Total Twist Angle Research Articles

Optical measurements of the twist constant and angle in nematic liquid crystal cells

We present a reliable optical method for measuring the twist elastic constant K2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {K}_2$$\\end{document} and for assessing the total twist angle in a standard nematic twist cell. The method relies on the use of a non-standard configuration of crossed polarisers and a twist cell, which allows us to measure accurately the twist-cell parameters by reducing the degeneracy between them. Grid patching and an efficient beam propagation method are utilised in the numerical models used for fitting the experimental data. The modelling shows that the polarisation dynamics in a twist cell is non-trivial and much more complex than in a planar cell. The twist elastic constant of three commonly used liquid crystals (5CB, 6CHBT and E7) was successfully extracted from cross-polarised intensity measurements.

Probing the twist angle of confined prominence eruption using SDO/AIA data

In this context, we utilized a simplified representation of the curved cylinder flux tube to approximate the helical structure of the prominence. By considering the bright helical features as indicators of the magnetic field, we measured the average twist angle of the prominence legs. To gather the necessary data, we obtained image data with a wavelength of 171 Å from the Solar Dynamic Observatory (SDO)/Advanced Imaging Assembly (AIA) archive. We employed some IDL routines within the SolarSoft (SSW) package to determine the flux rope’s total twist angle for a confined prominence eruption. Specifically, we focus on a confined prominence eruption that occurred at the south-east limb of the Sun for an active region (AR) NOAA (AR 11 117) observed on October 21, 2010. The eruption commenced on 2010-10-21 at 21:56:18 UT and lasted until 2010-10-22 at 01:24:58 UT. During this event, a B2.6 flare class that occurred on 2010-10-21 at 23:17 UT, located at heliographic position of N20E84. Our results indicate that the distance between the two footpoints is up to 18 670 km. Initially, when the event began the height (h) was found to be 21 162.1 km, but the height was increased to reach 80 362.4 km at the end of eruption. The flux rope’s average twist angle (ϕ, in radian) at the beginning of eruption was ϕ = 13.4π. As the prominence ascended to higher levels, the twist angle was decreased gradually due to the magnetic field relaxation reached to ϕ = 3.6π. We determined that the flux ropes average twist angle (ϕ) that exceed the threshold for the helical kink instability. Therefore, we conclude that the eruption was caused by helical kink instability, as a result it is in consistent with other investigations.

Rapid Rotation of an Erupting Prominence and the Associated Coronal Mass Ejection on 13 May 2013

In this paper, we report the multiwavelength observations of an erupting prominence and the associated coronal mass ejection (CME) on 13 May 2013. The event occurs behind the western limb in the field of view of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) spacecraft. The prominence is supported by a highly twisted magnetic flux rope and shows rapid rotation in the counterclockwise direction during the rising motion. The rotation of the prominence lasts for ∼ 47 minutes. The average period, angular speed, and linear speed are ∼ 806 sec, ∼ 0.46 rad min−1, and ∼ 355 km s−1, respectively. The total twist angle reaches ∼ 7 $\pi$ , which is considerably larger than the threshold for kink instability. Writhing motion during 17:42 – 17:46 UT is clearly observed by SWAP in 174 Å and Extreme-UltraViolet Imager (EUVI) on board the behind Solar Terrestrial Relations Observatory (STEREO) spacecraft in 304 Å after reaching an apparent height of ∼ 405 Mm. Therefore, the prominence eruption is most probably triggered by kink instability. A pair of conjugate flare ribbons and post-flare loops are created and observed by STA/EUVI. The onset time of writhing motion is consistent with the commencement of the impulsive phase of the related flare. The 3D morphology and positions of the associated CME are derived using the graduated cylindrical shell (GCS) modeling. The kinetic evolution of the reconstructed CME is divided into a slow-rise phase (∼ 330 km s−1) and a fast-rise phase (∼ 1005 km s−1) by the writhing motion. The edge-on angular width of the CME is a constant (60∘), while the face-on angular width increases from 96∘ to 114∘, indicating a lateral expansion. The latitude of the CME source region decreases slightly from ∼ 18∘ to ∼ 13∘, implying an equatorward deflection during propagation.

