Complex Symmetry Research Articles

Ferromagnetic Resonance Study of Magnetic Anisotropy in Epitaxial Fe<sub>3</sub>O<sub>4</sub> Thin Film

Ferromagnetic resonance (FMR) is used to investigate the magnetic anisotropy of a 25.5 nm thin Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> film above and below its Verwey transition temperature (TV). Epitaxial smooth film of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> is deposited by oxygen-assisted molecular beam epitaxy. FMR spectra are recorded using a 9.49 GHz Brucker EMX system from 80 K to room temperature with a magnetic field applied along [100] direction. The resonance field (Hr) and linewidth (AH) are extracted by fitting the FMR line with a Lorentzian function. Temperature dependence of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> and ΔH shows a transition at T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> . Furthermore, the data of in-plane angular dependence of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> at 300 and 83 K indicated a change in symmetry from fourfold to twofold below TV, consistent with a transformation of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> from cubic (fourfold) to monoclinic (twofold) structure with its easy axis switching from [110] to [100]. Complex symmetry pattern is found in angular dependence of ΔH below TV, which is attributed to the in-plane twinning of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> lattice.

Design of 4-electrode optical device for application of vector electric fields to self-assembled quantum dot complexes

Self-assembled InAs quantum dots (QDs) are of great interest as components of optoelectronic devices that can operate at the quantum limit. The charge configuration, interdot coupling, and symmetry of complexes containing multiple QDs can all be tuned with applied electric fields, but the magnitude and angle of the electric field required to control each of these parameters depend on the orientation of the QD complex. We present a 4-electrode device compatible with optical excitation and emission that allows application of electric fields with arbitrary magnitudes and angles relative to isolated QD complexes. We demonstrate the electric field tunability of this device with numerical simulations.

Real‐Time Symmetry‐Preserving Deformation

AbstractIn this paper, we address the problem of structure‐aware shape deformation: We specifically consider deformations that preserve symmetries of the shape being edited. While this is an elegant approach for obtaining plausible shape variations from minimal assumptions, a straightforward optimization is numerically expensive and poorly conditioned. Our paper introduces an explicit construction of bases of linear spaces of shape deformations that exactly preserve symmetries for any user‐defined level of detail. This permits the construction of low‐dimensional spaces of low‐frequency deformations that preserve the symmetries. We obtain substantial speed‐ups over alternative approaches for symmetry‐preserving shape editing due to (i) the sub‐space approach, which permits low‐res editing, (ii) the removal of redundant, symmetric information, and (iii) the simplification of the numerical formulation due to hard‐coded symmetry preservation. We demonstrate the utility in practice by applying our framework to symmetry‐preserving co‐rotated iterative Laplace surface editing of models with complex symmetry structure, including partial and nested symmetry.

Lie and Noether symmetries of systems of complex ordinary differential equations and their split systems

The Lie and Noether point symmetry analyses of a kth-order system of m complex ordinary differential equations (ODEs) with m dependent variables are performed. The decomposition of complex symmetries of the given system of complex ODEs yields Lie- and Noether-like operators. The system of complex ODEs can be split into 2m coupled real partial differential equations (PDEs) and 2m Cauchy–Riemann (CR) equations. The classical approach is invoked to compute the symmetries of the 4m real PDEs and these are compared with the decomposed Lie- and Noether-like operators of the system of complex ODEs. It is shown that, in general, the Lie- and Noether-like operators of the system of complex ODEs and the symmetries of the decomposed system of real PDEs are not the same. A similar analysis is carried out for restricted systems of complex ODEs that split into 2m coupled real ODEs. We summarize our findings on restricted complex ODEs in two propositions.

