Synthesis and characterisation of heterometallic molecular triangles using ambidentate linker: self-selection of a single linkage isomer

The coordination driven self-assembly of discrete molecular triangles from a non-symmetric ambidentate linker 5-pyrimidinecarboxylate (5-pmc) and Pd(II)/Pt(II) based 90◦ acceptors is presented. Despite the possibility of formation of a mixture of isomeric macrocycles (linkage isomers) due to different connectivity of the ambidentate linker, formation of a single and symmetrical linkage somer in both the cases is an interesting observation. Moreover, the reported macrocycles represent the first example of discrete metallamacrocycles of bridging 5-pmc. While solution composition in both the cases was characterised by multinuclear NMR study and electrospray ionization mass spectrometry (ESI-MS), the identity of the assemblies in the solid state was established by X-ray single crystals structure analysis. Variable temperature NMR study clearly ruled out the formation of any other macrocycles by [4 + 4] or [2 + 2] self-assembly of the reacting components.

Medium-Voltage Drive for Induction Machine With Multilevel Dodecagonal Voltage Space Vectors With Symmetric Triangles

Multilevel inverters with dodecagonal (12-sided polygon) voltage space vector structure have advantages, such as complete elimination of fifth and seventh harmonics, reduction in electromagnetic interference, reduction in device voltage ratings, reduction of switching frequency, extension of linear modulation range, etc., making it a viable option for high-power medium-voltage drives. This paper proposes two power circuit topologies capable of generating multilevel dodecagonal voltage space vector structure with symmetric triangles (for the first time) with minimum number of dc-link power supplies and floating capacitor H-bridges. The first power topology is composed of two hybrid cascaded five-level inverters connected to either side of an open-end winding induction machine. Each inverter consists of a three-level neutral-point-clamped inverter, which is cascaded with an isolated H-bridge making it a five-level inverter. The second topology is for a normal induction motor. Both of these circuit topologies have inherent capacitor balancing for floating H-bridges for all modulation indexes, including transient operations. The proposed topologies do not require any precharging circuitry for startup. A simple pulsewidth modulation timing calculation method for space vector modulation is also presented in this paper. Due to the symmetric arrangement of congruent triangles within the voltage space vector structure, the timing computation requires only the sampled reference values and does not require any offline computation, lookup tables, or angle computation. Experimental results for steady-state operation and transient operation are also presented to validate the proposed concept.

An Open-End winding IM drive with Multilevel 12-sided Polygonal Vectors with Symmetric Triangles

Multilevel inverters with hexagonal voltage space vector structures have improved performance of induction motor drives compared to that of the two level inverters. Further reduction in the torque ripple on the motor shaft is possible by using multilevel dodecagonal (12-sided polygon) voltage space vector structures. The advantages of dodecagonal voltage space vector based PWM techniques are the complete elimination of fifth and seventh harmonics in phase voltages for the full modulation range and the extension of linear modulation range. This paper proposes an inverter circuit topology capable of generating multilevel dodecagonal voltage space vectors with symmetric triangles, by cascading two asymmetric three level inverters with isolated H-Bridges. This is made possible by proper selection of DC link voltages and the selection of resultant switching states for the inverters. In this paper, a simple PWM timing calculation method is proposed. Experimental results have also been presented in this paper to validate the proposed concept.

Self-Assembled Pd(II) Metallocycles Using an Ambidentate Donor and the Study of Square-Triangle Equilibria

The self-assembly reaction of a cis-blocked 90° square planar metal acceptor with a symmetrical linear flexible linker is expected to yield a [4 + 4] self-assembled square, a [3 + 3] assembled triangle, or a mixture of these.However, if the ligand is a nonsymmetrical ambidentate, it is expected to form a complex mixture comprising several linkage isomeric squares and triangles as a result of different connectivities of the ambidentate linker. We report instead that the reaction of a 90° acceptor cis-(dppf)Pd(OTf)2 [where dppf ) 1,1′-bis(diphenylphosphino)- ferrocene] with an equimolar amount of the ambidentate unsymmetrical ligand Na-isonicotinate unexpectedly yields a mixture of symmetrical triangles and squares in the solution. An analogous reaction using cis-(tmen)Pd(NO3)2 instead of cis-(dppf)Pd(OTf)2 also produced a mixture of symmetrical triangles and squares in the solution. In both cases the square was isolated as the sole product in the solid state, which was characterized by a single crystal structure analysis. The equilibrium between the triangle and the square in the solution is governed by the enthalpic and entropic contributions. The former parameter favors the formation of the square due to less strain in the structure whereas the latter one favors the formation of triangles due to the formation of more triangles from the same number of starting linkers. The effects of temperature and concentration on the equilibria have been studied by NMR techniques. This represents the first report on the study of square-triangle equilibria obtained using a nonsymmetric ambidentate linker. Detail NMR spectroscopy along with the ESI-mass spectrometry unambiguously identified the components in the mixture while the X-ray structure analysis determined the solid-state structure.