On the Kink Instability of Twisted Coronal Loops: Nonneutralized Electric Current

Based on linear magnetohydrodynamic equations and an energy principle we analyze the ideal kink instability of a twisted force-free coronal loop (flux rope) surrounded by an outer potential magnetic field by using the sharp-boundary approximation at the surface. Unlike Tsap et al., a magnetic flux rope with nonneutralized (uncompensated) electric current is considered. We have shown that the twist angle of magnetic field lines is closely related to coronal mass ejections and solar flares. The kink instability condition does not depend on the radial profile of the magnetic field inside a flux rope in the long-wavelength limit but depends strongly on the reverse electric currents at the surface. The total critical twist angle of magnetic field lines, which determines the kink instability threshold, can be much greater than π radians due to reverse azimuthal surface current. This agrees with observations and illustrates the importance of the role of reverse currents for stabilization of a flux rope. Additional arguments in favor of the energy release models based on the uncompensated electric currents are presented.

Oblique light incidence method to study topological defects in nematic layers with conical boundary conditions

A polarization microscopy method to investigate the orientational structures and boojums formed in the chiral and achiral nematic layers under conical (tilted) boundary conditions has been developed. Oblique light incidence on nematic layer is used, due to which the phase difference between the ordinary and extraordinary waves depends on the director’s azimuthal angle. The phase difference gets maximal when the director azimuthal angle of achiral nematic varphi (x,y) = 0 and an azimuthal angle at the center of the chiral nematic layer varphi _0(x,y) = 0 independently of the total twist angle varphi _{TOTAL}. It has been found that the m=+1 boojums with the phase xi = pm 90^circ and xi = (-90^circ + varphi _{TOTAL}/2) are formed in achiral and chiral nematics, respectively, at the director tilt angle theta _{d/2} cong 40^circ at the interface. In addition, the defectless structure of chiral nematic with the periodically variable azimuthal director angle on the substrates has been studied.

Performance Characterization of a Kenics Static Mixer Using Slotted Elements

The pharmaceutical, biomedical, bioenergy, and consumer products industries rely heavily on the mixing of fluids. The bulk of the processes that are undergone in these industries are laminar flowing fluids with the attendant need for low-pressure losses which the Kenics static mixers are better suited for. The mixing of fluids is achieved through the splitting and shearing at successive element junctions and stretching and folding along the length of the elements. The performance of Kenics static mixers can be enhanced by optimizing the total blade twist angle, however, the blade pitch has little or no impactful effect. The device geometry optimization is a criterion for its performance enhancement. This study investigates the output mixture strength of the Kenics static mixer using slotted mixer elements solved numerically with Finite Element Method code; COMSOL Multiphysics. The Kenics static mixer performance was optimized with the use of slotted mixer elements as it was observed that the slot width size and a varying number of slots on the mixer elements had an impact on its performance.

Investigation on the effects of twisted wind flow on the wind loads on a square section megatall building

In most wind load codes, the wind direction is assumed to be the same along the height in the atmospheric boundary layer (ABL). But actually, due to the Earth's rotation (Coriolis force), the wind direction in the ABL changes along the height. This twisted wind flow (TWF) will obviously make a difference to the wind loads on megatall buildings. In this study, two kinds of TWFs with total wind twist angles of 25° and 15° are generated in a boundary layer wind tunnel. The effects of TWFs on wind pressures and aerodynamic forces acting on a square section megatall building model are investigated. It is found that the TWF significantly changes the distribution of wind pressure, and it makes the wind force that acts on the megatall building vary with the total wind twist angle. It is interesting to also find that the peak value of power spectra of the lateral wind force is also sharp in TWF. The wind direction where the sharp peak occurs merely changes from that in the corresponding equivalent straight wind flow (SWF). Also, the magnitude levels of correlation coefficient and coherence of wind forces in TWF are almost as strong as those in SWF. These factors further indicate that a relatively small wind-induced response may not be expected to be acquired in TWF. The results of this study have led to a comprehensive understanding of the effects of TWF on the characteristics of wind loads on a square section megatall building.

Wind tunnel simulation of wind flows with the characteristics of thousand-meter high ABL

The accurate simulation of wind flow in the boundary layer wind tunnel is very important for the relevant research on the environmental and structural wind engineering. Due to the earth's rotation, an Ekman spiral shaped wind direction profile would be generated, which is a common phenomenon in the thousand-meter high atmospheric boundary layer (ABL). However, the simulation of wind direction was overlooked in previous studies. In this study, based on the objectives of wind profiles determined by the field measurement, two twisted wind flows (TWFs) with the characteristics of thousand-meter high ABL are successfully simulated using the modified passive simulation technology, i.e. a combination of a self-developed vane system and the traditional passive simulation facilities. In the two TWFs, the wind speed profiles follow the power-law. The maximum wind twist angles are 24.2° and 14.7° respectively, and the variations of wind directions follow the Ekman spiral. The turbulence intensities fluctuate within the stipulations in Chinese Load Code, indicating that the results obtained in the wind tunnel test are reasonable. The power spectra of wind speed show good agreement with the von Karman spectrum. In order to evaluate the effect of TWF, the simulation of multi targets equivalent straight wind flow (SWF) is achieved. Then, the effect of TWF on the wind loads of megatall building is discussed so as to illustrate the importance of accurate simulation of wind flow. It is found that due to the existence of wind twist angle, for any specified wind direction, the wind force that acts on a thousand-meter high building is no longer a specific value, but varies with the total wind twist angle.

