Triangular Boundary Research Articles

New discovery of ZnO whisker in SnZn/Cu solder joints interconnection in concentrator silicon solar cells solder layer

In this work, we have found the formation of ZnO whiskers in SnZn/Cu solder joints interconnection in concentrator silicon solar cells solder layer. Different morphologies of ZnO whiskers were precipitated from rich-Zn phase. During oxidation, the diffusion of Zn atoms induces the formation of voids. The volume expansion (near surface zone) and volume shrinkage (inner zone) both appear in the microstructure matrix, and the tensile stress resulting from oxidation is the driving force for ZnO whisker growth. Net-type oxidation morphology along the triangular grain boundary resulting from that Zn diffuses onto the free surface along the grain boundaries of Sn was found synchronously.

Finite Element Analysis of Porous Medical Grade Cobalt Chromium Alloy Structures Produced by Selective Laser Melting

The recent introduction of selective laser melting (SLM) for the processing of medical grade cobalt chromium (CoCr) alloy has led to a complex shape fabrication of porous custom CoCr alloy implants with controlled porosity to meet the requirements of the anatomy and functions at the region of implantation. This paper discusses finite element (FE) analysis and mechanical characterization of porous medical grade CoCr alloy in cubical structures with volume based porosity ranging between 60% and 80% produced using SLM rapid manufacturing process. Analysis by FE is considered beneficial to predict the effective mechanical properties of the porous structures manufactured by SLM due to minimization of the need for expensive and time consuming physical testing. Cellular structures modelling for fabrication with Direct Metal Laser Sintering machine were designed to vary between 60% and 80% to study the effect of structural variation on mechanical properties of the cellular porous structure. ANSYS 14.0 FE modelling software was used to predict the effective elastic modulus of the samples and comparisons were made with the experimental data. FE results show that with the material properties in the functions of porosities, minimum mesh size of 0.2 mm for triangular shape mesh and boundary as well as load conditions as applied in this study, agreement in equivalent stress, strain and deformation with the experimental results can be achieved to some extent. The technique for FE in this study can be used to investigate stress distribution in three dimensional model of real bone.

A Novel Multivariate Classification Model using Triangular Boundary based Outlier Detection (TBOD) Algorithm to Discover Suspicious Transaction Activity

There is an immense regulatory overhaul over the Money Laundering (ML) threats in financial systems. To build trust and confidence there is an industry wide push to invest more in the Anti-Money Laundering (AML) programs which includes Know Your Customer (KYC), Transaction Monitoring(TM), Trade Surveillance, Fraud Detection and Prevention. These great deals of critical processes require detecting money laundering in the real world financial systems in response to mounting concern over money laundering. Data mining plays a major role to accommodate various types of meaningful and useful information from banking systems. Outlier detection mechanism helps to discover the abnormal behavior in the dataset to identify the suspicious activities in today's world. This paper proposes a novel technique called Triangular Boundary based Outlier Detection (TBOD) Algorithm to detect suspicious activity in banking environments. Segmentation is the preliminary step applied on the dataset to cluster/group the customer based on product usage and associated customer risk. For each customer segment, the profile is modeled to set the boundaries based on historical transaction behaviors. Then, Multivariate classification is applied on the clustered dataset to identify the outliers. Distinct TBOD algorithm has been proposed to model the system and validate it to detect suspicious transactions. The records are arranged as triangular matrix, which visualizes the upper and lower levels of records. The abnormal behavior is identified based on the boundary condition proposed. Various performance measures have been taken to examine the results. The proposed method results in higher precision, recall, sensitivity and specificity values with lesser MAE than the existing SVM K-cross validation, LDOF and K-Means IBK algorithms. It guarantees the accurate detection of outliers in the dataset.

