Finite element implementation of boundary conditions for the pressure Poisson equation of incompressible flow

In this paper we address the problem of the implementation of boundary conditions for the derived pressure Poisson equation of incompressible flow. It is shown that the direct Galerkin finite element formulation of the pressure Poisson equation automatically satisfies the inhomogeneous Neumann boundary conditions, thus avoiding the difficulty in specifying boundary conditions for pressure. This ensures that only physically meaningful pressure boundary conditions consistent with the Navier-Stokes equations are imposed. Since second derivatives appear in this formulation, the conforming finite element method requires C¹ continuity. However, for many problems of practical interest (i.e. high Reynolds numbers) the second derivatives need not be included, thus allowing the use of more conventional C⁰ elements. Numerical results using this approach for a wall-driven contained flow within a square cavity verify the validity of the approach. Although the results were obtained for a two-dimensional problem using the p-version of the finite element method, the approach presented here is general and remains valid for the conventional h-version as well as three-dimensional problems.     

An Alternative Method to Study Positivity in N-Higgs-Doublet Potentials

N-Higgs-doublet models (NHDM) introduce new sources of CP-violation in an extension of the standard model in the Higgs sector. The NHDMs must satisfy some conditions including the positivity constraint. While the study of positivity in NHDMs is not easy, we present a simple method to study positivity in the case of N doublets by making use of hyperspherical coordinates. This constraint is of great importance as it imposes limits on the coupling constants and thereby on the masses predicted within the model when combined with other constraints such as the positivity of the mass matrix elements.     

A generalization of Eagon–Reiner’s theorem and a characterization of bi-CMt bipartite and chordal graphs

We give a generalization of Eagon-Reiner’s theorem relating Betti numbers of the Stanley-Reisner ideal of a simplicial complex and the CM_t property of its Alexander dual. Then we characterize bi-CM_t bipartite graphs and bi-CM_t chordal graphs. These are generalizations of recent results due to Herzog and Rahimi.     

A framework of irregularity enlightenment for data pre-processing in data mining

Irregularities are widespread in large databases and often lead to erroneous conclusions with respect to data mining and statistical analysis. For example, considerable bias is often resulted from many parameter estimation procedures without properly handling significant irregularities. Most data cleaning tools assume one known type of irregularity. This paper proposes a generic Irregularity Enlightenment (IE) framework for dealing with the situation when multiple irregularities are hidden in large volumes of data in general and cross sectional time series in particular. It develops an automatic data mining platform to capture key irregularities and classify them based on their importance in a database. By decomposing time series data into basic components, we propose to optimize a penalized least square loss function to aid the selection of key irregularities in consecutive steps and cluster time series into different groups until an acceptable level of variation reduction is achieved. Finally visualization tools are developed to help analysts interpret and understand the nature of data better and faster before further data modeling and analysis.     

Influence of Compatibilizer-Type and Processing Approach on the Dispersion of OMMT in High-Density Polyethylene Matrix

High-density polyethylene/organoclay nanocomposites were prepared via melt intercalation in an internal mixer using both a direct mixing and master batching method. Two types of maleic anhydride grafted polyethylene, high-density polyethylene grafted maleic anhydride, and linear low-density polyethylene grafted maleic anhydride, (HDPE-g-MA, LLDPE-g-MA) were used as compatibilizers to enhance the dispersibility of nanoclay in HDPE. Dispersion of organoclay in the nanocomposites was characterized by using X-ray diffraction (XRD), transmission electron microscopy (TEM), and rheological mechanical spectroscopy (RMS). Effects of clay content and degree of clay dispersion on the rheological and tensile properties were also investigated. Furthermore, the effect of order of mixing on the dispersion and distribution of the clay layers was studied. The obtained results showed that organoclay in the nanocomposites were dispersed homogeneously and exfoliated better when HDPE-g-MA and the direct mixing route were used. Although in the master batching method clay intercalated better, clay layers chiefly remain in compatibilizer rich areas. On the other hand, direct mixing was observed to lead to clay particles being dispersed in the HDPE matrix or at the interface of the matrix and compatibilizer and, consequently, better improvement in the tensile modulus was achieved. It was determined that the compatibilizer with the higher miscibility with the matrix was the key factor for achieving better exfoliation of clay sheets.     

A New Construction for Cohen–Macaulay Graphs

Let G be a finite simple graph on a vertex set V(G) = {x ₁₁,…, x _n1}. Also let m ₁,…, m _n  ≥ 2 be integers and G ₁,…, G _n be connected simple graphs on the vertex sets V(G _i ) = {x _i1,…, x _{im i} }. In this article, we provide necessary and sufficient conditions on G ₁,…, G _n for which the graph obtained by attaching the G _i to G is unmixed or vertex decomposable. Then we characterize Cohen–Macaulay and sequentially Cohen–Macaulay graphs obtained by attaching the cycle graphs or connected chordal graphs to arbitrary graphs.     

Experimental investigations of the functional morphology of dragonfly wings

Nowadays, the importance of identifying the flight mechanisms of the dragonfly, as an inspiration for designing flapping wing vehicles, is well known. An experimental approach to understanding the complexities of insect wings as organs of flight could provide significant outcomes for design purposes. In this paper, a comprehensive investigation is carried out on the morphological and microstructural features of dragonfly wings. Scanning electron microscopy （SEM） and tensile testing are used to experimentally verify the functional roles of different parts of the wings. A number of SEM images of the elements of the wings, such as the nodus, leading edge, trailing edge, and vein sections, which play dominant roles in strengthening the whole structure, are presented. The results from the tensile tests indicate that the nodus might be the critical region of the wing that is subjected to high tensile stresses. Considering the patterns of the longitudinal corrugations of the wings obtained in this paper, it can be supposed that they increase the load-bearing capacity, giving the wings an ability to tolerate dynamic loading conditions. In addition, it is suggested that the longitudinal veins, along with the leading and trailing edges, are structural mechanisms that further improve fatigue resistance by providing higher fracture toughness, preventing crack propagation, and allowing the wings to sustain a significant amount of damage without loss of strength.     

Relativistic symmetries in the Hulth6n scalar-vector-tensor interactions

In the presence of spin and pseudospin （p-spin） symmetries, the approximate analytical bound states of the Dirac equation for scalar-vector-tensor Hulth6n potentials are obtained with any arbitrary spin-orbit coupling number using the Pekeris approximation. The Hulth6n tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov-Uvarov （NU） method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given.     

A simple efficient methodology for Dirac equation in minimal length quantum mechanics

We solve the modified Dirac equation by adding a harmonic oscillator potential and implementing the Nikiforov–Uvarov technique. The closed forms of solutions are reported in a quite simple and systematic manner.