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Journal articles on the topic 'Toroidal rings'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Ley Koo, E., H. Torres-Bustamante, and A. Góngora T. "Spherical symmetry breaking in electric, magnetic and toroidal multipole moment radiations in spherical toroidal resonant cavities and optimum-efficiency antennas." Revista Mexicana de Física 67, no. 2 Mar-Apr (July 15, 2021): 174–79. http://dx.doi.org/10.31349/revmexfis.67.174.

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This Letter reports the breaking of the spherical symmetry in the complete electromagnetic multipole expansion when its sources are distributed on spherical toroidal surfaces, identifying the specic geometrical and physical changes fromthe familiar case of sources on a spherical surface. In fact, for spherical toroids dened by concentric spherical rings and symmetric conical rings, the boundary conditions at the latter are not compatible in general with integer values for the orbital angular momentum label of the multipole moments: the polar angle eigenfunctions become Legendre functions of order λ and associativity m represented as innite series with a denite parity, and their complementary associated radial functions are spherical Bessel functions of the same order λ. Consequently, the corresponding multipole sources for the electric, magnetic and toroidal moments and their connections are identied within the Debye formalism, and theappropriate outgoing wave Green functions are constructed in the new basis of eigenfunctions of the Helmholtz equation. Our familiarity with the exact solutions, for the cases of the complete sphere and of cylindrical toroids, allow us to give a preliminary account of the electromagnetic elds for the spherical toroids via the integration of their sources and the Green function for resonant cavities and optimum effciency antennas.

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2

Hingorani, Manju M., and Mike O'Donnell. "Toroidal proteins: Running rings around DNA." Current Biology 8, no. 3 (January 1998): R83—R86. http://dx.doi.org/10.1016/s0960-9822(98)70052-1.

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3

Dikpati, Mausumi, Aimee A. Norton, Scott W. McIntosh, and Peter A. Gilman. "Dynamical Splitting of Spot-producing Magnetic Rings in a Nonlinear Shallow-water Model." Astrophysical Journal 922, no. 1 (November 1, 2021): 46. http://dx.doi.org/10.3847/1538-4357/ac1359.

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Abstract We explore the fundamental physics of narrow toroidal rings during their nonlinear magnetohydrodynamic evolution at tachocline depths. Using a shallow-water model, we simulate the nonlinear evolution of spot-producing toroidal rings of 6° latitudinal width and a peak field of 15 kG. We find that the rings split; the split time depends on the latitude of each ring. Ring splitting occurs fastest, within a few weeks, at latitudes 20°–25°. Rossby waves work as perturbations to drive the instability of spot-producing toroidal rings; the ring split is caused by the “mixed stress” or cross-correlations of perturbation velocities and magnetic fields, which carry magnetic energy and flux from the ring peak to its shoulders, leading to the ring split. The two split rings migrate away from each other, the high-latitude counterpart slipping poleward faster due to migrating mixed stress and magnetic curvature stress. Broader toroidal bands do not split. Much stronger rings, despite being narrow, do not split due to rigidity from stronger magnetic fields within the ring. Magnetogram analysis indicates the emergence of active regions sometimes at the same longitudes but separated in latitude by 20° or more, which could be evidence of active regions emerging from split rings, which consistently contribute to observed high-latitude excursions of butterfly wings during the ascending, peak, and descending phases of a solar cycle. Observational studies in the future can determine how often new spots are found at higher latitudes than their lower-latitude counterparts and how the combinations influence solar eruptions and space weather events.

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4

Abad, M., M. Guilleumas, R. Mayol, and M. Pi. "Vortex rings in toroidal Bose-Einstein condensates." Laser Physics 18, no. 5 (May 2008): 648–52. http://dx.doi.org/10.1134/s1054660x08050162.

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5

Selvakumar, Krishnan, and Manoharan Subajini. "Classification of rings with toroidal Jacobson graph." Czechoslovak Mathematical Journal 66, no. 2 (June 2016): 307–16. http://dx.doi.org/10.1007/s10587-016-0257-y.

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6

Wu, Chunyan, Chunhua Hu, and Yuzhou Liu. "Hyperbranched polysiloxane with highly constrained rings and the effect of the attached arms on the assembly behavior." Polymer Chemistry 8, no. 42 (2017): 6490–95. http://dx.doi.org/10.1039/c7py01177f.

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7

Baniodeh, Amer, Nicola Magnani, Stefan Bräse, Christopher E. Anson, and Annie K. Powell. "Ligand field variations: tuning the toroidal moment of Dy6 rings." Dalton Transactions 44, no. 14 (2015): 6343–47. http://dx.doi.org/10.1039/c5dt00237k.

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8

Sanchez del Rio, Manuel, Kenneth A. Goldberg, Valeriy V. Yashchuk, Ian Lacey, and Howard A. Padmore. "Simulations of applications using diaboloid mirrors." Journal of Synchrotron Radiation 28, no. 4 (June 1, 2021): 1041–49. http://dx.doi.org/10.1107/s160057752100401x.