Quantitation of Zygomatic Complex Symmetry Using 3-Dimensional Computed Tomography

To improve the clinical evaluation of the symmetry of the zygomatic complex (ZMC), the authorsdeveloped a new method to measure the eminence and width of the ZMC using 3-dimensional (3D) computed tomography (CT). The accuracy and reproducibility of the ZMC symmetry evaluation using this method were investigated. Spiral CT was carried out in 50 volunteers with visually symmetric faces. Based on an exact craniofacial midsagittal plane, a 3D coordinate system was constructed and used to measure the eminence and width of the ZMC. Absolute differences between the bilateral eminences and widths were calculated as ΔE and ΔW, respectively. The ZMC eminence also was measured based on traditional methods using anatomic landmarks, and the bilateral absolute difference was calculated to serve as a control (ΔcE). The ΔE value was lower than the ΔcE value (0.6 vs 1.75mm; P < .001). None of the results for ΔE were larger than 2mm, and 7 results (3.5%) for ΔW were larger than 2mm. By comparison, 57 results (28.5%) for ΔcE were larger than 2cm (P < .001). The intraclass correlation coefficient (ICC) indicated almost perfect agreement for inter- and intraexaminer reliabilities for ΔE (ICC, 0.82 to 0.86) and ΔW (ICC, 0.81 to 0.85) measurements, and moderate agreement for inter- and intraexaminer reliabilities was obtained for ΔcE (ICC, 0.61 to 0.68) measurements. This new method is practical and valuable in the clinical evaluation of ZMC symmetry.

The Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS): exploiting symmetry for faster subgraph enumeration.

Subgraph matching algorithms are used to find and enumerate specific interconnection structures in networks. By enumerating these specific structures/subgraphs, the fundamental properties of the network can be derived. More specifically in biological networks, subgraph matching algorithms are used to discover network motifs, specific patterns occurring more often than expected by chance. Finding these network motifs yields information on the underlying biological relations modelled by the network. In this work, we present the Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS), an improved version of the Index-based Subgraph Matching Algorithm (ISMA). ISMA quickly finds all instances of a predefined motif in a network by intelligently exploring the search space and taking into account easily identifiable symmetric structures. However, more complex symmetries (possibly involving switching multiple nodes) are not taken into account, resulting in superfluous output. ISMAGS overcomes this problem by using a customised symmetry analysis phase to detect all symmetric structures in the network motif subgraphs. These structures are then converted to symmetry-breaking constraints used to prune the search space and speed up calculations. The performance of the algorithm was tested on several types of networks (biological, social and computer networks) for various subgraphs with a varying degree of symmetry. For subgraphs with complex (multi-node) symmetric structures, high speed-up factors are obtained as the search space is pruned by the symmetry-breaking constraints. For subgraphs with no or simple symmetric structures, ISMAGS still reduces computation times by optimising set operations. Moreover, the calculated list of subgraph instances is minimal as it contains no instances that differ by only a subgraph symmetry. An implementation of the algorithm is freely available at https://github.com/mhoubraken/ISMAGS.

Complex symmetry of composition operators induced by involutive ball automorphisms

Suppose H \mathcal {H} is a weighted Hardy space of analytic functions on the unit ball B n ⊂ C n \mathbb {B}_n\subset \mathbb {C}^n such that the composition operator C ψ C_\psi defined by C ψ f = f ∘ ψ C_{\psi }f=f\circ \psi is bounded on H \mathcal {H} whenever ψ \psi is a linear fractional self-map of B n \mathbb {B}_n . If φ \varphi is an involutive Moebius automorphism of B n \mathbb {B}_n , we find a conjugation operator J \mathcal {J} on H \mathcal {H} such that C φ = J C φ ∗ J C_{\varphi }=\mathcal {J} C^*_{\varphi }\mathcal {J} . The case n = 1 n=1 answers a question of Garcia and Hammond.

