Spherical Rings Research Articles

Enhancing acoustic levitation capacity through array geometry optimization

The contactless micromanipulation capability and microgravity environment provided by the acoustic levitation technology have excellent application prospects in many fields, such as droplet dynamics, solidification state physics, life sciences, etc. However, the applications are severely constrained by the limitation of the transducer power. In this paper, we explore an array geometry optimization framework to improve the levitation capability. First, the acoustic pressure attenuation and directional characteristics of commercial transducers are analyzed to uncover the mechanism of the array geometry affecting the acoustic radiation force (ARF). Second, based on the Gor'kov potential theory, the array geometry form of N-elements is derived, and the arrangement in the spherical ring (ASR) method is proposed to obtain the element coordinates. Then, spherical radius and array height are adjusted to obtain the optimal array geometry. On this basis, the directional angle of each transducer is further optimized. Finally, simulation and physical verification are carried out. The simulation results indicate that the ARF increases and then decreases with the spherical radius and array height, which are the existing maximum values. Directional angle optimization (DAO) can improve the ARF, particularly when the array height exceeds the sphere diameter. These findings are consistent with the analytical results. Notably, we built a prototype physical system, and the physical experiments showed that the optimized array improved the axial ARF by 201.2% and the radial ARF by 115.9% over the conventional array. The works presented in this paper offer a valuable design approach for acoustic levitation arrays, thereby contributing to the advancement and application of ultrasonic array levitation technology.

On the geometric fixed points of real topological cyclic homology

AbstractWe give a formula for the geometric fixed‐points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to carry out computations in the fundamental examples of spherical group rings, perfect ‐algebras and 2‐torsion‐free rings with perfect modulo 2 reduction. Our calculations agree with the normal L‐theory spectrum in the cases where the latter is known, as conjectured by Nikolaus.

An Equivariant Generalisation of McDuff–Segal’s Group–Completion Theorem

Abstract In this short note, we prove a $G$–equivariant generalisation of McDuff–Segal’s group–completion theorem for finite groups $G$. A new complication regarding genuine equivariant localisations arises and we resolve this by isolating a simple condition on the homotopy groups of $\mathbb{E}_{\infty }$–rings in $G$–spectra. We check that this condition is satisfied when our inputs are a suitable variant of $\mathbb{E}_{\infty }$–monoids in $G$–spaces via the existence of multiplicative norm structures, thus giving a localisation formula for their associated $G$–spherical group rings.

Thermofluidic analysis around a heated hollow spherical ring immersed in air

Efforts are made to report a numerical investigation on natural convection flow around a heated vertical hollow spherical ring with negligible wall thickness exposed in quiescent air within laminar regime. Both inner and outer walls are maintained at a constant temperature throughout the study. Thermal and flow fields are predicted thoroughly over the wide range of following governing pertinent parameters: height-to-diameter ratio and Rayleigh number ( First, thermal plumes are employed to understand the thermofluidic behavior around the spherical ring qualitatively. A high-temperature zone inside the spherical ring is identified at higher value aspect ratio almost for all values of due to the entrapment of the heated plume. It is also noticed that the cooling rate from inner wall first increases with and finds a maximum value then starts to drop with a further rise of for a constant value of This maximum value is almost 7.1 times higher at 107 compared to 103, whereas it is approximately 3.75 times higher at 106 compared to 103. However, the heat loss rate from outer wall increases continually with the progressive rise of for a fixed value of However, the mean Nusselt number on both inner and outer walls reduces with the increase of for all cases of Again, the pattern of mass flow rate through the ring is also predicted for various values of and The mass flow rate reduces progressively with the continual rise of for a fixed value of Lastly, the study is concluded by developing a suitable correlation for net Nusselt number based on the computed data points which shows a satisfactory agreement within ±6% of the computational data.

