Spherical Rings Research Articles

1152 VORTEX STRUCTURE BEHIND A CYLINDER ATTACHED SPHERICAL RINGS USING CONDITIONAL SAPMLING METHOD

Vortex induced vibration is caused by the fluid interaction behind a circular cylinder. The flow resistance, acoustic noise, and flow-induced vibration are triggered by this phenomenon. In order to control this phenomenon, the aim of the present study is to suppress the vortex shedding generated from a circular cylinder attached spherical rings. In this paper, the flow behavior in the wake and the drag coefficients are measured by the hot-wire anemometer and three-components balance. To observe the flow structure, the phase averaged velocity is calculated by the conditional sampling method in the wake. As a result, the drag coefficients decrease due to the enhancement of the velocity recovery behind these rings.

Angular tension of black holes

Angular tension is an ADM charge that contributes a work term to the first law of black hole mechanics when the range of an angular coordinate is varied and leads to a new Smarr formula for stationary black holes. A phase diagram for singly-spinning D=5 black holes shows that angular tension resolves the degeneracies between spherical black holes and (dipole) black rings and captures the physics of the black ring balance condition. Angular tension depends on the behavior of the metric at rotational axes and we speculate on its relation to rod/domain structure characterizations of higher dimensional black holes and black hole uniqueness theorems.

Highly sensitive laser-based sensor for nanoparticles in air using a dual-ring-mirror setup

One of the most frequently applied techniques to detect nanoparticles in air is analyzing laser light scattering. This technique is very flexible while offering high accuracy and reliability. Yet its functionality highly depends on the sensitivity of the measurement system components. Especially for miniaturized sensor devices with limited space, additional techniques are needed to preserve high intensity of scattered light. In our work we demonstrate a technique using two spherical ring mirrors to identify nanoparticles with diameters below 100 nm in a forward-scattering setup. We succeeded measuring polystyrene particles with diameters of 92 nm with a signal-to-noise-ratio of more than 10.

Heat and Fluid Flow Around a Sphere With Cylindrical Bore

This work is devoted to the numerical investigation of heat and fluid flow past a sphere with a centric, cylindrical bore. Such spherical rings are of interest in many technological processes. In chemical reactors, for example, spherical rings are used as a catalyst with an increased reacting surface. Motivated by this fact, we considered spherical rings with different bores and different orientations in flow regimes corresponding to Reynolds numbers from 10 up to 300. The results show a significant influence of the bore diameter on the symmetry and hence the steadiness of the flow field. The Nusselt number can be increased, which leads to a moderate rise in the drag coefficient. Thereby, the effect of the borehole depends on the Reynolds number, the bore diameter, and the angle of attack. For that reason, drag forces and total heat transfers do not simply follow the heat exchanging surface area. Based on the presented results, new correlations are given for both the drag coefficient and the Nusselt number; correlations which incorporate the bore geometry and the bore orientation in the flow field.

S053045 球形リングを設置した円柱後流の流れの挙動に関する研究

S053045 球形リングを設置した円柱後流の流れの挙動に関する研究

Quantum Ring Models and Action-Angle Variables

We suggest to use the action-angle variables for the study of properties of (quasi)particles in quantum rings. For this purpose we present the action-angle variables for three two-dimensional singular oscillator systems. The first one is the usual (Euclidean) singular oscillator, which plays the role of the confinement potential for the quantum ring. We also propose two singular spherical oscillator models for the role of the confinement system for the spherical ring. The first one is based on the standard Higgs oscillator potential. We show that, in spite of the presence of a hidden symmetry, it is not convenient for the study of the system's behaviour in a magnetic field. The second model is based on the so-called CP(1) oscillator potential and respects the inclusion of a constant magnetic field.