Diagnosing the Magnetic Field Structure of a Coronal Cavity Observed during the 2017 Total Solar Eclipse

Abstract We present an investigation of a coronal cavity observed above the western limb in the coronal red line Fe x 6374 Å using a telescope of Peking University and in the green line Fe xiv 5303 Å using a telescope of Yunnan Observatories, Chinese Academy of Sciences, during the total solar eclipse on 2017 August 21. A series of magnetic field models is constructed based on the magnetograms taken by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO) one week before the eclipse. The model field lines are then compared with coronal structures seen in images taken by the Atmospheric Imaging Assembly on board SDO and in our coronal red line images. The best-fit model consists of a flux rope with a twist angle of 3.1π, which is consistent with the most probable value of the total twist angle of interplanetary flux ropes observed at 1 au. Linear polarization of the Fe xiii 10747 Å line calculated from this model shows a “lagomorphic” signature that is also observed by the Coronal Multichannel Polarimeter of the High Altitude Observatory. We also find a ring-shaped structure in the line-of-sight velocity of Fe xiii 10747 Å, which implies hot plasma flows along a helical magnetic field structure, in the cavity. These results suggest that the magnetic structure of the cavity is a highly twisted flux rope, which may erupt eventually. The temperature structure of the cavity has also been investigated using the intensity ratio of Fe xiii 10747 Å and Fe x 6374 Å.

Investigation on characteristics of thousand-meter height wind profiles at non-tropical cyclone prone areas based on field measurement

Accurate representation of the atmospheric wind profiles is very important for the relevant research works on the environmental wind engineering and wind-resistance design of buildings. Recently, the characteristics of thousand-meter height wind field in the atmospheric boundary layer (ABL) are investigated based on the field measurement by a wind profiler, which was installed in a coastal area of China (121.75°E, 39.05°N). Specifically, mean wind velocity profiles and wind direction profiles measured during 16 strong windy days (synoptic wind) are analyzed in the present paper. It is found that based on the agglomerative clustering analysis, the mean wind velocity profiles can be divided into two categories, namely, I and R categories. For I category, the wind velocity increases with height monotonously. While for R category, the wind velocity reaches a maximum value at a height of 500–600 m, and then recedes with height. In most cases, I category wind velocity profile can envelope that of R category, and thus becomes the main consideration for the wind−resistance design of megatall buildings. Furthermore, for I category, the log−law can be used to describe the variation of wind velocities below the height of 360 m, while the power−law is valid up to 1000 m. With the increment of total twist angle and wind velocity, the variation of measured wind directions shows a better agreement with that implied by Ekman spiral. And the total wind twist angles can reach 5°–40° over the first 1000 m.

Twist transitions and force generation in cholesteric liquid crystal films

The response of a cholesteric liquid crystal film to mechanical confinement is theoretically investigated considering planar anchoring conditions on the limiting surfaces and pure twist distortion of the liquid crystal director. We evaluate the total twist angle and normal force acting on the surfaces as a function of the film thickness. Assuming the Rapini-Papoular functional form for the surface anchoring energy, we show that the surface twist angle undergoes discontinuous jumps or continuous transitions as a function of the film thickness and anchoring strength. The transitions take place at well-defined film thicknesses, related to the intrinsic periodicity of the cholesteric liquid crystal, and produce oscillations in the normal force and position of the optical band-gap as the film thickness is varied.

Eshelby twist and correlation effects in diffraction from nanocrystals

Molecular dynamics simulations were used to model the Eshelby dislocation inside Pd and Ir nanowires and to predict the powder diffraction pattern using the Debye scattering equation. We find that the ideal dislocation solution by Eshelby is in good agreement with the observed twist angle and deviatoric strain, even though it ignores both the splitting of the Eshelby dislocation into two partials and surface stress. Surface stress plays a significant role only for nanorods with small aspect ratio (∼1:1). We also find that Wilson's prediction on the diffraction peak broadening for the Eshelby dislocation is overestimated because it ignores the fact that the Eshelby twist relaxes the deviatoric strain. Moreover, the twist loosens the correlation along the nanorod, causing additional line profile broadening, which is read by diffraction as a decrease of coherent domain size when the total twist angle is bigger than 1.5°. Overall, our findings suggest a novel way to predict and analyze the dislocations as well as the resulting strain fields in the twisted nanocrystalline rods.

