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Journal articles on the topic 'Double-Torus'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

Hajac, Piotr M., and Tetsuya Masuda. "Quantum double-torus." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 327, no. 6 (September 1998): 553–58. http://dx.doi.org/10.1016/s0764-4442(98)89162-3.

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2

OZAWA, MAKOTO. "SATELLITE DOUBLE TORUS KNOTS." Journal of Knot Theory and Its Ramifications 10, no. 01 (February 2001): 133–42. http://dx.doi.org/10.1142/s0218216501000779.

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We characterize satellite double torus knots. Especially, if a satellite double torus knot is not a cable knot, then it has a torus knot companion. This answers Question 12 (a) raised by Hill and Murasugi in [4].

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3

Hayashi, Chuichiro. "Trivial Double-Torus Knot." Journal of Knot Theory and Its Ramifications 12, no. 05 (August 2003): 579–88. http://dx.doi.org/10.1142/s0218216503002652.

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A knot K in a closed connected orientable 3-manifold M is called a double-torus knot, if it is in a genus two Heegaard splitting surface H of M. We give a necessary and sufficient condition for a double-torus knot to be the trivial knot in words of meridian disks of genus two handlebodies obtained by splitting M along H.

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4

OZAWA, MAKOTO. "TANGLE DECOMPOSITIONS OF DOUBLE TORUS KNOTS AND LINKS." Journal of Knot Theory and Its Ramifications 08, no. 07 (November 1999): 931–39. http://dx.doi.org/10.1142/s0218216599000584.

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5

HILL, PETER, and KUNIO MURASUGI. "ON DOUBLE-TORUS KNOTS (II)." Journal of Knot Theory and Its Ramifications 09, no. 05 (August 2000): 617–67. http://dx.doi.org/10.1142/s0218216500000359.

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A double-torus knot is a knot embedded in a genus two Heegaard surface [Formula: see text] in S3. We consider double-torus knots L such that [Formula: see text] is connected, and consider fibred knots in various classes.

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6

NORWOOD, RICK. "TURNING DOUBLE-TORUS LINKS INSIDE OUT." Journal of Knot Theory and Its Ramifications 08, no. 06 (September 1999): 789–98. http://dx.doi.org/10.1142/s0218216599000493.

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7

HILL, PETER. "ON DOUBLE-TORUS KNOTS (I)." Journal of Knot Theory and Its Ramifications 08, no. 08 (December 1999): 1009–48. http://dx.doi.org/10.1142/s0218216599000651.

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A double-torus knot is knot embedded in a genus two Heegaard surface [Formula: see text] in S3. After giving a notation for these knots, we consider double-torus knots L such that [Formula: see text] is not connected, and give a criterion for such knots to be non-trivial. Various new types of non-trivial knots with trivial Alexander polynomial are found.

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8

LEE, KYUNG BAI, and FRANK RAYMOND. "MAXIMAL TORUS ACTIONS ON SOLVMANIFOLDS AND DOUBLE COSET SPACES." International Journal of Mathematics 02, no. 01 (February 1991): 67–76. http://dx.doi.org/10.1142/s0129167x91000065.

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Any compact, connected Lie group which acts effectively on a closed aspherical manifold is a torus Tk with k ≤ rank of [Formula: see text], the center of π1 (M). When [Formula: see text], the torus action is called a maximal torus action. The authors have previously shown that many closed aspherical manifolds admit maximal torus actions. In this paper, a smooth maximal torus action is constructed on each solvmanifold. They also construct smooth maximal torus actions on some double coset spaces of general Lie groups as applications.

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9

Álvarez, Miguel Carrión, Joseph Corneli, Genevieve Walsh, and Shabnam Beheshti. "Double Bubbles in the Three-Torus." Experimental Mathematics 12, no. 1 (January 2003): 79–89. http://dx.doi.org/10.1080/10586458.2003.10504713.

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10

Gillard, Mike, and Paul Sutcliffe. "Domain walls and double bubbles." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2109 (July 8, 2009): 2911–25. http://dx.doi.org/10.1098/rspa.2009.0227.

