Common Edge Research Articles

Crystal structure and hydrogenation properties of Pd5As

The crystal structure of Pd5As was refined simultaneously from laboratory X-ray, synchrotron and neutron powder diffraction data (space group C2/m, a = 551.82(2) pm, b = 774.50(3) pm, c = 842.13(4), β = 99.037(2)°, Z = 4). This is in contrast to earlier work, which describes the structure in the non-centrosymmetric space group C2. Eight palladium atoms form a bicapped trigonal prism around arsenic. Two such polyhedra are connected by a common edge to double prisms (average distance As–Pd 252 pm). Palladium has got coordination numbers of 11 (average distance 276 pm) or 12 (average distance of 278 pm). The crystal structure of Pd5As represents a strongly distorted cubic closest packing as proven by crystallographic group–subgroup relationships. Pd5As does not take up hydrogen up to 5.0 MPa hydrogen pressure and temperatures up to 723 K. Quantum-mechanical calculations using DFT methods using an ab initio evolutionary algorithm confirm the crystal structure of Pd5As and reveal the stability of a hypothetical hydride Pd5AsH. The lack of reactivity might be due to kinetic hindrance because of an endothermic rearrangement of the metal matrix necessary for hydrogen incorporation. Above 5.8 GPa, however, this phase transition becomes thermodynamically favourable, making hydrogenation of Pd5As likely to occur.

Phason space analysis and structure modelling of 100 Å-scale dodecagonal quasicrystal in Mn-based alloy

The dodecagonal quasicrystal classified into the five-dimensional space group P126/mmc, recently discovered in a Mn–Cr–Ni–Si alloy, has been analysed using atomic-resolution spherical aberration-corrected electron microscopy, i.e. high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and conventional transmission electron microscopy. By observing along the 12-fold axis, non-periodic tiling consisting of an equilateral triangle and a square has been revealed, of which common edge length is a = 4.560 Å. These tiles tend to form a network of dodecagons of which size is a ≈ 17 Å in diameter. The tiling was interpreted as an aggregate of 100 Å-scale oriented domains of high- and low-quality quasicrystals with small crystallites appearing at their boundaries. The quasicrystal domains exhibited a densely filled circular acceptance region in the phason space. This is the first observation of the acceptance region in an actual dodecagonal quasicrystal. Atomic structure model consistent with the electron microscopy images is a standard Frank-Kasper decoration of the triangle and square tiles that can be inferred from the crystal structures of Zr4Al3 and Cr3Si. Four kinds of layers located at z = 0, ±1/4 and 1/2 are stacked periodically along the 12-fold axis, and the atoms at z = 0 and 1/2 form hexagonal anti-prisms consistently with the 126-screw axis. The validity of this structure model was examined by means of powder X-ray diffraction.

The Fano Plane and the Strong Independence Ratio in Hypergraphs of Maximum Degree 3

AbstractA set S of vertices in a hypergraph H is strongly independent if no two vertices in S belong to a common edge. The strong independence number of H, denoted , is the maximum cardinality of a strongly independent set in H. The rank of H is the size of a largest edge in H. The hypergraph H is k‐uniform if every edge of H has size k. The transversal number, denoted , of H is the minimum number of vertices that intersect every edge. Our main result is that for all , the strong independence ratio of a hypergraph H with rank k and maximum degree 3 satisfies and this bound is achieved for all . In particular, this bound is achieved for the Fano plane. As an application of our result, we show that if H is a k‐uniform hypergraph on n vertices with m edges and with maximum degree 3 and vertices of degree 3, then . This improves a result due to Chvátal and McDiarmid [Combinatorica 12 (1992), 19–26] who proved that in the case when is even and H has maximum degree 3.

On the sum of the two largest Laplacian eigenvalues of unicyclic graphs

Let G be a simple graph and $S_{2}(G)$ be the sum of the two largest Laplacian eigenvalues of G. Guan et al. (J. Inequal. Appl. 2014:242, 2014) determined the largest value for $S_{2}(T)$ among all trees of order n. They also conjectured that among all connected graphs of order n with m ( $n \leq m\leq2n -3$ ) edges, $G_{m,n}$ is the unique graph which has maximal value of $S_{2}(G)$ , where $G_{m,n}$ is a graph of order n with m edges which has $m-n+1$ triangles with a common edge and $2n-m-3$ pendent edges incident with one end vertex of the common edge. In this paper, we confirm the conjecture with $m=n$ .

