Symmetric Clusters Research Articles

Strong isotopic effect in the electron-mediated nuclear-nuclear interaction in solids

We studied the nuclear-nuclear spin interaction mediated by an unpaired electron spin, focusing on an isotopic effect by electron nuclear double resonance (ENDOR) spectroscopy. We investigated a linear cluster Ga-Ti3+-Ga in titanium-doped gallium oxyde β − Ga2O3, whereby the unpaired electron spin density of Ti3+ is equally delocalized on the nuclear spins I = 3/2 of nearest-neighboring 69Ga and 71Ga nuclei. The linear geometry of the spin arrangement allowed us to easily identify the ENDOR spectra for the three possible isotopic configurations: 69Ga-Ti-71Ga 69Ga-Ti-69Ga and 71Ga-Ti-71Ga. Despite the magnetic moments of 71Ga and 69Ga nuclei differing by only by 27%, the experimental effect of the electron-mediated nuclear-nuclear interaction (pseudodipolar interaction) on the ENDOR spectra is one order of magnitude larger ( 1 MHz) for the symmetrical clusters (69Ga-Ti-69Ga and 71Ga-Ti-71Ga, respectively) than for the asymmetrical cluster 69Ga-Ti-71Ga (<0.1 MHz). This important isotopic effect in the internuclear interaction is a consequence of the cluster symmetry with a local inversion center for the symmetrical configurations, which is lacking in the asymmetrical configuration. These symmetrical clusters thus combine a resolved nuclear-nuclear spin interaction, a nuclear spin monitoring by an unpaired electron, and a large nuclear spin quantum register, which make them attractive for quantum information processing whereby nuclear qubits can be monitored by short selective radiofrequency pulses.

Multipeaked fundamental and vortex solitons in azimuthally modulated Bessel lattices

We demonstrate the existence of multipeaked fundamental and vortex solitons in defocusing Kerr media with an imprinted azimuthally modulated Bessel lattice. Multipeaked solitons emanating from the fundamental linear lattice modes are stable in their entire existence domains. The number of soliton peaks is determined by the azimuthal index. Multipeaked vortex solitons with high topological charges in lattices exhibit special amplitude and phase distributions that resemble those of azimuthons. We reveal that the “stability rule” for vortex solitons in defocusing Kerr media is exactly opposite to that in focusing media. Multipeaked vortex solitons we obtained may provide a missing link between the radially symmetric vortices and nonrotating soliton clusters.

Assembly of four copper(II)–2,2′-biimidazole complex-supported Strandberg-type phosphomolybdates

Four Strandberg-type phosphomolybdate-based Cu(II) complexes of 2,2′-biimidazole (C6H6N4, H2biim) and H2O molecules, namely [Cu(H2biim)2(H2O)][Cu(H2biim)2(HPO4)2(Mo5O15)]·2H2O (1), [{Cu(H2biim)(H2O)}2{μ-Cu(H2biim)(H2O)}(P2Mo5O23)]2·20H2O (2), [Cu(H2biim)2][{Cu(H2biim)(H2O)2}{Cu(H2biim)2}(HPO4)(PO4)(Mo5 O15)]2·20H2O (3), and [Cu(H2biim)2(H2O)][Cu(H2biim)2(HPO4)2(Mo5O15)]·6H2O (4) have been synthesized and characterized by physico-chemical and spectroscopic methods. Single-crystal X-ray diffraction analysis reveals that compound 1 consists of a mono-supporting heteropolyoxoanion [Cu(H2biim)2(H2P2Mo5O23)]2−and an isolated [Cu(H2biim)2(H2O)]2+ cation. Compound 2 is composed of two tetra-supporting heteropolyoxoanions linked via two Cu(II) complex fragments. In compound 3, there exist two symmetrical bi-supported polyoxoanion clusters and an isolated [Cu(H2biim)2]2+ fragment lying in the center of the clusters. Compound 4 is also constructed from a [Cu(H2biim)2(H2P2Mo5O23)]2− polyoxoanion and a [Cu(H2biim)2(H2O)]2+ cation, but it has a different space group and packing interactions compared with compound 1.

