Odd Rings Research Articles

Design of linear photonic crystal fiber with all-positive/negative ultraflattened chromatic dispersion for the whole telecom band

Ultraflattened dispersion of optical fibers is urgently needed for ultrawideband and ultralong-haul transmission in dense wavelength division multiplexing (DWDM) systems. A systematic solution is finely developed to adjust and control the ultraflattened dispersion curves in high accuracy. The validity is verified by designing two photonic crystal fibers (PCFs) with ultraflattened chromatic dispersion across the whole telecom band (1260 to 1625 nm). Numerical results confirm that line PCF with near-zero, all-positive, and ultraflatten dispersion ranging 0.32 ± 0.17 ps / ( nm · km ) can support 1600-km line transmission in DWDM, whereas the dispersion-compensating PCF with low negative and ultraflattened dispersion ranging −15.57 ± 0.37 ps / ( nm · km ) has a high dispersion compensation efficiency of up to 33 times for line PCF. An improved PCF structure is proposed by introducing three extra small air-holes between the standard lattices of odd rings. Moreover, other fiber parameters such as nonlinear coefficient (<1.1 w − 1 · km − 1), numerical aperture (>0.189), and confinement loss (<0.09 dB / km for line PCF) implied that both PCFs presented can support long-haul linear scheme in the whole telecom band.

The roommate problem with externalities

This paper extends the roommate problem to include externalities, allowing preferences for a partner to depend on the situation of others. Stability concepts for matchings and partitions of the set of agents are proposed and characterized, conditional on all agents having prudent expectations about other agents’ reactions to deviations. We prove that any roommate problem with externalities has a stable partition and that a stable matching exists if there is a stable partition without odd rings. These results allow us to find restrictions on the space of preferences ensuring the existence of a stable matching. We also show that some classical properties are lost in the presence of externalities: the existence of paths to stability from any unstable matching, the coincidence of the core with the set of stable matchings, and the invariance of the set of agents who are alone in a stable matching.

Injective stability for odd unitary K 1

Abstract We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we give a self-contained proof of injective stability for the odd unitary K 1 {K_{1}} -functor under the stable rank condition.

Aromaticity and Antiaromaticity in the Excited States of Porphyrin Nanorings.

Aromaticity can be a useful concept for predicting the behavior of excited states. Here we show that π-conjugated porphyrin nanorings exhibit size-dependent excited-state global aromaticity and antiaromaticity for rings containing up to eight porphyrin subunits, although they have no significant global aromaticity in their neutral singlet ground states. Applying Baird’s rule, even rings ([4n] π-electrons) are aromatic in their lowest excited states, whereas the lowest excited states of odd rings ([4n + 2] π-electrons) are antiaromatic. These predictions are borne out by density functional theory (DFT) studies of the nucleus-independent chemical shift (NICS) in the T1 triplet state of each ring, which reveal the critical importance of the triplet delocalization to the emergence of excited-state aromaticity. The singlet excited states (S1) are explored by measurements of the radiative rate and fluorescence peak wavelength, revealing a subtle odd–even alternation as a function of ring size, consistent with symmetry breaking in antiaromatic excited states.

The local structural differences in amorphous Ge-Sb-Te alloys

Chalcogenide alloys in pseudobinary line between Sb2Te3 and GeTe are extensively utilied in phase change memories for optical and electronic contrast between crystalline and amorphous phases. Different from the crystalline structure, the understanding of amorphous structures is still insufficient due to disorder and distortion. By employing first-principle molecular dynamics simulations and atomistic cluster alignment analysis, the short-range orders and the associated distortions of amorphous Sb2Te3, Ge1Sb2Te4, Ge2Sb2Te5, Ge3Sb2Te6 and GeTe are investigated to explore the origin of nature difference. The results reveal that GeGe and SbSb bonds present a notable competitive mechanism with GeTe content. The GeTe content has a great influence on Ge- and Te-centered short-range orders but little influence on the structures of Sb-centered clusters, especially for the octahedral sites and unidentified structures. The tetrahedrons in Ge-centered clusters of each alloy show a close proportion, but the fraction of tetrahedrons in total clusters increases with the increasing GeTe content due to the increase in the ratio of Ge atom. As for the distortions of clusters, the distorted tetrahedrons in Ge2Sb2Te5 are closest to the standard tetrahedron, the Peierls distortion of Ge-centered 6-fold octahedron reduces with an increase in GeTe content whereas that of Sb-centered 6-fold octahedron shows a little change. Additionally, it is found that GeTe content can inhibit the formation of nanocavity but contribute to the formation of the odd rings. Our findings deepens the understanding of amorphous structures, which can promote the design and application of phase-change materials.