Discovery of hard-magnetic domains in two-dimensional arrays of soft-magnetic Fe3O4 nanocubes

In this study, abnormal hard-magnetic domains were discovered in Fe3O4@C composite material, in which well-ordered 16-nm-sized Fe3O4 cubes were tightly embedded into carbon sheets of tens of nanometers thick. It was found that ca. 40 columns of Fe3O4 nanocubes magnetically self-assembled into a single strip-type domain with perpendicular magnetic anisotropy. More strikingly, remarkable domain misalignments, which were very similar to common edge dislocations among atomic planes in crystal lattices, were clearly observed and termed as “domain dislocation” in this work. The hard-magnetic properties of Fe3O4@C material, including large coercivity of 2150 Oe, high MR/MS value of 0.9, and strong anisotropy energy of 3.772 × 105 erg/cm3, were further ascertained by carefully designed electromagnetic absorption contrast experiments. It is anticipated that the discovery of hard-magnetic domains and domain dislocations within 2-D arrays of soft-magnetic nanomaterials will shed new light on the development of high-density perpendicular magnetic recording industry.

Adaptive cell-centered finite volume method for diffusion equations on a consistent quadtree grid

Models applied in image processing are often described by nonlinear PDEs in which a good approximation of gradient plays an important role especially in such cases where irregular finite volume grids are used. In image processing, such a situation can occur during a coarsening based on quadtree grids. We present a construction of a deformed quadtree grid in which the connection of representative points of two adjacent finite volumes is perpendicular to their common boundary enabling us to apply the classical finite volume methods. On the other hand, for such an adjusted grid, the intersection of representative points connection with a finite volume boundary is not a middle point of their common edge and standard methods cannot achieve a good accuracy. In this paper we present a new cell-centered finite volume method to evaluate solution gradients, which results into a solution of a simple linear algebraic system and we prove its unique solvability. Finally we present numerical experiments for the regularized Perona-Malik model in which we applied this new method.

The condition for first slip in a common edge contact subject to in-plane and anti-plane loading

A contact is formed from two elastically similar cylinders of the same diameter and having ends cut at the same angle, not necessarily perpendicular to their axes, pressed end to end. The interface experiences Coulomb friction and the assembly is subject to transverse shear and remote torsion. This constitutes a contact with a mutually defined extent. The condition for and location of the point of first slip are found. It is shown that torsion (anti-plane loading) encourages edge slip and transverse (in-plane) shear encourages slip from an interior point. The necessary condition for adhesion at the edge under the most general condition is derived.

Sound Radiation from a Surface Source Located at the Bottom of the Wedge Region

AbstractApplying rigorous analytical methods, formulas describing the sound radiation have been obtained for the wedge region bounded by two transverse baffles with a common edge and bottom. It has been assumed that the surface sound source is located at the bottom. The presented formulas can be used to calculate the sound pressure and power inside the wedge region. They are valid for any value of the wedge angle and represent a generalization of the formulas describing the sound radiation inside the two and three-wall corner region. Moreover, the presented formulas can be easily adapted for any case when more than one sound source is located at the bottom. To demonstrate their practical application, the distribution of the sound pressure modulus and the sound power have been analyzed in the case of a rectangular piston located at the wedge’s bottom. The influence of the transverse baffle on the sound power has been investigated. Based on the obtained formulas, the behaviour of acoustic fields inside a wedge can be predicted.