Reinterpretation of the vibrational spectroscopy of the medicinal bioinorganic synthon c,c,t-[Pt(NH3)2Cl2(OH)2

The Pt(IV) complex c,c,t-[Pt(NH3)2Cl2(OH)2] is an important intermediate in the synthesis of Pt(IV) anticancer prodrugs and has been investigated as an anticancer agent in its own right. An analysis of the vibrational spectroscopy of this molecule was previously reported (Faggiani et al., Can. J. Chem. 60:529, 1982), in which crystallographic determination of the structure of the complex permitted a site group approach. The space group, however, was incorrectly assigned. In the present study we have redetermined at high resolution crystal structures of c,c,t-[Pt(NH3)2Cl2(OH)2] and c,c,t-[Pt(NH3)2Cl2(OH)2]·H2O2, which makes possible discussion of the effect of hydrogen bonding on the N-H and O-H vibrational bands. The correct crystallographic site symmetry of the platinum complex in the c,c,t-[Pt(NH3)2Cl2(OH)2] structure is used to conduct a new vibrational analysis using both group-theoretical and modern density functional theory methods. This analysis reveals the nature and symmetry of the "missing band" described in the original publication and suggests a possible explanation for its disappearance.

Continuous symmetry measures for complex symmetry group

Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.

Reversible Achiral-to-Chiral Switching of Single Mn–Phthalocyanine Molecules by Thermal Hydrogenation and Inelastic Electron Tunneling Dehydrogenation

Induction of chirality in planar adsorbates by hydrogenation of phthalocyanine molecules on a gold surface is demonstrated. This process merely lowers the molecular symmetry from 4- to 2-fold, but also breaks the mirror symmetry of the entire adsorbate complex (molecule and surface), thus rendering it chiral without any realignment at the surface. Repositioning of single molecules by manipulation with the scanning tunneling microscope (STM) causes interconversion of enantiomers. Dehydrogenation of the adsorbate by means of inelastic electron tunneling restores the mirror symmetry of the adsorbate complex. STM as well as density functional theory (DFT) calculations show that chirality is actually imprinted into the electronic molecular system by the surface, i.e., the lowest unoccupied orbital is devoid of mirror symmetry.

Synthesis, Spectral Characterization, Magnetic Moment, Mass, X-Ray Diffraction, and Kinetic (TGA) Studies of Cr(III) Complex with Metformin: An Oral Antidiabetic Drug

The present work describes synthesis, spectral characterization, and X-ray diffraction studies of Cr(III) with “metformin,” an oral antidiabetic drug. The conductometric titration using monovariation method indicates that complex is ionic and of L2M type. Analytical data agree with the molecular formula of complex namely, [(C4H11N5)2Cr(H2O)2]2Cl. Geometry of complex assigned is octahedral, supported by IR, electronic spectra, magnetic moments,1H-NMR and mass studies, and proposed structure (I) for complex. X-ray diffraction data also supports the complex formation and symmetry of complex and various parameters like particle size, porosity, volume of unit cell, and density have been calculated. The Freeman-Carroll and Sharp-Wentworth methods have been used to calculate activation energy and thermal stability. The activation energy(Ea)calculated with the help of these methods are in agreement with each other. Thermodynamic parameters such as free energy change (ΔF) and entropy change are also determined on the basis of TG curves and by using data of the Freeman-Carroll method.

Prepare and deliver an effective presentation

Abstract Defecation in the ctenophore Mnemiopsis leidyi is a stereotyped sequence of effector responses that occur with a regular ultradian rhythm. Time intervals between repeated defecations of individual animals depend on body size, ranging from ~10 min in small larvae to ~1 hr in large adults. New features and corrections of previous reports of the gastrovascular system during and between defecations are described in detail by video microscopy. Contrary to the scientific literature, the defecating organ of the excretory complex is just one of the two anal canals which possesses the animal’s only anal pore. The anal pore is not visible as a permanent structure as depicted in textbooks, but appears at defecation and disappears afterward. DIC microscopy reveals that opening and closing of the anal pore resemble a reversible ring of tissue fusion between apposed endodermal and ectodermal layers at the aboral end. Mnemiopsis thus appears to have an intermittent anus and therefore an intermittent through-gut that reoccur at regular intervals. The temporality of a visible anal pore in Mnemiopsis is novel, and may shed light on the evolution of a permanent anus and through-gut in animals. In addition, mirror image dimorphism of the diagonal anal complex occurs in larval ctenophores but not in adults, indicating developmental flexibility in diagonal symmetry of the anal complex.

