Toroidal Form Research Articles

On Degree-Based Topological Indices of Kagome Graphene, and Carbon Kagome Nanotubes and Nanotori

Approaches based on graph descriptors have been used in cheminformatics and bioinformatics for molecular property prediction. In this article, we apply partition technique and simple counting schemes to describe the structure of a two-dimensional (2D) kagome graphene and then derive the closed form of various degree-based topological indices (graph descriptor) of 2D kagome graphene, and its tubular and toroidal forms.

Optical Asymmetry and Structural Complexity in Hierarchically Organized Chiral CuO Nanostructures: Insight into the Geometric and Crystallographic Effects on Cooperative Chirality.

Optical asymmetry and structural complexity across different length scales were realized in flower-shaped CuO nanostructures, prepared through refluxing an aqueous solution of copper acetate, sodium hydroxide, and D-tartaric acid, as well as in their toroid-like forms obtained on calcination at 600 °C. Atomic scale chirality in the flower morphology could be visualized as putative Boerdijk-Coexter-Bernal like tetrahelical fragments, while that in the toroid form could be identified as screw dislocation-driven helicity. The fraction of asymmetry in the nanostructures has been evaluated from their chiroptical responses based on Kuhn asymmetry factor (g) from circular dichroism (CD) spectroscopy in the entire UV-vis range. The origin of chirality in the two CuO nanostructures has been assigned to the helical arrangement of the Cu-O-Cu network in accordance with their microscopic and spectroscopic observations. Attempts have been made to interpret the crystallographic and geometric chiralities in the two CuO nanostructures based on the redshift and augmented intensity of the CD signal along with an increase in their corresponding anisotropic factor on calcination. Further, the diverse interaction of the toroid-shaped CuO nanostructures with enantiomeric tryptophan moieties has been illustrated from the measurement of their corresponding thermodynamic parameters.

Drag reduction and power optimization due to an innovative, toroidal hull form of an AUV

The use of unconventional design has become a norm for mission-specific underwater autonomous craft. Geometrical characteristics and drag optimized shapes of single-hulled underwater vehicles are known since 1970s and a few significant improvements have been possible since then. These are mostly related to the efficiency of a wake adapted propeller, positioned at the stern in wake of the hull. In a novel effort, when the propeller is integrated into the craft at center-line, and the hull in its entirety is designed to act as the duct, the drag of the hull is further reduced. This craft uses a toroidal hull form that distributes payload axi-symmetrically around an internal ducted thruster. The craft is designed to operate at an economic cruise speed of 2kn. The power consumption is optimized to achieve an endurance of over 500 miles through this implementation of a ducted thruster. The hydrodynamic characteristics of the new toroidal hull are compared to those of a reference design which is slender and conventionally shaped. This conventional design is intended for the same volume and dimensions of payload. A reduction of 13% in drag from the first to final design iteration is achieved. This reduction in drag is due to a higheer effective length to thickness ratio of the ducted AUV, quantified in terms of a new parameter defined as Ih . The reduction of the wetted surface area also contributes to the drag optimization. The article shows that the shape of the leading edge of the toroidal hull becomes important to achieve low drag. The process of design and optimization using CFD, with the most appropriate turbulence models is detailed. The beneficial effect of the acceleration induced in the flow at the leading edge and trailing edge of the hull by the integrated thruster is studied and explained with the help of CFD results.