Boundary element analysis of non-planar three-dimensional cracks using complex variables

This paper reports new developments on the complex variables boundary element approach for solving three-dimensional problems of cracks in elastic media. These developments include implementation of higher order polynomial approximations for the boundary displacement discontinuities and more efficient analytical techniques for evaluation of integrals. The approach employs planar triangular boundary elements and is based on the integral representations written in a local coordinate system of an element. In-plane components of the fields involved in the representations are separated and arranged in certain complex combinations. The Cauchy–Pompeiu formula is used to reduce the integrals over the element to those over its contour and evaluate the latter integrals analytically. The system of linear algebraic equations to find the unknown boundary displacement discontinuities is set up via collocation. Several illustrative numerical examples involving a single (penny-shaped) crack and multiple (semi-cylindrical) cracks are presented.

Diagonal Discrete Hodge Operators for Simplicial Meshes Using the Signed Dual Complex

We present a technique to extend the geometric construction of diagonal discrete Hodge operators to arbitrary triangular and tetrahedral boundary conforming Delaunay meshes in the frequent case of piecewise uniform and isotropic material parameters. The technique is based on the novel concept of signed dual complex that originates from a physical argument. In particular, it is shown how the positive definiteness of the mass matrix obtained with the signed dual complex is easily ensured for all boundary conforming Delaunay meshes without requiring-as expected by the common knowledge-that each circumcenter has to lie inside the corresponding element. Eliminating this requirement, whose fulfillment presents otherwise formidable practical difficulties, enables one to easily obtain efficient, consistent, and stable schemes.

BrainPrint: A discriminative characterization of brain morphology

We introduce BrainPrint, a compact and discriminative representation of brain morphology. BrainPrint captures shape information of an ensemble of cortical and subcortical structures by solving the eigenvalue problem of the 2D and 3D Laplace–Beltrami operator on triangular (boundary) and tetrahedral (volumetric) meshes. This discriminative characterization enables new ways to study the similarity between brains; the focus can either be on a specific brain structure of interest or on the overall brain similarity. We highlight four applications for BrainPrint in this article: (i) subject identification, (ii) age and sex prediction, (iii) brain asymmetry analysis, and (iv) potential genetic influences on brain morphology. The properties of BrainPrint require the derivation of new algorithms to account for the heterogeneous mix of brain structures with varying discriminative power. We conduct experiments on three datasets, including over 3000 MRI scans from the ADNI database, 436 MRI scans from the OASIS dataset, and 236 MRI scans from the VETSA twin study. All processing steps for obtaining the compact representation are fully automated, making this processing framework particularly attractive for handling large datasets.

Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases

The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a set of Bethe roots with cardinality equal to N the length of the chain and which satisfies a set of Bethe equations with an additional term. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-12 chain on the segment with two upper triangular boundaries.

Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation

It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace׳s and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy.

An alternative BE–FE formulation for a raft resting on a finite soil layer

This work presents a numerical tool for simulating the interaction of a raft with the soil, which can be a half space or a finite layer supported by a rigid base. The soil is modelled using the boundary element method (BEM) with Kelvin fundamental solutions. Infinite boundary elements (IBEs) are employed for the far field simulation, allowing computational cost reduction without compromising the accuracy. The IBE formulation is based on a triangular boundary element with linear shape functions instead of the commonly used quadrilateral IBEs. Displacements are restrained at the rigid base, when it exists. The raft is modeled with the finite element method (FEM) using a triangular element, which is obtained by combining bending effects and membrane effects. For the FEM–BEM coupling, the BEM tractions are considered as nodal reactions in the FEM formulation. The coupling is established using equilibrium and compatibility conditions, obtaining a system of equations that represents the complete problem.

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

Form factors of the half-infinite XXZ spin chain with a triangular boundary

.The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of form factors of local operators are proposed using bosonization. Sufficient conditions such that the expressions for triangular boundary conditions coincide with those for diagonal boundary conditions are identified. The expressions are compared with known results upon specializations. Using the spin-reversal property, which relates the Hamiltonian with upper and lower triangular boundary conditions, new identities between multiple integrals of infinite products are extracted.