S054024 球形リング設置による円柱からの渦放出抑制([S05402]噴流,後流,およびはく離流れの基礎と応用:最前線(2))

S054024 球形リング設置による円柱からの渦放出抑制([S05402]噴流,後流,およびはく離流れの基礎と応用:最前線(2))

Low-Q Electrically Small Spherical Magnetic Dipole Antennas

Three novel electrically small antenna configurations radiating a TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> spherical mode corresponding to a magnetic dipole are presented and investigated: multiarm spherical helix (MSH) antenna, spherical split ring resonator (S-SRR) antenna, and spherical split ring (SSR) antenna. All three antennas are self-resonant, with the input resistance tuned to 50 ohms by an excitation curved dipole/monopole. A prototype of the SSR antenna has been fabricated and measured, yielding results that are consistent with the numerical simulations. Radiation quality factors (Q) of these electrically small antennas (in all cases ka <; 0.26) approach the limit of 3.0 times the Chu lower bound for a given antenna size, which is in line with a theoretical prediction made by Wheeler in 1958.

Which Surfaces of Revolution Core Like a Sphere?

SummaryIf a cylindrical drill bit bores through a solid sphere along an axis, removing a capsule from the sphere, the object that remains is called a spherical ring. A surprising property of the sphere that is often presented in calculus courses is that any two spherical rings whose cylindrical inner boundaries have the same height also have the same volume, regardless of the radii of the spheres from which they were cut. In this article, we pose and answer the question: to what extent does this property characterize the sphere among surfaces of revolution?

Considering data gaps in geoid modelling by modifying Stokes’ formula

There are numerous methods to modify Stokes’ formula with the usually common feature of reducing the truncation error committed by the lack of gravity data in the far-zone, resulting in an integral formula over the near-zone combined with an Earth Gravity Model that mainly contributes with the long-wavelength information. Here we study the reverse problem, namely to estimate the geoid height with data missing in a cap around the computation point but available in the far-zone outside the cap. Secondly, we study also the problem with gravity data available only in a spherical ring around the computation point. In both cases the modified Stokes formulas are derived using Molodensky and least squares types of solutions. The numerical studies show that the Molodensky type of modification is useless, while the latter method efficiently depresses the various errors contributing to the geoid error. The least squares methods can be used for estimating geoid heights in regions with gravity data gaps, such as in Polar Regions, over great lakes and in some developing countries with lacking gravity data.

ROTATING ELECTROMAGNETIC WAVES IN TOROID-SHAPED REGIONS

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three-dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hill's type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.

Open discrete mappings having local ACL n inverses

We consider open, discrete mappings between domains from R n satisfying condition (N), having local ACL n inverses on D∖B f , so that μ n (B f ) = 0, H*(·, f) < ∞ on B f and . For this class of mappings (or even for larger classes of open, discrete mappings) we generalize the important modular inequality of Poleckii, also using the modular estimates of the spherical rings from Cristea (Local homeomorphism having local ACL n inverses, Complex Var. Elliptic Equ. 53(1) (2008), 77–99). We continue the work from the same paper by generalizing some basic facts from the theory of quasiregular mappings. We give equicontinuity results, Picard, Montel and Liouville type theorems, estimates of the modulus of continuity, analogues of Schwarz's lemma, eliminability results and boundary extensions theorems. Together with the multiple extensions of Zoric's theorem from the paper, we establish strong generalizations of one of the most important theorems from the theory of quasiregular mappings. We also extend similar results given in some recent classes of functions larger than the class of quasiregular functions, as the class of mappings of finite distortion and satisfying condition (𝒜), or the class of mappings of finite dilatation with dilatation in the bounded mean oscillation class.

A proposed design and fabrication of lenses and mirrors from a set of spherical rings that produce desired energy distributions for solar energy applications

The amount of energy contained in the solar aureole affects the performance of solar systems. Solar optical systems are, therefore, dependent on the characteristics of the shape of the sun in a specific geographical location. For this reason, the present study proposes the design of solid lenses and mirrors modelled from a set of concentric spherical rings that give a desired distribution of energy in the focal plane. One hundred spherical rings, whose optimum curvature radius values were calculated by Genetic Algorithms, were employed in the modelling process. The study also proposes a design of a petal tool to polish lens and mirror surfaces.

Ned sets on a hyperplane

Under study are the sets in ℝn (NED sets) each of which does not affect the conformal capacity of any condenser with connected plates disjoint from this set. These sets are removable singularities of quasiconformal mappings, which explains our interest in them. For compact sets on a hyperplane we obtain a geometric criterion of the NED property; we point out a simple sufficient condition for an NED set in terms of the connected attainability of its points from its complement in the hyperplane. For compact sets on a hypersphere we obtain a criterion for an NED set in terms of the reduced module at a pair of points in its complement. We establish that a compact set on a hypersphere S, removable for the capacity in at least one spherical ring concentric with S and containing S, is an NED set.