Roommate Problems with Externalities

This paper extends the roommate problem to include externalities, allowing preferences for a partner to depend on the situation of the others. Assuming that everyone has prudent expectations about other agents' reactions to deviations, stability concepts for matchings and partitions of the set of agents are proposed and characterized. We prove that any roommate problem with externalities has a stable partition and that a stable matching exists if there is a stable partition without odd rings. These results allow us to find restrictions on the space of preferences ensuring the existence of a stable matching. We also show that some classical properties are lost in the presence of externalities: the existence of paths to stability from any unstable matching, the coincidence of the core with the set of stable matchings, and the invariance of the set of agents who are alone in a stable matching.

ChemInform Abstract: Novel Carbons: Habits and Oddities

AbstractReview: discussion of crystal structure predictions of novel carbon polymorphs with even and odd rings; 47 refs.

Computational Studies of Carbodiimide Rings

Computational studies of alicyclic carbodiimides (RN═C═NR) (rings five through twelve) at the MP2/6-31G(d,p)//MP2/6-31G(d,p) level of theory were conducted to locate the transition states between carbodiimides isomers. Transition states for rings six through twelve were found. The RNCNR dihedral angle is ∼0° for even-numbered rings, but deviates from 0° for rings seven, nine, eleven, and twelve. The even- and odd-numbered ring transition states have different symmetry point groups. Cs transition states (even rings) have an imaginary frequency mode that transforms as the asymmetric irreducible representation of the group. C2 transition states (odd rings) have a corresponding mode that transforms as the totally symmetric representation. Intrinsic reaction coordinate analyses followed by energy minimization along the antisymmetric pathways led to enantiomeric pairs. The symmetric pathways give diastereomeric isomers. The five-membered ring carbodiimide is a stable structure, possibly isolable. A twelve-membered ring transition state was found only without applying symmetry constraints (C1). Molecular mechanics and molecular dynamics studies of the seven-, eight-, and nine-membered rings gave additional structures, which were then minimized using ab initio methods. No structures beyond those found from the IRC analyses described were found. The potential for optical resolution of the seven-membered ring is discussed.

Novel Carbons: Habits and Oddities

AbstractCarbon is a surprising material in all respects. In this Review, we present results of metadynamics calculations for crystal structure prediction of novel carbon polymorphs with even and odd rings. So‐called superhard graphite results from cold‐compressing graphite. We review the results of molecular dynamics simulations on the graphite‐to‐diamond phase transition, that yields Oganov's M‐carbon. The latter, like some of the modifications predicted by metadynamics, features five‐ and seven‐membered odd rings. We identify the role of odd rings at times of phase nucleation, and we speculate on the preference for odd‐membered rings over even motifs in a context of nucleation and phase growth.

A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings

The term "frustration" in the context of magnetism was originally used by P. W. Anderson and quickly adopted for application to the description of spin glasses and later to very special lattice types, such as the kagomé. The original use of the term was to describe systems with competing antiferromagnetic interactions and is important in current condensed matter physics in areas such as the description of emergent magnetic monopoles in spin ice. Within molecular magnetism, at least two very different definitions of frustration are used. Here we report the synthesis and characterization of unusual nine-metal rings, using magnetic measurements and inelastic neutron scattering, supported by density functional theory calculations. These compounds show different electronic/magnetic structures caused by frustration, and the findings lead us to propose a classification for frustration within molecular magnets that encompasses and clarifies all previous definitions.