An alternative description for the interaction between the Eu3+ ion and its nearest neighbours

The LiYF4:Eu3+ and the Eu (btfa)3(4,4-bipy)(EtOH) compounds are being revisited by the method of equivalent nearest neighbours (MENNs) and the simple overlap model, this time to suggest a comparison between: the europium local symmetry in complexes containing β-diketones and the S4 symmetry in the LiYF4:Eu3+; and the ionic bonding in lanthanide containing compounds as pure electrostatic attraction. The 7F1 level splitting was satisfactorily predicted in both cases by very similar sets of charge factors. This similarity indicates that the lanthanide ion treats the chemical species (N, O and F) in its first neighbourhood merely as negative charges.

Thermodynamic and Structural Trends in Hexavalent Actinyl Cations: Complexation of Dipicolinic Acid with NpO22+ and PuO22+ in Comparison with UO22+

The complexation of NpO2(2+) and PuO2(2+) with dipicolinic acid (DPA) has been investigated in 0.1 M NaClO4 by spectrophotometry, microcalorimetry, and single crystal diffractometry. Formation of 1:1 and 1:2 (metal/ligand molar ratio) complexes of DPA with NpO2(2+) and PuO2(2+) were identified and the thermodynamic parameters were determined and compared with those of UO2(2+) . All three hexavalent actinyl cations form strong 1:1 DPA complexes with slightly decreasing but comparable stability constants from UO2(2+) to PuO2(2+), whereas the stability constants of the 1:2 complexes (logβ2) decrease substantially along the series (16.3 for UO2L2(2-), 15.17 for NpO2L2(2-), and 14.17 for PuO2L2(2-) at 25 °C). The enthalpies of complexation for the 1:2 complexes become less exothermic from UO2L2(2-) (-28.9 kJ mol(-1)), through NpO2L2(2-) (-27.2 kJ mol(-1)), and to PuO2L2(2-) (-22.7 kJ mol(-1)). The trends in the thermodynamic parameters are discussed in terms of the effective charge of the cations and the steric constraints in the structures of the complexes. In addition, the features of the absorption spectra, including the wavelength and intensity of the absorption bands, are related to the perturbation of the ligand field and the symmetry of the actinyl complexes.

Symmetry Constraint for Foreground Extraction

Symmetry as an intrinsic shape property is often observed in natural objects. In this paper, we discuss how explicitly taking into account the symmetry constraint can enhance the quality of foreground object extraction. In our method, a symmetry foreground map is used to represent the symmetry structure of the image, which includes the symmetry matching magnitude and the foreground location prior. Then, the symmetry constraint model is built by introducing this symmetry structure into the graph-based segmentation function. Finally, the segmentation result is obtained via graph cuts. Our method encourages objects with symmetric parts to be consistently extracted. Moreover, our symmetry constraint model is applicable to weak symmetric objects under the part-based framework. Quantitative and qualitative experimental results on benchmark datasets demonstrate the advantages of our approach in extracting the foreground. Our method also shows improved results in segmenting objects with weak, complex symmetry properties.

Optimal fold symmetry of LH2 rings on a photosynthetic membrane

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order.

