Helix Radius Research Articles

Tunable bandgaps in an elastic meta-plate with shape memory alloy springs

In this paper, a tunable metamaterial based on shape memory alloy springs is designed, which can achieve bandgap tuning by spring's unique shape memory effect. The variation mechanism of shear modulus and geometrical parameters of shape memory alloy springs is investigated by considering a detailed phase transition mechanism. For any specific temperatures, the energy band structure and frequency response spectrum of the metamaterial are calculated by numerical simulation. And the theoretical prediction models of bandgap boundary frequency and tuning range at different temperatures are established. The experimental test of vibration transmission of metamaterial is finally presented. The results show that (1) By varying the spring's shear modulus and height, the metamaterial exhibits excellent vibration isolation characteristics and bandgap tuning in low-frequency range of 124–226Hz. (2) The bandgap boundaries and tuning ranges can be predicted by the theoretical prediction model, which shows good agreement with both the simulation results and the experimental data. (3) By artificially designing shape memory alloy springs with larger shear modulus and wire radius, smaller helix radius and number of turns, the bandgap moves to higher frequencies. The current work can provide a reference for further engineering applications with the tunable elastic/acoustic metamaterials.

A new model of thermo-mechanical actuation for twisted and coiled polymer muscles with initial curvature

The twisted and coiled polymer (TCP) artificial muscle is one type of novel soft actuator for mimicking natural skeletal muscle that can provide large linear and torsional actuation and energy density. Twisting and coiling are the pivotal steps in fabricating TCP muscles. The influence of twisting on the actuation response of TCP muscles has been extensively investigated recently. However, the influence of coiling remains unclear. Based on the finite strain theory, we establish a new thermo-mechanical actuation model for TCP muscles with initial curvature. The theoretical predictions based on the model align well with the finite element simulations, accurately capturing the actuation response of thermally-activated TCP muscles. It is revealed that twisting contributes positively to the actuation, while coiling has a passive effect. Geometrical parameters, such as the helix radius and helix angle, can effectively regulate the actuation performance of TCP muscles. Furthermore, an optimal bias angle is identified that maximizes both the recovery torque and the linear actuation. This study sheds light on the structural optimization design of TCP muscles.

Cholesteric liquid crystal phase variations within nanotubes: an in-depth analysis of the influences of twist radius and molecular pitch

ABSTRACT This study investigates the self-assembly and phase transitions of cholesteric liquid crystals (CLCs) when confined in nanotubes, specifically focusing on the variations in their molecular structures. A dissipative particle dynamics method was used to investigate how the changes in helix radius ( r LC ) and pitch ( P ) affect the behaviour of the LCs. For pitches of 24, 12, and 6, the orientation order parameter ( P 2 ) showed distinct trends during cooling. Smaller helix radii resulted in isotropic to nematic to smectic phase transitions, whereas larger radii resulted in a novel smectic phase with spiral structures (Sm s ). Circumferential local-order parameters ( P 2 r and P 2 z ) were introduced to better characterise the phases, and a disordered spiral-structure phase (Sm s 2 ) with local perturbations was observed. The transitions between isotropic, nematic, and smectic phases, highlighting the influence of the pitch and helix radius, were observed from the phase diagrams. Smaller pitches and radii prevented the formation of stable structures; however, specific combinations induced characteristic spiral structures in the smectic phase. These results provide new insights into the self-assembly of confined CLCs, which have potential applications in the design of photonic devices and LC-based sensors. This study advances our understanding of phase control in quasi-one-dimensional systems and highlights the importance of molecular variations in liquid crystal behaviour.