Charge transport through a molecular wire for flexible electronics

In the present work we used a system consisting of a molecular wire of multiple thiophene rings bridged between gold electrodes to study the charge transport mechanism, the effect of the tilt angle, the temperature dependence, the atomic configuration of the gold electrodes, the molecule–electrode interaction and the effect of rotation of the molecular wire on the conductance of the studied system. We found that, for shorter molecular lengths, the charge transport can be explained by tunneling, but, as the molecular length increases, it changes to hopping, which is supported by modeling the conductance of the molecular wire with a change in the temperature of the system. The results show that shorter molecular wires exhibit temperature-invariant behavior, and longer molecular wires exhibit highly temperature-variant behavior. The geometrically optimized symmetries of thiophene molecules with even and odd orientation are different, which leads to a difference in the contact configurations between the molecule and the electrodes, and results in a larger coupling parameter for thiophene molecules with even thiophene rings than for thiophene molecules with odd thiophene rings.

Front Cover (Phys. Status Solidi B 5/2010)

The front cover illustration refers to the Editor's Choice article by Kapko, Drabold, and Thorpe. They study the electronic properties of a realistic atomistic model of amorphous graphene. The model contains odd-membered rings, particularly five and seven membered rings and no coordination defects. The presence of odd rings in amorphous graphene leads to a very significant increase in the density of states in the vicinity of the Fermi level. The cover picture shows a graphene monolayer together with the calculated density of states. For more details go to page 1197.

Formation of hydrogenated amorphous carbon films containing fullerene-like structures

Abstract Hydrogenated amorphous carbon films containing fullerene-like structures were obtained by magnetron sputtering of a titanium target in methane and argon atmosphere. The microstructure of the film was investigated by transmission electron microscopy and Raman spectra. Additionally, the three stage model proposed by Ferrari and Robertson was used to explain the formation process of fullerene-like structures. The results show that titanium target was covered by a hydrocarbon layer, and the new-produced hydrocarbon layer on titanium target rather than the titanium surface was sputtered during deposition. The product of the sputtering can serve as ‘seeds’ for the formation of fullerene-like structures. These ‘seeds’ or nuclei are proposed to be open graphene structures, at the effect of ions bombardment, more defects are introduced and the curved structure arises due to incorporation of odd member rings into the graphene sheets, which resulted in the formation of curved planes with small radii of curvature and closed fullerene-like structure.

Li 8[B 16O 26(OH) 4] · 6H 2O: A novel lithium borate with a larger polyborate anion

A novel hydrated lithium borate, Li 8[B 16O 26(OH) 4] · 6H 2O, has been hydrothermally synthesized and characterized by single crystal X-ray diffraction, FT-IR spectroscopy, and simultaneous TGA–DTA. Its crystal structure consists of Li–O polyhedra and polyborate anionic layers constructed by the unprecedented [B 16O 26(OH) 4] 8− unit. The layered networks are stacked by ABAB fashion and each sheet contains the largest odd 13-membered boron rings.

Stress and structural relaxation in amorphous hydrogenated carbon films

The correlation between the residual stress and the atomic-bond structure has been investigated in detail in hydrogenated amorphous films (a-C:H). The relaxation process was studied in relation with the Raman characteristics evolution and the induced metric distortions during growth. The analysis of the Raman data shows that the metric distortions alone cannot explain the stress relaxation in the deposited films. The creation of some topological defects, such as odd rings, is required to explain both the Raman features behavior and the structural relaxation in the a-C:H samples.

Synthesis and Structure of KBGe2O6: The First Chiral Zeotype Borogermanate with 7‐Ring Channels.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Synthesis and Structure of KBGe2O6: the first chiral zeotype borogermanate with 7-ring channels.