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We study configurations of intersecting domain walls in a Wess–Zumino model with three vacua. We introduce a volume-preserving flow and show that its static solutions are configurations of intersecting domain walls that form double bubbles, that is, minimal area surfaces which enclose and separate two prescribed volumes. To illustrate this field theory approach to double bubbles, we use domain walls to reconstruct the phase diagram for double bubbles in the flat square two-torus and also construct all known examples of double bubbles in the flat cubic three-torus.

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11

Khayutin, Ilya. "Arithmetic of double torus quotients and the distribution of periodic torus orbits." Duke Mathematical Journal 168, no. 12 (September 2019): 2365–432. http://dx.doi.org/10.1215/00127094-2019-0016.

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12

Choi, Doo Ho, and Ki Hyoung Ko. "Parameterizations of 1-Bridge Torus Knots." Journal of Knot Theory and Its Ramifications 12, no. 04 (June 2003): 463–91. http://dx.doi.org/10.1142/s0218216503002445.

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A 1-bridge torus knot in a 3-manifold of genus ≤ 1 is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal form we give algorithms to determine the number of components and to compute the fundamental group of the complement when the normal form determines a knot. We also give a description of the double branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by using its Conway's normal form and obtain an explicit formula for the first homology of the double cover.

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13

Zhang, Xue-Guang. "A practicable estimation of opening angle of dust torus in Type-1.9 AGN with double-peaked broad Hα." Monthly Notices of the Royal Astronomical Society 519, no. 3 (January 9, 2023): 4461–66. http://dx.doi.org/10.1093/mnras/stad024.

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ABSTRACT In this manuscript, an independent method is proposed to estimate opening angle of dust torus in AGN, through unique properties of Type-1.9 AGN with double-peaked broad Hα (Type-1.9 DPAGN) coming from central accretion disc. Type-1.9 AGN without broad Hβ can be expected by the commonly accepted unified model of AGN, considering central BLRs seriously obscured by dust torus with its upper boundary in the line of sight. For the unique Type-1.9 DPAGN, accretion disc originations of double-peaked broad Hα can be applied to determine the inclination angle of the central accretion disc, which is well accepted as substitute of the half opening angle of the central dust torus. Then, among low redshift Type-1.9 DPAGN in SDSS, SDSS J1607+3319 at redshift 0.063 is collected, and the half opening angle of the central dust torus is determined to be around 46 ± 4°, after considering the disfavoured BBH system to explain the double-peaked broad Hα through long-term none variabilities and disfavoured local physical conditions to explain the disappearance of broad Hβ through virial BH mass properties. The results indicate that more detailed studying on dust torus of AGN can be appropriately done through Type-1.9 DPAGN in the near future.

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14

Monera, M. G., V. Gómez-Gutiérrez, and F. Sánchez-Bringas. "Lines of Curvature on the Double Torus." Lobachevskii Journal of Mathematics 43, no. 1 (January 2022): 98–109. http://dx.doi.org/10.1134/s1995080222040138.

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15

LANE, S., H. NORWOOD, and R. NORWOOD. "ERRATUM: "TURNING DOUBLE-TORUS LINKS INSIDE OUT"." Journal of Knot Theory and Its Ramifications 22, no. 05 (April 2013): 1392002. http://dx.doi.org/10.1142/s0218216513920028.

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16

Brubaker, Nicholas D., Stephen Carter, Sean M. Evans, Daniel E. Kravatz, Sherry Linn, Stephen W. Peurifoy, and Ryan Walker. "Double Bubble Experiments in the Three-Torus." Math Horizons 15, no. 4 (April 2008): 18–21. http://dx.doi.org/10.1080/10724117.2008.11974768.

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17

Zhu, Zhiwen, and Zhong Liu. "Strange Nonchaotic Attractors of Chua's Circuit with Quasiperiodic Excitation." International Journal of Bifurcation and Chaos 07, no. 01 (January 1997): 227–38. http://dx.doi.org/10.1142/s0218127497000169.