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The diaboloid is a reflecting surface that converts a spherical wave to a cylindrical wave. This complex surface may find application in new Advanced Light Source bending-magnet beamlines or in other beamlines that now use toroidal optics for astigmatic focusing. Here, the numerical implementation of diaboloid mirrors is described, and the benefit of this mirror in beamlines exploiting diffraction-limited storage rings is studied by ray tracing. The use of diaboloids becomes especially interesting for the new low-emittance storage rings because the reduction of aberration becomes essential for such small sources. The validity of the toroidal and other mirror surfaces approximating the diaboloid, and the effect of the mirror magnification, are discussed.

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9

Cherkasova, O. A., A. A. Skripkin, and S. A. Cherkasova. "Computer Simulation of a Radial Contactless Magnetic Suspension on a Permanent Magnet System." Vestnik Tambovskogo gosudarstvennogo tehnicheskogo universiteta 27, no. 4 (2021): 543–54. http://dx.doi.org/10.17277/vestnik.2021.04.pp.543-554.

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The distributions of magnetic induction and magnetic field strength are obtained. It was found that with a parallel arrangement of toroidal rings of elliptical cross-section in a magnetic suspension, the magnetic induction is 1.7 times higher than with a perpendicular arrangement of the same rings. The calculation of the ponderomotive and magnetomotive forces between two toroidal annular permanent magnets with a radial magnetization of an elliptical section in a contactless magnetic suspension system is carried out. Quasi-elastic stiffness coefficients and static load capacity were calculated for both models. It is shown that the rigidity of the suspension decreases monotonically with a decrease in the size of the gap, regardless of the model.

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10

Kalaimurugan, G., P. Vignesh, and T. Tamizh Chelvam. "On zero-divisor graphs of commutative rings without identity." Journal of Algebra and Its Applications 19, no. 12 (December 5, 2019): 2050226. http://dx.doi.org/10.1142/s0219498820502266.

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Let [Formula: see text] be a finite commutative ring without identity. In this paper, we characterize all finite commutative rings without identity, whose zero-divisor graphs are unicyclic, claw-free and tree. Also, we obtain all finite commutative rings without identity and of cube-free order for which the corresponding zero-divisor graph is toroidal.

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11

Никулин, В. В., and Е. А. Чашников. "Коэффициент расширения тороидального воздушного пузыря в воде." Письма в журнал технической физики 48, no. 13 (2022): 46. http://dx.doi.org/10.21883/pjtf.2022.13.52745.19241.

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The rise of a toroidal bubble in water obtained by injecting a pulsed jet of air into the water through a nozzle vertically upwards has been experimentally investigated. It was found that despite the decrease in the cross-section of the toroidal bubble during the ascent, its radius, depending on the distance traveled, grows linearly, as in the case of self-similar vortex rings. The coefficient of expansion of the bubble at different volumes of injected air is determined. A comparison was made with toroidal bubbles obtained when balloons burst in water. A qualitative explanation of the observed differences is given.

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12

Di, Chenyang, Jian Zhang, Fang Wang, and Yu Zhang. "Numerical and Experimental Buckling and Post-Buckling Analyses of Sphere-Segmented Toroidal Shell Subject to External Pressure." Metals 13, no. 1 (December 26, 2022): 64. http://dx.doi.org/10.3390/met13010064.

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This study determined the buckling characteristics of sphere-segmented toroidal shells subjected to external pressure. The proposed toroidal vessel comprises six spheres and six rings. Two laboratory models with the same nominal dimensions were manufactured, measured, tested, and evaluated. To investigate whether sphere-segmented toroidal shells are imperfection-sensitive structures with closely spaced eigenvalues, the subspace algorithm was applied to evaluate the first 50 eigenmodes, and the modified Riks algorithm was used to obtain post-buckling characteristics. The results indicated that the deviation between the results of the experimental and numerical analyses was within a reasonable range. The proposed sphere-segmented toroidal shells were highly imperfection-sensitive structures with closely spaced eigenvalues. Subsequently, imperfection sensitivity analysis confirmed this conclusion. In numerical analyses, the first eigenmode could be considered as the worst eigenmode of sphere-segmented toroidal shells. The trend of the equilibrium path of sphere-segmented toroidal shells was consistent with spherical shells, revealing instability. In addition, ellipticity and completeness exerted a negligible effect on the buckling load of sphere-segmented toroidal shells.

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13

Buelk, Samuel, Ben Cox, and Elizabeth Jurisich. "A Wakimoto Type Realization of Toroidal 𝔰𝔩n+1." Algebra Colloquium 19, spec01 (October 31, 2012): 841–66. http://dx.doi.org/10.1142/s1005386712000727.

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The authors construct a Wakimoto type realization of toroidal 𝔰𝔩n+1. The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor product of two polynomial rings in infinitely many commuting variables.

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14

Hymas, Kieran, and Alessandro Soncini. "The Role of Magnetic Dipole—Dipole Coupling in Quantum Single-Molecule Toroics." Magnetochemistry 8, no. 5 (May 23, 2022): 58. http://dx.doi.org/10.3390/magnetochemistry8050058.