The vortex ring state of a rotor and its comparison with the collapse of an annular jet in counterflow

The vortex ring state (VRS) of a rotor is associated with the development of the trailed vortex system in powered descending flight, where the topology of the vortex wake changes from its usual helical form into a toroidal form. In the VRS, the toroidal vortex ring envelops the entire rotor, and it sheds and reforms in an unsteady manner. In previous attempts to understand the basic phenomenology of the VRS, the focus was on the role of the trailed vortices in the transition to the VRS: computational and experimental work utilized rotor models to generate the trailing vortex wake, and mechanisms for the emergence of the VRS were postulated based on the interaction of the trailed vortices. In this paper, a different approach is taken: a set of experiments on a core annular jet flow are described, where the jet flow in counterflow is used to simulate a rotor in powered descent. It is shown that this leads to the formation of a flow field that shares many of the features of the VRS of a rotor system. This brings into question the role of the rotor blade trailing vortices in the development of the rotor wake VRS, and it is proposed instead that the interaction between the mean flow and counterflow drives the VRS phenomenon.

Dissimilar cavitation dynamics and damage patterns produced by parallel fiber alignment to the stone surface in holmium:yttrium aluminum garnet laser lithotripsy.

Recent studies indicate that cavitation may play a vital role in laser lithotripsy. However, the underlying bubble dynamics and associated damage mechanisms are largely unknown. In this study, we use ultra-high-speed shadowgraph imaging, hydrophone measurements, three-dimensional passive cavitation mapping (3D-PCM), and phantom test to investigate the transient dynamics of vapor bubbles induced by a holmium:yttrium aluminum garnet laser and their correlation with solid damage. We vary the standoff distance (SD) between the fiber tip and solid boundary under parallel fiber alignment and observe several distinctive features in bubble dynamics. First, long pulsed laser irradiation and solid boundary interaction create an elongated "pear-shaped" bubble that collapses asymmetrically and forms multiple jets in sequence. Second, unlike nanosecond laser-induced cavitation bubbles, jet impact on solid boundary generates negligible pressure transients and causes no direct damage. A non-circular toroidal bubble forms, particularly following the primary and secondary bubble collapses at SD = 1.0 and 3.0 mm, respectively. We observe three intensified bubble collapses with strong shock wave emissions: the intensified bubble collapse by shock wave, the ensuing reflected shock wave from the solid boundary, and self-intensified collapse of an inverted "triangle-shaped" or "horseshoe-shaped" bubble. Third, high-speed shadowgraph imaging and 3D-PCM confirm that the shock origins from the distinctive bubble collapse form either two discrete spots or a "smiling-face" shape. The spatial collapse pattern is consistent with the similar BegoStone surface damage, suggesting that the shockwave emissions during the intensified asymmetric collapse of the pear-shaped bubble are decisive for the solid damage.

Study of Toroidal Core Multilimb Transformer (TCMLT) for High-Power DC Application

Multimodule isolated converters incorporating excellent features of galvanic isolation, bidirectional power flow, and simple control are widely adopted in medium-voltage (MV) high-power dc-dc applications. However, the converter size and dc-link capacitor voltage balancing are significant concerns in galvanically isolated cascaded dc-dc converters. This article proposes a new design of an integrated transformer implementing toroidal cores named toroidal core multilimb transformer (TCMLT), employed in a dc-dc modular isolated bidirectional dual-active-bridge (IB-DAB) resonant converter topology. The modular design structure of the proposed transformer can be conveniently constructed and implemented for more number of participating modules conforming the compactness constraint. Moreover, an external coupling winding is implemented in the TCMLT structure to resolve the dc-link voltage balancing issue. This coupling winding method substitutes the expensive complex control circuits, which consequently results in cost reduction and reliability enhancement. Besides, the reluctance model of the proposed structure is analyzed. Based on the reluctance model, a common mode-difference mode (CM-DM) electrical circuit is realized for the proposed scheme. Furthermore, unlike the conventional approach of implementing U, UI, and EI cores for multilimb transformer (MLT) structure with separate limbs, a synthesis method of TCMLT in toroidal form is proposed. The comparative study of the proposed design with the conventional U-core MLT confirms that the proposed TCMLT offers less leakage inductance with significant size reduction. Finally, to validate the efficacy of TCMLT, a three-limb laboratory-scale prototype is employed in a 6-kW cascaded IB-DAB resonant converter topology.