Triangular inequality-based rotation-invariant boundary image matching for smart devices

Nowadays there are many efforts to develop image matching applications exploiting a large number of images stored in smart devices such as smartphones, smart pads, and smart cameras. Boundary image matching converts boundary images to time-series and identifies similar boundary images using time-series matching on those time-series. In boundary image matching, computing the rotation-invariant distance between image time-series is a very time-consuming process since it requires a lot of Euclidean distance computations for all possible rotations. To support the boundary image matching in smart devices, we need to devise a simple but fast computation mechanism for rotation-invariant distances. For this purpose, in this paper we propose a novel rotation-invariant matching solution that significantly reduces the number of distance computations using the triangular inequality. To this end, we first present the notion of self-rotation distance and formally show that the self-rotation distance with the triangular inequality produces a tight lower bound and prunes many unnecessary distance computations. Using the self-rotation distance, we then propose a triangular inequality-based solution to rotation-invariant image matching. We next present the concept of k-self rotation distance as a generalized version of the self-rotation distance and formally show that this $$k$$ k -self rotation distance produces a tighter lower bound and prunes more unnecessary distance computations. Using the $$k$$ k -self rotation distance we also propose an advanced triangular inequality-based solution to rotation-invariant image matching. Experimental results show that our self-rotation distance-based algorithms significantly outperform the existing algorithms by up to one or two orders of magnitude, and we believe that this performance improvement makes our algorithms very suitable for smart devices.

A new BE formulation coupled to the FEM for simulating vertical pile groups

Abstract The aim of this work is to obtain a numerical tool for pile–soil interaction analysis. The soil is modeled as an infinite domain in radial directions. The piles, considered cylindrical, are modeled with the finite element method (FEM), using one-dimensional elements. Displacements and tractions along the shaft are approximated by polynomial functions. The soil is modeled using the boundary element method (BEM) with Kelvin fundamental solutions. Infinite boundary elements (IBEs) are employed for the far field simulation, allowing computational cost reduction without compromising the accuracy. The IBE formulation is based on a triangular boundary element with linear shape functions instead of the commonly used quadrilateral IBEs. By coupling the FEM–BEM formulations, a single system of equations which represents the complete pile–soil interaction problem is obtained.

Correlation functions of the half-infinite XXZ spin chain with a triangular boundary

The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of correlation functions are proposed using bosonization. Sufficient conditions such that the expressions for triangular boundary conditions coincide with those for diagonal boundary conditions are identified. As an application, summation formulae of the boundary expectation values 〈σ1a〉 with a=z,± are obtained. Exploiting the spin-reversal property, relations between n-fold integrals of elliptic theta functions are extracted.

BrainPrint: identifying subjects by their brain.

Introducing BrainPrint, a compact and discriminative representation of anatomical structures in the brain. BrainPrint captures shape information of an ensemble of cortical and subcortical structures by solving the 2D and 3D Laplace-Beltrami operator on triangular (boundary) and tetrahedral (volumetric) meshes. We derive a robust classifier for this representation that identifies the subject in a new scan, based on a database of brain scans. In an example dataset containing over 3000 MRI scans, we show that BrainPrint captures unique information about the subject's anatomy and permits to correctly classify a scan with an accuracy of over 99.8%. All processing steps for obtaining the compact representation are fully automated making this processing framework particularly attractive for handling large datasets.

Research on damage evolution and damage model of 316LN steel during forging

The tensile tests and unloading tensile experiments of 316LN steel were conducted. The damage evolution processes were investigated by optical microscope. The fracture was studied using a Scanning Electron Microscope (SEM) and optical microscope, of which, the chemical compositions were analyzed by Energy Dispersive Spectrometer (EDS). The results show that voids nucleate by decohesion of Al2O3 inclusions–matrix interface and mainly along the grain boundary, especially, at triangular grain boundary junctions. The tensile processes were simulated by Deform2D under different deformation conditions. The critical damage values were obtained. The model between the critical damage value, temperature and strain rate was established by regression analysis. A combination of numerical simulation and upsetting experiments was applied for verifying the accuracy and reliability of critical damage value. These damage values can be used to predict the initiation of voids during 316LN steel hot forging. So, they have important instructional effects on designing forging technology of 316LN steel.

