Circular Filaments Research Articles

Calculation of magnetic stiffness over torque between two current-carrying circular filaments arbitrarily positioning in the space

The sets of expressions for calculation of sixteen components of magnetic stiffness over torque between two current-carrying circular filaments arbitrarily positioning in the space are derived by using mutual inductance and Grover’s method. The expressions are presented in the analytical form via integral equations, whose kernels include the elliptic functions of first and second kinds. The derived sets of formulas were mutually validated and results of calculation of components of magnetic stiffness agree well to each other.

Rearrangement of sunspot magnetic field caused by an X1.5 solar flare

ABSTRACT Solar flares will cause the change of the photospheric magnetic field and sunspot structure. However, the exact physical processes involved remain unclear. Here, we study the changes of photospheric magnetic field before and after an X1.5 flare caused by a circular filament eruption in the active region NOAA 13006. The magnetic field structure of this active region is a fan-spine structure with a circular polarity inversion line (PIL). We found that the sunspot structure contracted towards the PIL as a whole after the flare. The penumbra away from the PIL gradually disappears, and the umbra and penumbra near the PIL gradually enhances. By analysing the local magnetic field, the Lorentz force (LF), and the photospheric velocity field in these three regions, we find that the magnetic flux in the region of the disappearing penumbra converges and contracts towards the PIL, leading to an enhancement of the umbra, while the enhancement of the penumbra potentially indicates that this region may be the footpoint of a reconnected magnetic field system. We suggest that this contracting motion is driven by the horizontal LF.

Calculation of mutual inductance between circular and arbitrarily shaped filaments via segmentation method

In this article, two analytical formulas for the calculation of mutual inductance between a circular filament and line segment arbitrarily positioning in the space are derived by using Mutual Inductance Method (MIM) and Babic’s Method (BM), respectively. Using the fact that any curve can be interpolated by a set of line segments, a method for calculation of mutual inductance between a circular filament and filament having an arbitrary shape in the space is proposed based on the derived analytical formulas. The derived two formulas and the proposed method (Segmentation Method) were numerically validated by using FastHenry software and reference examples from the literature. In particular, the proposed method was successfully applied to the calculation of mutual inductance between the circular filament and the following special curves such as circle, circular arc, elliptic arc, ellipse, spiral, helices and conical helices. All results of the calculation are in good agreement with the reference examples.

DcAFF (Discontinuous Aligned Fibre Filament) – Mechanical properties investigation on multilayer 3D printed parts

DcAFF (Discontinuous Aligned Fibre Filament) is a novel thermoplastic filament developed for 3D printing. This filament is reinforced with highly aligned discontinuous fibres and is based on the High Performance Discontinuous Fibre (HiPerDiF) method which produces thin tapes suitable for a range of different composite manufacturing processes. The HiPerDiF, using fibres longer than the critical length, provides mechanical performance comparable to continuous fibre composites with the high formability typical of short fibre composites. Thanks to the development of the third-generation HiPerDiF machine and the DcAFF filament forming method, circular DcAFF filaments can be produced consistently and at high rates. In this paper, both the physical properties and the internal architecture of the produced filament were investigated. In particular, μCT scanning and image post-processing were used to quantify fibre alignment. The designed filament-forming process ensures that the large fraction of the fibres in the final product are well aligned with the longitudinal axis of the filament. The mechanical properties of the multilayer DcAFF 3D printing part are presented for the first time in this paper with tensile, short beam shear (SBS), and open-hole tensile testing. The comparison with the previous studies and data in the literature shows comparable or indeed superior stiffness of DcAFF over existing methods for 3D printing composite parts; however, to be able to consider this material as a viable candidate for high-performance 3D printing further improvements are required in term of strength, e.g. increasing fibre-matrix adhesion or substituting the proof-of-concept PLA matrix with a high performance one.

Experimental investigation on the role of turbulent buffeting on the dynamics of a flexible filament in airflow

This paper documents the results of an experiment conceived to explore and quantitatively assess the role of turbulent buffeting on the dynamics of a flexible filament exposed to airflow. In the experiment, a circular cross-section flexible filament was tested in a wind tunnel where the turbulence level was modified with a square-mesh grid. Measurements were carried out with and without the grid to assess the role of turbulent buffeting on the dynamics of the filament. A hot wire anemometer was used to measure the turbulent airflow, whilst fast video imaging was employed to resolve the filament motion in 3D. The inclusion of the grid and subsequent increase in turbulence level yielded a higher amplitude of motion during the post-flutter regime, thus providing evidence of the role of turbulent buffeting on the flapping dynamics of the filament, hence confirming a conjecture advanced in previous research but not proved yet. Interestingly, the higher amplitude of motion due to turbulent fluctuation was confined only to the vertical plane, suggesting a role of the filament attachment angle in the propagation of disturbances from turbulent fluctuations. No detectable role of turbulent buffeting was observed on the onset of flapping which, based on a comparison with literature data, has been classified as a fluid-elastic instability. Finally, no detectable role of turbulent buffeting was observed in the qualitative dynamics of the filament during flutter and post-flutter.

