Helix Pitch Angle Research Articles

Double-Helical Tiled Chain Structure of the Twist-Bend Liquid Crystal Phase in CB7CB

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πRmol, where Rmol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain.

Real model for micro swimmer and the study of the relationship between the swimming speed, pitch angle, and rotation rate for the flagellum

This study focuses on the fluid mechanics of a microswimmer and explores the relationship between speed, pitch angle, and rotation rate for the flagellar during bacterial swimming. Based on the simulation using MATLAB, it is concluded that when the pitch angle of the flagellar helix is in the range of 0 to 90 degrees, the value of swimming speed increases firstly and decreases. When the angle reaches 46.83 degrees, the speed reaches the maximum point. The radius of the body of the microswimmer is determined by the Buckingham Pi theory. After calculating by using the equations in the related paper and measuring by the real model, we derive that the relationship between swimming speed and the rotation rate for the flagellar filament should be proportional at the low rotation rate so that it can be obtained to optimize the artificial micro swimming device with higher swimming efficiency.

Fluorinated Biphenylpyrimidine as a Possible Matrix for Ferroelectric Liquid Crystal Mixtures

The results of the synthesis and study of a new fluorinated achiral smectic C liquid crystal, namely, 2-(3-fluoro-4'-pentylbiphenyl-4-yl)-5-hexylpyrimidine, are presented. The possibility to use this compound as a matrix for ferroelectric liquid crystal (FLC) mixtures is evaluated. Two mixtures have been prepared: one (FLC-691-F) is based on new fluorinated compound and another (FLC-691) on its non-fluorinated analogue. The diester of optically active 2-octanol and terphenyldicarboxylic acid was used as a chiral dopant for both mixtures. Investigation of these FLC mixtures parameters: phase transition temperatures, helix pitch, spontaneous polarization and tilt angle show significant influence of fluorine atom. When comparing the phase sequence of FLC-691 and FLC-691-F mixtures, one can note that in the fluorine containing mixture an additional smectic A phase arises. At the same temperatures, the helix pitch of FLC-691-F is 2 – 2.5 times less than the helix pitch of FLC-691. The tilt angle of FLC-691-F is much smaller than that of FLC-691 but its value approaches the optimal value of 22.5 degrees, which ensures maximum light transmittance of electro-optical cells. At the same time the presence of fluorine atom in the matrix is a reason for the decrease of the mixture spontaneous polarization and a significant decrease (almost 4 times) in the driving voltage of electro-optical light shutters. As a result, it was shown that the fluorinated matrix provides new possibilities for controlling the mixture parameters.

Complex Mode Dispersion Characteristics of Dielectric Loaded Radially Thick Helix

In this article, a generalized analytical and computational numerical theory, for both the guided and leaky modes, has been developed to investigate the dispersive behavior of dielectric-loaded radially thick helix (DLRTH). The complex root finding Muller iterative algorithm is used to compute the normalized phase and attenuation constants. A unique way has been adopted for the classification of HE and EH hybrid modes present in the proposed structure, and based on that, for the first time, we report that this structure shows physical leaky and trapped surface wave propagation characteristics. Furthermore, in the guided mode, it is seen that both slow wave (SW) and backward wave (BW) exist due to the inherently skewed boundary of the helical geometry. The parametric study of helix radius and pitch angle as well as dielectric constant gives optimized parameter values, which help in designing the proposed structure in the desired mode and at the desired frequencies. Moreover, it is reported that pitch angle aids in controlling and figuring out the leaky mode bandwidth. The analytical cum numerical MATLAB results are successfully verified using CST Microwave Studio computational analysis and are found to be in good agreement. The improved characteristic equations for guided mode find practical applications in the design and performance evaluation of the SW structure (SWS) for the phase delay applications. The leaky mode will find application for beam scanning helical antennas.

On The Free Vibration of Doubly Clamped Single-Walled Coiled Carbon Nanotubes: A Novel Size Dependent Continuum Model

In this paper, the size dependent vibration behavior of doubly clamped single-walled coiled carbon nanotubes (CCNTs) is investigated using nonlocal helical beam model. This model is based on Washizu’s beam theory so that all displacement components of CCNT in the equations of motion are defined at the centroidal principal axis and transverse shear deformations are considered. After deriving the nonlocal free vibration equations, they are solved by the generalized differential quadrature method (GDQM). Then, the natural frequencies and corresponding mode shapes are determined for the clamped-clamped boundary conditions (BCs). After that, a parametric study on the effect of different parameters, including the helix cylinder to the tube diameters ratio , the number of pitches, the helix pitch angle, and the nonlocal parameter on the natural frequencies is conducted. It is worth noting that the results of the proposed method would be useful in the practical applications of CCNTs such as using in nanoelectromechanical systems.

