Torus Structure Research Articles

Coxeter and Dynkin Diagrams and Their Associated Twisted Partition Functions for the Virasoro Minimal Models

To a pair (G′, G″) of ADE Dynkin diagrams one can associate five types of sesquilinear forms on the space of Virasoro characters. These forms can be interpreted, in terms of minimal models, as twisted partition functions. Our classification rests on the possibility of twisting the “torus structures” of the two diagrams G′ and G″. For the torus structure of a given diagram, one can introduce a single twist, two twists, or no twist at all. We describe the general situation and study an example pertaining to the case of the Virasoro minimal models.

Giant single-molecule magnets: a [Mn84] torus and its supramolecular nanotubes.

The discovery a decade ago that individual molecules can function as magnetizable magnets provided a new, 'bottom-up' approach to nanoscale magnetic materials, and such molecules have since been called single-molecule magnets (SMMs). Each molecule functions as a nanoscale, single-domain magnetic particle that, below its blocking temperature (TB), exhibits the classical macroscale property of a magnet, namely magnetization hysteresis. In addition, they straddle the classical/quantum interface in also displaying quantum tunnelling of magnetization (QTM) and quantum phase interference, the properties of the atomic or microscale. SMMs have a number of potential applications, including very high density information storage, where each bit would be stored as the magnetization orientation of an individual molecule, and as quantum bits for quantum computing, taking advantage of the quantum superposition of states provided by the QTM. To facilitate development of techniques for addressing individual SMMs for such applications, and other reasons, it has been of interest to us to explore whether very large examples (by molecular standards) could be synthesized. In effect, can the molecular (or 'bottom-up') approach reach the size regime of the classical (or 'top-down') approach to nanoscale magnetic materials? Indeed, here we sure that a giant Mn84 SMM can be prepared with a torus structure of 4 nm dimensions, that it displays both magnetization hysteresis and QTM, and that it crystallizes as highly ordered, supramolecular nanotubes.

Giant Single‐Molecule Magnets: A {Mn84} Torus and Its Supramolecular Nanotubes

The discovery a decade ago that individual molecules can function as magnetizable magnets provided a new, 'bottom-up' approach to nanoscale magnetic materials, and such molecules have since been called single-molecule magnets (SMMs). Each molecule functions as a nanoscale, single-domain magnetic particle that, below its blocking temperature (TB), exhibits the classical macroscale property of a magnet, namely magnetization hysteresis. In addition, they straddle the classical/quantum interface in also displaying quantum tunnelling of magnetization (QTM) and quantum phase interference, the properties of the atomic or microscale. SMMs have a number of potential applications, including very high density information storage, where each bit would be stored as the magnetization orientation of an individual molecule, and as quantum bits for quantum computing, taking advantage of the quantum superposition of states provided by the QTM. To facilitate development of techniques for addressing individual SMMs for such applications, and other reasons, it has been of interest to us to explore whether very large examples (by molecular standards) could be synthesized. In effect, can the molecular (or 'bottom-up') approach reach the size regime of the classical (or 'top-down') approach to nanoscale magnetic materials? Indeed, here we sure that a giant Mn84 SMM can be prepared with a torus structure of 4 nm dimensions, that it displays both magnetization hysteresis and QTM, and that it crystallizes as highly ordered, supramolecular nanotubes.

Efficient SERS substrates made by electroless silver deposition into patterned silicon structures