Energy harvesting from underwater torsional vibrations of a patterned ionic polymer metal composite

In this paper, we study underwater energy harvesting from torsional vibrations of an ionic polymer metal composite (IPMC) with patterned electrodes. We focus on harmonic base excitation of a centimeter-size IPMC, which is modeled as a slender beam with thin cross-section vibrating in a viscous fluid. Large-amplitude torsional vibrations are described using a complex hydrodynamic function, which accounts for added mass and nonlinear hydrodynamic damping from the surrounding fluid. A linear black box model is utilized to predict the IPMC electrical response as a function of the total twist angle. Model parameters are identified from in-air transient response, underwater steady-state vibrations, and electrical discharge experiments. The resulting electromechanical model allows for predicting energy harvesting from the IPMC as a function of the shunting resistance and the frequency and amplitude of the base excitation. Model results are validated against experimental findings that demonstrate power harvesting densities on the order of picowatts per millimeter cubed.

OBSERVATION OF KINK INSTABILITY DURING SMALL B5.0 SOLAR FLARE ON 2007 JUNE 4

Using multi-wavelength observations of SoHO/MDI, SOT-Hinode/blue-continuum (4504 \AA), G-band (4305 \AA), Ca II H (3968 \AA) and TRACE 171 \AA, we present the observational signature of highly twisted magnetic loop in AR 10960 during the period 04:43 UT-04:52 UT at 4 June, 2007. SOT-Hinode/blue-continuum (4504 \AA) observations show that penumbral filaments of positive polarity sunspot have counter-clock wise twist, which may be caused by the clock-wise rotation of the spot umbrae. The coronal loop, whose one footpoint is anchored in this sunspot, shows strong right-handed twist in chromospheric SOT-Hinode/Ca II H (3968 \AA) and coronal TRACE 171 \AA\, images. The length and the radius of the loop are $L\sim$80 Mm and $a\sim$4.0 Mm respectively. The distance between neighboring turns of magnetic field lines (i.e. pitch) is estimated as $\approx$ 10 Mm. The total twist angle, $\Phi\sim$12$\pi$ (estimated for the homogeneous distribution of the twist along the loop), is much larger than the Kruskal -Shafranov instability criterion. We detected clear double structure of the loop top during 04:47-04:51 UT on TRACE 171 \AA \ images, which is consistent with simulated kink instability in curved coronal loops (T{\"o}r{\"o}k et al. 2004). We suggest, that the kink instability of this twisted magnetic loop triggered B5.0 class solar flare, which occurred between 04:40 UT and 04:51 UT in this active region.

Characterization of Liquid Crystal Layer and Cholesteric Film by Renormalized Spectroscopic Ellipsometry

Renormalized transmission spectroscopic ellipsometry (RTSE) is used to evaluate the device parameters of liquid crystal display (LCD). To determine the reduced dielectric and elastic constants, threshold voltage, pretilt angle, cell gap, and surface polar anchoring energy coefficient, symmetrically oblique incidence transmission ellipsometry (SOITE) was applied to vertical-alignment (VA) LCD. It is suggested that the rubbing process on the alignment films for VA LCD does not disturb the measurement of the genuine surface polar anchoring energy coefficient. RTSE is also applicable to the determination of the total twist angle of the cholesteric film.

Influence of the magnetic and laser fields on the director structures of a ferrocholesteric liquid crystal in homeotropic cells

We study the influence of the magnetic and laser fields on the director structures of a ferrocholesteric liquid crystal in homeotropic cells. Using the analytical method based on the Euler–Lagrange equations, we find a correlation between the fields intensities and the confinement ratio r = d / p , ( d is the cell thickness and p is the cholesteric pitch) at the limit of the transition from the homeotropic alignment to the translationally invariant configuration (TIC) with uniform in plane twist. We discuss this correlation as a function of the sign of the magnetic and dielectric anisotropies. If both anisotropies are positive and the magnetic field and the laser beam are perpendicular to the cell walls, the magnetic field preserves the homeotropic alignment while the laser beam pushes the system towards the TIC. The control parameters of the transition are the laser beam intensity and the confinement ratio. If the magnetic anisotropy is negative and the dielectric one is positive both fields concur in driving the system towards the TIC. The spinodal surface separating the metastable homeotropic configuration from the instable TIC is an ellipsoid whose halfaxes are smaller that in the case of a pure liquid crystal by a factor depending on the material constants and the cell thickness. We find also the total twist angle across the sample witch can be varied between a lower and an upper limit by changing the light intensity or the magnetic field strength. Our results can be useful in designing magneto-optical devices.

