Toroidal Helix Research Articles

Study on the toroidal helix and manufacturing method of enveloping hourglass worm tooth surface

As a complex space enveloped surface, the tooth surface of dual-lead helical gear enveloping hourglass worm is characteristic with difference tooth profile, unequal pitch and variable tooth thickness. To grasp the geometry characteristics and precision manufacturing method of it, the analytical method for toroidal helix is presented. The mathematical model of toroidal helix is developed, and the geometry characteristics of helix angle, axial tooth thickness, and tooth surface undercutting are analyzed. The helix angle of toroidal helix presents the convex shape, and the undercutting characteristic is affected by the pressure angle, helix angle, transmission ratio, and normal modulus. Based on the toroidal helix of tooth surface, the precision manufacturing method is proposed, and the measuring method is developed. The hourglass worm sample was manufactured and measured, and the transmission accuracy of hourglass worm drive is tested. The results show that the manufacturing and measuring method of toroidal helix is effective and feasible.

Magnetic induction communication using toroidal helix coil

Magnetic induction communication using toroidal helix coil

Driven toroidal helix as a generalization of the Kapitza pendulum.

We explore a model system consisting of a particle confined to move along a toroidal helix while being exposed to a static potential as well as a driving force due to a harmonically oscillating electric field. It is shown that in the limit of a vanishing helix radius, the governing equationsof motion coincide with those of the well-known Kapitza pendulum-a classical pendulum with oscillating pivot-implying that the driven toroidal helix represents a corresponding generalization. It is shown that the two dominant static fixed points present in the Kapitza pendulum are also present for a finite helix radius. The dependence of the stability of these two fixed points on the helix radius, the driving amplitude, and the static potential are analyzed analytically. These analytical results are subsequently compared to results corresponding of numerical simulations. Additionally, the most prominent deviations of the driven helix from the Kapitza pendulum with respect to the resulting phase space are investigated and analyzed in some detail. These effects include an unusual transition to chaos and an effective directed transport due to the simultaneous presence of multiple chaotic phase space regions.

External-field-induced dynamics of a charged particle on a closed helix.

We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For small driving amplitudes and a linearly polarized field, we find a split up of the chaotic part of the phase space, which prevents the particle from inverting its direction of motion. This allows for a nonzero average velocity of chaotic trajectories without breaking the well-known symmetries commonly responsible for directed transport. Within our chosen normalized units, the resulting average transport velocity is constant and does not change significantly with the driving amplitude. A very similar effect is found in case of the circularly polarized field and low driving amplitudes. Furthermore, when driving with a circularly polarized field, we unravel a second mechanism of the split up of the chaotic phase space region for very large driving amplitudes. There exists a wide range of parameter values for which trajectories may travel between the two chaotic regions by crossing a permeable cantorus. The limitations of these phenomena, as well as their implication on manipulating directed transport in helical geometries are discussed.

Circular intensity differential scattering of light to characterize the coronavirus particles

Angle-resolved circularly polarized light scattering calculations are demonstrated to identify virus particles from nonvirus particles. A coronavirus particle is modeled as having a spherical shaped envelope with cylindrical spikes projected from the envelope surface, and the single-stranded ribonucleic acid (RNA) genome polymer has been mimicked with a toroidal helix. The influence of genome polymer packaged as a standard helix in the virion core is also demonstrated. We investigated four different electromagnetic models: (i) a nucleated sphere with spikes that is a coronavirus particle, (ii) a nucleated sphere with no spikes, (iii) a homogeneous sphere, and (iv) a respiratory fluid containing a virus particle. The angular pattern of scattered circularly polarized light, the circular intensity differential scattering of light (CIDS), served as a particle’s signature. This scattering signature is found sensitive to the chiral parameters that reveal information about the particles. The effect of changes in the RNA polymer, changes in its packaging, number of turns, handedness, and size are demonstrated on the scattering calculations. Additionally, the extinction efficiency, the depolarization ratio, the total scattered intensity, and the effect of changes in the wavelength of incident light on these scattering quantities are investigated. This biophysical method can offer a label-free identification of virus particles and can help understand their interaction with light.

Tunable order of helically confined charges.