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This paper focuses attention on strange nonchaotic attractor of Chua's circuit with two-frequency quasiperiodic excitation. Existence of the attractor is confirmed by calculating several characterizing quantities such as Lyapunov exponents, Poincaré maps, double Poincaré maps and so on. Two basic mechanisms are described for the development of the strange nonchaotic attractor from two-frequency quasiperiodic state (torus solution). One of them is torus-doubling bifurcation followed by a smooth transition from the torus attractor to the strange nonchaotic attractor; and another is that the torus does not undergo period-doubling bifurcation at all; instead, the torus attractor gradually becomes wrinkled, and eventually becomes strange but nonchaotic.

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18

Liu, Xiaolei, and Motohiko Murai. "Engineering Possibility Studies of a Novel Cylinder-Type FOWT Using Torus Structure with Annular Flow." Energies 15, no. 13 (July 5, 2022): 4919. http://dx.doi.org/10.3390/en15134919.

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This paper proposes and researches a novel cylinder-type FOWT using a neutrally buoyant double-layer torus structure with annular flow; its oscillatory motion in severe sea conditions is controlled by a spinning top device designed as a neutrally buoyant double-layer torus structure with annular flow water in a torus structure with a small internal radius, and welded to the periphery of the cylinder-type FOWT underwater buoyancy-providing part. The rotational axis retention effect and the gyroscopic effect are considered appropriate approaches to suppress the oscillating motion of FOWT. To obtain a better hydrodynamic response, the scale of the torus structure, such as its radius, the radius of the internal annular flow water, and the angular velocity of the annular flow water are taken as the design parameters, and a large number of comparative calculations based on the fluid–solid coupling theory of potential flow are carried out to determine the appropriate design parameters. Eventually, on the basis of the obtained suitable design parameters, the proposed conceptual design approach is demonstrated to be feasible in view of the energy consumption.

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19

Pandey, Vipul Kumar, and Bhabani Prasad Mandal. "Double Hodge Theory for a Particle on Torus." Advances in High Energy Physics 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6124189.

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We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.

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20

Samuelson, Peter. "Iterated Torus Knots and Double Affine Hecke Algebras." International Mathematics Research Notices 2019, no. 9 (September 4, 2017): 2848–93. http://dx.doi.org/10.1093/imrn/rnx198.

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21

Liu, Wenna, and Chuanzhong Li. "Symmetries of the q-NKdV hierarchy." International Journal of Modern Physics A 36, no. 06 (February 28, 2021): 2150040. http://dx.doi.org/10.1142/s0217751x21500408.

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In this paper, the additional symmetries and the string equation of the [Formula: see text]-NKdV hierarchy are established basing on the Orlov–Shulman’s [Formula: see text] operator, and then some properties are also given. Next, we construct the quantum torus symmetry of the [Formula: see text]-NKdV hierarchy and further derive the quantum torus constraints on the tau function of the [Formula: see text]-NKdV hierarchy. Comparing to the [Formula: see text] infinite-dimensional Lie symmetry, this quantum torus symmetry has a nice algebraic structure with double indices. Finally, we study the ghost symmetry of the multicomponent [Formula: see text]-NKdV hierarchy.

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22

Elliot, Ross, and Sergei Gukov. "Exceptional knot homology." Journal of Knot Theory and Its Ramifications 25, no. 03 (March 2016): 1640003. http://dx.doi.org/10.1142/s0218216516400034.

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The goal of this paper is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called hyperpolynomials that address the “problem of negative coefficients” often encountered in DAHA-based approaches to homological invariants of torus knots and links. Furthermore, from the physics of BPS states and the spectra of singularities associated with Landau–Ginzburg potentials, we also describe a rich structure of differentials that act on homological knot invariants for exceptional groups and uniquely determine the latter for torus knots.

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23

Bardiev, Dilshodbek, Martin Kološ, Daniela Pugliese, and Zdeněk Stuchlík. "GRMHD Evolution of Interacting Double Accretion Tori Orbiting a Central Black Hole." Astrophysical Journal 941, no. 2 (December 1, 2022): 173. http://dx.doi.org/10.3847/1538-4357/aca0a3.