Spin-orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model

Specific features of orbital and spin structure of transition metal compounds in the case of the face-sharing MO$_6$ octahedra are analyzed. In this geometry, we consider the form of the spin--orbital Hamiltonian for transition metal ions with double ($e_g^{\sigma}$) or triple ($t_{2g}$) orbital degeneracy. Trigonal distortions typical of the structures with face-sharing octahedra lead to splitting of $t_{2g}$ orbitals into an $a_{1g}$ singlet and $e_g^{\pi}$ doublet. For both doublets ($e_g^{\sigma}$ and $e_g^{\pi}$), in the case of one electron or hole per site, we arrive at a symmetric model with the orbital and spin interaction of the Heisenberg type and the Hamiltonian of unexpectedly high symmetry: SU(4). Thus, many real materials with this geometry can serve as a testing ground for checking the prediction of this interesting theoretical model. We also compare general trends in spin--orbital ("Kugel--Khomskii") exchange interaction for three typical situations: those of MO$_6$ octahedra with common corner, common edge, and the present case of common face, which has not been considered yet.

Temperature dependence of interfacial structures and acidity of clay edge surfaces

In the pursuit of a microscopic understanding of the effects of temperature on the surface reactivity of clay minerals, we conducted first principles molecular dynamics (FPMD) simulations to study the interfacial structures and acidity of clay edge surfaces at elevated temperatures. The common edge surfaces ((010) and (110) types) of phyllosilicates were investigated at 348K and 423K, and the results were compared with those previously derived at ambient conditions. We found that the stable surface sites are the same as at ambient conditions, including Al(OH2)2 (6-fold Al), Al(OH2) (5-fold Al) and Si(OH) on the (010) facet, and Al(OH2), Al(OH)Si and Si(OH) on the (110) surface. The FPMD-based vertical energy gap technique was applied to compute the acidity constants of edge sites and the resulting pKa values show a decreasing trend with temperature. The results demonstrate that although changes in the point of zero charge of the entire material are insignificant up to 348K, the decrease in surface pKa can be 3pKa units, while it can be as large as 6pKa units up to 423K. The derived interface structures and pKa values can be used in future experimental and modeling research, e.g., in interpreting experiments and predicting the surface complexation of metal cations and organics. This study therefore provides a physical basis for investigating the interfacial processes of clay minerals in environments that experience elevated P–T conditions, such as sedimentary basins and geological nuclear waste repositories.

Dodecagonal quasicrystal in Mn-based quaternary alloys containing Cr, Ni and Si

A dodecagonal quasicrystal showing 12-fold symmetry forms in Mn-rich quaternary alloys containing 5.5 or 7.5 at.% Cr, 5.0 at.% Ni and 17.5 at.% Si. After annealing at 700 °C for 130 h, the quasicrystal precipitated in a matrix of β-Mn-type crystalline phase. The shape of the quasicrystal is needle-like having a length of several tens of micrometres. Electron diffraction as well as powder X-ray diffraction experiments has revealed the following characteristics of the quasicrystal: diffraction symmetry 12/mmm, the presence of systematic extinction for h1h2h2h1h5-type reflections with odd h5 index, and then five-dimensional space group P126/mmc. Indexing of the reflections indicated that the dimension of the common edge in the equilateral triangle–square tiling is 4.560 Å, and the periodicity is 4.626 Å along the 12-fold axis. This is the first example of the dodecagonal quasicrystal synthesized by ordinary metallurgical method in 3-d transition-metal alloys.

Synthesis, Crystal Structures, and Characterization of Three Novel Copper Complexes Based on N-acylsalicylhydrazone and Different Secondary Ligands

The reactions of copper acetate and (2-hydroxybenzylidene)-2-phenylacetohydrazide (L1) and/or (2-chlorophenoxy)-N’-(2-hydroxybenzylidene) acetohydrazide (L2) in the presence of different secondary ligands, piperazine (pipe), pyridine (Py), and urotropine (Ur), in the solution of methanol and dimethyl formamide (V:V = 10:2) yielded three novel copper complexes, formulated as [CuL1]2(pipe)·2DMF 1, [Cu(Py)(L2)]2 2, and [Cu(L2)](Ur)·DMF 3, respectively. These three compounds have been characterized structurally using single-crystal diffraction. In 1, the copper complexes are bridged by pipe ligands to result in dimers. The pipe ligand serves as a μ2 bridge. In 2, two square-pyramids Cu(N2O3) polyhedrons share a common edge to form a dinuclear compound. In 3, the copper complexes are linked by Ur ligands to result in the formation of chain structure. The three compound exhibit similar luminescence at λmax = 440, 460, and 680 nm upon excitation at 354 nm, respectively.