We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates with the particle distance and allows for the existence of stable bound states, despite the purely repulsive character of the Coulomb interaction. We design an order parameter to classify these bound states and use it to identify a structural crossover of the particle order, occurring when the electric field strength is varied. Amorphous particle configurations for a vanishing electric field and crystalline order in the regime of a strong electric field are observed. We study the impact of parameter variations on the particle order and conclude that the crossover occurs for a wide range of parameter values and even holds for different helical systems.

Toroidal Ferrite Transformers With Conformal Laser Direct Structured Windings

Many applications in communications and power electronics demand inductive components that operate at high frequency or a broad range of frequencies. For applications requiring miniature devices with large inductance values, most often the components are manufactured imprecisely in the traditional method where magnetic cores are wound with a fine gauge wire. To achieve the best high-frequency performance, there is a desire to use a practical manufacturing method that removes the imprecision of wire winding. In this article, a unique 3-D laser exposure system is used to direct-write conformal winding patterns on the surface of MnZn ferrite toroids. The toroidal helix windings were fabricated by both an additive laser direct structuring (LDS) process and a subtractive laser-written mask-and-etch process. Both methods were performed on both enamel-coated ferrites and bare ferrites. The performance and equivalent circuit model parameters of the transformers were measured up to 1.5 GHz and will be presented. The transformers fabricated on the enamel-coated cores were found to have comparable or better inductances and broadband coupling than wire-wound transformers of matching construction.

Analysis of Rectangular Cross-Section Toroidal Helix Geometry for Winding Length Optimization

Recent advances in additive direct-write circuit technology have enabled the fabrication of inductive winding geometries previously considered impossible by conventional methods. In this letter, a winding fabricated around a rectangular cross-section toroidal core is considered. As an extension of research embedding toroidal cores within printed circuit board, this letter considers the minimization of the winding length when the vertical path, along the toroidal z-direction, is not restricted to be perfectly vertical, which is only possible with direct-write techniques. It will be shown that the exact analysis results in a transcendental equation for the optimized vertical midpoints of the winding turns. However, a few reasonable approximations allow an analytical expression for this optimized midpoint to be found. Comparisons of this approximate analytical solution to the exact solution found by numerical methods will be presented for typical toroid dimensions. The accuracy of this approximate solution with changing turn density will also be presented. For typical toroid dimensions, it was found that the choice of midpoint can change the total winding length by as much as 10%. The analytical approximate solution for the midpoint was found to deviate by 2.75% of angular gap from the exact solution, which resulted in an error in the minimum winding length of only 0.07%, a result which will be discussed in this letter.

Study of a toroidal-helical pipe as an innovative static mixer in laminar flows

In this paper we present the design of a novel, passive mixer, to enhance mixing and residence time distribution for promoting transport and reaction mechanisms in such devices. The goal is to understand and optimize the flow patterns for enhancing mixing in laminar flows through toroidal helical pipes, inspired by the coiled flow inverter (CFI) (Saxena and Nigam, 1984). A toroidal helix is a smooth analytical curve winding around a torus. It is characterized by three parameters: the radius of the torus’ centerline, the radius of the torus’ cross-section, and the number of turns it winds around the torus. Unlike the torus or the straight helix which have constant curvatures, the toroidal helix has a spatially oscillating curvature. We found that this causes the otherwise separated pair of Dean vortices to couple together, periodically re-orient, shrink and grow within each turn of the pipe. The resultant complex streamlines span the entire cross-section and enhances mixing via advective means. By constraining the total pipe length, a meaningful comparison of mixing efficiency within a given volume of pipe can be assessed as the torus’s cross-section radius and the number of helix turns are systematically varied. Reynolds number of up to 400 is explored with the number of turns of 3, 5, 7 and 8. The optimization study shows that the best mixing performance is achieved using a moderate number of turns. Apart from flow pattern and mixing efficiency, we also studied the pressure drop to monitor increased energy consumption and residence time distribution of the flow to monitor degree of mixing.

Degeneracy and inversion of band structure for Wigner crystals on a closed helix

We explore the formation of Wigner crystals for charged particles on a toroidal helix. Focusing on certain commensurate cases we show that the ground state undergoes a pitchfork bifurcation from the totally symmetric polygonic to a zig-zag-like configuration with increasing radius of the helix. Remarkably, we find that for a specific value of the helix radius, below the bifurcation point, the vibrational frequency spectrum collapses to a single frequency. This allows for an essentially independent small-amplitude motion of the individual particles and consequently localized excitations can propagate in time without significant spreading. Increasing the radius beyond the degeneracy point, the band structure is inverted, with the out-of-phase oscillation mode becoming lower in frequency than the mode corresponding to the center of mass motion.