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For single-molecule toroics (SMTs) based on noncollinear Ising spins, intramolecular magnetic dipole–dipole coupling favours a head-to-tail vortex arrangement of the semi-classical magnetic moments associated with a toroidal ground state. However, to what extent does this effect survive beyond the semi-classical Ising limit? Here, we theoretically investigate the role of dipolar interactions in stabilising ground-state toroidal moments in quantum Heisenberg rings with and without on-site magnetic anisotropy. For the prototypical triangular SMT with strong on-site magnetic anisotropy, we illustrate that, together with noncollinear exchange, intramolecular magnetic dipole–dipole coupling serves to preserve ground-state toroidicity. In addition, we investigate the effect on quantum tunnelling of the toroidal moment in Kramers and non-Kramers systems. In the weak anisotropy limit, we find that, within some critical ion–ion distances, intramolecular magnetic dipole–dipole interactions, diagonalised over the entire Hilbert space of the quantum system, recover ground-state toroidicity in ferromagnetic and antiferromagnetic odd-membered rings with up to seven sites, and are further stabilised by Dzyaloshinskii–Moriya coupling.

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15

UJEVIC, MAXIMILIANO, PATRICIO S. LETELIER, and DANIEL VOGT. "RELATIVISTIC RING MODELS." International Journal of Modern Physics D 20, no. 12 (November 25, 2011): 2291–304. http://dx.doi.org/10.1142/s0218271811020305.

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Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin–Toomre family of disks. In particular, we present systems with one ring, two rings and a disk with a ring. Also, the circular velocity of a test particle and its stability when performing circular orbits are presented in all these models. In general, we find that regions of non-stability appear between the rings when they become thinner.

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16

Alanazi, Abdulaziz M., Mohd Nazim, and Nadeem Ur Rehman. "Classification of Rings with Toroidal and Projective Coannihilator Graph." Journal of Mathematics 2021 (June 12, 2021): 1–7. http://dx.doi.org/10.1155/2021/4384683.

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Let S be a commutative ring with unity, and a set of nonunit elements is denoted by W S . The coannihilator graph of S , denoted by A G ′ S , is an undirected graph with vertex set W S ∗ (set of all nonzero nonunit elements of S ), and α ∼ β is an edge of A G ′ S ⇔ α ∉ α β S or β ∉ α β S , where δ S denotes the principal ideal generated by δ ∈ S . In this study, we first classify finite ring S , for which A G ′ S is isomorphic to some well-known graph. Then, we characterized the finite ring S , for which A G ′ S is toroidal or projective.

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17

LI, SHUAI, SHI-PING WANG, and A.-MAN ZHANG. "CHARACTERISTICS OF THE JET IMPACT DURING THE INTERACTION BETWEEN A BUBBLE AND A WALL." International Journal of Modern Physics: Conference Series 42 (January 2016): 1660157. http://dx.doi.org/10.1142/s2010194516601575.

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The dynamics of a toroidal bubble splitting near a rigid wall in an inviscid incompressible fluid is studied in this paper. The boundary integral method is adopted to simulate the bubble motion. After the jet impact, the vortex ring model is used to handle the discontinued potential of the toroidal bubble. When the toroidal bubble is splitting, topology changes are made tear the bubble apart. Then, the vortex ring model is extended to multiple vortex rings to simulate the interaction between two toroidal bubbles. A typical case is discussed in this study. Besides, the velocity fields and pressure contours surrounding the bubble are used to illustrate the numerical results. An annular high pressure region is generated at the splitting location, and the maximum pressure may be much higher than the jet impact. More splits may happen after the first split.

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18

Warren, W. E., and J. A. Weese. "The Deformation of O-Rings Compressed by Smooth Rigid Plates." Journal of Energy Resources Technology 119, no. 2 (June 1, 1997): 73–80. http://dx.doi.org/10.1115/1.2794979.

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Three-dimensional effects of symmetrically compressing an O-ring with rigid plates are investigated. The O-ring is assumed to be an incompressible elastic material and the mixed boundary value problem is formulated within the framework of classical the linear elasticity theory. Transversely compressing the O-ring between flat rigid plates increases the toroidal radius and induces a reduction in the O-ring cross-sectional radius. This reduction depends strongly on the conditions of contact between plate and O-ring, and the reduced contact pressure may threaten the integrity of the seal. For O-rings compressed radially inward compressed radially inward or outward, most of the radial displacement is accommodated by a change in the toroidal radius with very little actual compression of the ring material. If this effect is not accounted for in the design of the seal, the contact pressure may not be sufficient to secure the seal.

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19

Bogoyavlenskij, Oleg. "Safety Factor for the New Exact Plasma Equilibria." Zeitschrift für Naturforschung A 74, no. 2 (January 28, 2019): 163–81. http://dx.doi.org/10.1515/zna-2018-0337.