A long-range hierarchical clustering model for constructing perfect quasicrystalline formations

Since their discovery, the unique structural signature of quasicrystals has posed a perplexing puzzle. Whereas significant progress has been made in determining their physical properties, a deeper understanding of the structure of quasicrystals remains an open question. Although available structural models provide important insights into understanding the quasiperiodic structural order, there is still significant information lacking concerning the determination of the long-range order of quasicrystals. A global multi-level hierarchical framework is presented that is able to describe the long-range translational and orientational order of the global empire pertaining to perfect Penrose tiling (PPT) models. In this order, the global empire is constructed of infinite levels of hierarchical clusters. Any cluster level, in this hierarchy, is composed of four smaller building clusters; two highly symmetrical clusters and their two fragments. Cluster configurations and the geometric arrangements of the multi-level clusters are determined entirely by a geometric progression of framework of nested decagrams. The proposed model suggests that the position of building units, locally and globally, is defined by one global framework, and not tiled based on local rules (matching or overlapping, etc). In this way, quasicrystal formations can grow rapidly ad infinitum without the need for any defects or mismatches.

Infrared spectrum of the CS2 trimer: observation of a structure with D3 symmetry

Infrared spectra of a carbon disulfide trimer formed in a pulsed supersonic slit-jet expansion are obtained via direct absorption of a tuneable diode laser in the region of the CS(2)ν(3) fundamental (∼1535 cm(-1)). This is the first high-resolution spectroscopic observation of (CS(2))(3). Two bands sharing the same lower state are assigned to ((12)C(32)S(2))(3). These correspond to the two infrared active trimer vibrations (a parallel and a perpendicular band) of the constituent CS(2) monomer asymmetric stretches. The weaker perpendicular band is centered at 1524.613 cm(-1), shifted by -10.74 cm(-1) with respect to the free CS(2) monomer. The parallel band is centered at 1545.669 cm(-1), a vibrational shift of +10.31 cm(-1). Transitions with K≠ 3n and those with K = 0, J = odd in the ground state are absent, establishing that this trimer has D(3) symmetry. The two parameters required to define this structure are determined to be 3.811 Å for the C-C bond distance and 61.8° for the angle between a monomer axis and the plane containing the C atoms. In addition, a parallel band arising from trimers with a single (34)S substitution is observed around 1544.46 cm(-1). Together with the recently observed cross-shaped CS(2) dimer, these results indicate a tendency for CS(2) to form highly symmetric clusters.

Large ion clusters H N+ of Rydberg Matter: Stacks of planar clusters H 7

Hydrogen and alkali atoms can form low-density metallic phases, in their most well-ordered form called Rydberg Matter (RM). RM consists mainly of small six-fold symmetric planar clusters in point group D 6h as shown by rotational spectroscopy. In their “sleeping top” (dark) state they can form stacks of clusters, as recently observed by 39K nuclear spin-flip transitions. Stacks of clusters H 7 are now directly observed by TOF-MS, using a laser intensity of <10 15 W cm −2. The TOF-MS resolution is high and the excitation level is found to be n B = 1. The Coulomb explosion process giving the ions observed involves rupture of an H 7 cluster in the stack and probably also addition of a proton to a cluster stack. Further mechanisms are discussed. RM clusters of the stack type can be larger than the previously observed limit for planar RM clusters of N = 91. That no N = 7 clusters but only larger planar RM clusters were detected in previous rotational spectroscopy studies is now suggested to be due to formation of cluster stacks.

Structure of an approximant crystal in Ni-rich Al71Ni22Co7

A novel approximant crystalline structure formed in an Al71Ni22Co7 alloy annealed at 973 K is reported, for which the S1-type superlattice decagonal quasicrystal forms as a major phase. Electron diffraction and atomic-resolution Z-contrast scanning transmission electron microscope investigations successfully identified the approximant as having a monoclinic unit cell with a = c = 3.2 nm (b = 0.4 nm), β = 108°; the structure is constructed by the five-fold symmetric decagonal clusters 2 nm across, which are arrayed by inverting their pentagonal directions between the neighbours (antiferro order of the cluster sense). A plausible atomic model of the approximant is proposed by referring to a model structure of the S1-type decagonal quasicrystal, which is composed of the similar local linkages of the five-fold symmetry clusters. The present approximant is shown to share some structural characteristics with the PD3c-approximant reported for a Co-rich Al71.5Ni12.5Co16 alloy.