A novel air core electromagnetic fault current limiter with rotational motion

AbstractThe authors deal with design and analysis of an air‐core electromagnetic fault current limiter (FCL) with rotary motion. The proposed device is characterised by a simple structure, fast operating speed and reversible operation. It consists of two movable concentric air core spherical reactor rings (i.e. inner and outer rings) with variable mutual angular displacement. At normal condition, reactors are approximately aligned, and subsequently, the effective inductance/impedance of the equipment and the respective voltage drop are low. At faulty conditions, the short circuit current exerts a repulsive rotary electromagnetic torque on the reactors, which results in a fast and steady increase of the reactors angular displacement. During this process, the effective inductance of the equipment rapidly rises up to a level that effectively limits the short circuit current. To determine the effectiveness of the proposed topology in limiting the network's fault current, the inductance profile of the proposed rotary FCL and the respective fault current characteristic are compared with similar case studies (a) with linear FCL and (b) without FCL. The analysis is carried out via a finite element (FE) and supported via analytical and theoretical discussion. Finally, a down‐scale prototype of the proposed FCL was built and tested to verify the functionality of the device in the lab environment.

Design of freeform mirrors using the concentric rings method

Through the methodology of optical surface design based on concentric rings, this paper proposes the design of freeform mirrors, initially by employing segmented rings, each of them with different spherical radii of curvature, and then by employing segmented conic rings with different conic constants in each of the segments. These surfaces will then produce the desired images. For the case of segmented spherical rings, mathematical expressions were deduced to obtain the image points as a function of the radii of curvature. Furthermore, it is shown that in the case where conic rings were used, there is a decrease in spherical aberration, which allows the manipulation of the generated image. Finally, several proposals are presented for the design of mirrors to generate both the desired size of the image and the desired distribution of energy, together with their analyses.

Scattered polarized radiation of extrasolar circumplanetary rings

Aims. We have investigated the impact of circumplanetary rings consisting of spherical micrometer-sized particles on the net scattered light polarization of extrasolar gas giants. Methods. Using the three-dimensional Monte Carlo radiative transfer code POLARIS, we studied the impact of the macroscopic parameters that define the ring, such as its radius and inclination, and the chemical composition of the ring particles on the net scattered polarization. For the spherical ring particles, we applied the Mie scattering theory. We studied the flux and polarization of the scattered stellar radiation as a function of planetary phase angle and wavelength from the optical to the near-infrared. Results. For the chosen grain size distribution, the dust particles in the ring show strong forward scattering at the considered wavelengths. Thus, the reflected flux of the planet dominates the total reflected and polarized flux at small phase angles. However, the scattered and polarized flux of the ring increase at large phase angles and exceeds the total reflected planetary flux. For large rings that contain silicate particles, the total reflected flux is dominated by the radiation scattered by the dust in the ring at all phase angles. As a result, the orientation of polarization is parallel to the scattering plane at small phase angles. In contrast, for a ring that contains water ice particles, the orientation of polarization is parallel to the scattering plane at large phase angles. Depending on the ring inclination and orientation, the total reflected and polarized flux show a specific distribution as well. Large particles show a strong polarization at large phase angles compared to smaller particles. For a Jupiter-like atmosphere that contains methane and aerosols, methane absorption features are missing in the spectrum of a ringed planet. Conclusions. Scattering of the stellar radiation by dust in circumplanetary rings of extrasolar planets results in unique features in the phase-angle- and wavelength-dependent reflected and polarized net flux. Thus, exoplanet polarimetry provides the means to study not only the planetary atmosphere and surface, but also to identify the existence and constrain the properties of exoplanetary rings.

Analytical Modeling of Rotary Electromagnetic Fault Current Limiter

Rotary electromagnetic fault current limiter (FCL) is an emerging technology for limiting fault currents in the power network. The device consists of two movable air-core spherical reactor rings (i.e., inner and outer rings). The movable feature allows the reactor rings to rotate, and form a proper mutual positional displacement. This can limit the fault current since the effective inductance of the device is dependent to the mutual angular position of the reactor rings. Due to the unconventional structure, to this date, the design process has solely been based on finite element (FE) method. This paper aims to analytically validate the theory and the overall functionality of the device in both the steady state and transient regime. For this propose, the resistance and the inductance of the device are first computed at normal operating condition using the basic theory of engineering electromagnetics. Next, performance characteristics such as electromagnetic torque, rotational displacement of the reactors, effective inductance of the device, and the network current are calculated at the faulty condition. For verification purposes, analytical results are compared with via FE simulation and experimental test.

