Parabolic Structure Research Articles

The Synthesis and Assembly Mechanism of Micro/Nano-Sized Polystyrene Spheres and Their Application in Subwavelength Structures.

The following study involved the utilization of dispersion polymerization to synthesize micron/nano-sized polystyrene (PS) spheres, which were then deposited onto a silicon substrate using the floating assembly method to form a long-range monolayer. Subsequently, dry etching techniques were utilized to create subwavelength structures. The adjustment of the stabilizer polyvinylpyrrolidone (PVP), together with changes in the monomer concentration, yielded PS spheres ranging from 500 nm to 5.6 μm in diameter. These PS spheres were suspended in a mixture of alcohol and deionized water before being arranged using the floating assembly method. The resulting tightly packed particle arrangement is attributed to van der Waals forces, Coulomb electrostatic forces between the PS spheres, and surface tension effects. The interplay of these forces was analyzed to comprehend the resulting structure. Dry etching, utilizing the PS spheres as masks, enabled the exploration of the effects of etching parameters on the resultant structures. Unlike traditional dry etching methods controlling RF power and etching gases, in the present study, we focused on adjusting the oxygen flow rate to achieve cylindrical, conical, and parabolic etched structures.

Topology optimization of an elliptical parabolic shell structure: effect of penalty factor and load type

Topology optimization of an elliptical parabolic shell structure: effect of penalty factor and load type

Observation of Boyer-Wolf Gaussian modes

Stable laser resonators support three fundamental families of transverse modes: the Hermite, Laguerre, and Ince Gaussian modes. These modes are crucial for understanding complex resonators, beam propagation, and structured light. We experimentally observe a new family of fundamental laser modes in stable resonators: Boyer-Wolf Gaussian modes. By studying the isomorphism between laser cavities and quadratic Hamiltonians, we design a laser resonator equivalent to a quantum two-dimensional anisotropic harmonic oscillator with a 2:1 frequency ratio. The generated Boyer-Wolf Gaussian modes exhibit a parabolic structure and show remarkable agreement with our theoretical predictions. These modes are also eigenmodes of a 2:1 anisotropic gradient refractive index medium, suggesting their presence in any physical system with a 2:1 anisotropic quadratic potential. We identify a transition connecting Boyer-Wolf Gaussian modes to Weber nondiffractive parabolic beams. These new modes are foundational for structured light, and open exciting possibilities for applications in laser micromachining, particle micromanipulation, and optical communications.

Vibration control of thin shallow paraboloidal shells with light-activated shape memory polymers

With the applications of thin-walled paraboloidal shell structure in aviation, aerospace and communication systems, smart-structure based active vibration control becomes essential to improve the performance of thin-walled parabolic structures. Light-activated shape memory polymer (LaSMP) is a novel actuator material that exhibits dynamic Young's modulus and strain properties under ultraviolet (UV) light exposures, which can be used for non-contact vibration control. This study focuses on investigating the vibration control performance of a shallow parabolic thin shell, with simply supported boundary conditions, with laminated LaSMP patches. Based on the LaSMP strain model, the vibration control effect of LaSMP patch on the thin shell is discussed. A finite element model of the simply supported parabolic thin shell is developed to obtain the natural frequencies. The modal expansion method is employed to investigate the vibration control of the shallow parabolic thin shell laminated with LaSMPs, and independent modal responses are calculated. According to the different control mode, the effects of LaSMP actuators on vibration control of shallow paraboloid shell are studied in three cases with varying actuation position and coverage area of LaSMP actuators. The results indicate that LaSMP can control the vibration of the thin shell by reducing the vibration amplitude and the final vibration control effect is determined by the mode shape, the initial LaSMP strain, and the location and area covered by LaSMP actuators. By establishing the model between the LaSMP actuator force and the attenuations in modal amplitude, this study provides an analytical tool for the application of LaSMPs in vibration control of flexible structures.

On the motives of moduli of parabolic chains and parabolic Higgs bundles

Analogous to the Higgs bundles on a Riemann surface which played an important role in the study of representations of the fundamental group of the surface, the parabolic Higgs bundles play also their importance in the study of the fundamental group but of the punctured surface. In this paper, we give an algorithm to calculate the (virtual) motive (i.e. in a suitable Grothendieck group) of the moduli spaces of parabolic Higgs bundles of fixed rank and fixed parabolic structure, using localization with respect to the circle action.