Closed-Form Solution to Electromagnetic Fields in Far Zone Radiated by Toroidal Antennas

In this paper, a single-wound toroidal helix antenna (SWTHA) and a contra-wound toroidal helix antenna (CWTHA) are analyzed in an analytical way. In this connection, the total winding length of a SHTA is estimated and a fairly accurate and closed-form expression of the length is obtained. Meanwhile, a closed form solution of the electromagnetic fields in far zone or their alternative vector potential components is obtained. The formulation is analytical, based on the assumption of uniform SWTHA and CWTHA currents and the large ratio a/b of the toroidal antenna radius a over the turn radius b. The solution is general enough for any number N of wound turns. The results are finally reduced to those existing results available elsewhere in literature by letting the radius b be zero (for infinitely thin wire and circular loop antennas) and the winding number N be zero (for the normal circular loop antennas). The reduced results of the potential components are the same as those in the textbooks. The analytical results are obtained for the first time, useful for antenna designers and also antenna engineering education.

A study of the CTHA based on analytical models

The first electromagnetic analysis of the contra-wound toroidal helix antenna (CTHA) is presented. This very-low-profile antenna is seen to have characteristics derivable from a transmission line with a standing current wave and an array of small loops. Formulas for the far-field radiation and efficiency are given. These are used, in conjunction with a numerical model, to develop some trends relating performance and design parameters.

Modes of the contrawound toroidal helix antenna

The contrawound toroidal helix antenna with constant current is examined; it has an omnidirectional pattern in the toroid plane. Radiation resistance is derived for the dipole mode, and results are validated by moment-method calculations. The radiation Qs of these antennas are greater than one million, making them unsuitable as dipole mode radiators. Ratios of loop-mode to dipole-mode radiation resistances range from several hundred to large values. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 365–368, 1999.

Calculation of the twist and the writhe for representative models of DNA

The geometric quantities twist ( Tw) and writhe ( Wr) are of primary importance for a complete description of the structure of DNA. In the case of a closed circular DNA, the sum of Tw and Wr is constant and equal to the linking number, Lk. In this paper we present a general method for calculation of the twist in terms of a pair of curves and a correspondence surface that joins them. The twist of any pair of curves (C 1 and C 2) may take on different values depending upon their ordering, and in general Tw(C 1, C 2) is not equal to Tw(C 2, C 1) . We describe four models that may be taken to represent the structure of DNA and compute the twist for both orderings in each case. The four models examined are: I, a regular helix about a linear axis; II, a toroidal helix about a closed circular axis; III, a superhelix about a regular helical axis; and IV, a superhelix about a closed toroidal helix. In cases II and IV these results are also used to calculate Lk and Wr. Case III is used to analyze the winding of DNA in a nucleosome.

X-ray scattering from the superhelix in circular DNA.

This communication presents measurements, made with a newly constructed position-sensitive detector, of the small-angle x-ray scattering from the first-order superhelix of native COP608 plasmid DNA. This instrument measures intensities free of slit effects and provides good resolution in the region of interest. The reported observations, made both in the presence and in the absence of intercalator, closely fit the scattering patterns calculated for noninterwound helical first-order superhelices. These results are consistent with a toroidal helical structure but not with interwound conformations. The pitch angle alpha and contour length per turn c are reported for the native molecule at several concentrations of the platinum intercalating compound. From these parameters, the best-fitting toroidal helix is constructed and its geometry is investigated. The specific linking difference of the native molecule is estimated to be delta Lk/Lk0 approximately equal to -0.055. If the best-fitting toroidal helix is taken to be the actual structure, the partitioning of superhelicity between twist and writhe occurs in the approximate ratio of 2:1.

The Fourier transforms of a coiled coil and a toroidal helix

The Fourier transform of a finite coiled coil containing an integral number of repeat units is evaluated analytically. The special cases where the coiled coil reduces either to a pure helix or to a toroidal helix are specifically included.