Inward and outward interaction of magneto-acoustic cylindrical and spherical solitary rings in spin-1/2 fermionic quantum plasma

Inward and outward interaction of magneto-acoustic cylindrical and spherical solitary rings in spin-1/2 fermionic quantum plasma

Kilohertz-Frequency Rotation of Acoustically Levitated Particles.

The achievable rotational frequency of acoustically levitated particles is limited by the suspension stability and the achievable driving torque. In this work, a spherical ring arrangement of piezoelectric transducers and an improved excitation concept are presented to increase the rotational speed of an acoustically levitated particle by more than a factor of 10 compared to previously published results. A maximum rotational frequency of 3.6 kHz using asymmetric expanded polystyrene (EPS) particles is demonstrated. At such rotational speeds, high-frequency resonances of the transducers cause disturbances of the acoustic field which present a previously unexplored limit to the achievable manipulation rate of the particle. This limit is investigated in this work by means of calculations based on an analytical model and high precision measurements of the transducer characteristics beyond the conventional frequency range.

Thermal radiative properties of zirconium oxide films in the near‐infrared wavelengths

AbstractThermal barrier coatings (TBCs) using yttria‐stabilized zirconium dioxide (YSZ) are widely used in gas turbines to protect metal components against the high combustion product temperature. Increasing combustion temperature and pressure, radiative heat transfer becomes an essential portion of the overall heat transfer in TBCs. This necessitates a greater understanding of the thermal radiative properties of YSZ films, especially in the near‐infrared wavelength range. The commonly used Kubelka–Munk (KM) method in the radiative property reduction from the measured transmittance and reflectance spectra of YSZ films can incur inaccurate results when the coating optical thickness is not sufficiently large. The discrete ordinates method with the asymmetric spherical ring angular quadrature can solve the radiative transfer equation with good accuracy in optically thin media. Considering the solution accuracy and computational efficiency, a hybrid approach of combining the KM and discrete ordinate methods is used to invert radiative properties. The absorption and scattering coefficients of air plasma sprayed YSZ films are determined over the wavelength range from 1 to 2.6 μm at room temperature. Over this near‐infrared wavelength range, the scattering coefficient decreases with the increasing wavelength, and the absorption coefficient is very small overall.

The structure and formation of giant Marimo (Aegagropila linnaei) in Lake Akan, Japan

Aegagropila linnaei is a freshwater green alga, which at one time was distributed widely in the northern hemisphere. The aggregate often forms beautiful spherical shapes known as “lake balls” or “Marimo”. The population of Marimo has been rapidly decreasing worldwide, and today the large Marimo, with a diameter of more than 12 cm, exit only in Lake Akan in Japan. However, how Marimo grow and maintain their unique spherical shape in natural habitats remains unsolved. Here we show that Marimo are “polished” into spheres by the rotation induced by wind waves. Such a process enhances the water exchange between the interior and exterior of the Marimo, thereby recycling nutrients for growth. Our results provide an intriguing model of a physical environment interacting with biological processes in a self-sustaining ecosystem. We also demonstrate that Marimo have a spherical annual ring structure, and their growth rate is associated with ice cover. The balance between the ecology of Marimo and the water environment in Lake Akan is highly vulnerable and at risk of irreversible degradation. We must endeavor to rescue Marimo from the fate of a "canary in the coal mine" of global climate change.

Affine Pieri rule for periodic Macdonald spherical functions and fusion rings

Let gˆ be an untwisted affine Lie algebra or the twisted counterpart thereof (which excludes the affine Lie algebras of type BCˆn=A2n(2)). We present an affine Pieri rule for a basis of periodic Macdonald spherical functions associated with gˆ. In type Aˆn−1=An−1(1) the formula in question reproduces an affine Pieri rule for cylindric Hall-Littlewood polynomials due to Korff, which at t=0 specializes in turn to a well-known Pieri formula in the fusion ring of genus zero slˆ(n)c-Wess-Zumino-Witten conformal field theories.