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Abstract The matter orbiting black holes (BHs) in microquasars or active galactic nuclei forms toroidal accretion disk structures, and multiple torus structures have been recently described as ringed accretion disks (RADs) in a full general relativistic approach. Here we realize full general relativistic magnetohydrodynamic (GRMHD) numerical simulations related to double toroidal structure immersed in the equatorial plane of the gravitomagnetic field of a central Schwarzschild BH in an asymptotically uniform magnetic field. We study the merging dynamics of an initial RAD structure constructed by two corotating or counterrotating tori, where accretion of matter from the outer torus is assumed onto the inner torus, using the 2.5D GRMHD simulation schemes with the HARM numerical code. We study the dynamics of the system assuming various initial conditions, and we have demonstrated that the initial matter density is the relevant factor governing the system evolution.

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24

Gomes, Eduardo Michel Vieira, Edson Donizete de Carvalho, Carlos Alexandre Ribeiro Martins, Waldir Silva Soares, and Eduardo Brandani da Silva. "Hyperbolic Geometrically Uniform Codes and Ungerboeck Partitioning on the Double Torus." Symmetry 14, no. 3 (February 23, 2022): 449. http://dx.doi.org/10.3390/sym14030449.

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Current research builds labelings for geometrically uniform codes on the double torus through tiling groups. At least one labeling group was provided for all of the 11 regular tessellations on the double torus, derived from triangular Fuchsian groups, as well as extensions of these labeling groups to generate new codes. An important consequence is that such techniques can be used to label geometrically uniform codes on surfaces with greater genera. Furthermore, partitioning chains are constructed into geometrically uniform codes using soluble groups as labeling, which in some cases results in an Ungerboeck partitioning for the surface. As a result of these constructions, it is demonstrated that, as in Euclidean spaces, modulation and encoding can be combined in a single step in hyperbolic space.

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25

Corneli, Joseph, Paul Holt, George Lee, Nicholas Leger, Eric Schoenfeld, and Benjamin Steinhurst. "The double bubble problem on the flat two-torus." Transactions of the American Mathematical Society 356, no. 9 (March 12, 2004): 3769–820. http://dx.doi.org/10.1090/s0002-9947-04-03551-2.

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26

Král', Daniel, and Matěj Stehlík. "Coloring of Triangle-Free Graphs on the Double Torus." SIAM Journal on Discrete Mathematics 22, no. 2 (January 2008): 541–53. http://dx.doi.org/10.1137/07067920x.

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27

Hikami, Kazuhiro. "DAHA and skein algebra of surfaces: double-torus knots." Letters in Mathematical Physics 109, no. 10 (June 13, 2019): 2305–58. http://dx.doi.org/10.1007/s11005-019-01189-5.

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28

TAMVAKIS, HARRY, and ELIZABETH WILSON. "Double theta polynomials and equivariant Giambelli formulas." Mathematical Proceedings of the Cambridge Philosophical Society 160, no. 2 (December 18, 2015): 353–77. http://dx.doi.org/10.1017/s0305004115000754.

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AbstractWe use Young's raising operators to introduce and study double theta polynomials, which specialize to both the theta polynomials of Buch, Kresch, and Tamvakis, and to double (or factorial) Schur S-polynomials and Q-polynomials. These double theta polynomials give Giambelli formulas which represent the equivariant Schubert classes in the torus-equivariant cohomology ring of symplectic Grassmannians, and we employ them to obtain a new presentation of this ring in terms of intrinsic generators and relations.

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29

Cruz-González, I., A. I. Gómez-Ruiz, A. Caldú-Primo, E. Benítez, J. M. Rodríguez-Espinosa, Y. Krongold, I. Aretxaga, et al. "Early science with the LMT: molecular torus in UGC 5101." Monthly Notices of the Royal Astronomical Society 499, no. 2 (September 25, 2020): 2042–50. http://dx.doi.org/10.1093/mnras/staa2949.