Criteria for Determining the Genesis of Placers and Their Different Sources Based on the Morphological Features of Placer Gold

Based on the identified typomorphic features of placer gold, a set of determined morphogenetic criteria is proposed to identify the genesis of placer gold content and different sources in the platform areas, which allow more correctly selecting search methods and improving the efficiency of forecasting ore and placer gold deposits. Gold particles larger than 0.25 mm with signs of wind-worn processing indicate the formation of autochthonous aeolian placers. Gold particles with signs of wind-worn processing with a size of 0.1–0.25 mm, forming an extensive halo of dispersion, indicate the formation of allochthonous placers in Quaternary deposits. Deflationary (autochthonous) placers of native gold can be found by the halo of its distribution of toroidal and spherical hollow forms, which, of course, are the search morphogenetic criterion of aeolian placers. The presence of disc-shaped and lamellar gold particles with ridgelike edges in alluvial placers is typical for placers of heterogeneous origin, formed due to deflation of proluvial placers. The discovery of pseudo-ore gold in alluvial placers indicates the arrival of gold from intermediate gold-bearing sources of different ages and not from primary sources, which is a morphogenetic criterion for determining different sources of the placer. In modern gold placers, the presence of gold of a pseudo-ore appearance can serve as a search criterion for the discovery of gold-bearing conglomerates with high gold content. The developed method for diagnosing the genotype of placer gold by its morphological characteristics (alluvial, aeolian, pseudo-ore) can be successfully used by industrial geological organizations to search and explore ore and placer gold deposits.

Characterization of normal and deformed red blood cells using simulated differential photoacoustic cross-section spectral data

Frequency dependent differential photoacoustic cross-section (DPACS) over a large frequency band (100–1000 MHz) has been computed and subsequently, morphological parameters of photoacoustic (PA) source have been quantified. Green’s function method has been employed for computing the DPACS for a series of ellipsoidal droplets (with varying aspect ratio), Chebyshev particles (with different waviness (n) and deformation (ϵ) parameters), healthy red blood cell (RBC) and cells suffering from hereditary disorders (spherocytosis, elliptocytosis and stomatocytosis). The tri-axial ellipsoid form factor (TAEFF), finite cylinder form factor (CFF) and toroid form factor (TFF) models have been used to fit the DPACS spectrum to obtain size and shape information of the PA source. The TAEFF model estimates the shape parameters of the ellipsoidal droplets accurately (error < 5%). It is found that volume estimation is better (error < 10%) for lower order (n = 2, ϵ = ± 0.25) and very higher order (n = 35, 45, ϵ = ± 0.05) Chebyshev particles compared to those of n = 4, 6 and ϵ = ± 0.25. The TAEFF model predicts shape parameters of stomatocyte with volume error ≈15% but it is ≤6% for other cells. The opposite trend is observed for the CFF model. The TFF model is able to estimate the shape parameters efficiently for normal erythrocyte and stomatocyte but gives relatively large errors (>15%) for other deformed RBCs. The inverse problem framework may motivate to develop a PA-based technology to assess single cell morphology.

Systematic analysis of frequency dependent differential photoacoustic cross-section data for source size estimation.

A frequency dependent differential photoacoustic cross-section (DPACS) over a large frequency band (100-1000 MHz) was computed, and subsequently, morphological parameters of a photoacoustic (PA) source were quantified. The Green's function approach was utilized for calculating the DPACS for spheroidal droplets with varying aspect ratios, Chebyshev particles with different waviness and deformation parameters, and normal red blood cells and cells affected by hereditary disorders (e.g., spherocytosis, elliptocytosis, and stomatocytosis). The theoretical framework considers that PA waves propagate through an acoustically dispersive and absorbing medium and are detected by a planar detector of finite size. The frequency dependent DPACS profile was fitted with tri-axial ellipsoid, finite cylinder, and toroid form factor models to obtain size and shape information of the PA source. The tri-axial ellipsoid form factor model was found to provide better estimates of the shape parameters compared to other models for a variety of sources. The inverse problem framework may motivate developing PA-based technology to assess single-cell morphology.