Study on the deformation mode and energy absorption characteristics of a corner-enhanced biomimetic spider web hierarchical structure

To improve the energy absorption properties of honeycomb structures based on the underlying mechanism of uniform stress dispersion and to effectively increase the strength of a spiderweb, a corner-enhanced spiderweb hierarchical honeycomb structure was proposed herein. This study involved a quasistatic compression test and simulation of a corner-enhanced spiderweb hierarchical structure complemented by 3D printing. The deformation pattern of the common spiderweb honeycomb (CSH) was //-shaped. However, the deformation pattern of the honeycomb after corner enhancement tended to be monolithic, forming an X shape. The deformation characteristics of both the CSH and the first-order local cellular elements were analyzed. The corner-enhanced honeycomb cellular elements dispersed the load onto the inner wall to achieve a common load-bearing effect. Further numerical simulation analysis was carried out in conjunction with the experiments, and local destruction analysis was performed for single-cell elements. Corner enhancement could increase the plastic hinge energy absorption of the structure, with a first-order corner-enhanced spiderweb honeycomb (CESH-F) exhibiting a 46.3 % improvement in specific energy absorption compared to that of a conventional CSH. The layers were reinforced to compress the load uniformly, and a third-order corner-enhanced spiderweb honeycomb (CESH-T) had a 25.7 % improvement in specific energy absorption compared to that of the CESH-F. In addition, optimization was performed for corner-enhanced spiderweb honeycomb (CESH) according to different helix radii. The effect of the radial line thickness on honeycomb-specific energy absorption was explored, and the radial line thickness was positively proportional to honeycomb-specific energy absorption. These findings offered valuable insights into the design of lightweight and high-energy-absorbing biomimetic structures.

Coiling of Secondary Tubes Formed from the Colloidal Exhaust of Primary Chemical Gardens.

Chemical gardens are self-organized precipitate structures such as thin-walled tubes and membrane-bound cells reminiscent of biological shapes. These usually inorganic precipitates compartmentalize the reaction system and allow the study of materials synthesis in very steep concentration gradients. We create such tubes by steadily injecting a mixture of MnCl2 and CuSO4 solutions into a large reservoir of sodium silicate solution. The growing tube is open at its tip and ejects a stream of colloidal particles that aggregate to form a secondary tube above the original one. This secondary tube can coil into a tightly wound nest-like structure, freely suspended underneath the solution-air interface. Using three-dimensional image reconstruction, we analyze the onset of coiling and show that the structure is helical with a helix radius that increases in the vertical direction. The height at which the coiling begins is lowered with each successive repeat of the growth experiment, suggesting that coiling is induced by small variations in the density of the silicate solution.

A multi-stable deployable quadrifilar helix antenna with radiation reconfigurability for disaster-prone areas

In disaster-prone areas, damaged infrastructure requires impromptu communications leveraging lightweight and adaptive antennas. Accordingly, we introduce a bi-stable deployable quadrifilar helix antenna that passively reconfigures its radiation characteristics in terms of pattern and polarization. The proposed structure is composed of counter-rotating helical strips, connected by rotational joints to allow a simultaneous change in the helix height and radius. Each helical strip is composed of a fiber-reinforced composite material to achieve two stable deployed states that are self-locking. The reconfiguration between an almost omnidirectional pattern and a circularly polarized directive pattern enables the antenna to be suitable for both terrestrial and satellite communication within the L-band. More specifically, the presented design in infrastructure-less areas achieves satellite localization with directive circularly polarized waves and point-to-point terrestrial connectivity with an almost omnidirectional state. Hence, we present a portable, agile, and passively reconfigured antenna solution for low-infrastructure areas.

A standard reference frame and geometry for nucleosomes.