Design and optimization of origami-inspired inflatable deployable tubular structures

Inflatable deployable structures inspired by origami have significant applications in space missions such as solar arrays and antennas. In this paper, a generalized Miura-ori tubular cell (GMTC) is presented as the basic cell to design a family of inflatable origami tubular structures with the targeted configuration. First, the classification of rigid foldable degree-4 vertices is studied thoroughly. Since the proposed GMTC is comprised of forming units (FU) and linking units (LU), types of FUs and LUs are investigated based on the classification of degree-4 vertices, respectively. The rigid foldability of the GMTC is presented by studying the kinematics of the FUs and LUs. Volume of the GMTC is analyzed to investigate multistable configurations of the basic cell. The variations in volume of the GMTC offer great potential for developing the inflatable tubular structure. Design method and parametric optimization of the tubular structure with targeted configuration are proposed. The feasibility of the approach is validated by the approximation of four different cases, namely parabolic, semicircular, trapezoidal, and straight-arc hybrid tubular structures.

Packing optimization and design of the deployable parabolic rigid antenna based on origami

This paper introduces a novel approach for optimizing the packing and design of deployable parabolic rigid antenna structures based on origami, tailored to meet specific requirements related to the number of solid-surface blocks and the size of the folded antenna. The study begins by selecting a single-vertex four-crease configuration with one degree of freedom from the origami pattern, guided by mobility analysis, to optimize block arrangement. Subsequently, a planar model is employed to qualitatively examine the impact of geometric parameters on the stowage efficiency of the antenna. Building upon the insights gained from the planar model, an optimization framework for the parabolic rigid deployable antenna structure is established. The objective function of the optimization is the stowage volume, while simultaneously adhering to stiffness, collision, and mobility constraints. The design parameters of the antenna structure are thoroughly analyzed. To mitigate collision risks during folding, design considerations are applied to placement of support nodes, location of rotating axes, and block division, leveraging the optimized parameters. The practicality of the proposed method is successfully demonstrated through the folding of a simulated 3D model and of a physical 3D printed model. These tangible representations show the feasibility of the presented approach, affirming its potential applicability in the optimization and design of deployable parabolic rigid antenna structures.

Modal signal analysis of parabolic shell structures with flexoelectric sensors

The flexoelectric effect, garnering extensive attention in recent years, is an electro-mechanical coupled gradient effect that widely exists in dielectric materials and holds great potential for applications in structural sensing and actuation. The parabolic shell structure, characterized by line focusing, finds widespread use in key structural components such as solar trough collectors and communication antennas. Distributed sensing of the structural states of these parabolic shells is critical for vibration control, health monitoring, and shape control of precision structural systems. Therefore, flexoelectric sensing research based on parabolic shell structure has become an important topic. This study establishes a mathematical model for flexoelectric sensing in a parabolic shell with four-sided simply supported boundary conditions. The model is based on the direct flexoelectric effect, and thin shell assumption, and incorporates specific Lamé parameters and curvature radius. The electro-mechanical strain gradient/signal generation characteristics and distributed modal flexoelectric signals on the parabolic shell are investigated. The sensing signal under the open-circuit conditions is deduced, and the flexoelectric sensing signal and sensing characteristics of different modes are analyzed. The formulation of the flexoelectric neural sensing signal for the parabolic shell structure is provided and divided into two components: a circumferential bending component and a longitudinal bending component. In the case studies, the effects of design parameters such as flexoelectric sensor thickness, size, and aspect ratios are evaluated and compared. The analysis and results of this study offer a theoretical foundation and reference for refining the design parameters of the flexoelectric sensor and determining its optimal sensing position, and potentially paving the way for new applications of flexoelectric sensing technology.

Thermal examination for double diffusive MHD Jeffrey fluid flow through the space of disc and cone apparatus subject to impact of multiple rotations

Non-Fourier’s and non-Fick’s models enhance predictions of transient heat transfer and mass transport, especially in situations where local equilibrium assumptions break down. In such fluids, the deformation rate and shear stress display a natural parabolic structure. In this study, we explore the flow of a Jeffrey fluid with dual diffusions, incorporating both non-Fourier's and non-Fick's assumptions, through the gap of disk-cone devices. Four scenarios have been investigated for fluid flow and heat transformation in this work comprising of (i) both disc and cone are rotating in opposite directions (ii) both disc and cone are rotating in same direction, (iii) cone is rotating while disc remains stationary, (iv) disc is rotating while cone remains stationary. After deriving the basic equations, a set of appropriate variables is used to convert them into dimension from form. RK-4 (Runge-Kutta 4th order) technique has been employed for the solution of nonlinear equations. As the magnetic and Maxwell factors experience a notable increase, whether the disk and cone move in tandem, in opposite directions, or involve a static cone with a gyrating disk, or a static disk with a gyrating cone, the transverse velocity panels consistently exhibit retardation in all scenarios. Additionally, a noteworthy observation is made when evaluating changes in both the Nusselt number and the Sherwood number, with significantly more pronounced variations detected at the surface of the disk compared to that of the cone. There has been a 35% increase observed in the thermal flow rate with variations in the thermophoresis factor.