Dynamic modelling and verification of a flexible clustered launch vehicle

Conceptual design of aerospace devices with low weight and high performance has currently been the aim of many researches and this has led to appearance of the flexibility in structures of these devices. These flexible behaviours have considerable effects on the flight dynamic and this problem in launch vehicles with cluster bodies is more important. Nonetheless, in the previous works, this aerospace device is only modelled as a single flexible body which is not enough for complete vibrational analysis. Hence, in this article, a non-linear dynamic model of a flexible clustered launch vehicle with one central core and two symmetrical clusters is extracted in the vector matrix format via the quasi-coordinate Lagrange method. Continuously, in order to verify the extracted dynamic model, the system is also modelled as a flexible multi-body in ADAMS software. Finally, parameters of the equation-based model and the ADAMS model are compared. Investigation on the results of this comparison shows satisfactory validation of the equations of motion.

Use of symmetry and stability for data clustering

An important consideration in clustering is the determination of an algorithm appropriate for partitioning a given data set. Thereafter identification of the correct model order and determining the corresponding partitioning need to be performed. In this paper, at first the effectiveness of the recently developed symmetry based cluster validity index named Sym-index which provides a measure of “symmetricity” of the different partitionings of a data set is shown to address all the above mentioned issues, viz., identifying the appropriate clustering algorithm, determining the proper model order and evolving the proper partitioning as long as the clusters possess the property of symmetry. Results demonstrating the superiority of the proposed cluster validity measure in appropriately determining the proper clustering technique as well as appropriate model order as compared to five other recently proposed measures, namely PS-index, I-index, CS-index, well-known XB-index, and stability based index, are provided for several clustering methods viz., two recently developed genetic algorithm based clustering techniques, the average linkage clustering algorithm, self organizing map and the expectation maximization clustering algorithm. Five artificial data sets and three real life data sets, are considered for this purpose. In the second part of the paper, a new measure of stability of clustering solutions over different bootstrap samples of a data set is proposed. Thereafter a multiobjective optimization based clustering technique is developed which optimizes both Sym-index and the measure of stability simultaneously to automatically determine the appropriate number of clusters and the appropriate partitioning of the data sets having symmetrical shaped clusters. Results on five artificial and five real-life data sets show that the proposed technique is well-suited to detect the number of clusters from data sets having point symmetric clusters.

Stability of small planar dust cluster in the presence of an external magnetic field

Oscillations and stability of planar symmetric dust clusters shaped as a regular polygon and a regular polygon with a particle at the center in the presence of an external uniform magnetic field are analyzed. The structure stability against small perturbations is considered. To this end, the equation of motion was linearized with respect to small coordinate variations. As a result, a dispersion relation (quartic algebraic equation) was derived and numerically studied for particular types of interactions between particles. A comparison of stability regions for a quadrangle and a triangle with a particle at the center, as well as a pentagon and a quadrangle with a particle at the center shows that there are ranges of parameters, where configurations without particle at the center are stable and configurations with a particle at the center are unstable, and vice versa.

A Multifaceted Cage Cluster, [CoII6O12 ⊃ X]− (X = Cl− or F−): Halide Template Effect and Frustrated Magnetism

Two hexanuclear CoII clusters, NHEt3[Co6(phendc)6 ⊃ X]·MeOH·3H2O (X = Cl− (1) or F− (2)), were obtained accidently by the in situ formation of the coordinating ligand H2phendc (1,10-phenanthroline-2,9-dicarboxylate) from the precursor ligand H2phenox (1,10-phenanthroline-2,9-dicarbaldehyde dioxime). Halides among the reactants used become the template around which a highly symmetric cluster is generated which display spin-glass magnetic behavior as a consequence of the severe magnetic frustration due to geometrical arrangement of the moments. Different anion-template effects were demonstrated by ESI-MS studies. Interestingly, 1 exists in solution; in its solid state, a rare and unique single-crystal to single-crystal transformation is observed upon desolvation, which is accompanied by the departure of NEt3. Both dc and ac magnetization data suggest the spin-glass behavior for 1 and its guest-free structure H[Co6(phendc)6Cl] (1′) at different blocking temperatures of 5.3 and 7.8 K, respectively. The absence of this observation for 2 raises an interesting question regarding its origin and provides a remarkable example of fine-tuning of frustrated magnetic properties via host−guest interactions.