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AbstractAn exact formula for the limit of the safety factor q at a magnetic axis is derived for the general up-down asymmetric plasma equilibria possessing axial symmetry, generalizing Bellan’s formula for the up-down symmetric ones. New exact axisymmetric plasma equilibria depending on arbitrary parameters α, ξ, bkn, zkn, where k = 1, ⋯, M, n = 1⋯, N, are constructed (α ≠ 0 is a scaling parameter), which are up-down asymmetric in general. The equilibria are not force-free if ξ ≠ 0 and satisfy Beltrami equation if ξ = 0. For some values of ξ the magnetic field and electric current fluxes have isolated invariant toroidal magnetic rings, for another ξ they have invariant spheroids (blobs) and for some values of ξ both invariant toroidal rings and spheroids (blobs). A generalization of the Chandrasekhar – Fermi – Prendergast magnetostatic model of a magnetic star is presented where plasma velocity V(x) is non-zero.

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20

Meger, R. A., M. R. Parker, and H. H. Fleischmann. "Anomalous losses from relativistic electron rings in decreasing toroidal fields." Physics of Fluids 28, no. 1 (January 1985): 13–16. http://dx.doi.org/10.1063/1.865174.

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21

Vogt, D., and P. S. Letelier. "Analytical potential-density pairs for flat rings and toroidal structures." Monthly Notices of the Royal Astronomical Society 396, no. 3 (July 1, 2009): 1487–98. http://dx.doi.org/10.1111/j.1365-2966.2009.14803.x.

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22

Liu, P., Y. W. Zhang, and C. Lu. "Structures and stability of defect-free multiwalled carbon toroidal rings." Journal of Applied Physics 98, no. 11 (December 2005): 113522. http://dx.doi.org/10.1063/1.2138371.

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23

Kalaimurugan, G., P. Vignesh, and T. Tamizh Chelvam. "Toroidal zero-divisor graphs of decomposable commutative rings without identity." Boletín de la Sociedad Matemática Mexicana 26, no. 3 (March 28, 2020): 807–29. http://dx.doi.org/10.1007/s40590-020-00282-3.

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24

Vasetsky, Yu M. "VIRIAL THEOREM LIMITATIONS FOR THE TOROIDAL MAGNETIC ENERGY STORAGE CAUSED BY THE LOCATION OF SUPPORT STRUCTURE ELEMENTS AND THEIR MECHANICAL PROPERTIES." Tekhnichna Elektrodynamika 2022, no. 1 (January 24, 2022): 3–16. http://dx.doi.org/10.15407/techned2022.01.003.

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Based on the virial theorem, the influence of the following factors to characteristics of mechanical support systems of toroidal magnetic energy storage is considered: the configuration of the coils, the support system elements location under compressive forces, the mechanical properties of the material, the distribution of the cross-sectional areas of the support rings and the corresponding distribution of radial forces. It is established that the volume of structure requirement depends only on the radii from which the coils transmit forces to the support rings. The found general relation, in contrast to the existing ones, establishes a relationship between all the parameters that determine the volume of the support structures. The characteristics of support systems are analyzed both for identical mechanical stresses and for identical mechanical properties of all support elements. The characteristics for specific examples of toroidal systems with circular coils are found. It is shown that systems with support elements in compression located on the side of the vertical axis of the torus have a significantly smaller volume of structure compared to other locations. The influence of the relative radial size of the torus cross-section and the distribution of the cross-sectional areas of the support rings on the structure requirement is analyzed. The relationship between dimensionless characteristics that determine the volume of elements subjected to mechanical stresses of compression and tension is noted. References 37, figures 8, table 1.

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25

Yang, Zhaoqi, Dawei Li, and Tianhu Li. "Design and synthesis of catenated rings based on toroidal DNA structures." Chemical Communications 47, no. 43 (2011): 11930. http://dx.doi.org/10.1039/c1cc14957a.

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26

Fulla, M. R., F. Rodriguez-Prada, and J. H. Marín Cadavid. "Spectral properties of two electrons vertically coupled in toroidal quantum rings." Superlattices and Microstructures 49, no. 3 (March 2011): 252–57. http://dx.doi.org/10.1016/j.spmi.2010.07.002.

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27

Marín, J. H., M. R. Fulla, F. Rodriguez-Prada, F. García, and J. C. Piña. "Energy spectrum of an artificial molecular complex in toroidal quantum rings." Superlattices and Microstructures 49, no. 3 (March 2011): 258–63. http://dx.doi.org/10.1016/j.spmi.2010.07.004.

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28

Stafeev, S. S., and V. V. Kotlyar. "Toroidal polarization vortices in tightly focused beams with singularity." Computer Optics 44, no. 5 (October 2020): 685–90. http://dx.doi.org/10.18287/2412-6179-co-734.

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In this paper, we numerically investigated tight focusing of cylindrical vector beams of the second order using Richards-Wolf formulae. It was shown that intensity rings where the Poynting vector was equal to zero appeared not only in the focal plane but also in nearby planes. For example, a lens with numerical aperture NA=0.95 was shown to generate periodical toroidal vortices with a 0.8-m period along the z-axis at a distance of about 0.45 m from the axis. The vortices were generated pairwise, with the closest-to-focus vortex having clockwise helicity and the subsequent being anticlockwise. The vortices were also characterized by saddle points. When focusing an optical beam passed through a narrow annular aperture, no toroidal vortices were observed.