A nano fabrication process using caesium chloride in an island lithography scheme has been used to make wells in a silicon dioxide layer on silicon. Silver structures have been made in these wells using an electroless process that involves the reduction of silver ions and oxidation of silicon in the presence of fluoride ions. The silver deposition process is found to be diffusion controlled. The 'electroless' solution composition determines the structure of the deposited silver. Thus structures can be generated that resemble a torus or a pillar or a small set of spheres. The torus structure was found to give SERS signals for pyridine about 100 times higher than other reported structures. The stability of the torus structure in pure water is limited, and it is therefore necessary to store these structures in alkaline media or with an adsorbate layer as a protector, so making long-term active substrate storage possible. The free energy difference that drives the conversion of tori to pillars has its origin in the excess surface energy, determined by the surface curvature. Optimized substrates have a SERS sensitivity of about 108 for pyridine and some ssDNA molecules. The laser spot to spot variation in SERS signal intensity over the substrate is small, ca. ±5%. For a molecule like R6G, where resonant absorption occurs, large enhancement is obtained such that a single molecule, in the field of view (3 micron spot size) of the Raman microscope, can be detected. The importance of the torus structure would seem to be empirically established. From a practical point of view, such as using SERS as an analytical tool or examining some resonant structure, these substrates offer a sensitive, uniform and reproducible adsorbent.

Torus structure on graphs and twisted partition functions for minimal and affine models

Using the Ocneanu quantum geometry of ADE diagrams (and of other diagrams belonging to higher Coxeter–Dynkin systems), we discuss the classification of twisted partition functions for affine and minimal models in conformal field theory and study several examples associated with the WZW, Virasoro and W 3 cases.

Different types of bursting calcium oscillations in non-excitable cells

In the paper different types of bursting Ca 2+ oscillations are presented. We analyse bursting behaviour in four recent mathematical models for Ca 2+ oscillations in non-excitable cells. Separately, regular, quasi-periodic, and chaotic bursting Ca 2+ oscillations are classified into several subtypes. The classification is based on the dynamics of separated fast and slow subsystems, the so-called fast–slow burster analysis. For regular bursting Ca 2+ oscillations two types of bursting are specified: Point–Point and Point–Cycle bursting. In particular, the slow passage effect, important for the Hopf–Hopf and SubHopf–SubHopf bursting subtypes, is explained by local divergence calculated for the fast subsystem. Quasi-periodic bursting Ca 2+ oscillations can be found in only one of the four studied mathematical models and appear via a homoclinic bifurcation with a homoclinic torus structure. For chaotic bursting Ca 2+ oscillations, we found that bursting patterns resulting from the period doubling root to chaos considerably differ from those appearing via intermittency and have to be treated separately. The analysis and classification of different types of bursting Ca 2+ oscillations provides better insight into mechanisms of complex intra- and intercellular Ca 2+ signalling. This improves our understanding of several important biological phenomena in cellular signalling like complex frequency–amplitude signal encoding and synchronisation of intercellular signal transduction between coupled cells in tissue.

Effect of solenoid magnetic current on the beam extraction of filtered vacuum arc source (FVAS)

In this study, a new type of filtered vacuum arc source (FVAS) was designed, which was composed of a torus structure with bending angle of 60°. The radius of torus and plasma duct was 266 mm and 80 mm, respectively, and the total length was 600 mm. The magnet part was composed of one permanent magnet, one magnetic yoke and five solenoid magnets. The cathode evaporation region with a modified magnetic mirror configuration was adapted. The plasma duct was electrically isolated from the ground so that a bias voltage could be applied. The cathode was made of graphite and was 80 mm in diameter. A computer simulation and experiment using the Taguchi method (design of experiment) studied the effects of a solenoid magnet on plasma extraction. The source and extraction magnet affected the arc stabilization. The extraction beam current was maximized with a low value of the source magnet current and a high value for the filtering magnet current. The maximized values of the beam current density of 1.8 mA cm 2 and average deposition rate of 5 Å/s were obtained at the conditions of the arc discharge current, source, extraction and bending magnet were 30 A, 1 A, 3 A and 3 A, respectively.

Discovery of an Edge-on Dust Disk around the [WC10] Central Star CPD −56°8032

We present Hubble Space Telescope ultraviolet and optical Space Telescope Imaging Spectrograph spectroscopy of the [WCL] planetary nebula central star CPD -56°8032, obtained during its latest light-curve minimum. The UV spectrum shows the central star's continuum light distribution to be split into two bright peaks separated by 010. We interpret this finding as due to an edge-on disk or torus structure that obscures direct light from the star, which is seen primarily via its light scattered from the disk's rims or lobes. CPD -56°8032 is an archetype of dual dust chemistry [WCL] planetary nebulae, which exhibit strong infrared emission features from both carbon-rich and oxygen-rich materials, and for which the presence of a disk harboring the O-rich grains had been suggested. Our direct observation of an edge-on occulting dust structure around CPD -56°8032 provides strong support for such a model and for binary interactions being responsible for the correlation between the dual dust chemistry phenomenon in planetary nebulae and the presence of a hydrogen-deficient [WCL] Wolf-Rayet central star.

