibacterial activity using agar well method. Many of these compounds showed satisfactory antibacterial activity as compared to standard drugs against all the bacteria tested.