Open Hole Tension of 3D Printed Aligned Discontinuous Composites

This paper explores the use of Discontinuous Aligned Fibre Filament (DcAFF), a novel discontinuous fibre reinforced thermoplastic filament for 3D printing, to produce structural complex parts. Compared to conventional composite manufacturing, 3D printing has great potential in steering fibres around small structural features. In this current study, the initial thin carbon fibre (CF)-poly(L-lactic acid) (PLA) tape, produced with the High Performance Discontinuous Fibre (HiPerDiF) technology, is now reshaped into a circular cross-section filament, the DcAFF, using a bespoke machine designed to be scalable to high production rates rather than using a labour-intensive manual moulding method as in previous work. The filaments are then fed to a general-purpose 3D printer. Tensile and open-hole tensile tests were considered in this paper for mechanical and processability of DcAFF. The 3D printed specimens fabricated with the DcAFF show superior tensile properties compared to other PLA-based 3D printed composites, even those containing continuous fibres. Curvilinear open-hole tensile test samples were fabricated to explore the processability and performances of such material in complex shapes. The mechanical performance of the produced specimens was benchmarked against conventionally laid-up specimens with a cut hole. Although the steered specimens produced have lower strength than the fully consolidated samples, the raster generated by the printing path has turned the failure mechanism of the composite from brittle to ductile.

Magnetic stiffness calculation for the corresponding force between two current-carrying circular filaments arbitrarily oriented in the space

In this article, sets of analytical formulas for calculation of nine components of magnetic stiffness of corresponding force arising between two current-carrying circular filaments arbitrarily oriented in the space are derived by using Babic’s method and the method of mutual inductance (Kalantarov–Zeitlin’s method). Formulas are presented through integral expressions, whose kernel function is expressed in terms of the elliptic integrals of the first and second kinds. Also, we obtained an additional set of expressions for calculation of components of magnetic stiffness by means of differentiation of Grover’s formula of the mutual inductance between two circular filaments with respect to appropriate coordinates. The derived sets of formulas were mutually validated and results of calculation of components of magnetic stiffness agree well to each other.

Modelling of Backscattering off Filaments Using the Code IPF-FD3D for the Interpretation of Doppler Backscattering Data.

Filaments or blobs are well known to strongly contribute to particle and energy losses both in L- and H-mode, making them an important plasma characteristic to investigate. They are plasma structures narrowly localized across a magnetic field and stretched along magnetic field lines. In toroidal devices, their development is observed to take place in the peripheral plasma. Filament characteristics have been studied extensively over the years using various diagnostic techniques. One such diagnostic is the Doppler backscattering (DBS) method employed at the spherical tokamak Globus-M/M2. It has been observed that the DBS signal reacts to the backscattering from filaments. However, the DBS data have proven difficult to analyze, which is why modelling was undertaken using the code IPF-FD3D to understand what kind of information can be extrapolated from the signals. A circular filament was thoroughly investigated in slab geometry with a variety of characteristics studied. Apart from that, the motion of the filaments in the poloidal and radial directions was analyzed. Additionally, other shapes of filaments were presented in this work. Modelling for the real geometry of the Globus-M/M2 tokamak was performed.

X-point and divertor filament dynamics from gas puff imaging on TCV

A new gas puff imaging diagnostic has been installed on the TCV tokamak, providing two-dimensional insights into scrape-off-layer (SOL) turbulence dynamics above, at and below the magnetic X-point. A detailed study in L-mode, attached, lower single-null discharges shows that statistical properties have little poloidal variations, while vast differences are present in the 2D behaviour of intermittent filaments. Strongly elongated filaments, just above the X-point and in the divertor far-SOL, show a good consistency in shape and dynamics with field-line tracing from filaments at the outboard midplane, highlighting their connection. In the near-SOL of the outer divertor leg, short-lived, high frequency and more circular (diameter ∼15 sound Larmor radii) filaments are observed. These divertor-localised filaments appear born radially at the position of maximum density and display a radially outward motion with velocity ≈400 m s−1 that is comparable to radial velocities of upstream-connected filaments. Conversely, in these discharges ( pointing away from the divertor), these divertor filaments’ poloidal velocities differ strongly from those of upstream-connected filaments. The importance of divertor-localised filaments upon radial transport and profile broadening is explored using filament statistics and in situ kinetic profile measurements along the divertor leg. This suggests that these filaments contribute significantly to electron density profile broadening in the divertor.