Notes on the Quantum Tetrahedron

This is a set of notes describing several aspects of the space of paths on ADE Dynkin diagrams, with a particular attention paid to the graph E6. Many results originally due to A. Ocneanu are here described in a very elementary way (manipulation of square or rectangular matrices). We define the concept of essential matrices for a graph and describe their module properties with respect to right and left actions of fusion algebras. In the case of the graph E6, essential matrices build up a right module with respect to its fusion algebra but a left module with respect to the fusion algebra of A11. We present two original results: 1) We show how to recover the Ocneanu graph of quantum symmetries of the Dynkin diagram E6 from the natural multiplication defined in the tensor square of its fusion algebra (the tensor product should be taken over a particular subalgebra); this is the Cayley graph for the two generators of the twelve dimensional algebra E6 ⊗A3 E6 (here A3 and E6 refer to the commutative fusion algebras of the corresponding graphs). 2) One already knows how to associate, with every point of the graph of quantum symmetries, a particular matrix describing the “ torus structure” of the chosen Dynkin diagram (Ocneanu construction). In the case of E6, one obtains in this way twelve such matrices of dimension 11 ×11; one of them is a modular invariant and encodes the partition function of the corresponding conformal field theory. We introduce a very simple algorithm that allows one to compute these matrices.

Physical Diagnostics from a Narrow Fe Kα Emission Line Detected byChandrain the Seyfert 1 Galaxy NGC 5548

We report the detection of a narrow Fe K? emission line in the Seyfert 1 galaxy NGC 5548 with the Chandra High-Energy Transmission Grating. In the galaxy frame we measure a center energy of 6.402 keV, a FWHM of 4515 km s-1, an intensity of 3.6 ? 10-5 photons cm-2 s-1, with an equivalent width of 133 eV (errors are 90% confidence for one parameter). The line is only marginally resolved at the 90% confidence level. The line energy is consistent with an origin in cold, neutral matter, but ionization states up to ~Fe XVIII are not ruled out. We cannot constrain the detailed dynamics but, assuming Keplerian motion, the velocity width is consistent with the line being produced in the outer optical/UV broad-line region (BLR) at about a light month from the central X-ray source. We cannot rule out some contribution to the narrow Fe K? line from a putative, parsec-scale, obscuring torus that is postulated to be a key component of active galactic nuclei (AGNs) unification models. The continuum intensity during the Chandra observation was a factor ~2 less than typical historical levels. If the X-ray continuum was at least a factor of 2 higher in the recent past before the Chandra observation and the narrow Fe K? intensity had not yet responded to such a change, then the predicted line intensity and equivalent width for an origin in the BLR is within the 90% measurement errors. Anisotropic X-ray continuum illumination of the BLR and/or additional line emission from a torus structure would improve the agreement with observation. Two out of three archival ASCA data sets are consistent with the narrow line being present with the same intensity as in the Chandra observation. However, there is strong evidence that the narrow-line intensity varied and was unusually low during one of the ASCA campaigns. In general, inclusion of the narrow line to model the overall broad Fe K? line profile in terms of a rotating disk plus black-hole model can have a non-negligible effect on the disk line intensity and variability properties. Variability of the broad disk line in NGC 5548 is difficult to reconcile with the expectations of the simple disk model, even when the narrow-line component is accounted for. It will be critical to ascertain the importance of a similar nondisk Fe K? line in other Seyfert 1 galaxies. Future monitoring of the narrow Fe K? component with large collecting area and high spectral resolution will enable reverberation mapping the BLR region, complementary to similar studies using the optical/UV lines, and therefore provide independent constraints on the black-hole mass.