Mitigation of disruption on IR-T1 tokamak by means of low-energy neutral beam injection to control runaway electron generation

In a tokamak, the poloidal magnetic field provided by the toroidal plasma current forms an essential part of the magnetic field confining the plasma. However, instabilities of magnetohydrodynamic equilibrium can lead to an uncontrolled sudden loss of plasma current and energy, which is called a disruption. Disruptions are of significant concern to future devices due to the large amount of energy released during the rapid quenching of the plasma. One important consequence of disruption is the generation of significant current carried in multi-MeV runaway electrons that are eventually lost into plasma components. They can damage the tokamak walls and its structure if they are not controlled. Disruption control by neutral beam injection has been performed on IR-T1 to study the effect on runaway electron generated by plasma disruptions. Noble gases are used for injection, pure Hydrogen, Helium and Argon. The use of these non-reactive gases for disruption control ensures they fast removed from the vessel after the termination of a tokamak discharge. A piezo-valve is used for injection which has the precision of 1 ms. The effect of runaway electron generation control during disruption is studied using a comparison between reference disruptive discharge and a discharge into which different impurity species are injected. The data collected can then be used to optimize the performance of these energetic electrons control generated in disruption.

Pyrometric imaging of soot processes in a pilot ignited direct injected natural gas engine

This work assesses the soot formation and oxidation processes in a high-pressure direct injection natural gas engine using simultaneous high-speed two-colour pyrometry and OH* chemiluminescence imaging. A parametric investigation considers the effects of fuel injection pressure, injection duration and relative pilot and natural gas injection timings. A typical combustion event consists of natural gas being ignited by diesel pilot combustion products, followed by partially premixed combustion of natural gas near the piston bowl wall. Soot is formed as natural gas is injected into this reaction zone. A toroidal soot cloud forms and grows towards the centre of the piston bowl. For the range of operating conditions tested, the peak apparent heat release rate and the onset of detectable soot were correlated, as were the timing of the peak soot fraction and end of natural gas injection. The latter indicates that the soot formation and transition to a net oxidation process are strongly influenced by the injection process, similar to diesel engines. Changes in the relative timing of the diesel pilot and natural gas injections influenced natural gas premixing times, with increased premixing leading to a higher peak apparent heat release rate and lower peak soot fraction. The injection pressure affected the peak soot fraction though enhanced oxidation was expected to ultimately reduce the engine-out soot for higher injection pressures. Based on this parametric investigation, an existing conceptual model of pilot ignited direct injected natural gas combustion is extended to also describe the soot formation and oxidation processes.

X-ray Charge Density Study of the Drug Methimazole with Z′ = 2: Differences in the Electronic Structure of the Thiourea Core due to Crystal Packing Effects

Herein we present a detailed experimental charge-density study for the low-temperature polymorph of antithyroid drug methimazole crystallized with two crystallographically independent molecules lacking conformational freedom. Quantum-topological analysis of experimental electron density allowed us to detect the distinctive differences in the electron distribution within their thiourea groups, arising primarily from crystal packing effects. Sulfur atom S(1a) features two separate regions of positive deformation density, whilst the other atom S(1b) is found to be more diffuse with positive density taking a toroidal form. In contrast to S(1a), the couple of the lone pairs of S(1b) derived by non-bonding charge concentrations takes a more significant turn relative to the molecular plane and proves to be distorted. We also report an ambiguous electronic structure of the heteroatoms, i.e. appearance of “false” Laplacian CPs (3, +3) or splitting of true ones, which is caused by neglecting or excessive use of Gra...