Computer modelling of the director configuration in a supertwist nematic liquid crystal cell

Abstract The director distribution in a supertwist nematic cell, containing La-Roche liquid crystal mixture 3010, has been studied extensively using Berreman's computer simulation approach. It is seen that the director distribution in the cell depends critically on the total twist angle θt, the surface tilt angle θo and the ratio of the cell thickness to the pitch d/p. The values of θo and φt have been optimized to yield a small bistability (ΔV = 0.06 V) and a relatively large change in the midplane tilt angle (Δθm = 51°) in an unstrained cell with Ŏt = (d/p) × 360°. The optimum values of θo and Ot were found to be 15° and 240°, respectively. The effect of varying d/p on the director distribution has also been studied in great detail in supertwist cells with θo = 30° and Ot = 270°. Some interesting features in understrained and overstrained cells have been observed.

Influence on the Hysteresis Effect of Various Parameters in Supertwisted Nematic Liquid Crystals

Abstract The influence of materials and cell parameters on the hysteresis effect in a supertwisted nematic LCD composed of chiral nematic layers is theoretically investigated. The variation of tilt angle of the director in a midplane of the LC layer with an applied voltage change is numerically calculated. Transition voltage Vn1 , recovery voltage Vn2 and reduced hysteresis width H=(Vn1 - Vn2)/Vn1 are evaluated under the different combinations of such parameters as the elastic constant ratios k = k33/k11 and ξ = k33/k22 , dielectric anisotropy Δe, pretilt angles θo on the electrode surfaces, total twist angle φ and the thickness of the LC layer d. The lower limits of the cell thickness and the pretilt angle, as well as the total twist angle, below which the bistable range completely disappears, are found to exist. The influence of various parameters on those characters are investigated.

Transmission of light through a twisted nematic liquid-crystal layer

A coupled-mode theory is used to find simple exact expressions for the transmission of light through a twisted nematic liquid-crystal layer. The thickness of the layer for zero transmission is shown to depend on the total twist angle. A previous theoretical model for tuning a liquid-crystal cell is shown to be in error and alternatives are suggested.

Twisted and non-twisted rhabdoms and their significance for polarization detection in the bee

1. In the dorsal retina of the worker bee twisted and non-twisted rhabdoms (resp. retinulae) are analysed by serial LM- and EM-reconstructions. The straight retinulae restricted to the most dorsal 4–5 horizontal rows of ommatidia contain 9 long visual cells, whereas the twisted retinulae are composed of 8 long cells (nos. 1–8) and one basal short visual cell (cell no. 9). The ninth cell and two of the overlying long twisted cells (nos. 1 and 2) are ultraviolet cells (UV cells) which are the only receptors engaged in polarized light detection. 2. By rhabdom geometry two mirror-imaged types of rhabdoms can be discriminated (X- andY-type), which are randomly distributed in the retina. One class of retinulae twists clockwise, the other counterclockwise. The twist rate amounts to about 1°μm−1. The total twist angle is about 180° for the long and about 40° for the small UV cells. 3. In the focal plane of the dorsal part of the retina the microvilli of the long UV cells are all oriented perpendicularly to the horizontalz-axis of the eye. The basal ninth cells replace one of the overlying long UV cells. At their tips, the microvilli are also perpendicularly oriented to thez-axis. 4. By optical analysis polarization sensitivity (PS) and direction for maximum sensitivity (Φmax) are computed for the long as well as for the short UV cells. If the effective birefringence of the rhabdom is very low PS of the long twisted UV cell decreases to unity. However, PS of the short basal UV cells remains pronounced (PS=4.2 for a dichroic ratio of 5 and 7.1 for a dichroic ratio of 10). As birefringence increases, PS of the long, twisted UV cells increases, but PS of the short ninth cell first decreases to a minimum PS-value of near unity before increasing to high values. We propose the hypothesis that the overall birefringence of the bee's fused rhabdoms is very low (Δn<10−3). 5. For low birefringence the two types of short, ninth cells are maximally sensitive at planes that differ by 36°. 6. Histological as well as optical analysis suggest a minimum model fore-vector detection involving the UV receptors of only two twisted ommatidia: two ninth cells of different twist type act as polarization sensitive channels and the long UV cell(s) as a polarization insensitive channel.