Design of a Deployable Broadband Mesh Reflector Antenna for a SIGINT Satellite System Considering Surface Shape Deformation.

In this paper, we propose a deployable broadband mesh reflector antenna for use in signals intelligence (SIGINT) satellite systems, considering performance degradation due to shape deformation. To maximize gain by increasing the diameter of the reflector while reducing the weight of the antenna, the reflector of the antenna is designed using lightweight silver-coated Teflon mesh. The mesh reflectors are typically expanded by tension to maintain their parabolic structure; thus, shape deformation cannot be avoided. This shape deformation results in shape differences between the surface of the mesh reflector and the ideal parabolic reflector, thus resulting in the degradation of the performance of the mesh reflector antenna. To observe this degradation, we analyze antenna performance according to the number of arms, the number of joints, the feed distance, and the distance from the reflector center to each joint. The performance of the mesh reflector antenna is examined using an effective lossy conducting surface (ELCS) that has the same reflectivity as the silver-coated Teflon mesh to reduce simulation time and computing resources. The designed silver-coated Teflon mesh reflector and the double-ridged feed antenna are fabricated, and the bore-sight gain is measured using the three-antenna method. The measured bore-sight gain of the proposed antenna is 31.6 dBi at 10 GHz, and the measured and simulated results show an average difference of 3.28 dB from 2 GHz to 18 GHz. The proposed deployable mesh reflector antenna can be used in a variety of applications where small stowed volume is required for mobility, such as mobile high-gain antennas as well as satellite antenna systems. Through this study, we demonstrate that shape deformation of the mesh reflector surface significantly affects the performance of reflector antennas.

Thermal performance of Parabolic Trough Solar Collector

The research progress of numerical simulation of parabolic trough solar collector was introduced. Especially the numerical simulation studies of the internal flow field in the collector tube and the external flow field of the concentrator were reviewed. In the study of the internal flow field in the collector tube, the type of heat transfer fluids and the characteristics of optical concentration have a significant effect on the heat collection performance and thermal stress distribution, especially in the water/steam medium heat collection loop. The unique gas-liquid two phase flow superposition of the non-uniform heat flux distribution outside the tube may lead to serious thermal stress bending deformation of the collector tube. In the study of the external flow field of the concentrator, due to the high actual wind speed and the low structural strength of the ultra-thin lens, the concentrator is subjected to wind load deformation, resulting in the loss of optical efficiency, and even leading to the failure of the parabolic trough collector structure, which directly affects the normal operation of the whole collector field.

Seshadri constants of parabolic vector bundles

Let X be a complex projective variety, and let E_* be a parabolic vector bundle on X with parabolic structure on a divisor. We introduce the notion of parabolic Seshadri constants of E_* . It is shown that these constants are analogous to the classical Seshadri constants of vector bundles, in particular they have parallel definitions and properties. We prove a Seshadri criterion for parabolic ampleness of E_* in terms of the parabolic Seshadri constants of it. We also compute parabolic Seshadri constants for symmetric powers and tensor products of parabolic vector bundles.

Stochastic simulation of electron transport in a strong electrical field in low-dimensional heterostructures

Abstract In this paper we develop a stochastic simulation algorithm for electron transport in a DA-pHEMT heterostructure. Mathematical formulation of the problem of electron gas transport in the heterostructure in the form of a coupled system of Poisson, Schrödinger and kinetic Boltzmann equations is given. A Monte Carlo model of electron transport in DA-pHEMT heterostructures which accounts for multivalley parabolic band structure, as well as relevant formulas for calculating electron scattering rates and scattering phase functions on polar optical, intervalley phonons and on impurities are developed. The results of a computational experiment involving the solution of the system of Poisson–Schrödinger–Boltzmann equations for the AlGaAs/GaAs/InGaAs/GaAs/AlGaAs heterostructure are presented. The distribution of electrons by energy subband in the main and satellite valleys and the field dependences of the electron drift velocity in each valley are calculated. It was discovered that there is no spatial transfer of electrons into wide-gap AlGaAs layers due to high barriers created by modulated-doped impurities. A comparative analysis of the electron drift velocities in the studied DA-pHEMT heterostructures and in the unstrained layer of the InGaAs is given.