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ABSTRACT As part of the Early Science Large Millimeter Telescope projects, we report the detection of nine double-peaked molecular lines, produced by a rotating molecular torus, in the ultraluminous infrared galaxies (ULIRG) – Compton-thick active galactic nuclei (AGN) galaxy UGC 5101. The double-peaked lines we report correspond to molecular transitions of HCN, HCO+, HNC, N2H+, CS, C18O, 13CO, and two CN lines; plus the detection of C2H that is a blend of six lines. The redshift search receiver spectra covers the 73–113 GHz frequency window. Low- and high-density gas tracers of the torus have different implied rotational velocities, with a rotational velocity of 149 ± 3 km s−1 for the low-density ones (C18O, 13CO) and 174 ± 3 km s−1 for high-density tracers (HCN, HCO+, HNC, N2H+, CS, and CN). In UGC 5101, we find that the ratio of integrated intensities of HCN to 13CO to be unusually large, probably indicating that the gas in the torus is very dense. Both the column densities and abundances are consistent with values found in AGN, starburst, and ULIRG galaxies. The observed abundance ratios cannot discriminate between X-ray and UV-field-dominated regions.

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30

Ruben, George C., and Kenneth A. Marx. "Torus Circumference and Thickness Parameters From a Linear DNA Size Series Suggest How Toruses Self-Assemble." Proceedings, annual meeting, Electron Microscopy Society of America 43 (August 1985): 522–23. http://dx.doi.org/10.1017/s0424820100119430.

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Certain double stranded DNA bacteriophage and viruses are thought to have their DNA organized into large torus shaped structures. Morphologically, these poorly understood biological DNA tertiary structures resemble spermidine-condensed DNA complexes formed in vitro in the total absence of other macromolecules normally synthesized by the pathogens for the purpose of their own DNA packaging. Therefore, we have studied the tertiary structure of these self-assembling torus shaped spermidine- DNA complexes in a series of reports. Using freeze-etch, low Pt-C metal (10-15Å) replicas, we have visualized the microscopic DNA organization of both calf Thymus( CT) and linear 0X-174 RFII DNA toruses. In these structures DNA is circumferentially wound, continuously, around the torus into a semi-crystalline, hexagonal packed array of parallel DNA helix sections.

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31

Chen, Tao, Xianli Liu, Changhong Wang, and Guangyue Wang. "Design and fabrication of double-circular-arc torus milling cutter." International Journal of Advanced Manufacturing Technology 80, no. 1-4 (March 31, 2015): 567–79. http://dx.doi.org/10.1007/s00170-015-7033-2.

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32

Hart, Evelyn L., and Edward C. Keppelmann. "Explorations in Nielsen periodic point theory for the double torus." Topology and its Applications 95, no. 1 (June 1999): 1–30. http://dx.doi.org/10.1016/s0166-8641(97)00277-0.

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33

Ponomaryov, G. A., K. P. Levenfish, and A. E. Petrov. "Jet and counter-jet in transonic pulsar wind nebulae." Journal of Physics: Conference Series 2103, no. 1 (November 1, 2021): 012021. http://dx.doi.org/10.1088/1742-6596/2103/1/012021.

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Abstract X-ray observations show that a jet and a counter-jet in pulsar wind nebulae often differ one from another. Sometimes one of the jets is not observed at all. We show that the most likely reason for this difference is the relative motion of a pulsar and an ambient matter. Even the slow (subsonic or transonic) ambient matter stream in the pulsar rest frame strongly affects the jets, making the windward jet bright and dynamic, and the leeward jet dim and diffuse. The effect is illustrated using a relativistic MHD model of a double-torus pulsar wind nebula. The model is shown to explain reasonably well the observational appearance of the jets in the Vela nebula - a double-torus object which evolves in a transonic stream initiated by the passage of the reverse shock of the parent supernova.

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34

Lamm, Tobias, and Reiner M. Schätzle. "Conformal Willmore tori in ℝ4." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 742 (September 1, 2018): 281–301. http://dx.doi.org/10.1515/crelle-2015-0101.

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Abstract For every two-dimensional torus {T^{2}} and every k \in \mathbb{N} , {k\geq 3} , we construct a conformal Willmore immersion f : T^{2} \to \mathbb{R}^{4} with exactly one point of density k and Willmore energy 4πk. Moreover, we show that the energy value {8\pi} cannot be attained by such an immersion. Additionally, we characterize the branched double covers T^{2} \to S^{2} \times \{ 0 \} as the only branched conformal immersions, up to Möbius transformations of {\mathbb{R}^{4}} , from a torus into {\mathbb{R}^{4}} with at least one branch point and Willmore energy {8\pi} . Using a perturbation argument in order to regularize a branched double cover, we finally show that the infimum of the Willmore energy in every conformal class of tori is less than or equal to {8\pi} .