Numerical investigation of toroidal bubble dynamics in a compressible fluid based on boundary integral method

The external liquid compressibility cannot be ignored because the speed of the bubble jet emerging at the end of bubble collapse reaches hundreds of meters per second. Additionally, when the bubble jet penetrates the surface of a bubble, a toroidal bubble forms and the singly connected flow domain changes to a doubly connected topology. As the Biot–Savart law is based on the assumption of incompressibility, the vortex ring model is very difficult to extend to compressible fluids. This paper describes the use of the boundary integral method to establish a numerical model of a toroidal bubble, considering the external liquid compressibility and the internal gas wave effect. A cut is introduced into the fluid domain so that it can be considered as singly connected, with the discontinuity of velocity across this cut equal to the circulation of the flow. Furthermore, the initial bubble condition is calculated by the volume acceleration model. The numerical model is validated through comparisons with experimental data from underwater explosions. The numerical results are found to correlate well with the experimental results. Then, the influence of buoyancy parameters and the internal gas wave effect on toroidal bubble dynamics in a gravitational field is investigated.

Simulation of Harmonic Temperature and Magnetic Fields Based on the Method of Separation of Variables in Regions of Complex Toroidal Forms

Basic boundary-value problems of calculating harmonic physical fields for toroidal forms (including the cases of complex sectors and nonlinear boundary-value conditions) are considered on the basis of exact analytical representation of the solution in the form of a series in toroidal harmonics. The results obtained can be used in calculating harmonic fields in problems of heat and mass transfer and of electromagnetism, coefficients of the medium of specific technical objects of toroidal form, as well as a test problem when employing other methods.

Low frequency acoustical scattering from dynamic schools of swim bladder fish

A time-domain computational model is used to describe the dynamic evolutions of fish schools. The individual and ensemble fish behaviors are governed by three radial parameters, representing attraction, orientation, and repulsion zones between fishes. Different combinations of these radii cause the schools to evolve into various discoid, swarming, parallelized, or toroidal geometric forms. A previously developed model [J. Acoust. Soc. Am. 99, 196–208 (1996)] is applied to study the variations in ensemble scattering from these school types for ensonification frequencies in the swim bladder resonance region, as a function of frequency and time, and predicts distinct characteristic features for the different school geometries. In particular, this work focuses on scattering from disk-shaped schools, by examining the computed resonance response for different school dimensions, packing density, and orientation, in order to identify specific features that are determinative for this type of arrangement. The ultimate goal of this work is to achieve a better understanding of the physical basis for variations in fish school scattering levels and to obtain a detailed statistical description of these objects. [Work supported by ONRG.]

The Spin Torus Energy Model and Electricity

Defining the electron to be a toroidal form of concentrated energy rather than a monopole point-charge, such as used for the Orbital Nuclear Atomic Model (ONAM), leads to a subtly different explanation for electricity and the dynamic nature of electromagnetic fields. The Spin Torus Energy Model (STEM) is used to define the electron and positron, which are then used to explain the nature of electric and magnetic fields, electric current generation from battery and induction sources, capacitor charge and discharge, and superconductivity. STEM supports the notion that free positrons exist within matter, and are equal in importance to electrons: as ONAM makes no provision for positrons within matter, this assertion has wide ranging implications for atomic structure models and chemistry.

Experimental and numerical study of the effects of a wall on the coalescence and collapse of bubble pairs

Two-bubble interaction is the most fundamental problem in multi-bubbles dynamics, which is crucial in many practical applications involving air-gun arrays and underwater explosions. In this paper, we experimentally and numerically investigate coalescence, collapse, and rebound of non-buoyant bubble pairs below a rigid wall. Two oscillating vapor bubbles with similar size are generated simultaneously near a rigid wall in axisymmetric configuration using the underwater electric discharge method, and the physical process is captured by a high-speed camera. Numerical simulations are conducted based on potential flow theory coupled with the boundary integral method. Our numerical results show excellent agreement with the experimental data until the splashing of the jet impact sets in. With different ranges of γbw (the dimensionless distance between the rigid wall and the nearest bubble center), the interaction between the coalesced bubble and the rigid wall is divided into three types, i.e., “weak,” “intermediate,” and “strong.” As γbw decreases, the contact point of the two axial jets migrates toward the wall. In “strong interaction” cases, only an upward jet towards the upper rigid wall forms and a secondary jet with a larger width appears at the base of the first jet. The collapsing coalesced bubble in a toroidal form splits into many smaller bubbles due to the instabilities and presents as bubble clouds during the rebounding phase, which may lead to a weakened pressure wave because the focusing energy associated with the collapsing bubble is disintegrated.

