Twist,tilt, and symmetric grain boundaries in hexagonal materials

Grain boundaries of characteristic geometry, e.g., twist, tilt, and symmetric boundaries are often used as reference boundaries in analyses of boundary networks in polycrystalline materials. This article deals with the issue of proper identification of characteristic boundaries in the case of materials with hexagonal D _6h symmetry. To identify all boundaries of characteristic types, both analytical calculations and numerical searches are used. The first approach provides exact parameters of the characteristic boundaries, whereas the second one gives boundaries which can be classified as characteristic if some tolerance is allowed. In both methods, all symmetrically equivalent boundary representations are taken into consideration. The obtained sets of twist, tilt, symmetric, and 180°-tilt boundaries are presented in the form of two-dimensional maps containing stereographic projections of the corresponding boundary plane normals for selected grain misorientations. These diagrams facilitate interpretation of experimental distributions of grain boundaries; with the representation used, they can be directly linked to experimental distributions. Examples of such diagrams for lattice parameter ratios c/a of $\sqrt{5/2}$ and $\sqrt{20/21}$ are presented. They are compared to example boundary distributions in Ti alloy and distributions of WC/WC boundaries in WC–Co composites available in the literature.     

“Smart” polymeric nanospheres as new materials for possible biomedical applications

Novel random terpolymers of N-isopropylacrylamide (NIPAM), sodium 2-acrylamido-2-methyl-1-propanesulfonate (AMPS), and cinnamoyloxyethylmethacrylate (CEMA) were synthesized by free radical copolymerization using AIBN as an initiator. Five terpolymers were obtained by copolymerization of the monomer mixtures containing a fixed amount of 10 mol % of AMPS while the content of CEMA ranged from 5 to 25 mol % and was changed in 5 mol % increments. The terpolymers obtained are water-soluble. Because of their amphiphilic nature they undergo self-organization in the aqueous solution with the formation of micelles capable of solubilizing sparingly water soluble organic compounds, such as drugs. The terpolymers are susceptible to three external stimuli, i.e. temperature, ionic strength and UV light. Due to the presence of NIPAM in the terpolymers they display the lower critical solution temperature (LCST), the presence of AMPS makes them sensitive to the ionic strength of the solution, while the light-responsiveness of the terpolymers is due to the presence of cinnamoyl chromophores, which undergo photodimerization when irradiated with UV light at about 280 nm. Application of any of these stimuli alone or in combination with other stimuli allows changing the copolymer properties in a controlled way.     

Iterative absolute electroanalytical approach to characterization of bulk redox conducting systems

A novel electroanalytical approach is proposed here, and it is demonstrated with the direct and simultaneous determination of two unknowns: the concentration of redox sites and the apparent diffusion coefficient for charge propagation in a single crystal of dodecatungstophosphoric acid. This Keggin-type polyoxometalate serves as a model bulk redox conducting inorganic material for solid-state voltammetry. The system has been investigated using an ultramicrodisk working electrode in the absence of external liquid supporting electrolyte. The analytical method requires numerical solution of the combination of two equations in which the first one describes current (or charge) in a well-defined (either spherical or linear) diffusional regime and the second general equation describes chronoamperometric (or normal pulse voltammetric current) under mixed (linear-spherical) conditions. The iterative approach is based on successive approximations through calculation and minimizing the least-squares error function. The method is fairly universal, and in principle, it can be extended to the investigation of other bulk systems including sol-gel processed materials, redox melts, and solutions on condition that they are electroactive and well behaved, they contain redox centers at sufficiently high level, and a number of electrons for the redox reaction considered is known.     

Triangular Bézier surface patches in modeling shape of boundary geometry for potential problems in 3D

This paper presents a new boundary shape representation for 3D boundary value problems based on parametric triangular Bézier surface patches. Formed by the surface patches, the graphical representation of the boundary is directly incorporated into the formula of parametric integral equation system (PIES). This allows us to eliminate the need for both boundary and domain discretizations. The possibility of eliminating the discretization of the boundary and the domain in PIES significantly reduces the number of input data necessary to define the boundary. In this case, the boundary is described by a small set of control points of surface patches. Three numerical examples were used to validate the solutions of PIES with analytical and numerical results available in the literature.     

Improving Clairvoyant: reduction algorithm resilient to imbalanced process arrival patterns

The Journal of Supercomputing - The Clairvoyant algorithm proposed in “A novel MPI reduction algorithm resilient to imbalances in process arrival times” was analyzed, commented and...     

Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis

The implementation of periodic boundary conditions (PBCs) is one of the most important and difficult steps in the computational analysis of structures and materials. This is especially true in cases such as mechanical metamaterials which typically possess intricate geometries and designs which makes finding and implementing the correct PBCs a difficult challenge. In this work, we analyze one of the most common PBCs implementation technique, as well as implement and validate an alternative generic method which is suitable to simulate any possible 2D microstructural geometry with a quadrilateral unit cell regardless of symmetry and mode of deformation. A detailed schematic of how both these methods can be employed to study 3D systems is also presented.

     

Consensus models: Computational complexity aspects in modern approaches to the list coloring problem

In the paper we study new approaches to the problem of list coloring of graphs. In the problem we are given a simple graph G=(V,E) and, for every v∈V, a nonempty set of integers S(v); we ask if there is a coloring c of G such that c(v)∈S(v) for every v∈V. Modern approaches, connected with applications, change the question—we now ask if S can be changed, using only some elementary transformations, to ensure that there is such a coloring and, if the answer is yes, what is the minimal number of changes. In the paper for studying the adding, the trading and the exchange models of list coloring, we use the following transformations:

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adding of colors (the adding model): select two vertices u, v and a color c∈S(u); add c to S(v), i.e. set S(v):=S(v)∪{c};

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trading of colors (the trading model): select two vertices u, v and a color c∈S(u); move c from S(u) to S(v), i.e. set S(u):=S(u)?{c} and S(v):=S(v)∪{c};

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exchange of colors (the exchange model): select two vertices u, v and two colors c∈S(u), d∈S(v); exchange c with d, i.e. set S(u):=(S(u)?{c})∪{d} and S(v):=(S(v)?{d})∪{c}.

Our study focuses on computational complexity of the above models and their edge versions. We consider these problems on complete graphs, graphs with bounded cyclicity and partial k-trees, receiving in all cases polynomial algorithms or proofs of NP-hardness.     

Evaluation of artery visualizations for heart disease diagnosis

Heart disease is the number one killer in the United States, and finding indicators of the disease at an early stage is critical for treatment and prevention. In this paper we evaluate visualization techniques that enable the diagnosis of coronary artery disease. A key physical quantity of medical interest is endothelial shear stress (ESS). Low ESS has been associated with sites of lesion formation and rapid progression of disease in the coronary arteries. Having effective visualizations of a patient's ESS data is vital for the quick and thorough non-invasive evaluation by a cardiologist. We present a task taxonomy for hemodynamics based on a formative user study with domain experts. Based on the results of this study we developed HemoVis, an interactive visualization application for heart disease diagnosis that uses a novel 2D tree diagram representation of coronary artery trees. We present the results of a formal quantitative user study with domain experts that evaluates the effect of 2D versus 3D artery representations and of color maps on identifying regions of low ESS. We show statistically significant results demonstrating that our 2D visualizations are more accurate and efficient than 3D representations, and that a perceptually appropriate color map leads to fewer diagnostic mistakes than a rainbow color map.