Effective field theories for topological insulators by functional bosonization

Effective field theories that describe the dynamics of a conserved U(1) current in terms of ``hydrodynamic'' degrees of freedom of topological phases in condensed matter are discussed in general dimension $D=d+1$ using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the ``primary series'' of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when $D$ is odd) or the $\ensuremath{\theta}$ (when $D$ is even) terms. For topological insulators characterized by a ${\mathbb{Z}}_{2}$ topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative ``fractional'' topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

Algebraic graph theory and its applications for mesh generation

AbstractMesh generation is an important step in many numerical methods. The authors present a novel approach to mesh generation, based on algebraic graph theory, that can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The mesh is expressed as a hierarchically symmetric graph that preserves both the hierarchical structure as well as the symmetry characteristics of such configurations. (© 2012 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Flame synthesis of zinc oxide nanocrystals

Abstract Distinctive zinc oxide (ZnO) nanocrystals were synthesized on the surface of Zn probes using a counter-flow flame medium formed by methane/acetylene and oxygen-enriched air streams. The source material, a zinc wire with a purity of ∼99.99% and diameter of 1 mm, was introduced through a sleeve into the oxygen rich region of the flame. The position of the probe/sleeve was varied within the flame medium resulting in growth variation of ZnO nanocrystals on the surface of the probe. The shape and structural parameters of the grown crystals strongly depend on the flame position. Structural variations of the synthesized crystals include single-crystalline ZnO nanorods and microprisms (ZMPs) (the ZMPs have less than a few micrometers in length and several hundred nanometers in cross section) with a large number of facets and complex axial symmetry with a nanorod protruding from their tips. The protruding rods are less than 100 nm in diameter and lengths are less than 1 μm. The protruding nanorods can be elongated several times by increasing the residence time of the probe/sleeve inside the oxygen-rich flame or by varying the flame position. At different flame heights, nanorods having higher length-to-diameter aspect-ratio can be synthesized. A lattice spacing of ∼0.26 nm was measured for the synthesized nanorods, which can be closely correlated with the (0 0 2) interplanar spacing of hexagonal ZnO (Wurtzite) cells. The synthesized nanostructures were analyzed by scanning electron microscopy (SEM), transmission electron microscopy (TEM), high resolution TEM (HR-TEM), X-ray energy dispersive spectroscopy (EDS), and selected area electron diffraction pattern (SAED). The growth mechanism of the ZnO nanostructures is discussed.

New insights in the bonding regime and ligand field in Wernerian complexes. A density functional study

We advance challenging new observations about the bonding regime and ligand field (LF) effects in the Wernerian complexes, with the help of several computer experiments realized exploiting the specific leverages of the ADF (Amsterdam density functional) code. Assembling the molecular systems from preliminarily prepared metal ion and individual ligand fragments and analyzing the components of the total bonding energy (Pauli repulsion, electrostatic interactions and orbital part), we noticed interesting correlations between the orbital part and the simple formulas of the qualitatively defined ligand field stabilization energy (LFSE). The facts are beyond the obvious or predictable comprehension, since the orbital components incorporate the subtle balance of intra- and inter-fragment density rearrangements, charge transfer and orbital mixing. The energy decomposition analysis was performed considering metal ions and ligand sets in their nominal oxidation states, or with fractional charges, resulted after a preliminary step of electronegativity equalization driven charge transfer. We worked on series of prototypic simple octahedral units: [MqF6]q−6 , [Mq(CN)6]q−6 and [Mq(H2O)6]q complexes with MII and MIII ions selected from the M=Cr to Cu 3d series. Besides, as illustration of observed regularities in the case of more complex ligands and intermediate symmetries, we considered [Mq(bpca)2]q−2 complexes (Hbpca=bis(2-pyridilcarbonyl)amine) with D2d symmetry. Using the ADF facilities of orbital population control and fractional occupation schemes, we devised two simple ways to estimate 10Dq parameters by numerical experiments that simulate the effects of Ligand Field stabilization and electron promotion. To the best of our knowledge, though simple, such considerations on bonding regime or methodological procedures designed to meet the phenomenological demands of LF models have not been discussed before. Interesting new aspects can yet be discovered exploring the subtle details of coordination bonding as intermediate between ionic and covalent bonding regime.