Drift resonance and stability of the Io plasma torus

The observed local time asymmetry of the Io plasma torus is generally attributed to the presence of a persistent dawn‐to‐dusk electric field in the Jovian magnetosphere. The local time asymmetry is modulated at the System 3 rotation period of Jupiter's magnetic field, suggesting that the dawn‐to‐dusk electric field may be similarly modulated. We argue that such a System 3 modulation would have a profound disruptive effect on the observed torus structure if the torus were to corotate at exactly the System 3 rate: the torus would be a resonantly forced harmonic oscillator, and would disintegrate in a few rotation periods, contrary to observations. This destabilizing effect is independent of, and in addition to, the more familiar effect of the centrifugal interchange instability, which is also capable of disrupting the torus in a few rotation periods in the absence of other effects. We conclude that the observed (few percent) corotation lag of the torus is essential to preserving the observed long‐lived torus structure by detuning the resonant frequency (the torus drift frequency) relative to the forcing frequency (System 3). A possible outcome of this confinement mechanism is a residual radial oscillation of the torus at the beat period (∼10 days) between System 3 and the torus drift period.

ASCA observations of the Seyfert 2 galaxy NGC 7582: Implications for the unified scheme of AGNs

ASCA observations of the Seyfert 2 galaxy NGC 7582 revealed that it was highly variable on the timescale of ∼ 2×10 4 s in the hard X-ray band (2–10 keV), while the soft X-ray (0.5-2 keV) flux remained constant. The normalized variability amplitude in the hard X-ray band was σ RMS ≈ 0.3, which is the same level as that of Seyfert 1 galaxies of the same luminosity ∼ 3×10 42 erg s −1 (2–10 keV). The spectral analysis suggests that this object is seen through an obscuring torus with the thickness of N H ∼ 1.0 × 10 23 cm −2. The hard X-ray is an absorbed direct continuum from a hidden Seyfert 1 nucleus, while the soft X-ray is dominated by the scattered central continuum from a spatially extended region. We have an obscured/absorbed and a scattered view of this source as expected from the unification model for Seyfert galaxies. An interesting point is that the inferred column density increased by ∼ 4 × 10 22 cm −2 from 1994 to 1996, suggesting a “patchy” torus structure, namely the torus might be composed of many individual clouds. The observed iron line near 6.4 keV with EW of 170 eV is consistent with the torus picture.

Nested elliptical orbits and their resemblance to a rolling torus structure

ABSTRA C T Wide dust lanes are believed to be a common feature of active galaxies, obscuring the bright central regions. Although these dust lane features appear to be long-lived, thick discs are widely believed to be unstable and tend to collapse into very thin discs, owing to high frictional dissipation caused by intersecting orbital paths. Individual gas and dust particles in the disc are believed to orbit the galactic centre, under purely gravitational forces, in precessing elliptical orbits which are inclined to the principal plane of the disc. If the eccentricity of the orbits is related in a simple way to the inclination of the orbital planes, then the orbital paths can be nested and need not intersect. In this special case, the motion of the disc will be ‘low-loss’ and almost free of friction. The envelope traced out by these nested orbits resembles a torus and there are severe restrictions on the permitted values of orbital elements. This torus executes a collective motion, it rotates toroidally (‘rolls round’) as it orbits the galactic centre. The rolling torus analogue of nested elliptical orbits is simple to model and predicts velocity dispersions all along the dust lane ‐ even in the line of sight to the nucleus. Evidence is presented for the dust lane of the radio galaxy Centaurus A being a torus which rolls as it orbits the centre. Non-circular velocities and ‘radial streaming motions’ are observed in the dust lane of Cen A at a range of wavelengths. The size of these anomalous velocities is in good numerical agreement with the predictions of this model. These velocities are difficult to explain in dust lane models based on circular orbits.