Free vibration analysis of functionally graded cylindrical helices with variable cross-section

The main purpose of this study is to investigate free vibrations of cylindrical helical rods with variable cross-section, composed of functionally graded materials, which may be used to model environmental effects. The material variation is considered to be along the rod axis. Governing differential equations of the free vibration are obtained via Timoshenko's beam theory, where axial and shear deformations and rotary inertia are taken into consideration. The governing equations are solved numerically by using the transfer matrix method. The effects of cross-section variation (βsec), material gradient index (βmat), helix pitch angle (α), and number of active coils (n) on the frequencies are investigated. All results are compared with the ANSYS solutions, in which a very well approximation is achieved.

Scattering due to uniaxial anisotropic chiral medium-coated PEC cylinder with conducting helix loading

ABSTRACT A perfect electrically conducting (PEC) cylinder (having a circular cross-section) encapsulated with uniaxial anisotropic chiral medium was studied emphasizing the features of scattering. A conducting sheath helix structure having a varying orientation with respect to the optical axis (or pitch angle) was assumed to be at the outermost surface. This allows alterations in scattering patterns. The echo width of the structure was evaluated under the assumption of parallel polarized oblique incidence of waves. The effect on scattering was evaluated under varying chirality and permittivity of the coating medium along with the variations in the helix pitch angle. The obtained results are compared with those achieved by replacing the chiral coating with a simple anisotropic kind of medium (without chirality).

Polarization and QPOs from jets in black hole systems

The historical observations of polarized jet emission for Blazars are reviewed and previous models are discussed. Motivated by this, a model for polarization of both steady and transient behavior using a helical magnetic field is presented. The variety of observed correlations and anti-correlations between the electric polarization angle, the degree of polarization and optical flux can be explained by this model. In addition, the phenomena of quasi-periodic oscillations (QPO) behavior seen in jets in X-ray Binaries (XRBs) is also explained by a model based on helical trajectories of emitting blobs and the resulting time scales and harmonics of the QPO are derived. In both the models, the input parameters are the inclination angle, the Lorentz factor of the jet and pitch angle of the magnetic helix.

A Closed-Form Buckling Formula for Open-Coiled and Properly Supported Circular-Bar Helical Springs

Abstract As a continuation of the author’s previous studies on the buckling analysis of helical springs, a closed-form formula having been obtained with the help of the artificial neural network (ANN) is proposed and discussed in detail for the first time for a cylindrical close/open-coiled helical spring with fixed ends and having a solid circular section. As far as the author knows there is no such a formula in the open-literature to consider the effects of all stress resultants (torsional and bending moments, axial and shearing forces), large helix pitch angles together with the axial and shear deformations on the buckled state. The present formula may be used in a wide range of the total number of active turns, the ratio of the free axial length to the mean helix diameter, and the spring index. It is yet again revealed that it is not appropriate to use the elementary theory to determine the critical buckling loads for open-coiled springs. The present formula may allow the deeper understanding of spring buckling mechanism and to be used directly and safely in the design processes of such closely/open-coiled springs.

A bioinspired study on the compressive resistance of helicoidal fibre structures.

Helicoidal fibre structures are widely observed in natural materials. In this paper, an integrated experimental and analytical approach was used to investigate the compressive resistance of helicoidal fibre structures. First, helicoidal fibre-reinforced composites were created using three-dimensionally printed helicoids and polymeric matrices, including plain, ring-reinforced and helix-reinforced helicoids. Then, load-displacement curves under monotonic compression tests were collected to measure the compressive strengths of helicoidal fibre composites. Fractographic characterization was performed using an X-ray microtomographer and scanning electron microscope, through which crack propagations in helicoidal structures were illustrated. Finally, mathematical modelling was performed to reveal the essential fibre architectures in the compressive resistance of helicoidal fibre structures. This work reveals that fibre-matrix ratios, helix pitch angles and interlayer rotary angles are critical to the compressive resistance of helicoidal structures.

Complex Copper Nanostructures for Fluid Sensing—a Comparative Study of the Performance of Helical and Columnar Thin Films

This communication is pivoted to the sensing of fluids by the use of nanoengineered thin films comprised of copper nano-helixes as well as copper nano-rods, in order to study the comparison of the performance of thin films having different morphological features. For this purpose, human blood samples having different concentrations of haemoglobin are taken into account as measurands. The sensing configuration exploits the use of nanostructured metallic thin films grown over glass substrate with the void regions filled up with measurands, and the features of absorption spectra are monitored. Two different wavelengths are used along with two different values of helix pitch angle as well as slanting angle of nano-rods, and the focus is put on the effect due to these parameters on the sensing characteristics. It is observed that in the case of nano-helix structured films, pitch angle affects spectral characteristics obtained due to the generation of plasmonic waves at the interface of two partnering mediums. Upon comparing the obtained results with those corresponding to thin films comprised of slanted copper nano-rods (having different angles of inclination), it has been found that the nano-helix embedded films provide better appreciable results than those exhibited by the columnar thin films, thereby making the former kind of nanostructured mediums more useful in sensing-related applications.