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29

Chelvam, T. Tamizh, K. Selvakumar, and V. Ramanathan. "Cayley sum graph of ideals of commutative rings." Journal of Algebra and Its Applications 17, no. 07 (June 13, 2018): 1850125. http://dx.doi.org/10.1142/s0219498818501256.

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Let [Formula: see text] be a commutative ring, [Formula: see text] the set of all ideals of [Formula: see text] and [Formula: see text], a subset of [Formula: see text]. The Cayley sum graph of ideals of [Formula: see text], denoted by Cay[Formula: see text], is a simple undirected graph with vertex set is the set [Formula: see text] and, for any two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] or [Formula: see text], for some [Formula: see text] in [Formula: see text]. In this paper, we study connectedness, Eulerian and Hamiltonian properties of Cay[Formula: see text]. Moreover, we characterize all commutative Artinian rings [Formula: see text] whose Cay[Formula: see text] is toroidal.

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30

Lorén-Aguilar, Pablo, and Matthew R. Bate. "Toroidal vortices and the conglomeration of dust into rings in protoplanetary discs." Monthly Notices of the Royal Astronomical Society: Letters 453, no. 1 (August 25, 2015): L78—L82. http://dx.doi.org/10.1093/mnrasl/slv109.

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31

Damiani, Rick, Gabor Vali, and Samuel Haimov. "The Structure of Thermals in Cumulus from Airborne Dual-Doppler Radar Observations." Journal of the Atmospheric Sciences 63, no. 5 (May 1, 2006): 1432–50. http://dx.doi.org/10.1175/jas3701.1.

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Abstract A newly developed technique for airborne dual-Doppler observations with the Wyoming Cloud Radar is used to characterize the velocity fields in vertical planes across cumulus turrets. The clouds sampled were continental in nature, with high bases (near 0°C) and with depths of 2–3 km. Clear evidence was found that the clouds evolved through sequences of bubbles, or thermals, with well-defined toroidal circulations, or vortex rings. The ring core and tube diameters were about 200–600 m, leading to turret sizes of 1–2 km in the horizontal. The largest updraft speeds were observed in the ring centers, but regions of turbulent, ascending air extended behind the thermals to distances comparable with the toroid sizes. Vertical shear of ambient winds, when present, led to a tilting of the updrafts and toroids. Patterns in the reflectivity and velocity fields indicated regions of major intrusions into the thermals, accompanied by entrainment of ambient air, or recycling of larger hydrometeors, depending on their location. In addition, at the upper cloud/environment interface, instability nodes contributed to further entrapment of cloud-free air. The observations presented in this paper constitute clear demonstrations and quantitative characterization of vortical circulations in growing cumulus turrets; they should provide a more reliable basis for the assessment of simulations and of model parameterizations.

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32

Xu, Yichao, and Vitali F. Nesterenko. "Propagation of short stress pulses in discrete strongly nonlinear tunable metamaterials." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2023 (August 28, 2014): 20130186. http://dx.doi.org/10.1098/rsta.2013.0186.

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The propagation of short pulses with wavelength comparable to the size of a unit cell has been studied in a one-dimensional discrete metamaterial composed of steel discs alternating with toroidal nitrile O-rings under different levels of precompression using experiments, numerical simulations and theoretical analysis. This strongly nonlinear metamaterial is more tunable than granular chains composed of linear elastic spherical particles and has better potential for attenuation of dynamic loads. A double power-law relationship for compressed O-rings was found to describe adequately their quasi-static and dynamic behaviour with significantly different elastic moduli. It is demonstrated that the double power-law metamaterial investigated allows a dramatic increase in sound speed and acoustic impedance of three to four times using a moderate force.

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33

Piazza, Ivan Di, and Michele Ciofalo. "Transition to turbulence in toroidal pipes." Journal of Fluid Mechanics 687 (October 18, 2011): 72–117. http://dx.doi.org/10.1017/jfm.2011.321.