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35

TRIPP, JAMES J. "THE CANONICAL GENUS OF WHITEHEAD DOUBLES OF A FAMILY TORUS KNOTS." Journal of Knot Theory and Its Ramifications 11, no. 08 (December 2002): 1233–42. http://dx.doi.org/10.1142/s0218216502002219.

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36

Kamiyama, Kyohei, Motomasa Komuro, Tetsuro Endo, and Kazuyuki Aihara. "Classification of Bifurcations of Quasi-Periodic Solutions Using Lyapunov Bundles." International Journal of Bifurcation and Chaos 24, no. 12 (December 2014): 1430034. http://dx.doi.org/10.1142/s0218127414300341.

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In continuous-time dynamical systems, a periodic orbit becomes a fixed point on a certain Poincaré section. The eigenvalues of the Jacobian matrix at this fixed point determine the local stability of the periodic orbit. Analogously, a quasi-periodic orbit (2-torus) becomes an invariant closed curve (ICC) on a Poincaré section. From the Lyapunov exponents of an ICC, we can determine the time average of the exponential divergence rate of the orbit, which corresponds to the eigenvalues of a fixed point. We denote the Lyapunov exponent with the smallest nonzero absolute value as the Dominant Lyapunov Exponent (DLE). A local bifurcation manifests as a crossing or touch of the DLE locus with zero. However, the type of bifurcation cannot be determined from the DLE. To overcome this problem, we define the Dominant Lyapunov Bundle (DLB), which corresponds to the dominant eigenvectors of a fixed point. We prove that the DLB of a 1-torus in a map can be classified into four types: A+(annulus and orientation preserving), A-(annulus and orientation reversing), M (Möbius band), and F (focus). The DLB of a 2-torus in a flow can be classified into three types: A+× A+, A-× M (equivalently M × A-and M × M), and F × F. From the results, we conjecture the possible local bifurcations in both cases. For the 1-torus in a map, we conjecture that type A+and A-DLBs correspond to a saddle-node and period-doubling bifurcations, respectively, whereas a type M DLB denotes a double-covering bifurcation, and type F relates to a Neimark–Sacker bifurcation. Similarly, for the 2-torus in a flow, we conjecture that type A+× A+DLBs correspond to saddle-node bifurcations, type A-× M DLBs to double-covering bifurcations, and type F × F DLBs to the Neimark–Sacker bifurcations. After introducing the mathematical concepts, we provide a DLB-calculating algorithm and illustrate all of the above bifurcations by examples.

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37

Jiang, Heping, Tonghua Zhang, and Yongli Song. "Delay-Induced Double Hopf Bifurcations in a System of Two Delay-Coupled van der Pol–Duffing Oscillators." International Journal of Bifurcation and Chaos 25, no. 04 (April 2015): 1550058. http://dx.doi.org/10.1142/s0218127415500583.

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In this paper, we investigate the codimension-two double Hopf bifurcation in delay-coupled van der Pol–Duffing oscillators. By using normal form theory of delay differential equations, the normal form associated with the codimension-two double Hopf bifurcation is calculated. Choosing appropriate values of the coupling strength and the delay can result in nonresonance and weak resonance double Hopf bifurcations. The dynamical classification near these bifurcation points can be explicitly determined by the corresponding normal form. Periodic, quasi-periodic solutions and torus are found near the bifurcation point. The numerical simulations are employed to support the theoretical results.

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38

Hanao, Takafumi, Nobuharu Oki, Takashi Nakayama, Takahiro Hyobu, Hidetoshi Hirono, Yusuke Kikuchi, Naoyuki Fukumoto, and Masayoshi Nagata. "Experiment of Double-pulsing Helicity Injection on Helicity Injected Spherical Torus Plasmas." IEEJ Transactions on Fundamentals and Materials 134, no. 9 (2014): 497–502. http://dx.doi.org/10.1541/ieejfms.134.497.