The nucleosome is often described as a histone-DNA complex containing eight histones and 145-147 base pairs of DNA. The reality is more complex. Here we evaluate approximately 500 nucleosomes from the Research Collaboratory for Structural Biology with the goal of establishing a reference frame and standard geometry for describing the internal structure of mono-nucleosomes and the stacking of nucleosomes in arrays and clusters. Our reference frame places the center of mass of the nucleosome's octameric core at the origin. The positive x-axis aligns with the symmetry axis of the nucleosome and passes through the central base pair or base pair step associated with the octamer. The z-axis is defined by fitting a regular helix (constant pitch and radius) to the nucleosome. The positive direction is determined by the choice of reading strand. Two methods for defining this helix are explored. One fits a helix to the center line of the DNA, which is itself determined according to a standard reference geometry for DNA base pairs. The other fits a helix to the centers of mass obtained from the histones. The z-axes, so defined, are slightly askew. Over 100 nucleosomes are used to define a standard reference geometry for the histones and for super helices with 145, 146 and 147 base pairs. In all structures, the cumulative sum of Rise, Twist and arclength are linear functions of base pair index with R2 values in excess of 0.999. The standard geometry supports a rigorous definition of entry-exit angle and identification of structural anomalies. Select examples demonstrate how generalizations of the inter and intra base pair parameters can be utilized to analyze the internal structure of mono-nucleosomes, their stacking in arrays and clusters, and the ab initio assembly of atomic and coarse-grained structures.

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.

Quasi-equilibrium states for helical vortices with swirl

We present a family of exact equilibrium solutions of the Euler equations consisting of a single helical vortex with an axial flow component along the vortex core. Relations between vorticity, velocity and streamfunction are analytically derived in the inviscid framework and constitute a generalization of relations valid for vortex rings (Batchelor, 1967 An Introduction to Fluid Dynamics. Cambridge University Press). Through Navier–Stokes simulations, it is shown that these relations hold for quasi-steady viscous solutions and become independent of the Reynolds number when sufficiently large. We also elaborate a procedure which generates a quasi-equilibrium with prescribed characteristics (circulation, helix radius, helical pitch, vortex core size, swirl level) and compare the obtained state with the results of an asymptotic theory. Finally, we illustrate how a strong axial flow jeopardizes such an evolution towards a quasi-equilibrium.

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.

Electrostatic free energies carry structural information on nucleic acid molecules in solution.

Over the last several decades, a range of experimental techniques from x-ray crystallography and atomic force microscopy to nuclear magnetic resonance and small angle x-ray scattering have probed nucleic acid structure and conformation with high resolution both in the condensed state and in solution. We present a computational study that examines the prospect of using electrostatic free energy measurements to detect 3D conformational properties of nucleic acid molecules in solution. As an example, we consider the conformational difference between A- and B-form double helices whose structures differ in the values of two key parameters-the helical radius and rise per basepair. Mapping the double helix onto a smooth charged cylinder reveals that electrostatic free energies for molecular helices can, indeed, be described by two parameters: the axial charge spacing and the radius of a corresponding equivalent cylinder. We show that electrostatic free energies are also sensitive to the local structure of the molecular interface with the surrounding electrolyte. A free energy measurement accuracy of 1%, achievable using the escape time electrometry (ETe) technique, could be expected to offer a measurement precision on the radius of the double helix of approximately 1 Å. Electrostatic free energy measurements may, therefore, not only provide information on the structure and conformation of biomolecules but could also shed light on the interfacial hydration layer and the size and arrangement of counterions at the molecular interface in solution.

Modeling of a bio-inspired soft arm with semicircular cross section for underwater grasping

Fluid-filled fiber-reinforced elastomeric enclosures (FREEs) with a circular cross section, inspired by the muscle structure of octopus arms, are a popular choice for actuators because of their high power density and relatively low manufacturing cost. However, the shape, flexibility, and grasping force of FREEs are slightly different from those of real octopus arms. A soft arm with a semicircular cross section has better bending performance than that of FREEs with a circular cross section and can thus more easily achieve flexible grasping. In this paper, to better describe the deformation of soft arm shape in an underwater environment, a model based on a constrained maximization volume is proposed for a semicylindrical soft arm. In particular, the model takes into account the effect of the expansion of the bottom on the semicylindrical soft arm and the proposed analytical model is used to analyze the factors that affect the helix radius of the soft arm, including the helix angles of the fibers, wall thickness, and inner radius of the soft arm. Then a method for fabricating soft arms with a semicircular cross section (length: 700 mm) and a method for extracting the helix radius are also proposed. Finally, a series of driving experiments is performed to measure the accuracy of the model using a hydraulic platform. Experimental results show that the maximum error rate of the helix radius is between 8.99% and 12.29%. The helix radius can be varied from 74.3 mm to 176 mm by changing the parameters of the soft arm.