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AbstractIncompressible flow in toroidal pipes of circular cross-section was investigated by three-dimensional, time-dependent numerical simulations using a finite volume method. The computational domain included a whole torus and was discretized by up to ${\ensuremath{\sim} }11. 4\ensuremath{\times} 1{0}^{6} $ nodes. Two curvatures $\delta $ (radius of the cross-section/radius of the torus), namely 0.3 and 0.1, were examined; a streamwise forcing term was imposed, and its magnitude was made to vary so that the bulk Reynolds number ranged between ${\ensuremath{\sim} }3500$ and ${\ensuremath{\sim} }14\hspace{0.167em} 700$. The results were processed by different techniques in order to confirm the spatio-temporal structure of the flow. Consecutive transitions between different flow regimes were found, from stationary to periodic, quasi-periodic and chaotic flow. At low Reynolds number, stationary flow was predicted, exhibiting a symmetric couple of Dean vortex rings and a strong shift of the streamwise velocity maximum towards the outer wall. For $\delta = 0. 3$, between $\mathit{Re}= 4556$ and $\mathit{Re}= 4605$ a first transition occurred from stationary to periodic flow, associated with a supercritical Hopf bifurcation and giving rise to a travelling wave which took the form of a varicose streamwise modulation of the Dean vortex ring intensity. A further transition, associated with a secondary Hopf bifurcation, occurred between $\mathit{Re}= 5042$ and $\mathit{Re}= 5270$ and led to a quasi-periodic flow characterized by two independent fundamental frequencies associated with distinct travelling waves, the first affecting mainly the Dean vortex rings and similar to that observed in purely periodic flow, the second localized mainly in the secondary flow boundary layers and manifesting itself as an array of oblique vortices produced at the edge of the Dean vortex regions. Both the periodic and the quasi-periodic regimes were characterized by an instantaneous anti-symmetry of the oscillatory components with respect to the equatorial midplane of the torus. For $\delta = 0. 1$, between $\mathit{Re}= 5139$ and $\mathit{Re}= 5208$ a direct (‘hard’) transition from steady to quasi-periodic flow occurred. Hysteresis was also observed: starting from a quasi-periodic solution and letting the Reynolds number decrease, both quasi-periodic and periodic stable solutions were obtained at Reynolds numbers below the critical value. A further decrease in $\mathit{Re}$ led to steady-state solutions. This behaviour suggests the existence of a subcritical Hopf bifurcation followed by a secondary Hopf bifurcation. The resulting periodic and quasi-periodic flows were similar to those observed for the higher curvature, but the travelling modes were now instantaneously symmetric with respect to the equatorial midplane of the torus. Also, the further transition from quasi-periodic to chaotic flow occurred with different modalities for the two curvatures. For $\delta = 0. 3$, a centrifugal instability of the main flow in the outer region occurred abruptly between $\mathit{Re}= 7850$ and $\mathit{Re}= 8160$, while a further increase of $\mathit{Re}$ up to 13 180 did not cause any relevant change in the distribution and intensity of the fluctuations. For $\delta = 0. 1$ the transition to chaotic flow was gradual in the range $\mathit{Re}= 6280$ to 8160 and affected mainly the inner region; only a further increase of $\mathit{Re}$ to 14 700 caused fluctuations to appear also in the outer region.

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34

Gourdie, Robert G., Tereance A. Myers, Alex McFadden, Yin-xiong Li, and Jay D. Potts. "Self-Organizing Tissue-Engineered Constructs in Collagen Hydrogels." Microscopy and Microanalysis 18, no. 1 (January 4, 2012): 99–106. http://dx.doi.org/10.1017/s1431927611012372.

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AbstractA novel self-organizing behavior of cellularized gels composed of collagen type 1 that may have utility for tissue engineering is described. Depending on the starting geometry of the tissue culture well, toroidal rings of cells or hollow spheroids were prompted to form autonomously when cells were seeded onto the top of gels and the gels released from attachment to the culture well 12 to 24 h after seeding. Cells within toroids assumed distinct patterns of alignment not seen in control gels in which cells had been mixed in. In control gels, cells formed complex three-dimensional arrangements and assumed relatively higher levels of heterogeneity in expression of the fibronectin splice variant ED-A—a marker of epithelial mesenchymal transformation. The tissue-like constructs resulting from this novel self-organizing behavior may have uses in wound healing and regenerative medicine, as well as building blocks for the iterative assembly of synthetic biological structures.

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35

Alanazi, Abdulaziz M., Mohd Nazim, and Nadeem Ur Rehman. "Planar, Outerplanar, and Toroidal Graphs of the Generalized Zero-Divisor Graph of Commutative Rings." Journal of Mathematics 2021 (August 10, 2021): 1–7. http://dx.doi.org/10.1155/2021/4828579.

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Let A be a commutative ring with unity and let set of all zero divisors of A be denoted by Z A . An ideal ℐ of the ring A is said to be essential if it has a nonzero intersection with every nonzero ideal of A . It is denoted by ℐ ≤ e A . The generalized zero-divisor graph denoted by Γ g A is an undirected graph with vertex set Z A ∗ (set of all nonzero zero-divisors of A ) and two distinct vertices x 1 and x 2 are adjacent if and only if ann x 1 + ann x 2 ≤ e A . In this paper, first we characterized all the finite commutative rings A for which Γ g A is isomorphic to some well-known graphs. Then, we classify all the finite commutative rings A for which Γ g A is planar, outerplanar, or toroidal. Finally, we discuss about the domination number of Γ g A .

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Arshad Ahmed, Kalilur Rahiman, J. Prasanna Naveen Kumar, Ashokkumar Shyam, Elumalai Natarajan, Selvarasan Iniyan, and Ranko Goic. "Experimental investigation on a solar parabolic trough receiver tube enhanced by toroidal rings." International Journal of Energy Research 46, no. 5 (December 28, 2021): 6637–53. http://dx.doi.org/10.1002/er.7599.