ASCA Observations of the Seyfert 2 Galaxy NGC 7582: An Obscured and Scattered View of the Hidden Nucleus

ASCA observations of the Seyfert 2 galaxy NGC 7582 revealed that it was highly variable on the timescale of ∼ 2×104 s in the hard X-ray band (2–10 keV), while the soft X-ray (0.5–2 keV) flux remained constant during the observations. The normalized variability amplitude in the hard X-ray band was σRMS ≈ 0.3, which is the same level as that of Seyfert 1 galaxies of the same luminosity ∼ 3 × 1042 erg s−1 (2–10 keV). The spectral analysis suggests that this object is seen through an obscuring torus with the thickness of NH ∼ 1.0× 1023 cm−2 . The hard X-rays are an absorbed direct continuum from a hidden Seyfert 1 nucleus, while the soft X-rays are dominated by the scattered central continuum from an extended spatial region. We have an obscured/absorbed and a scattered view of this source as expected from the unification model for Seyfert galaxies. More interestingly, the inferred column density increased by ∼ 4×1022 cm−2 from 1994 to 1996, suggesting a “patchy” torus structure, namely the torus might be composed of many individual clouds. The observed iron-line feature near 6.4 keV with the equivalent width of 170 eV is also consistent with the picture of the transmission of nuclear X-ray continuum through a non-uniform torus.

Impairment of Proliferating Cell Nuclear Antigen-dependent Apurinic/Apyrimidinic Site Repair on Linear DNA

Repair of apurinic/apyrimidinic (AP) sites by mammalian cell extracts was compared using circular and linear DNA substrates. Extracts prepared from DNA polymerase beta (polbeta)-proficient mouse fibroblasts repaired AP sites on both circular and linear DNA. However, extracts from the isogenic polbeta-knockout cells repaired AP sites on circular DNA but not efficiently on linear DNA. The circularity-dependent repair by the polbeta-knockout cell extract was completely inhibited by anti-proliferating cell nuclear antigen (PCNA) antibody but fully restored by addition of purified PCNA. Pretreatment of the linear DNA with AP endonuclease did not improve repair, indicating that impairment of AP site repair on linear DNA by polbeta-knockout cell extracts is not due to inefficiency of damage incision but rather to deficiency at the subsequent steps. These results indicate that AP sites can be repaired on circular DNA by the PCNA-dependent pathway in addition to the polbeta-dependent pathway and that the PCNA-dependent repair mechanism is poorly functional on linear DNA in vitro.

3.33. A close look at NGC1068 by adaptive optics: dust torus and micro-spiral structure

As the closest Seyfert nucleus, NGC 1068 is a key object to establish on firm grounds the model of active galactic nuclei (AGN). Two important questions relative to AGNs are : i) can we actually see the parsec-scale torus of dust and molecular gas around the central engine predicted by the popular Unified Model model (e.g. Antonucci, 1993)?; ii) how the gas is brought down to the parsec scale to feed the monster, and, in particular, is there a micro spiral/bar system that could produce the required torque ? Adaptive Optics in the near-IR has potential advantages to make a significant progress in those two questions : the low dust opacity and the excellent angular resolution.

The SUPRENUM supercomputer: Goals, achievements, and lessons learned

SUPRENUM is a highly parallel supercomputer for numerical applications. The 5-GFLOPS peak performance of the 256-node system made it the most powerful MIMD architecture of the ‘first generation.’ Each node is a complete, single-board vector machine with 20 Mflops peak performance (IEEE double precision). SUPRENUM is a distributed memory architecture, resulting in a highly scalable system that can be made fault-tolerant. Message passing is accelerated by dedicated communication hardware in each node. Array access is performed by an ‘intelligent’ DMA address generator. The SUPRENUM architecture was the first to be based on two-level interconnection structure, consisting of a number of clusters with each cluster consisting of a number of nodes. At the cluster level the nodes are interconnected by two very fast parallel buses. At the system level the clusters are interconnected by a torus structure consisting of serial ring buses. The nodes run under the proprietary, distributed PEACE operating system. Significant efforts were undertaken to make the system programmable, by providing a host of software tools, libraries, and application software packages. The paper discusses the rationale for the SUPRENUM architecture, the goals achieved, and the lessons learned.