Detection of band edge frequencies in symmetric/asymmetric dielectric loaded helix slow‐wave structures

AbstractThe significant contribution of this paper is to present a comprehensive analysis and design of π‐point and band edge frequencies of reported helix SWSs including not only a microwave but also millimeter‐wave operation frequencies considering the methods in available literature which are the Coupled Mode Analysis (CMA), the Exact Floquet Approach (EFA), and the Auxiliary Functions of Generalized Scattering Matrix (AFGSM) as a comparative study. A different approach called as effective rod model is applied to circular/T‐shaped dielectric support rod helix SWSs in order to obtain ladder circuit representation of one turn of related helix SWSs for the first time. Scattering matrices of equivalent circuit representation of interested helix SWSs are obtained by using microstrip line model of helix SWS which slits helical tape at the effective helix radius along the direction normal to the helix winding direction and flattens it out for the EFA, the AFGSM, and the CMA methods. Additionally, comparisons are given for investigated methods together with the results of Computer Simulation Technology (CST) design environment, and good agreement has been observed among numerical results of different helix SWSs in a broad frequency range.

Multi-ciliated microswimmers\u2013metachronal coordination and helical swimming

The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number N (with 5< N < 60) of cilia with length comparable to the body radius, is investigated by mesoscale hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e., the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity is found to increase with the cilia number N with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.Graphic abstract

Edge states supported by different boundaries of two helical lattices with opposite helicity

We discuss linear and nonlinear topological edge states on the bearded-bearded edge (BBE) and armchair-armchair edge (AAE) of two helical waveguide arrays with opposite helicity. The robustness of the linear topological edge state can be controlled by the helix radius, the angle of the incidence, and the amplitude of lattice potentials. In the nonlinear regime, multipole-like lattice quasisolitons may be found with a certain saturable nonlinear factor for AAE. The long-distance propagation dynamics of such quasisolitons are numerically studied from the evolution of their intensity patterns and the “center of mass”. On the contrary, no quasisoltion exists for BBE under the same conditions.

Helical toroid phantom for 3D flow imaging investigations

The medical physics community has hitherto lacked an effective calibration phantom to holistically evaluate the performance of three-dimensional (3D) flow imaging techniques. Here, we present the design of a new omnidirectional, three-component (3-C) flow phantom whose lumen is consisted of a helical toroid structure (4 mm lumen diameter; helically winded for 5 revolutions over a torus with 10 mm radius; 5 mm helix radius). This phantom’s intraluminal flow trajectory embraces all combinations of x, y, and z directional components, as confirmed using computational fluid dynamics (CFD) simulations. The phantom was physically fabricated via lost-core casting with polyvinyl alcohol cryogel (PVA) as the tissue mimic. 3D ultrasound confirmed that the phantom lumen expectedly resembled a helical toroid geometry. Pulsed Doppler measurements showed that the phantom, when operating under steady flow conditions (3 ml s−1 flow rate), yielded flow velocity magnitudes that agreed well with those derived from CFD at both the inner torus (−47.6 ± 5.7 versus −52.0 ± 2.2 cm s−1; mean ± 1 S.D.) and the outer torus (49.5 ± 4.2 versus 48.0 ± 1.7 cm s−1). Additionally, 3-C velocity vectors acquired from multi-angle pulsed Doppler showed good agreement with CFD-derived velocity vectors (<7% and 10° difference in magnitude and flow angle, respectively). Ultrasound color flow imaging further revealed that the phantom’s axial flow pattern was aligned with the CFD-derived flow profile. Overall, the helical toroid phantom has strong potential as an investigative tool in 3D flow imaging innovation endeavors, such as the development of flow vector estimators and visualization algorithms.