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Bakhtyiari, Moharram, Reza Nikandish, and Mohammad Javad Nikmehr. "When the annihilator graph of a commutative ring is planar or toroidal?" Acta et Commentationes Universitatis Tartuensis de Mathematica 24, no. 2 (December 31, 2020): 281–90. http://dx.doi.org/10.12697/acutm.2020.24.19.

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Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. The annihilator graph of R is defined as the undirected graph AG(R) with the vertex set Z(R)* = Z(R) \ {0}, and two distinct vertices x and y are adjacent if and only if ann_R(xy) \neq ann_R(x) \cup ann_R(y). In this paper, all rings whose annihilator graphs can be embedded on the plane or torus are classified.

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Han, J. L., and G. J. Qiao. "On Galactic magnetic field derived from RMs of pulsars." International Astronomical Union Colloquium 160 (1996): 485–86. http://dx.doi.org/10.1017/s0252921100042196.

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AbstractRMs of all 262 pulsars are used to see the large scale magnetic field of our Galaxy. We find that: (1). RMs of 91 pulsars at high galactic latitude (|b| > 8.6°) show two toroidal magnetic rings antisymmetric with respect to galactic plane. These data shouldn’t be used for modelling the large scale field in Galactic disk; (2). pulsars at low galactic latitude are concentrated on the spiral arms; (3). the directions of fields have a similar pitch angle to that of spiral arms.

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Zdagkas, Apostolos, Nikitas Papasimakis, Vassili Savinov, Mark R. Dennis, and Nikolay I. Zheludev. "Singularities in the flying electromagnetic doughnuts." Nanophotonics 8, no. 8 (June 22, 2019): 1379–85. http://dx.doi.org/10.1515/nanoph-2019-0101.

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AbstractFlying doughnuts (FDs) are exact propagating solutions of Maxwell equations in the form of single-cycle, space-time non-separable toroidal pulses. Here we review their properties and reveal the existence of a complex and robust fine topological structure. In particular, the electric and magnetic fields of the FD pulse vanish across a number of planes, spherical shells and rings, and display a number of point singularities including saddle points and vortices. Moreover, the instantaneous Poynting vector of the field exhibits a large number of singularities, which are often accompanied by extended areas energy backflow.

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Zhang, Jingyu, Chang Liu, Hengli Feng, Dongchao Fang, Jincheng Wang, Zuoxin Zhang, Yachen Gao, and Yang Gao. "Dual-Channel Mid-Infrared Toroidal Metasurfaces for Wavefront Modulation and Imaging Applications." Nanomaterials 12, no. 19 (September 22, 2022): 3300. http://dx.doi.org/10.3390/nano12193300.

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In this paper, we propose a dual-channel mid-infrared toroidal metasurface that consists of split equilateral triangular rings. The electromagnetic responses are analyzed by the finite-difference-time-domain (FDTD) method and temporal coupled-mode theory (TCMT). The results show that one channel of the metasurface is insensitive to the polarization angle of the incident light and temperature, while the other channel is sensitive. The reflectance and resonance wavelength can be manipulated by the polarization angle and temperature independently. Based on such a mechanism, we propose metasurfaces for two-bit programmable imaging and thermal imaging. The metasurfaces are believed to have potential applications in information processing and thermal radiation manipulation.

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Oliinyk, Artem, Igor Yatsuta, Boris Malomed, and Alexander Yakimenko. "Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates." Symmetry 11, no. 10 (October 19, 2019): 1312. http://dx.doi.org/10.3390/sym11101312.

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We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction with tunneling through the barrier) and strong (rings merging across a reduced barrier) interactions. For the weakly interacting toroidal Bose–Einstein condensates, formation of rotational fluxons (Josephson vortices) is associated with spontaneous breaking of the rotational symmetry of the tunneling superflows. The influence of a controllable symmetry breaking on the final state of the merging counter-propagating superflows is investigated in the framework of a weakly dissipative mean-field model. It is demonstrated that the population imbalance between the merging flows and the breaking of the underlying rotational symmetry can drive the double-ring system to final states with different angular momenta.

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Simon, Laurent, and Juan Ospina. "Transient analysis of drug delivery from a toroidal membrane: Applications for medicated vaginal rings." European Journal of Pharmaceutical Sciences 141 (January 2020): 105114. http://dx.doi.org/10.1016/j.ejps.2019.105114.

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Yusupaliev, U., S. A. Shuteev, E. E. Vinke, and P. U. Yusupaliev. "Vortex rings and plasma toroidal vortices in a homogeneous infinite medium. I. Maximum vortex path." Bulletin of the Lebedev Physics Institute 37, no. 8 (August 2010): 227–33. http://dx.doi.org/10.3103/s1068335610080014.

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Alsmadi, A. M., A. Alatas, J. Y. Zhao, M. Y. Hu, L. Yan, and E. E. Alp. "Microfocusing options for the inelastic X-ray scattering beamline at sector 3 of the Advanced Photon Source." Journal of Synchrotron Radiation 21, no. 3 (March 14, 2014): 488–96. http://dx.doi.org/10.1107/s1600577514000940.