Fano resonances in planar silver nanosphere clusters

The plasmonic properties of silver nanosphere clusters are investigated using the finite element and the plasmon hybridization methods. The nanoparticle clusters are found to exhibit multiple plasmon resonances with large induced electromagnetic field enhancements. For symmetric clusters, we show how group theory can be used to identify the microscopic nature of the plasmon resonances. For larger clusters, we show that narrow Fano resonances are frequently present in their optical spectra.

Regulation of dynamic polarity switching in bacteria by a Ras-like G-protein and its cognate GAP

The rod-shaped cells of the bacterium Myxococcus xanthus move uni-directionally and occasionally undergo reversals during which the leading/lagging polarity axis is inverted. Cellular reversals depend on pole-to-pole relocation of motility proteins that localize to the cell poles between reversals. We show that MglA is a Ras-like G-protein and acts as a nucleotide-dependent molecular switch to regulate motility and that MglB represents a novel GTPase-activating protein (GAP) family and is the cognate GAP of MglA. Between reversals, MglA/GTP is restricted to the leading and MglB to the lagging pole defining the leading/lagging polarity axis. For reversals, the Frz chemosensory system induces the relocation of MglA/GTP to the lagging pole causing an inversion of the leading/lagging polarity axis. MglA/GTP stimulates motility by establishing correct polarity of motility proteins between reversals and reversals by inducing their pole-to-pole relocation. Thus, the function of Ras-like G-proteins and their GAPs in regulating cell polarity is found not only in eukaryotes, but also conserved in bacteria.

Bromide‐Induced Formation of a Highly Symmetric Silver Thiolate Cluster Containing 36 Silver Atoms from an Infinite Polymeric Silver Thiolate

AbstractOwing to its good affinity with Ag+, Br– is able to truncate a silver thiolate polymer and induce the formation of a high‐nuclearity silver thiolate nanocluster, [Br@Ag36(SC6H4tBu‐4)36]–. The nanocluster has a disc‐like structure with one Br– anion trapped at the center of the cluster in an octahedral coordination.

Common Forms of Alkali Metals—New Rydberg Matter Clusters of Potassium and Hydrogen

Alkali metals can form low-density metallic phases, in their most well-ordered form called Rydberg Matter (RM). RM consists mainly of planar metallic clusters, with the number of atoms in each cluster not exceeding 100 according to experiments. Six-fold symmetric RM clusters in the most stable series K19, K37, K61 and K91 were observed by rotational radio-frequency spectroscopy and shown to be planar in point group D6h (Holmlid, J Mol Struct 885:122, 2008). Here, the RM clusters formed by K and H atoms are studied by neutral time-of-flight after pulsed laser fragmentation of RM formed from K and H. The kinetic energy of the fragments is due to laser initiated Coulomb explosions. Novel RM clusters of the type KN with N = 6, 9, 10, 13 and 15 are ejected from the material. They are necessarily planar due to the RM bonding, with two- or three-fold symmetry axes perpendicular to the plane. Pure hydrogen atom RM clusters HN are observed, demonstrating once more that H indeed is an alkali metal. Mixed clusters KMHN similar to hydrogen clusters where each K replaces an H atom as in KH6 are now also positively identified.

Form, symmetry and packing of biomacromolecules. II. Serotypes of human rhinovirus