Efficient algorithms for computing Reeb graphs

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. We describe an algorithm that constructs the Reeb graph of a Morse function defined on a 3-manifold. Our algorithm maintains connected components of the two dimensional levels sets as a dynamic graph and constructs the Reeb graph in O(nlogn+nlogg(loglogg)3) time, where n is the number of triangles in the tetrahedral mesh representing the 3-manifold and g is the maximum genus over all level sets of the function. We extend this algorithm to construct Reeb graphs of d-manifolds in O(nlogn(loglogn)3) time, where n is the number of triangles in the simplicial complex that represents the d-manifold. Our result is a significant improvement over the previously known O(n2) algorithm. Finally, we present experimental results of our implementation and demonstrate that our algorithm for 3-manifolds performs efficiently in practice.

A Pulsewidth Modulated Control of Induction Motor Drive Using Multilevel 12-Sided Polygonal Voltage Space Vectors

In this paper, a novel 12-sided polygonal space vector structure is proposed for an induction motor drive. The space vector pattern presented in this paper consists of two 12-sided concentric polygons with the outer polygon having a radius double the inner one. As compared to previously reported 12-sided polygonal space vector structures, this paper subdivides the space vector plane into smaller sized triangles. This helps in reducing the switching frequency of the inverters without deteriorating the output voltage quality. It also reduces the device ratings and dv/dt stress on the devices to half. At the same time, other benefits obtained from the existing 12-sided space vector structure, such as increased linear modulation range and complete elimination of 5th and 7th order harmonics in the phase voltage, are also retained in this paper. The space vector structure is realized by feeding an open-end induction motor with two conventional three-level neutral point clamped (NPC) inverters with asymmetric isolated dc link voltage sources. The neutral point voltage fluctuations in the three-level NPC inverters are eliminated by utilizing the switching state multiplicities for a space vector point. The pulsewidth modulation timings are calculated using sampled reference waveform amplitudes and are explained in detail in this paper. Experimental verification on a laboratory prototype shows that this configuration may be considered suitable for high power drives.

A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl6 suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown.

Efficient computation of volume fractions for multi-material cell complexes in a grid by slicing

The paper presents a novel slicing based method for computation of volume fractions in multi-material solids given as a B-rep whose faces are triangulated and shared by either one or two materials. Such objects occur naturally in geoscience applications and the said computation is necessary for property estimation problems and iterative forward modeling. Each facet in the model is cut by the planes delineating the given grid structure or grid cells. The method, instead of classifying the points or cells with respect to the solid, exploits the convexity of triangles and the simple axis-oriented disposition of the cutting surfaces to construct a novel intermediate space enumeration representation called slice-representation, from which both the cell containment test and the volume-fraction computation are done easily. Cartesian and cylindrical grids with uniform and non-uniform spacings have been dealt with in this paper. After slicing, each triangle contributes polygonal facets, with potential elliptical edges, to the grid cells through which it passes. The volume fractions of different materials in a grid cell that is in interaction with the material interfaces are obtained by accumulating the volume contributions computed from each facet in the grid cell. The method is fast, accurate, robust and memory efficient. Examples illustrating the method and performance are included in the paper.

Localization of handwritten text in documents using moment invariants and Delaunay triangulation

This paper describes an approach based on Zernike moments and Delaunay triangulation for localization of hand-written text in machine printed text documents. The Zernike moments of the image are first evaluated and we classify the text as hand-written using the nearest neighbor classifier. These features are independent of size, slant, orientation, translation and other variations in handwritten text. We then use Delaunay triangulation to reclassify the misclassified text regions. When imposing Delaunay triangulation on the centroid points of the connected components, we extract features based on the triangles and reclassify the text. We remove the noise components in the document as part of the preprocessing step so this method works well on noisy documents. The success rate of the method is found to be 86%. Also for specific hand-written elements such as signatures or similar text the accuracy is found to be even higher at 93%.

Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

A structural study of Li2S---B2S3 glasses by neutron diffraction

The radial distribution functions (RDFs) of five xLi2S.(1 - x)B2S3 glasses (x = 0.55, 0.60, 0.67, 0.71 and 0.75) have been determined from neutron diffraction experiments performed at the Institut Laue-Langevin, Grenoble. These glasses are prepared by casting a molten mixture of boron, sulphur and Li2S inside a controlled atmosphere glovebox. Addition of the Li2S Modifier is found gradually to suppress all peaks corresponding to interatomic distances > 3.5 angstrom, which implies that the structural entities present in these glasses become segmented, and therefore more ionic, as x increases. The assumption of the existence of four main structural entities based on four- and three-coordinated borons (the latter carrying bridging and/or non-bridging sulphurs) accounts for all the peaks present in the RDFs as a function of composition. Furthermore, in the most modified glass (x = 0.75), that which contains only 'isolated' BS33- triangles, there seems to be evidence for either octahedral or tetrahedral coordination of Li+ by S- ions

Structural Hypotheses And Raman-Spectroscopy Investigations Of Glasses Belonging To The B2s3-Li2s-Lii System

A previous B-11 nuclear magnetic resonance investigation of glasses belonging to the B2S3-Li2S-LiI system had allowed the authors to determine the variation of the number of three and four coordinated boron atoms with composition. These results, in addition to the observation that vitreous B2S3 quite easily forms fibres during casting, have led us to propose structural hypotheses for B2S3 based glasses, which are supported by the present Raman spectroscopy study. For vitreous B2S3 the spectra were accounted for on the basis of the various types of BS3/2 triangles proposed by the model. Molecular orbital considerations allowed us to assign the most significant lines for the binary glasses by assuming that BS3/2 triangles (with or without nonbridging sulphur atoms) and BS4 tetrahedra were present. In the ternary system, lithium iodide has been found to interact slightly on the structural entities, altering their vibrational characteristics without fundamentally modifying their nature.

Acto-myosin contractility rotates the cell nucleus

The nucleus of the eukaryotic cell functions amidst active cytoskeletal �laments, but its response to the stresses carried by these �laments is largely unexplored. We report here the results of studies of the translational and rotational dynamics of the nuclei of single �broblast cells, with the e�ects of cell migration suppressed by plating onto �bronectin-coated micro-fabricated patterns. Patterns of the same area but di�erent shapes and/or aspect ratio were used to study the e�ect of cell geometry on the dynamics. On circles, squares and equilateral triangles, the nucleus undergoes persistent rotational motion, while on high-aspect-ratio rectangles of the same area it moves only back and forth. The circle and the triangle showed respectively the largest and the smallest angular speed. We show that our observations can be understood through a hydrodynamic approach in which the nucleus is treated as a highly viscous inclusion residing in a less viscous uid of orientable �laments endowed with active stresses. Lowering actin contractility selectively by introducing blebbistatin at low concentrations drastically reduced the speed and persistence time of the angular motion of the nucleus. Time-lapse imaging of actin revealed a correlated hydrodynamic ow around the nucleus, with pro�le and magnitude consistent with the results of our theoretical approach. Coherent intracellular ows and consequent nuclear rotation thus appear to be a generic property that cells must balance by speci�c mechanisms in order to maintain nuclear homeostasis

Fixed-orientation equilateral triangle matching of point sets

Given a point set P and a class C of geometric objects, G(C)(P) is a geometric graph with vertex set P such that any two vertices p and q are adjacent if and only if there is some C is an element of C containing both p and q but no other points from P. We study G(del)(P) graphs where del is the class of downward equilateral triangles (i.e., equilateral triangles with one of their sides parallel to the x-axis and the corner opposite to this side below that side). For point sets in general position, these graphs have been shown to be equivalent to half-Theta(6) graphs and TD-Delaunay graphs. The main result in our paper is that for point sets P in general position, G(del)(P) always contains a matching of size at least vertical bar P vertical bar-1/3] and this bound is tight. We also give some structural properties of G(star)(P) graphs, where is the class which contains both upward and downward equilateral triangles. We show that for point sets in general position, the block cut point graph of G(star)(P) is simply a path. Through the equivalence of G(star)(P) graphs with Theta(6) graphs, we also derive that any Theta(6) graph can have at most 5n-11 edges, for point sets in general position. (C) 2013 Elsevier B.V. All rights reserved.