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Synchrotron radiation from third-generation high-brilliance storage rings is an ideal source for X-ray microbeams. The aim of this paper is to describe a microfocusing scheme that combines both a toroidal mirror and Kirkpatrick–Baez (KB) mirrors for upgrading the existing optical system for inelastic X-ray scattering experiments at sector 3 of the Advanced Photon Source.SHADOWray-tracing simulations without considering slope errors of both the toroidal mirror and KB mirrors show that this combination can provide a beam size of 4.5 µm (H) × 0.6 µm (V) (FWHM) at the end of the existing D-station (66 m from the source) with use of full beam transmission of up to 59%, and a beam size of 3.7 µm (H) × 0.46 µm (V) (FWHM) at the front-end of the proposed E-station (68 m from the source) with a transmission of up to 52%. A beam size of about 5 µm (H) × 1 µm (V) can be obtained, which is close to the ideal case, by using high-quality mirrors (with slope errors of less than 0.5 µrad r.m.s.). Considering the slope errors of the existing toroidal and KB mirrors (5 and 2.9 µrad r.m.s., respectively), the beam size grows to about 13.5 µm (H) × 6.3 µm (V) at the end of the D-station and to 12.0 µm (H) × 6.0 µm (V) at the front-end of the proposed E-station. The simulations presented here are compared with the experimental measurements that are significantly larger than the theoretical values even when slope error is included in the simulations. This is because of the experimental set-up that could not yet be optimized.

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Khonina, Svetlana N., Sergey I. Kharitonov, Sergey G. Volotovskiy, and Viktor A. Soifer. "Caustics of Non-Paraxial Perfect Optical Vortices Generated by Toroidal Vortex Lenses." Photonics 8, no. 7 (July 5, 2021): 259. http://dx.doi.org/10.3390/photonics8070259.

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In this paper, we consider the comparative formation of perfect optical vortices in the non-paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex lenses, as well as a vortex axicon in combination with a parabolic lens. The theoretical analysis of the action of these optical elements, as well as the calculation of caustic surfaces, is carried out using a hybrid geometrical-optical and wave approach. Numerical analysis performed on the basis of the expansion in conical waves qualitatively confirms the results obtained and makes it possible to reveal more details associated with diffraction effects. Equations of 3D-caustic surfaces are obtained and the conditions of the ring radius dependence on the order of the vortex phase singularity are analyzed. In the non-paraxial mode, when small light rings (several tens of wavelengths) are formed, a linear dependence of the ring radius on the vortex order is shown. The revealed features should be taken into account when using the considered optical elements forming the POV in various applications.

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Yusupaliev, U., S. A. Shuteev, E. E. Vinke, and V. G. Elenskii. "Vortex rings and plasma toroidal vortices in homogeneous infinite media. III. Diffusion anisotropy effect in vortices." Bulletin of the Lebedev Physics Institute 39, no. 3 (March 2012): 89–94. http://dx.doi.org/10.3103/s1068335612030050.

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Arshad Ahmed, K., and E. Natarajan. "Thermal performance enhancement in a parabolic trough receiver tube with internal toroidal rings: A numerical investigation." Applied Thermal Engineering 162 (November 2019): 114224. http://dx.doi.org/10.1016/j.applthermaleng.2019.114224.

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Parsapour, A., K. Khashyarmanesh, M. Afkhami, and Kh Ahmad Javaheri. "Classification of finite commutative rings with planar, toroidal, and projective line graphs associated with Jacobson graphs." Mathematical Notes 98, no. 5-6 (November 2015): 813–19. http://dx.doi.org/10.1134/s0001434615110103.

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49

Moreno-Insertis, F., M. Schüssler, and A. Ferriz-Mas. "Storage of Magnetic Flux in the Overshoot Region." Symposium - International Astronomical Union 157 (1993): 41–44. http://dx.doi.org/10.1017/s0074180900173838.

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The combined action of the subadiabatic ambient stratification in the overshoot region below the convection zone and the inertial forces associated with the solar rotation is shown to lead to the suppression of the escape of magnetic flux in the form of toroidal flux tubes both toward the surface and toward higher latitudes. We show that a flux ring initially in thermal equilibrium with its environment and rotating with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding, field-free gas. We conclude that flux rings with B≲ 105 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e. δ = ▿ – ▿ad≲–10−5; below that field strength the poleward drift is also reduced to a latitudinal oscillation of moderate amplitude, δθ ≲ 20 deg. Flux rings with significantly larger field strength cannot be kept in the equatorial parts of the overshoot region: their equilibrium configuration is located at high latitudes far outside the solar activity belts and, at any rate, requires unrealistic values of δ.

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Yusupaliev, U., N. P. Savenkova, Yu V. Troshchiev, S. A. Shuteev, S. A. Skladchikov, E. E. Vinke, and N. G. Gusein-zade. "Vortex rings and plasma toroidal vortices in homogeneous unbounded media. II. The study of vortex formation process." Bulletin of the Lebedev Physics Institute 38, no. 9 (September 2011): 275–82. http://dx.doi.org/10.3103/s1068335611090065.

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