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39

Zhao, Yaping, Jianyi Kong, Gongfa Li, and Tianchao Wu. "Tooth flank modification theory of dual-torus double-enveloping hourglass worm drives." Computer-Aided Design 43, no. 12 (December 2011): 1535–44. http://dx.doi.org/10.1016/j.cad.2011.06.024.

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40

Kramer, Peter, and Miguel Lorente. "The double torus as a 2D cosmos: groups, geometry and closed geodesics." Journal of Physics A: Mathematical and General 35, no. 8 (February 18, 2002): 1961–81. http://dx.doi.org/10.1088/0305-4470/35/8/312.

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41

MA, SUQI, QISHAO LU, and S. JOHN HOGAN. "DOUBLE HOPF BIFURCATION FOR STUART–LANDAU SYSTEM WITH NONLINEAR DELAY FEEDBACK AND DELAY-DEPENDENT PARAMETERS." Advances in Complex Systems 10, no. 04 (December 2007): 423–48. http://dx.doi.org/10.1142/s0219525907001227.

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A Stuart–Landau system under delay feedback control with the nonlinear delay-dependent parameter e-pτ is investigated. A geometrical demonstration method combined with theoretical analysis is developed so as to effectively solve the characteristic equation. Multi-stable regions are separated from unstable regions by allocations of Hopf bifurcation curves in (p,τ) plane. Some weak resonant and non-resonant oscillation phenomena induced by double Hopf bifurcation are discovered. The normal form for double Hopf bifurcation is deduced. The local dynamical behavior near double Hopf bifurcation points are also clarified in detail by using the center manifold method. Some states of two coexisting stable periodic solutions are verified, and some torus-broken procedures are also traced.

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LIPIŃSKI, Z. "YANGIAN DEFORMATION OF THE LIE ALGEBRA dĩff(T2)." Modern Physics Letters A 13, no. 20 (June 28, 1998): 1611–22. http://dx.doi.org/10.1142/s0217732398001698.

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New solution of a classical Yang–Baxter equation on a loop extended, "modified" Lie algebra of a diffeomorphism group of a torus dĩff(T2)[λ]is given. Lie bialgebra structure on dĩff(T2)[λ] is defined. By quantization of a defined Lie bialgebra, a Yangian algebra Y(dĩff(T2)) is obtained. Existence of a quantum double and a quantum R-matrix for Y(dĩff(T2)) is considered.

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Ichihara, Kazuhiro, and Makoto Ozawa. "Hyperbolic knot complements without closed embedded totally geodesic surfaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 3 (June 2000): 379–86. http://dx.doi.org/10.1017/s1446788700001476.

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AbstractIt is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces cannot be totally geodesic.

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Baptista, M. S., and I. L. Caldas. "Dynamics of the two-frequency torus breakdown in the driven double scroll circuit." Physical Review E 58, no. 4 (October 1, 1998): 4413–20. http://dx.doi.org/10.1103/physreve.58.4413.

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Kuznetsov A.P., Sedova Yu.V., and Stankevich N.V. "Two coupled quasiperiodic generators excited by external force." Technical Physics 67, no. 14 (2022): 2174. http://dx.doi.org/10.21883/tp.2022.14.55214.145-21.

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A system of two dissipatively coupled generators, which can exhibit autonomous quasiperiodic oscillations, excited by a harmonic signal, is studied. Lyapunov charts are presented that reveal the regimes of invariant tori of different dimensions and chaos. Phase portraits in stroboscopic section and double Poincare section are presented. The coexistence of different regimes, in particular, the bifurcations of invariant tori, is discussed. Keywords: quasiperiodic oscillations, coupled generators, Lyapunov charts, invariant torus, Poincare section, quasiperiodic bifurcation.

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Spong, Matthew. "A construction of complex analytic elliptic cohomology from double free loop spaces." Compositio Mathematica 157, no. 8 (July 26, 2021): 1853–97. http://dx.doi.org/10.1112/s0010437x21007363.