A dynamo in a torus as an explanation of magnetic fields in the outer rings of galaxies

It is currently generally believed that magnetic fields in the disks of spiral galaxies are generated by the dynamo mechanism, which is based on the joint action of differential rotation and the alpha effect, associated with turbulent motions in the interstellar gas. Together with their disks, outer rings are also encountered in galaxies, where magnetic fields may be present. In earlier studies, the generation of magnetic fields has been described in a planar approximation, whose essence is that the size of rings perpendicular to the plane of the galaxy is much smaller than their size in the radial direction. However, it is plausible that these sizesmay sometimes be comparable, so that it would be more logical to suppose that a ring has a toroidal form. A model for a dynamo in a toroidal ring is constructed in this study. This model describes the magnetic field using two functions, corresponding to the toroidal component of the field and the part of the vector potential characterizing its poloidal component. The possible generation of magnetic field in various cases is shown, with both quadrupolar symmetry (close to the fields obtained in the planar approximation) and dipolar symmetry (when two layers with oppositely directed magnetic fields form in the ring). The parameter values for which the generation of fields with one or the other type of symmetry is possible are estimated. The results can also be used to describe the evolution of the magnetic fields in other toroidal astrophysical objects.

Circulation, hydrography, and transport over the summit of Axial Seamount, a deep volcano in the Northeast Pacific

AbstractA numerical model of ocean flow, hydrography, and transport is used to extrapolate observations of currents and hydrography and infer patterns of material flux in the deep ocean around Axial Seamount, a destination node of NSF's Ocean Observatories Initiative's Cabled Array. Using an inverse method, the model is made to approximate measured deep ocean flow around this site during a 35 day time period in the year 2002. The model is then used to extract month‐long mean patterns and examine smaller‐scale spatial and temporal variability around Axial. Like prior observations, model month‐long mean currents flow anticyclonically around the seamount's summit in toroidal form with maximum speeds at 1500 m depth of 10–11 cm/s. As a time mean, the temperature (salinity) anomaly distribution takes the form of a cold (briny) dome above the summit. Passive tracer material continually released at the location of the ASHES vent field exits the caldera primarily through its southern open end before filling the caldera. Once outside the caldera, the tracer circles the summit in clockwise fashion, fractionally reentering the caldera over lower walls at its north end, while gradually bleeding southwestward during the modeled time period into the ambient ocean. A second tracer release experiment using a source of only 2 day duration inside and near the CASM vent field at the northern end of the caldera suggests a residence time of the fluid at that locale of 8–9 days.

Assessment of the Structure and Core Losses Pertaining to Magnetic Toroids Made from Powder and Cast in One Production Step

This paper presents the results of a comparison of two methods for the preparation of permalloy-type material. The nominal blend composition was Ni80-Fe14.7-Mo4.5-Mn0.5-Si0.3. Samples were prepared in the form of toroids using powder metallurgy and an induction casting method. The following measurements were carried out on samples: computer tomography, VSM, XRD, and measurement of the total magnetic losses at different frequencies and the magnetic induction. Both technologies were found to create a crystalline material with similar phases. The sample prepared by the induction casting method exhibited high coercivity, low magnetization saturation and high excess losses in comparison with the sample that had been subjected to a 24h and 120h milling duration.