Exact determination of the global tip deflection of both close-coiled and open-coiled cylindrical helical compression springs having arbitrary doubly-symmetric cross-sections

A general formulation of the static deflection under an axial force is required for accurate static, buckling and dynamic analyses. Even today, however, the helical spring formulas derived in 1960s still continue to be used in the spring design. So designers maintain to design helical springs with limited options in making a change in both the helix pitch angles and cross-section types. In this study, in order to carry out such formulation and get closed-form solutions for the vertical tip deflection, Castigliano's first theorem is directly employed to the linear elastic problem of cylindrical helical springs with large pitch angles. Derivation takes into account for the whole effect of the stress resultants such as axial and shearing forces, bending and torsional moments on the deformations. Cylindrical helical springs having doubly symmetric cross-sections such as a solid/hollow circle, a square, a horizontal/vertical rectangle, and a horizontal/vertical ellipse made of isotropic and homogeneous linear elastic materials are all handled in this work. For each shape of cross-section considered in the study, a closed form global formula in a compact form is offered for users with the common notations and common design parameters as currently used. These formulas may be directly used without hesitation for both closed-coiled (CC), α≤10°, and open-coiled (OC), α≥10°, cylindrical helical springs. That is one may use those formulas without the need for any extra information than he already has and without involving any design chart and correction factor. Some of formulas derived in this study are compared to the commonly used formulas in the available literature. It is verified that those formulas may be obtained readily from the present formulas by considering their certain assumptions. Benefits of this study related to previous ones are also discussed. Present global formulas are also verified with available recent experiments and finite element solutions. The groundwork for the data to be used directly in Castigliano's first theorem was obtained by using differential geometry of a helical structure from a general spatial rod, and governing equations derived by using equilibrium equations, constitutive equations and geometrical compatibility relations in vector forms. As a result, the author expects that a designer is to be free to design more accurate springs by using the global analytical formulas presented in this study.

Determination of the stability lobes with multi-delays considering cutter’s helix angle effect for machining process

As a common phenomenon, chatter is one of the most important factors that inhibit the improvement of productivity and deteriorate the machined surface quality in milling process. In this article, the mathematical model of the dynamic machining process is first constructed with multi-delays, in which the effect of the cutter’s helix angle on the chatter is considered. And a new integral interpolation method is proposed to predict the stability lobes. Based on this method, the mathematical model which is divided into two parts is calculated respectively with an interpolation method and an integration method. Using the Floquet theory, the stability limits of the dynamic milling system for an arbitrary point can thus be precisely predicted. Subsequently, the convergence rate of this integral interpolation method is analyzed. In order to verify the mathematical model, the stability lobes with uniform and variable cutter pitch angle are computed and the results show a good agreement with published experimental data; also one experiment is conducted to validate the proposed model and the method. Simultaneously, the simulation of a stability lobe with non-zero helix angle is also performed and the results validate the fact that the proposed method is capable of predicting stability limits with high accuracy. Finally, the influences of the cutter and process parameters such as helix angle, pitch angle, down-milling or up-milling and radial cutting depth on the milling chatter are analyzed.

Parametric Study on the Influence of Warping Deformation upon Natural Frequencies of Die Springs

The free vibrational characteristics of die springs are examined by Riccati transfer matrix method in this study. The warping deformation of spring’s cross section, as a new design factor, is incorporated into the differential equation of motion. Numerical simulations show that the warping deformation is a significant role of the behavior of natural frequencies of die springs and should be considered carefully. Approximately 40% of the errors may occur if warping is neglected. The change laws of warping effect with the parameter variations of springs are also explored, including the height-to-width ratio of the cross section, the cylinder diameter, the helix pitch angle, and the number of coils. The warping effect exhibits the most remarkable changes with the variation in the height-to-width ratio of the cross section. However, this effect is not fairly sensitive to the changes in other parameters, and it is particularly significant when the cross section is relatively narrow regardless of the changes in other parameters. This study evidently answers the key scientific question: “under what working condition should the warping effect be considered or ignored?” The analysis results can be used to guide spring designers in engineering.