The differentiation of the human rhinovirus into serotypes, all having very similar structures and the same architecture, is shown to be related to the packing of the viruses in the crystal and to its space-group symmetry. The molecular crystallographic properties (here described in terms of a molecular lattice Lambda(M) instead of the form lattice Lambda(F) considered in previous publications) appear to be compatible with the crystal structure and with the packing lattice Lambda(P), introduced in Part I [Janner (2010). Acta Cryst. A66, 301-311]. On the basis of the enclosing forms of the capsid, a sphere packing is considered, where the spheres touch at kissing points. Residues of each of the four coat proteins (VP1, VP2, VP3, VP4), having a minimal distance from the kissing points, define a set of kissing point related (KPR) residues. In this set only four different residues occur, one for each coat protein, ordered into symmetric clusters {already classified in a previous publication [Janner (2006). Acta Cryst. A62, 270-286]} and indexed by neighbouring lattice points of Lambda(P) (or equivalently of Lambda(M)). The indexed KPR residues allow a fingerprint characterization of the five rhinovirus serotypes whose structures are known (HRV16, HRV14, HRV3, HRV2 and HRV1A). In the fingerprint they occur as internal (if inside the given capsid), as external (if belonging to the neighbouring viruses) or as a contact residue (if at a kissing point position). The same fingerprint, periodically extended, permits a coarse-grained reconstruction of the essential properties of the crystal packing, invariant with respect to the space group of the serotype.

SPHERICALLY SYMMETRIC STELLAR CLUSTERS WITH ANISOTROPY AND CUTOFF ENERGY IN MOMENTUM DISTRIBUTION. II. THE RELATIVISTIC REGIME

We numerically construct models of spherically symmetric relativistic stellar clusters with anisotropic distribution functions. Newtonian solutions obtained in Paper I are generalized as isotropic Maxwellian ones with energy cutoff in their distribution function. We consider distributions with different levels of anisotropy and discuss some general characteristics of the models.

Porous ionic/molecular crystal composed of highly symmetric magnetic clusters

A porous ionic/molecular crystal composed of discrete triakis tetrahedral Co(8) clusters with an ideal T(d) symmetry shows interesting magnetism and porosity.

The dopaminergic system in the aging brain of Drosophila.

Drosophila models of Parkinson's disease are characterized by two principal phenotypes: the specific loss of dopaminergic (DA) neurons in the aging brain and defects in motor behavior. However, an age-related analysis of these baseline parameters in wildtype Drosophila is lacking. Here we analyzed the DA system and motor behavior in aging Drosophila. DA neurons in the adult brain can be grouped into bilateral symmetric clusters, each comprising a stereotypical number of cells. Analysis of TH > mCD8::GFP and cell type-specific MARCM clones revealed that DA neurons show cluster-specific, stereotypical projection patterns with terminal arborization in target regions that represent distinct functional areas of the adult brain. Target areas include the mushroom bodies, involved in memory formation and motivation, and the central complex, involved in the control of motor behavior, indicating that similar to the mammalian brain, DA neurons in the fly brain are involved in the regulation of specific behaviors. Behavioral analysis revealed that Drosophila show an age-related decline in startle-induced locomotion and negative geotaxis. Motion tracking however, revealed that walking activity, and exploration behavior, but not centrophobism increase at late stages of life. Analysis of TH > Dcr2, mCD8::GFP revealed a specific effect of Dcr2 expression on walking activity but not on exploratory or centrophobic behavior, indicating that the siRNA pathway may modulate distinct DA behaviors in Drosophila. Moreover, DA neurons were maintained between early- and late life, as quantified by TH > mCD8::GFP and anti-TH labeling, indicating that adult onset, age-related degeneration of DA neurons does not occur in the aging brain of Drosophila. Taken together, our data establish baseline parameters in Drosophila for the study of Parkinson's disease as well as other disorders affecting DA neurons and movement control.

Assessment of Regional Differences in Tariquidar-Induced P-Glycoprotein Modulation at the Human Blood–Brain Barrier

We attempted to assess regional differences in cerebral P-glycoprotein (P-gp) function by performing paired positron emission tomography (PET) scans with the P-gp substrate (R)-[(11)C]verapamil in five healthy subjects before and after i.v. infusion of tariquidar (2 mg/kg). Comparison of tariquidar-induced changes in distribution volumes (DVs) in 42 brain regions of interest (ROIs) failed to detect significant differences among brain ROIs. Statistical parametric mapping analysis of parametric DV images visualized symmetrical bilateral clusters with moderately higher DV increases in response to tariquidar administration in cerebellum, parahippocampal gyrus, olfactory gyrus, and middle temporal lobe and cortex, which might reflect moderately decreased P-gp function and expression.