Asymptotic behaviour of global vortex rings

In this paper, we are concerned with nonlinear desingularization of steady vortex rings in with a general nonlinearity f. Using the improved vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in the whole space. The requirements on f are very general, and it may not satisfy the Ambrosetti–Rabinowitz condition. Some qualitative and asymptotic properties are also established.

Calculation of magnetic force and torque between two arbitrarily oriented circular filaments using Kalantarov–Zeitlin’s method

In this article, formulas for calculation of magnetic force and torque between two circular filaments arbitrarily oriented in space were derived by using Kalantarov–Zeitlin’s method. Formulas are presented in an analytical form through integral expressions, whose kernel function is expressed in terms of the elliptic integrals of the first and second kinds, and provide an alternative formulation to Babič’s expressions. The derived new formulas were validated via comparison with a series of reference examples. Also, we obtained additional expressions for calculation of force and torque between two circular filaments by means of differentiation of Grover’s formula for the mutual inductance between two circular filaments with respect to appropriate coordinates. These additional expressions allow to verifying comprehensively and independently derived new formulas.

Magnetic Stiffness Calculation for the Corresponding Force between Two Current-Carrying Circular Filaments Arbitrarily Oriented in the Space

Magnetic Stiffness Calculation for the Corresponding Force between Two Current-Carrying Circular Filaments Arbitrarily Oriented in the Space

Batch production and fused filament fabrication of highly aligned discontinuous fibre thermoplastic filaments

Fused filament fabrication (FFF), which is a thermoplastic layer-by-layer additive manufacturing technique, called as 3D printing, can quickly build complex geometries, reducing design limitations and production costs of conventional manufacturing methods. Using a fibrous reinforcement strengthens the thermoplastic matrix, allowing FFF to be used in more structural complex-shape small-size applications in engineering. Aligned discontinuous fibre composites (ADFRC) incorporate a high-performance reinforcement architecture that, owing to a sufficient fibre length and high level of alignment, results in mechanical performance comparable to those of continuous fibre composites. Moreover, it can offer higher formability and, fewer manufacturing defects. In this paper, ADFRC preforms, produced with the High Performance Discontinuous Fibre (HiPerDiF) technology, were impregnated with poly(L-lactic acid) (PLA) and then reshaped to a circular-shaped 3D printing filament using a customised manual moulding and pultrusion method. Two different mould types were compared to maximise the filament quality and reduce the amount of trapped voids. The printability of the circular filaments was investigated by varying three parameters: deposition speed, processing temperature, and layer thickness. Finally, the tensile properties of samples from each manufacturing step: moulded, filament, single raster printed, and full height rectangular part, were investigated. Overall, the HiPerDiF-PLA filament can be printed using an 3D printer. Although the tensile properties of filament in each stage reduced as the result of the shape transformation process, the deposited layer of HiPerDiF-PLA part has greater stiffness and strength than other PLA composite materials. At this stage of technology development, the material has lower mechanical performance yet than the nylon continuous fibre composites printed with commercially available machines. However, there are clear routes forward for the improved performance of the HiPerDiF FFF printed filaments.

On the Static Pull-In of Tilting Actuation in Electromagnetically Levitating Hybrid Micro-Actuator: Theory and Experiment

This work presents the results of the experimental and theoretical study of the static pull-in of tilting actuation executed by a hybrid levitation micro-actuator (HLMA) based on the combination of inductive levitation and electrostatic actuation. A semi-analytical model to study such a pull-in phenomenon is developed, for the first time, as a result of using the qualitative technique based on the Lagrangian approach to analyze inductive contactless suspensions and a recent progress in the calculation of mutual inductance and force between two circular filaments. The obtained non-linear model, accounting for two degrees of freedom of the actuator, allows us to predict accurately the static pull-in displacement and voltage. The results of modeling were verified experimentally and agree well with measurements.

Precise Modeling of Mutual Inductance for Planar Spiral Coils in Wireless Power Transfer and Its Application

In magnetic coupling resonant wireless power transfer devices, planar spiral coils are often used as the coupling mechanism. In such application area, the coils are often wound sparsely with wide screw pitches and often under complex relative position. An accurate model of mutual inductance for planar spiral coils wound either densely or sparsely is established in this article. Utilizing Euler Angles, an exact expression of mutual inductance for a couple of planar spiral coils under arbitrary relative position is proposed. Based on this expression and geometric mean distance principle, a self-inductance expression for planar spiral coils is derived. Based on numerical calculation of the expressions proposed in this article, the influence of precession and spin angle on mutual inductance is studied; the method of determining radius of each turn when using traditional concentric circular filaments cluster approximation model for self- and mutual inductance calculation is studied; the difference of calculation results between the accurate model and the traditional approximation model is compared. Finite element simulation and experimental results verify the correctness of the proposed models.