A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method

A new method (the sinh–sigmoidal method) is proposed for the numerical evaluation of both nearly weakly and nearly strongly singular integrals on triangular boundary elements. These integrals arise in the 3D boundary element method when the source point is very close to the element of integration. The new polar coordinate-based method introduces a sinh transformation in the radial direction and a sigmoidal transformation in the angular direction, before the application of Gaussian quadrature. It also uses approximately twice as many quadrature points in the angular direction as in the radial direction, in response to a finding that the evaluation of these types of integrals is particularly sensitive to the placement of the quadrature points in the angular direction. Comparisons with various other methods demonstrate its accuracy and competitiveness. A major advantage of the new method is its ease of implementation and applicability to a wide class of integrals.

Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes

In this paper we develop a new limiter for linear reconstruction on non-coordinate-aligned meshes in two space dimensions, with focus on Cartesian embedded boundary grids. Our limiter is inherently two dimensional and linearity preserving. It separately limits the $x$ and $y$ components of the gradient, as opposed to a scalar limiter which limits all components simultaneously with one scalar. The limiter is based on solving a tiny linear program (LP) on each cell, using a very efficient version of the simplex method. A variety of computational results on triangular and embedded boundary meshes are presented. They demonstrate that the LP limiter successfully removes oscillations and significantly increases solution accuracy compared to a scalar limiter.

Modeling cooling of ready-to-eat meats by 3D finite element analysis: Validation in meat processing facilities

A three-dimensional (3D) finite element model for simulating heat transfer during cooling of irregular-shaped ready-to-eat meat products was developed and validated. The heat transfer model considered conduction as the governing equation, subject to convection, radiation and moisture evaporation boundary conditions. A 3D finite element algorithm developed in Java™ was used to solve the model. The algorithm generated solutions for meshes containing 4-node tetrahedral volume elements and 3-node triangular boundary elements. Product geometries were generated from CT-scan images of the meat products. The model was adapted to receive input parameters that can be easily provided by a meat processors including air relative humidity, air temperature, air velocity, type of casing, duration of water shower, product weight, and estimated core temperature of product prior to entering the cooling chamber. Model validation was conducted in four commercial facilities, under normal processing conditions. Temperatures predicted by the model were in agreement with observed values. Average root-mean-square error (RMSE) was 1.19±0.54°C for core temperatures, 1.73±0.48°C for temperatures 0.05m from core to surface, and 2.01±1.01°C for surface temperatures. The developed heat transfer model was integrated with predictive microbiology models through a food safety website: numodels4safety.unl.edu. The integration can be useful for estimating the severity of cooling deviations and resulting microbiological safety caused by unexpected cooling process disruptions.

Application of group representation theory to derive Hermite interpolation polynomials on a triangle

Current methods used to devise sets of Hermite interpolation polynomials of minimal order that ensure C(n) continuity across triangular element boundaries in two dimensions are not readily extensible to higher dimensions. The extension of such methods is especially difficult when the number of degrees of freedom afforded by data at points is different from the number of degrees of freedom determined by the coefficients of a complete polynomial basis to a particular order. This work introduces a formalism based on group representation theory that can accomplish this task in general. The method is introduced through the derivation of C(1) continuous Hermite polynomials that interpolate data at the three vertices of an equilateral triangular element. These interpolation polynomials are reported here for the first time. The polynomials derived here are compared to the standard polynomials defined in a right triangle by using the two sets of polynomials to solve the Laplace equation over finite elements. The methodology presented here is of use in higher dimensional elements when the complete polynomial degrees of freedom exceed the total C(n) degrees of freedom at the nodes.