In Situ Phase Separation Following Dehydration in Bimetallic Sulfates: A Variable-Temperature X-Ray Diffraction Study

Phase separation resulting in a single-crystal-single-crystal transition accompanied by a polycrystalline phase following the dehydration of hydrated bimetallic sulfates [Na(2)Mn(1.167)(SO(4))(2)S(0.33)O(1.167) x 2 H(2)O and K(4)Cd(3)(SO(4))(5) x 3 H(2)O] has been investigated by in situ variable-temperature single-crystal X-ray diffraction. With two examples, we illustrate the possibility of generating structural frameworks following dehydration in bimetallic sulfates, which refer to the possible precursor phases at that temperature leading to the mineral formation. The room-temperature structure of Na(2)Mn(1.167)(SO(4))(2)S(0.33)O(1.167) x 2 H(2)O is trigonal, space group R3. On heating the crystal in situ on the diffractometer, the diffraction images display spherical spots and concentric rings suggesting phase separation, with the spherical spots getting indexed in a monoclinic space group, C2/c. The structure determination based on this data suggests the formation of Na(2)Mn(SO(4))(2). However, the diffraction images from concentric rings could not be indexed. In the second example, the room-temperature structure is determined to be K(4)Cd(3)(SO(4))(5) x 3 H(2)O, crystallizing in a monoclinic space group, P2(1)/n. On heating the crystal in situ, the diffraction images collected also have both spherical spots and diffuse rings. The spherical spots could be indexed to a cubic crystal system, space group P2(1)3, and the structure is K(2)Cd(2)(SO(4))(3). The possible mechanism for the phase transition in the dehydration regime resulting in this remarkable single-crystal to single-crystal transition with the appearance of a surrogate polycrystalline phase is proposed.

Pulsed jet dynamics of squid hatchlings at intermediate Reynolds numbers

Squid paralarvae (hatchlings) rely predominantly on a pulsed jet for locomotion, distinguishing them from the majority of aquatic locomotors at low/intermediate Reynolds numbers (Re), which employ oscillatory/undulatory modes of propulsion. Although squid paralarvae may delineate the lower size limit of biological jet propulsion, surprisingly little is known about the hydrodynamics and propulsive efficiency of paralarval jetting within the intermediate Re realm. To better understand paralarval jet dynamics, we used digital particle image velocimetry (DPIV) and high-speed video to measure bulk vortex properties (e.g. circulation, impulse, kinetic energy) and other jet features [e.g. average and peak jet velocity along the jet centerline (U(j) and U(jmax), respectively), jet angle, jet length based on the vorticity and velocity extents (L(omega) and L(V), respectively), jet diameter based on the distance between vorticity peaks (D(omega)), maximum funnel diameter (D(F)), average and maximum swimming speed (U and U(max), respectively)] in free-swimming Doryteuthis pealeii paralarvae (1.8 mm dorsal mantle length) (Re(squid)=25-90). Squid paralarvae spent the majority of their time station holding in the water column, relying predominantly on a frequent, high-volume, vertically directed jet. During station holding, paralarvae produced a range of jet structures from spherical vortex rings (L(omega)/D(omega)=2.1, L(V)/D(F)=13.6) to more elongated vortex ring structures with no distinguishable pinch-off (L(omega)/D(omega)=4.6, L(V)/D(F)=36.0). To swim faster, paralarvae increased pulse duration and L(omega)/D(omega), leading to higher impulse but kept jet velocity relatively constant. Paralarvae produced jets with low slip, i.e. ratio of jet velocity to swimming velocity (U(j)/U or U(jmax)/U(max)), and exhibited propulsive efficiency [eta(pd)=74.9+/-8.83% (+/-s.d.) for deconvolved data] comparable with oscillatory/undulatory swimmers. As slip decreased with speed, propulsive efficiency increased. The detection of high propulsive efficiency in paralarvae is significant because it contradicts many studies that predict low propulsive efficiency at intermediate Re for inertial forms of locomotion.

