Evaluation of linear and nonlinear convection schemes on multidimensional non‐orthogonal grids with applications to KVLCC2 tanker

Almost all evaluations of convection schemes reported in the literature are conducted using simple problems on uniform orthogonal grids; thus, having limited contribution when solving industrial computational fluid dynamics (CFD), where the grids are usually non‐orthogonal with distortions. Herein, several convection schemes are assessed in uniform and distorted non‐orthogonal grids with emphasis on industrial applications. Linear and nonlinear (TVD) convection schemes are assessed on analytical benchmarks in both uniform and distorted grids. To evaluate the performance of the schemes, four error metrics are used: dissipation, phase and L₁ errors, and the schemes' effective order of accuracy. Qualitative and quantitative deterioration of these error metrics as a function of the grid distortion metrics are investigated, and rigorous verifications are performed. Recommendations for effective use of the convection schemes based on the range of grid aspect ratio (AR), expansion ratio (ER) and skewness (Q) are included. A ship hydrodynamics case is studied, involving a Reynolds averaged Navier–Stokes simulation of a bare‐hull KVLCC2 tanker using linear and nonlinear convection schemes coupled with isotropic and anisotropic Reynolds‐stress (ARS) turbulence models using CFDShip‐Iowa v4. Predictions of local velocities and turbulent quantities from the midships to the nominal wake plane are compared with experimental fluid dynamics (EFD), and rigorous verification and validation analyses for integral forces and moments are performed for 0° and 12° drift angles. Best predictions are observed when coupling a second‐order TVD scheme with the anisotropic turbulence model. Further improvements are observed in terms of prediction of the vortical structures for 30° drift when using TVD2S‐ARS coupled with DES. Copyright © 2009 John Wiley & Sons, Ltd.     

Relative T -Injective Modules and Relative T -Flat Modules

Let T be a Wakamatsu tilting module. A module M is called (n, T)-copure injective (resp. (n, T)-copure flat) if ɛ _T ¹ (N, M) = 0 (resp. Γ₁ ^T (N, M) = 0) for any module N with T-injective dimension at most n (see Definition 2.2). In this paper, it is shown that M is (n, T)-copure injective if and only if M is the kernel of an I _n (T)-precover f: A → B with A ∈ Prod T. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is (n, T)-copure injective.     

Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral calculus, each subtype is exemplified. The developed dimension may enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to develop and align educational objectives, teaching activities, and assessments in integral calculus, or how metacognition and metacognitive knowledge could be used to support teaching and learning.     

On a Class of Recursively Enumerable Sets

We define a class of so-called ∑(n)-sets as a natural closure of recursively enumerable sets W_n under the relation “∈” and study its properties.     

Roughness evolution of highly ordered nanoporous anodic aluminum oxide films

In this paper, we report on the surface roughness evolution of highly ordered anodic aluminum oxide (AAO) films based on an atomic force microscopy (AFM) study. Root mean square of the surface roughness was measured on AFM images taken from highly ordered AAO films produced by two-step anodization under different conditions including electrolyte type, anodization voltage, and anodization time. Surface roughness of highly ordered AAO films increases step by step through the two-step anodizing process including electropolishing, first-step anodization, dissolution, and second-step anodization. However, increase of the surface roughness is proportional to the anodization voltage and time. The surface roughness of AAO films changes as a function of length scale until it finally approaches a maximum termed the saturation roughness. The variation of roughness of the growth of AAO could be scaled with an anomalous dynamic behavior as it saturates over a critical length scale while the saturation roughness is dependent on the anodizing time and voltage.     

Study of kinetic,thermodynamic, and isotherm of Sr adsorption from aqueous solutions on graphene oxide (GO) and (aminomethyl)phosphonic acid–graphene oxide (AMPA–GO)

Journal of Radioanalytical and Nuclear Chemistry - In this work, graphene oxide (GO) and (aminomethyl)phosphonic acid–Graphene oxide (AMPA–GO) adsorbents were prepared by the modified...     

A distance function for computing on finite subsets of Euclidean spaces

In practical purposes for some geometrical problems, specially the fields in common with computer science, we deal with information of some finite number of points. The problem often arises here is: “How are we able to define a plausible distance function on a finite three dimensional space?” In this paper, we define such a distance function in order to apply it to further purposes, e.g. in the field settings of transportation theory and geometry. More precisely, we present a new model for traveling salesman problem and vehicle routing problem for two dimensional manifolds in three dimensional Euclidean space, the second problem on which we focus on this line is, three dimensional triangulation.     

Weyl’s Law and Connes’ Trace Theorem for Noncommutative Two Tori

We prove the analogue of Weyl’s law for a noncommutative Riemannian manifold, namely the noncommutative two torus ${\mathbb{T}_{\theta}^{2}}$ equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is achieved by studying the asymptotic distribution of the eigenvalues of the perturbed Laplacian on ${\mathbb{T}_{\theta}^{2}}$ . We also prove the analogue of Connes’ trace theorem by showing that the Dixmier trace and a noncommutative residue coincide on pseudodifferential operators of order ?2 on ${\mathbb{T}_{\theta}^{2}}$ .     

The simple chaotic model of passive dynamic walking

Recent findings on the dynamical analysis of human locomotion characteristics such as stride length signal have shown that this process is intrinsically a chaotic behavior. The passive walking has been defined as walking down a shallow slope without using any muscular contraction as an active controller. Based on this definition, some knee-less models have been proposed to present the simplest possible models of human gait. To maintain stability, these simple passive models are compelled to show a wide range of different dynamics from order to chaos. Unfortunately, based on simplifications, for many years the cyclic period-one behavior of these models has been considered as the only stable response. This assumption is not in line with the findings about the nature of walking. Thus, this paper proposes a novel model to demonstrate that the knee-less passive dynamic models also have the ability to model the chaotic behavior of human locomotion with some modifications. The presented novel model can show chaotic behavior as a stable and acceptable answer using a chaotic function in heel-strike condition. The represented chaotic model is also able to simulate different types of motor deficits such as Parkinson’s disease only by manipulating the value of chaotic parameter. Our model has extensively examined in complexity and chaotic behavior using different analytical methods such as fractal dimension, bifurcation and largest Lyapunov exponent, and it was compared with conventional passive models and the stride signal of healthy subjects and Parkinson patients.