Spherical symmetry breaking in electric, magnetic and toroidal multipole moment radiations in spherical toroidal resonant cavities and optimum-efficiency antennas

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.

Research on DC Corona Test of Typical Electrodes and Corona Limited Electric Field Magnitude for Valve Hall Fittings

In order to prevent the surface corona of valve hall fittings and obtain the corona limited electric field magnitude, the research designed dc corona test of spherical electrode and ring electrode with the different radius of curvature. The electrodes were used to imitate valve tower shield plate, grading ring, grading ball and grading shield for bushing. By the reason that the uneven electric field of irregular conductor can’t be calculated theoretically or measured accurately, the three-dimensional finite element model is used for simulating calculation. The variation of typical electrode corona inception electric field is analyzed and threshold value of corona inception electric field of valve hall fittings is acquired. With adequate modification, limited electric field magnitude for the project is proposed. The corona inception electric field magnitude of electrical equipment under the equivalent diameter of 200mm is 2000Vmm−1, and that of electrical equipment with an equivalent diameter of more than 200 mm is 1200 V • mm−1.

The modulus of a family of curves on an abstract surface over a spherical ring

The modulus of a family of curves on an abstract surface over a spherical ring

Vortex rings produced by non-parallel planar starting jets

Abstract

Organ Culture and Grafting of Choroid Plexus into the Ventricular CSF of Normal and Hydrocephalic HTx Rats

Choroid plexus (CP) may aid brain development and repair by secreting growth factors and neurotrophins for CSF streaming to ventricular and subventricular zones. Disrupted ventricular/subventricular zone progenitors and stem cells lead to CNS maldevelopment. Exploring models, we organ cultured the CP and transplanted fresh CP into a lateral ventricle of postnatal hydrocephalic (hyHTx) and nonhydrocephalic (nHTx) rats. After 60 days in vitro, the cultured choroid ependyma formed spherical rings with beating cilia. Cultured CP expressed endocytotic caveolin 1 and apical aquaporin 1 and absorbed horseradish peroxidase from medium. Transthyretin secretory protein was secreted by organ-cultured CP into medium throughout 60 days in vitro. Fresh CP, surviving at 1 week after lateral ventricle implantation of nHTx or hyHTx did not block CSF flow. Avascular 1-week transplants in vivo expressed caveolin 1, aquaporin 1, and transthyretin, indicating that grafted CP may secrete trophic proteins but not CSF. Our findings encourage further exploration on CP organ culture and grafting for translational strategies. Because transplanted CP, though not producing CSF, may secrete beneficial molecules for developing brain injured by hydrocephalus, we propose that upon CP removal in hydrocephalus surgery, the fractionated tissue could be transplanted back (ventricular autograft).

Study on numerical analysis of dynamic parameters of mobile walking robot

A dynamic model of a walking robot is proposed for moving along surfaces of different topologies and orientations to the horizon. The principal difference between walking robot mechanisms is that they are made in the form of flexible pedipulators. Actually the pedipulators are a set of spherical rings with a hydraulic or pneumatic drive. The patented design (Patent UA No 117065, publ. 2018.06.11) of the robot's feet is anthropomorphic and allows the robot to work in the angular coordinate system inherent in the human walking machine. The proposed mathematical model allows us to calculate the dynamic parameters (forces and moments) and compare these parameters with the allowable technological load that a walking robot can perform without losing adhesion with the displacement surface.

Split Injectivity ofA-Theoretic Assembly Maps

AbstractWe construct an equivariant coarse homology theory arising from the algebraic $K$-theory of spherical group rings and use this theory to derive split injectivity results for associated assembly maps. On the way, we prove that the fundamental structural theorems for Waldhausen’s algebraic $K$-theory functor carry over to its nonconnective counterpart defined by Blumberg–Gepner–Tabuada.