Plant beta‐diversity is enhanced around grassland–forest edges within a traditional agricultural landscape

AbstractQuestionsAre there positive edge effects on beta‐ and alpha‐diversity of plant species across semi‐natural grassland–secondary forest gradients located within a traditional agricultural landscape? Is beta‐diversity (dissimilarity in plant species composition between two given plots) well explained by environmental differences for both grasslands and forests? Do gradients of environmental factors created by forest edges influence spatial variation in alpha‐diversity from edges to grasslands and forests?LocationSemi‐natural grasslands and secondary forests (or conifer plantation) around paddy fields in a traditional agricultural landscape, western Japan.MethodsVegetation survey and environmental (soil water content and sunlight) measurements were conducted on 11 transects passing through grassland–forest ecosystems. Spatial variations in plant beta‐ and alpha‐diversity and environmental variables and their relationships were examined.ResultsWe quantitatively demonstrated common positive edge effects on beta‐diversity in both grasslands and forests. Our results suggest that among‐edge variations in light conditions, which likely depend on edge aspect and forest type, promote high grassland plant beta‐diversity in the vicinity of edges. However, the high beta‐diversity of forest floor communities in the proximity of edges cannot be explained by this mechanism. Alpha‐diversity tended to be lower within grassland plots located around edges than in grassland interiors, while the richness of the forest community increased toward the edge. This alpha‐diversity pattern was suggested to be attributable to resource gradients created by the forest edges.ConclusionsAlthough plant alpha‐diversity may not be consistently high in the vicinity of edges, beta‐diversity in the communities bordering grassland–forest edges will generally be high in the traditional agricultural landscape. Thus, maintenance of environmental heterogeneity among grassland–forest edges in agricultural ecosystems should be prioritized for local biodiversity conservation.

Joint reconstruction of multi-channel, spectral CT data via constrained total nuclear variation minimization

We explore the use of the recently proposed ‘total nuclear variation’ (TVN) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued images and has the advantage of encouraging common edge locations and a shared gradient direction among image channels. We show how it can be incorporated into a general, data-constrained reconstruction framework and derive update equations based on the first-order, primal-dual algorithm of Chambolle and Pock. Early simulation studies based on the numerical XCAT phantom indicate that the inter-channel coupling introduced by the TVN leads to better preservation of image features at high levels of regularization, compared to independent, channel-by-channel TV reconstructions.

Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar

In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establishing a rooted cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the nine unique 6-bar linkages with ground-connected inputs that can be constructed from the five distinct 6-bar mechanisms, Watt I–II and Stephenson I–III. Results also automatically produced the loop equations for all 153 unique linkages with a ground-connected input that can be constructed from the 71 distinct 8-bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1DOF linkages with revolute joints up to 8 bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.

First Principles Study on Structural Stability of Belite

A first-principles study was carried out to investigate the stability of the crystal structure of beta-form belite (beta-C2S) substituted by Sr atoms as trace impurities for Ca atoms in CaOx polyhedra. The effect of the connection types of CaOx polyhedral, in the form of common-edge bond and common-face bond, upon the crystal stability is described. The Ca-Ca interatomic distance closely relates to the hydraulic activity of beta-C2S. The beta-C2S substituted by an Sr atom for Ca(1) atoms having seven Ca-O bonds is energetically more stable than that substituted by an Sr atom for Ca(2) atoms having eight Ca-O bonds. The Sr-doped beta-C2S having a common face bond with SrOx polyhedra is energetically more favorable and results in structural stability compared with that having a common edge bond with SrOx polyhedra.