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We construct a complex analytic version of an equivariant cohomology theory which appeared in a paper of Rezk, and which is roughly modelled on the Borel-equivariant cohomology of the double free loop space. The construction is defined on finite, torus-equivariant CW complexes and takes values in coherent holomorphic sheaves over the moduli stack of complex elliptic curves. Our methods involve an inverse limit construction over all finite-dimensional subcomplexes of the double free loop space, following an analogous construction of Kitchloo for single free loop spaces. We show that, for any given complex elliptic curve $\mathcal {C}$, the fiber of our construction over $\mathcal {C}$ is isomorphic to Grojnowski's equivariant elliptic cohomology theory associated to $\mathcal {C}$.

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Antonucci, Robert. "Unified Models: Religion and Science." Symposium - International Astronomical Union 159 (1994): 301–9. http://dx.doi.org/10.1017/s0074180900175205.

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The Unified Model states that the classification of individual AGN is a function of orientation, and that orientation effects are key to understanding the different classes. In its most extreme form, it states that every AGN has a featureless continuum (FC) source and a broad line region (BLR), both enclosed in an opaque torus. The torus is perpendicular to the associated radio structure axis. For the powerful radio sources (in Elliptical galaxy hosts), the jets undergo bulk relativistic motion, giving rise to phenomena such as superluminal motion associated with the blazar class. All strong radio sources have diffuse double radio lobes, although in the blazars one is sometimes seen projected onto the other. To take this to the extreme, we can suppose that all opaque tori are made of dust and have the same opening angle and that the radio jets are all narrow and have the same bulk-motion Γ factor.

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Kameno, Seiji, Makoto Inoue, Kiyoaki Wajima, Satoko Sawada-Satoh, and Zhi-Qiang Shen. "Dense Plasma Torus in the GPS Galaxy NGC 1052." Publications of the Astronomical Society of Australia 20, no. 1 (2003): 134–39. http://dx.doi.org/10.1071/as03003.

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AbstractWe report results from nearly simultaneous pentachromatic VLBI observations towards a nearby GPS galaxy NGC 1052. The observations at 1.6 and 4.8 GHz with the VSOP, and at 2.3, 8.4, and 15.4 GHz with VLBA, provide linear resolutions of ∼0.1 pc. Convex spectra of a double-sided jet imply that synchrotron emission is obscured through foreground cold dense plasma, in terms of free–free absorption (FFA). We found a central condensation of the plasma which covers about 0.1 and 1 pc of the approaching and receding jets, respectively. A simple model with a geometrically thick plasma torus perpendicular to the jets is established to explain the asymmetric distribution of FFA opacities.

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MARQUES, F., J. M. LOPEZ, and J. SHEN. "Mode interactions in an enclosed swirling flow: a double Hopf bifurcation between azimuthal wavenumbers 0 and 2." Journal of Fluid Mechanics 455 (March 25, 2002): 263–81. http://dx.doi.org/10.1017/s0022112001007285.

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A double Hopf bifurcation has been found of the flow in a cylinder driven by the rotation of an endwall. A detailed analysis of the multiple solutions in a large region of parameter space, computed with an efficient and accurate three-dimensional Navier-Stokes solver, is presented. At the double Hopf point, an axisymmetric limit cycle and a rotating wave bifurcate simultaneously. The corresponding mode interaction generates an unstable two-torus modulated rotating wave solution and gives a wedge-shaped region in parameter space where the two periodic solutions are both stable. By exploring in detail the three-dimensional structure of the flow, we have identified the two mechanisms that compete in the neighbourhood of the double Hopf point. Both are associated with the jet that is formed when the Ekman layer on the rotating endwall is turned by the stationary sidewall.

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FROLOV, S. A. "GAUGE-INVARIANT HAMILTONIAN FORMULATION OF LATTICE YANG-MILLS THEORY AND THE HEISENBERG DOUBLE." Modern Physics Letters A 10, no. 34 (November 10, 1995): 2619–31. http://dx.doi.org/10.1142/s0217732395002751.

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It is known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge A0=0 one should place on each link a cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting case of a so-called Heisenberg double of a Lie group which is one of the basic objects in the theory of Lie-Poisson and quantum groups. It is shown in the paper that there is a generalization of the usual Hamiltonian formulation to the case of the Heisenberg double. The physical phase space of the (1+1)-dimensional γ-deformed Yang-Mills model is proved to be equivalent to the moduli space of flat connections on a two-dimensional torus.

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