Among the known zeolite topologies, odd rings are rare with the exception of 5-ring. We report here the hydrothermal synthesis and structural characterization of a novel compound, KBGe(2)O(6), the first germanate-based zeotype material with 7-ring channels. It crystallized in the orthorhombic system, space group P2(1)2(1)2(1) (No. 19), a = 4.8037(3) A, b = 10.2063(7) A, c = 10.7402(10) A, V = 526.57(5) A(3), Z = 3. The framework topology of this compound is previous unknown with the vertex symbol 4.6.4.6.6.7(2)(vertex1), 4.6.4.6.6.7(2)(vertex2), and 6.6.6.6.6(2) x 7(2)(vertex3). It is worth noting that the structure of the compound is chiral containing helices condensed from GeO(4) tetrahedra, which arrange around 2(1) screw axes. Furthermore, the K(+) ions within the channels are mobile and can be partially ion-exchanged with Na(+) at room temperature.

Structure, odd lines and topological entropy of disorder of amorphous silicon.

A continuous random network model of amorphous silicon, subject to periodic boundary conditions, is partitioned into cells bounded by irreducible rings. An algorithm has been developed to find the cells and the rings that bound them. A thread can be imagined to pass through odd rings (rings containing an odd number of atoms) without passing through even rings. Such a thread is an algorithmic realization of an odd line, which is the only topological defect in glass or amorphous condensed matter. The topological entropy of disorder associated with these odd lines is found to be approximately 80% of the value for an ideal tetrahedrally bonded random network of atoms for which the rings that bound the cells are statistically independent.

First principles molecular dynamics study of amorphous AlxGa1−xN alloys

We have systematically investigated atomic structures, electronic and dynamical properties of amorphous aluminum–gallium–nitride alloys (a-AlGaN) by performing first principles local basis molecular dynamics simulations. The network topology and defects of the amorphous 216-atom model system have been analyzed with the radial distribution function, the angular distribution function, the ring statistics, and the local coordination. It was found that the models have mixed threefold and fourfold coordinations, and the number of threefold (fourfold) coordinated atoms in alloys decreased (increased) with increasing Al composition. No odd rings are found, indicating that no wrong bonds (homonuclear bonds) appear in the a-AlxGa1−xN alloys. The Ga–N and Al–N bond lengths show a small variation with the Al composition, which is in agreement with recent extended x-ray absorption fine structure experimental measurements. The electronic properties examined by the electronic density of states and local bonding character demonstrate that no mid-band-gap states exist. The band-gap dependence on Al fraction x in a-AlxGa1−xN alloys shows a nearly linear variation with Al composition, and exhibits a small downward bowing behavior. It was also shown that valence band tail states are mostly localized on the threefold coordinated N sites, while the conduction band tail states are mostly localized on the threefold coordinated Ga and Al sites, and the electronic localization tends to become weaker with the addition of Al. We find a mixture of sp3 and sp2 bonds present in the network and their interaction plays a key role in the dynamical properties of a-AlxGa1−xN alloys.

Ring Current Patterns in Annelated Bicyclic Polyenes

Ring-current maps are constructed by Huckel-London theory for the 36 bicyclic systems C N H N - 2 derived by formal cross-linking of even [N]annulenes (N ≤ 18). The patterns of circulation are classified according to thelength of perimeter and position of the cross-link, described by the five possible combinations of perimeter and constituent ring sizes. The qualitative predictions are tested by ab initio distributed-origin (CTOCD) calculations of the maps for a subset of 15 bicycles in planar geometries. The ab initio calculations confirm the graph-theoretical prediction that the main current follows the Huckel rule: diatropic for 4n + 2 and paratropic for 4n π electrons. A perimeter current is found in the ab initio maps, when the bicycle is formed by fusion of two odd rings ([2l + 1], [2m + 1]), two equal antiaromatic rings ([4l, 4l]) or two (not necessarily equal) aromatic rings ([4l + 2], [4m + 2]). Orbital analysis shows that these perimeter currents are four-electron diatropic or two-electron paratropic, as in the monocycles. In the other cases, of a 4n + 2 bicycle formed by fusion of two unequal antiaromatic rings ([4l, 4m]) or of a 4n bicycle formed from fusion of an antiaromatic and an aromatic ring ([4l, 4m + 2]), the current is concentrated in one of the component rings.