Synthesis, Crystal Structure, and Properties of Mn(PO3F)(H2O)2

AbstractSingle crystals of manganese(II) fluorophosphate dihydrate, Mn(PO3F)(H2O)2, were grown in a metathesis reaction from aqueous solutions of MnCl2 and (NH4)2(PO3F). The crystal structure [P$\bar{1}$, Z = 2, a = 5.5280(7), b = 5.6357(7), c = 8.2570(10) Å, α = 81.279(2), β = 75.156(2), γ = 71.722(2)°, 1345 structure factors, 86 parameter, R[F2 > 2σ(F2)] = 0.0322, wR(F2 all) = 0.0771] consists of [MnO4(H2O)2] octahedra that share a common edge to form isolated double octahedra of the type [Mn2O2/2O4/1(H2O)4/1]. Each double octahedron is bridged by the oxygen atoms of six (PO3F) tetrahedra to six neighboring double octahedra into a layered arrangement parallel to (001). Adjacent layers are held together through weak O–H···O hydrogen bonds, and no significant hydrogen bonding interactions of the type O–H···F are observed. Vibrational spectra are discussed in terms of a site‐symmetry approximation for the (PO3F)2– anion. The thermal decomposition of Mn(PO3F)(H2O)2 starts above 130 °C. In a multi‐stage mechanism the end‐product Mn2P2O7 is formed at temperatures above 500 °C. Magnetic measurements suggest an antiferromagnetic ordering of Mn(PO3F)(H2O)2 at 3.4 K.

The removal of additional edges in the edge detection of potential field data

Edge detection results of potential field data are used to delineate the horizontal locations of the causative sources, and there are many edge detection filters to finish this work. However, most of balanced edge detection filters produce additional edges which interpret the potential field data that contain positive and negative anomalies. First, we test the application effect of several common balanced edge detection filters, and then analyze the reason that produces additional edges. We present several new edge detection filters depending on the distribution features of different derivatives that will not produce additional edges. The new filters are demonstrated on synthetic gravity anomalies, which show the edges more precisely, and are insensitive to noise. We also apply them to real potential field data because they display the locations of the stratigraphic markers more precisely and clearly.

Arithmetical rank of the edge ideals of some $n$-cyclic graphs with a common edge

In this paper, we present some lower bounds and upper bounds on the arithmetical rank of the edge ideals of some n-cyclic graphs with a common edge. For some special n-cyclic graphs with a common edge, we prove that the arithmetical rank equals the projective dimension of the corresponding quotient ring.

Total Transversals in Hypergraphs and Their Applications

Let $H = (V,E)$ be a hypergraph with vertex set $V$ and edge set $E$ of order ${n_{_H}} = |V|$ and size ${m_{_H}} = |E|$. The hypergraph $H$ is $k$-uniform if every edge of $H$ has size $k$. Two vertices in $H$ are adjacent if they belong to a common edge in $H$. A transversal in $H$ is a subset of vertices in $H$ that has a nonempty intersection with every edge of $H$. A total transversal in $H$ is a transversal $T$ in $H$ with the additional property that every vertex in $T$ is adjacent to some other vertex of $T$. The total transversal number $\tau_t(H)$ of $H$ is the minimum cardinality of a total transversal in $H$. For $k \ge 2$, let $b_k = \sup_{H \in {\cal H}_k} \, {\tau_t}(H) / ({n_{_H}} + {m_{_H}})$, where ${\cal H}_k$ denotes the class of all $k$-uniform hypergraphs containing no isolated vertices or isolated edges or multiple edges. It is known that $b_2 = 2/5$, $b_3 = 1/3$, $b_4 \le 1/3$, and $b_5 \le 2/7$. In this paper, we show that $b_4 = 2/7$ and $b_6 \le 1/4$. Further, for $k \ge 7$, we show that $b_7 \le 2/9$. These results on total transversals have applications in total domination in hypergraphs. A total dominating set in $H$ is a subset of vertices $D \subseteq V$ such that every vertex in $H$ is adjacent to some vertex in $D$. The total domination number $\gamma_t(H)$ is the minimum cardinality of a total dominating set in $H$. The following relationship between the total transversal number and the total domination number of uniform hypergraphs is known: For $k \ge 3$ and $H \in {\cal H}_k$, we have ${\gamma_t}(H) \le ( \max \{ \frac{2 }{k+1}, b_{k-1} \} ) \times {n_{_H}}$. As a consequence of our results on the total transversal number, for $k \in \{2,3,4,5,6,7,8\}$ and a hypergraph $H \in {\cal H}_k$, we have ${\gamma_t}(H) \le 2{n_{_H}}/(k+1)$.