Analytical Expressions for the Magnetic Field Generated by a Circular Arc Filament Carrying a Direct Current

This paper presents a simple, didactical and compact solution for the components of the magnetic vector potential and magnetic field generated by a circular arc filament carrying a direct current using the well-known incomplete elliptic integrals, their properties and formulas. Using a well-defined method, the expressions are obtained in Cartesian coordinates and then easily transformed to a compact expression in cylindrical coordinates. The paper provides numerical data for different study cases where arbitrary arc filaments are considered. Through Gauss' magnetic law, special cases, and comparisons with numerical methods, a degree of validation is provided for the derived expressions.These solutions represent a computational advantage for magnetic field calculations for applications like wireless power transfer. Finally, new integral formulas are derived using elliptic integrals.

Physical Modeling of a Sliding Clamp Mechanism for the Spreading of ParB at Short Genomic Distance from Bacterial Centromere Sites.

SummaryBacterial ParB partitioning proteins involved in chromosomes and low-copy-number plasmid segregation are cytosine triphosphate (CTP)-dependent molecular switches. CTP-binding converts ParB dimers to DNA clamps, allowing unidimensional diffusion along the DNA. This sliding property has been proposed to explain the ParB spreading over large distances from parS centromere sites where ParB is specifically loaded. We modeled such a “clamping and sliding” mechanism as a typical reaction-diffusion system, compared it to the F plasmid ParB DNA binding pattern, and found that it can account neither for the long range of ParB binding to DNA nor for the rapid assembly kinetics observed in vivo after parS duplication. Also, it predicts a strong effect on the F plasmid ParB binding pattern from the presence of a roadblock that is not observed in ChIP-sequencing (ChIP-seq). We conclude that although “clamping and sliding” can occur at short distances from parS, another mechanism must apply for ParB recruitment at larger genomic distances.

Desingularization of vortex rings in 3 dimensional Euler flows

In this paper, we are concerned with nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler fluids. We focus on the case when the vorticity function has a simple discontinuity, which corresponding to a jump in vorticity at the boundary of the cross-section of the vortex ring. Using the vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in several kinds of domains. The precise localization of the asymptotic singular vortex filament is proved to depend on the circulation and the velocity at far fields of the vortex ring, and the geometry of the domains. Some qualitative and asymptotic properties are also established.

The neuroactive substances and associated muscle system in Rhipidocotyle campanula (Digenea, Bucephalidae) from the intestine of the pike Esox lucius.

We report about the muscular system and the serotonergic and FMRFamidergic components of the nervous system of the Bucephalidae trematode, Rhipidocotyle campanula, an intestinal parasite of the pike. We use immunocytochemical methods and confocal scanning laser microscopy (CLSM). The musculature is identified by histochemical staining with fluorescently labeled phalloidin. The body wall musculature of R. campanula contains three layers of muscle fibres - the outer thin circular, intermediate longitudinal and inner diagonal muscle fibres running in two opposite directions. The digestive system of R. campanula possess of a well-developed musculature: radial, longitudinal and circular muscle elements are detected in the pharynx, circular and longitudinal muscle filaments seen in the oesophagus, and longitudinal and the circular muscle fibres were found in the intestinal wall. Specific staining indicating the presence of actin muscle filaments occurs in the cirrus sac localized in the posterior body region. The frontal region of anterior attachment organ, the rhynchus, in R. campanula is represented by radial muscle fibres. The posterior part of the rhynchus comprise of radial muscles forming the organ's wall, and several strong longitudinal muscle bundles. Serotonergic and FMRFamidergic structures are detected in the central and peripheral compartments of the nervous system of R. campanula, that is, in the paired brain ganglia, the brain commissure, the longitudinal nerve cords, and connective nerve commissures. The innervations of the rhynchus, pharynx, oesophagus and distal regions of the reproductive system by the serotonergic and FMRFamidergic nervous elements are revealed. We compare our findings obtained on R. campanula with related data for other trematodes.

Static Pull-In Behavior of Hybrid Levitation Microactuators: Simulation, Modeling, and Experimental Study

In this article, a systematic and comprehensive approach based on finite element analysis and analytical modelling for studying static pull-in phenomena in hybrid levitation micro-actuators is presented. A finite element model of electromagnetic levitation micro-actuators based on the Lagrangian formalism is formulated and developed as a result of recent progress in the analytical calculation of mutual inductance between filament loops. In particular, the developed finite element model allows us to calculate accurately and efficiently a distribution of induced eddy current within a levitated micro-object. At the same time, this fact provides a reason for formulating the analytical model in which the distribution of the induced eddy current can be approximated by one circuit represented by a circular filament. In turn, both developed models predict the static pull-in parameters of hybrid levitation micro-actuators without needs for solving nonlinear differential equations. The results of modelling obtained by means of the developed quasi-finite element and analytical model are verified by the comparison with experimental results.