Enhancing Swimming Performance by Optimizing Structure of Helical Swimmers.

Untethered microrobots provide the prospect for performing minimally invasive surgery and targeted delivery of drugs in hard-to-reach areas of the human body. Recently, inspired by the way the prokaryotic flagella rotates to drive the body forward, numerous studies have been carried out to study the swimming properties of helical swimmers. In this study, the resistive force theory (RFT) was applied to analyze the influence of dimensional and kinematical parameters on the propulsion performance of conventional helical swimmers. The propulsion efficiency index was applied to quantitatively evaluate the swimming performance of helical swimmers. Quantitative analysis of the effect of different parameters on the propulsion performance was performed to optimize the design of structures. Then, RFT was modified to explore the tapered helical swimmers with the helix radius changing uniformly along the axis. Theoretical results show that the helical swimmer with a constant helix angle exhibits excellent propulsion performance. The evaluation index was found to increase with increased tapering, indicating that the tapered structures can produce more efficient motion. Additionally, the analysis method extended from RFT can be used to analyze the motion of special-shaped flagella in microorganisms.

Talbot effect in arrays of helical waveguides.

We demonstrate that periodic self-imaging of light patterns with certain input periods can be effectively realized in one-dimensional and two-dimensional helical waveguide arrays. The band structure is drastically dependent on the helix radius and period, and the complete collapse of quasi-energy bands occurs for a certain helix radius and period, which strongly affects the intensity carpet and the Talbot length of the Talbot self-imaging effect. Talbot length would extend to infinity, as the helix radius and period approach the corresponding critical values corresponding to the band collapse, where the inversion of intensity distribution between even and odd waveguides is observed for the binary input pattern with π/2 phase shift between the adjacent waveguides.

Distinct chemotactic behavior in the original Escherichia coli K-12 depending on forward-and-backward swimming, not on run-tumble movements

Most motile bacteria are propelled by rigid, helical, flagellar filaments and display distinct swimming patterns to explore their favorable environments. Escherichia coli cells have a reversible rotary motor at the base of each filament. They exhibit a run-tumble swimming pattern, driven by switching of the rotational direction, which causes polymorphic flagellar transformation. Here we report a novel swimming mode in E. coli ATCC10798, which is one of the original K-12 clones. High-speed tracking of single ATCC10798 cells showed forward and backward swimming with an average turning angle of 150°. The flagellar helicity remained right-handed with a 1.3 μm pitch and 0.14 μm helix radius, which is consistent with the feature of a curly type, regardless of motor switching; the flagella of ATCC10798 did not show polymorphic transformation. The torque and rotational switching of the motor was almost identical to the E. coli W3110 strain, which is a derivative of K-12 and a wild-type for chemotaxis. The single point mutation of N87K in FliC, one of the filament subunits, is critical to the change in flagellar morphology and swimming pattern, and lack of flagellar polymorphism. E. coli cells expressing FliC(N87K) sensed ascending a chemotactic gradient in liquid but did not spread on a semi-solid surface. Based on these results, we concluded that a flagellar polymorphism is essential for spreading in structured environments.

Vibration analysis of nonuniform hyperboloidal and barrel helices made of functionally graded material

This study is in investigation of free vibration behavior of functionally graded hyperboloidal and barrel helices with variable cross section. Material and geometric variations of noncylindrical helices are assumed to be along the rod axis. Governing differential equations of motion, including rotatory inertia, axial and shear deformations are derived by the Timoshenko beam theory. Then, transfer matrix and stiffness matrix methods are employed for the numerical solution of obtained ordinary differential equations. Effects of material gradient index diameter variation parameter ), and ratio of helix radius at end section and middle section on the natural frequencies are investigated through a parametric study considering barrel and hyperboloidal geometries. Comparisons with available literature studies and ANSYS solutions are made regarding obtained results.