A path model for geodesics in Euclidean buildings and its applications to representation theory

In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex reductive Lie groups and to spherical Hecke rings associated with split nonarchimedean reductive Lie groups. Our main application is a generalization of the saturation theorem of Knutson and Tao for SLn to other complex semisimple Lie groups.

Weak localization of electromagnetic waves and radar polarimetry of Saturn's rings

We use a state-of-the-art physics-based model of electromagnetic scattering to analyze average circular polarization ratios measured for the A and B rings of Saturn at a wavelength of 12.6 cm. This model is directly based on the Maxwell equations and accounts for the effects of polarization, multiple scattering, weak localization of electromagnetic waves, and ring particle nonsphericity. Our analysis is based on the assumption that the observed polarization ratios are accurate, mutually consistent, and show a quasi-linear dependence on the opening angle. Also, we assume that the ring system is not strongly stratified in the vertical direction. Our numerical simulations rule out the model of spherical ring particles, favor the model of ring bodies in the form of nearly spherical particles with small-scale surface roughness, and rule out nonspherical particles with aspect ratios significantly exceeding 1.2. They also favor particles with effective radii in the range 4-10 cm and definitely rule out effective radii significantly smaller than 4 cm. Furthermore, they seem to rule out effective radii significantly greater than 10 cm. The retrieved ring optical thickness values are in the range 2-3 or even larger. If the rings do have a wake-like horizontal structure, as has been recently suggested, then these optical thickness values should be attributed to an average wake rather than to the optical thickness averaged over the entire horizontal extent of the rings.

Swimming dynamics and propulsive efficiency of squids throughout ontogeny

Squids encounter vastly different flow regimes throughout ontogeny as they undergo critical morphological changes to their two locomotive systems: the fins and jet. Squid hatchlings (paralarvae) operate at low and intermediate Reynolds numbers (Re) and typically have rounded bodies, small fins, and relatively large funnel apertures, whereas juveniles and adults operate at higher Re and generally have more streamlined bodies, larger fins, and relatively small funnel apertures. These morphological changes and varying flow conditions affect swimming performance in squids. To determine how swimming dynamics and propulsive efficiency change throughout ontogeny, digital particle image velocimetry (DPIV) and kinematic data were collected from an ontogenetic range of long-finned squid Doryteuthis pealeii and brief squid Lolliguncula brevis swimming in a holding chamber or water tunnel (Re = 20-20 000). Jet and fin wake bulk properties were quantified, and propulsive efficiency was computed based on measurements of impulse and excess kinetic energy in the wakes. Paralarvae relied predominantly on a vertically directed, high frequency, low velocity jet as they bobbed up and down in the water column. Although some spherical vortex rings were observed, most paralarval jets consisted of an elongated vortical region of variable length with no clear pinch-off of a vortex ring from the trailing tail component. Compared with paralarvae, juvenile and adult squid exhibited a more diverse range of swimming strategies, involving greater overall locomotive fin reliance and multiple fin and jet wake modes with better defined vortex rings. Despite greater locomotive flexibility, jet propulsive efficiency of juveniles/adults was significantly lower than that of paralarvae, even when juvenile/adults employed their highest efficiency jet mode involving the production of periodic isolated vortex rings with each jet pulse. When the fins were considered together with the jet for several juvenile/adult swimming sequences, overall propulsive efficiency increased, suggesting that fin contributions are important and should not be overlooked in analyses of the swimming performance of squids. The fins produced significant thrust and consistently had higher propulsive efficiency than did the jet. One particularly important area of future study is the determination of coordinated jet/fin wake modes that have the greatest impact on propulsive efficiency. Although such research would be technically challenging, requiring new, powerful, 3D approaches, it is necessary for a more comprehensive assessment of propulsive efficiency of the squid dual-mode locomotive system.

Laser self-induced thermo-optical effects in a magnetic fluid

The laser self-induced thermo-optical effects in a magnetic fluid are studied in this work. We study the origin of these effects theoretically, and then experiments are done to investigate the relationship between the divergence angle of the laser beam and the incident power. From the experimental results, we find out that the divergence angle increases linearly with the incident power to some critical power, which is in good agreement with the theory. To the high incident power side, the divergence angle will deviate from the linear relationship and the spherical aberration interference rings will be blurred due to the occurrence of the convective currents.