The concept of drastically easy maintenance (DREAM) tokamak reactor

Abstract One of the most important features of a power plant is high availability. An easy maintenance scheme is indispensable for high availability operation. For the easy maintenance scheme, a plasma configuration with high aspect ratio (with slender doughnut shape) of about 6 and a small number of 12 torus sectors is introduced. The adjacent torus sectors are jointed mechanically by a bolt-flange structure. The plasma vacuum region comprises a cryostat system and 12 horizontal access doors. A whole section of each torus sector is pulled out horizontally in a single radial straight motion between the adjacent toroidal field (TF) coils. The TF coil system is imbedded in the reactor building and can be repaired independent of the torus structure. The torus structure consists of a shield integrated vacuum vessel, a divertor structure and a tritium fuel breeding blanket structure. The divertor or blanket system is replaced from the transverse (toroidal) direction after the torus structure is pulled out. Even in the torus inboard region, there is a gap of 1 m between adjacent TF coils because of the high aspect ratio reactor configuration. Therefore, all the piping and feeder systems are gathered at the torus inboard region. The overall machine size is determined by a fusion power of 3 GW and almost 100% bootstrap current with a moderate Troyon coefficient of 3.5, magnetohydrodynamic safety factor of 5 and plasma elongation of 1.6.

Embedding of rings and meshes onto faulty hypercubes using free dimensions

Fault tolerance in hypercubes is achieved by exploiting inherent redundancy and executing tasks on faulty hypercubes. The authors consider tasks that require linear chain, ring, mesh, and torus structure, which are quite useful in parallel and pipeline computations. They assume the number of faults is on the order of the number of dimensions of the hypercube. The techniques are based on a key concept called free dimension, which can be used to partition a cube into subcubes such that each subcube contains, at most, one faulty node. Subgraphs are embedded in each subcube and then merged to form the entire graph.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Ionization Cones in the Seyfert Galaxy NGC 5728

view Abstract Citations (118) References (25) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Ionization Cones in the Seyfert Galaxy NGC 5728 Wilson, A. S. ; Braatz, J. A. ; Heckman, T. M. ; Krolik, J. H. ; Miley, G. K. Abstract We report high-resolution (0.1") observations of the Seyfert 2 galaxy NGC 5728 with the Hubble Space Telescope. Images have been obtained in the light of [O III] λλ4959, 5007, Hα+[N II] λλ6548, 6583 and green and red continua. The emission-line images reveal a spectacular biconical structure with overall extent 1.8 kpc. The two cones share a common axis and apex. The cones' axis coincides to within ~3^deg^ with that of the one-sided nuclear radio continuum emission but is not aligned with the rotation axis of the galaxy disk. No [O III] and only weak Hα + [N II] emissions are seen at the apex itself where the continuum is also weak and its color red. These results suggest our line of sight to the cones' apex is obscured or blocked. The apex almost certainly reflects the location of the "true" active nucleus, for it coincides with the radio nucleus, the gaseous kinematical center, and the geometrical center of the circumnuclear star-forming ring (which has been interpreted in terms of an inner Lindblad resonance). Bright, barlike features are seen in continuum light and may represent either a kpc-scale stellar bar or scattered nuclear light. Our data provide strong support for unified models of Seyfert galaxies, in which Seyfert 2 nuclei are blocked from direct view by an optically thick torus or other structure, with optical and ultraviolet radiation escaping preferentially along and around the torus axis. Publication: The Astrophysical Journal Pub Date: December 1993 DOI: 10.1086/187137 Bibcode: 1993ApJ...419L..61W Keywords: GALAXIES: ACTIVE; GALAXIES: INDIVIDUAL NGC NUMBER: NGC 5728; GALAXIES: ISM; GALAXIES: NUCLEI; GALAXIES: SEYFERT; GALAXIES: SPIRAL full text sources ADS | data products SIMBAD (7) NED (1) MAST (1) ESA (1)