On the conducting sheath double-helix loaded liquid crystal optical fibers

This work presents analysis of wave propagation in a rather new type of three-layer optical fiber wherein the outermost region being composed of radially anisotropic liquid crystal, and conducting sheath helix loadings exist at the core–inner clad as well as the inner clad–outer liquid crystal clad interfaces. The fiber structure offers two-way control on wave propagation through it. Focus is, however, made on the wave confinements in fiber due to the helix structures, as characterized by the respective pitch angles. Specific values of helix pitch angles at the two layer interfaces are taken into account, and the confinement patterns are analyzed. The dominant property of sheath helix structure over confinement patterns is quite an obvious fact. Clearly, the helix pitch angle greatly controls over the power confinement characteristics, which can be altered upon suitable adjustments of helical windings. Treatments have been made to illustrate the power patterns in all possible scenarios for critical pitch variations in each layer interface.

Conducting tape helix loaded radially anisotropic liquid crystal clad optical fiber

The paper reports investigation of a rather new type of optical fiber composed of three layers with the outermost region being radially anisotropic liquid crystal material, and the inner two regions as linear, homogeneous, and isotropic dielectrics. As such, the anisotropy remains in the outermost section of fiber. The core–clad interface of the inner dielectric regions is assumed to be loaded with conducting tape helix structure. It has been found that the width of the tape as well as the helix pitch angle are the effective parameters to govern the dispersion characteristics. Taking into account the zero-order guided modes, the effects on confinements due to the amalgamation of birefringence (optical property of liquid crystal) and tape helix pitch (geometrical/structural property of perfect conductor) are reported. The obtained results are compared with the case of a conducting sheath helix loaded liquid crystal fiber structure, and it has been found that the conducting tape helix loadings would be more useful than the sheath helix loaded fibers.

Dispersion Features of Conducting Sheath Helix Embedded Elliptical and Circular Fibers with Chiral Nihility Core

Discussions have been made of the electromagnetic wave propagation through optical fibers of elliptical and circular cross‐sections with the loadings of conducting sheath helix at the core‐clad interface with particular orientations. In both geometrical situations, the core section of fiber is assumed to be composed of chiral nihility medium, and the clad remains linear, homogeneous, isotropic, and nonmagnetic dielectric. Dispersion relations are deduced for both fiber structures, followed by the analysis of dispersion features considering a few low‐order EH modes. Furthermore, the effects of conducting helix pitch angle on the features of wave propagation are also discussed.

Transmission characteristics of circular and elliptical helically cladded optical fibers – A comparative analysis

Lightwave propagation through complex structured optical fibers, viz. twisted clad fibers with circular as well as elliptical cross-sections, are taken into account. Twists in the fiber are considered in the form of conducting sheath helix structures introduced at the core–clad interface. Wave propagation in such fibers can be controlled by suitably adjusting the helix pitch angle – the prime motivation of this work, which is tuned to emphasize on the power confinement patterns (or the fractional modal power) of these on a comparative platform. Taking into account a few low-order hybrid modes, variations of confinement are studied for the aforesaid two fiber types in respect of changes in the helix pitch angle. The obtained results indicate profound impact of introducing the helical structure – the feature that would find potential technological applications. Furthermore, helical clad elliptical fibers are found to be more responsive than the circular ones in terms of the variations in pitch angle.

On the control of optical confinement in sheath helix-loaded elliptical dielectric guide

An investigation has been made of the propagation of electromagnetic waves through dielectric optical guide loaded with conducting sheath helix at the core–clad interface. The guide structure falls into the category of complex media, wherein it has been assumed that the helix sheath remains continuous in nature along with each of the turns being isolated from the adjacent ones. Power confinement factors in the two regions of guide under consideration have been evaluated under the situation of varying values of helix pitch angle – from its orientation being parallel to the optical axis to the perpendicular orientation. Two different illustrative values of guide dimensions have been taken into account, and the effect on the propagation of power have been demonstrated under the variations in helix pitch angle.

Waves in Microstructured Conducting Sheath Helix Embedded Optical Guides with Chiral Nihility and Chiral Materials

The paper deals with the sustainment of electromagnetic waves in circularly cylindrical optical guide with chiral nihility and chiral materials in the core and the clad sections, respectively. A perfectly conducting tightly wound helix is introduced at the core‐clad interface. The eigenvalue relation for such a complex optical microstructured guide is deduced by applying suitable boundary conditions at the core‐clad interface, and the dispersion behavior is analyzed by varying the pitch angle of helix. The sustainment of energy flux density in such optical guides is estimated under various structural conditions, and the density patterns in core‐clad sections are anatomized analytically.