Effect of parabolic structure potentials on electron mobility in AlxGa1-xAs quantum well based field effect transistor structure

Here, we theoretically calculate and analyze electron mobility μ in AlxGa1-xAs double parabolic and semi-parabolic quantum well (DPQW and DSPQW) based field effect transistor structures. We compute μ as a function of applied electric field F by considering ionized impurity (II) and alloy disorder (AL) screened scattering potentials (VscrII/AL) and show that μ(DPQW) > μ (DSPQW). The symmetric property of VscrII/AL makes μ to vary symmetrically around F = 0 at which two subbands are occupied. The shape of the DSPQW structure potential, compared to DPQW, causes the subband wave functions ψ0 and ψ1 to lie nearer and also penetrate more into the central barrier. Accordingly, the II-scattering is reduced due to increased distance of the electrons from the ionized donors (lying in the side barriers), while AL-scattering is enhanced through increased scattering in the central barrier. As a result, we obtain for F = 0, μII (DSPQW) > μII (DPQW) and μAL (DSPQW) < μAL (DPQW). Further, we show that μ enhances in DPQW by increasing design parameters such as well width, spacer width, and central barrier width. However, μ reduces with the increase in alloy concentrations inside the well through intersubband interaction. The obtained results reflect the suitability of parabolic potential based quantum well structures in emerging optoelectronic devices to enhance the transport and optical properties.

Design and optimization of kirigami-inspired rotational parabolic deployable structures

Deployable structures designed through diverse methodologies have become crucial in contemporary engineering applications. Despite their distinct advantages, the exploration of kirigami techniques for designing parabolic deployable structures remains nascent. In this study, we explored the potential of kirigami for developing a parabolic deployable structure with a large deployment ratio and few degrees of freedom. According to the plane-symmetric kirigami pattern endowed with thickness, two distinctive deployable structural configurations were introduced. Based on these configurations, a geometric model and corresponding optimization method were proposed. A rigorous analysis was conducted to examine the effects of the array number and array row number on the deployment ratio. Finally, the deployment ability of the designed parabolic deployable structure and the surface morphology of the paraboloid were evaluated through computational simulations and prototype manufacturing. The results indicated that the kirigami-inspired deployable structure had an excellent deployment ability and closeness to the aimed paraboloid. This study provides an innovative methodology for designing curved deployable structures for engineering applications.

Moduli Spaces for the Fifth Painlevé Equation

Isomonodromy for the fifth Painlevé equation ${\rm P}_5$ is studied in detail in the context of certain moduli spaces for connections, monodromy, the Riemann-Hilbert morphism, and Okamoto-Painlevé spaces. This involves explicit formulas for Stokes matrices and parabolic structures. The rank 4 Lax pair for ${\rm P}_5$, introduced by Noumi-Yamada et al., is shown to be induced by a natural fine moduli space of connections of rank 4. As a by-product one obtains a polynomial Hamiltonian for ${\rm P}_5$, equivalent to the one of Okamoto.

Interstellar scintillation observations for PSR J0835−4510 at 6656 MHz

ABSTRACT Scintillation phenomena of pulsars provide an important tool for studying interstellar scattering screens and their properties. In this paper, we report pulsar scintillation phenomena of the PSR J0835−4510 at multiple epochs between MJD 58592 and MJD 58843 using the Kunming 40 m radio telescope at a centre frequency of 6656 MHz. We have measured the dynamic spectrum, and derived the scintillation time, bandwidth, and secondary spectrum at each observation epoch. For the first time, we report the detection of parabolic arc structure in the secondary spectra of PSR J0835−4510. Parabolic arcs with varying curvatures appear at all our observation epochs. We used both anisotropic and isotropic scattering screen models to fit the annual variations of arc curvature. While both models can fit the arc curvature variations equally well, the anisotropic model also explains the parabolic arc morphology and its time variation. In this model, the scattering is located at a fractional distance of s = 0.35 ± 0.10, or a distance Ds = 0.19 ± 0.03 kpc from the Earth, likely corresponding to the boundary of the Local Bubble.

Tuning and interpretation of electronic transport properties with

Electronic transport coefficients such as the electrical conductivity, the termo-power, and the charge carrier concentration are routinely measured in a variety of application areas such as electronics or thermoelectric power-generation and cooling. Using fitting procedures, those measurements are used to infer microscopic features of the samples. The code ▪ facilitates the estimation of electronic structure parameters such as the effective masses and band energies improving the current approach by increasing the complexity of the band structure representation. The software is designed with a server-client architecture to enhance performance and scalability. The server is implemented in the Julia programming language. We illustrate the design and the efficiency of the code with selected applications, which are relevant to the optimization of thermoelectric materials. Program summaryProgram Title:▪CPC Library link to program files:https://doi.org/10.17632/494nj6ftbv.1Developer's repository link:https://github.com/marcofornari/etransport.gitLicensing provisions: GPLv3Programming language: Julia, Python.Nature of problem: Electronic transport measurements are routinely used to link the functional properties exploited in electronics and energy sciences applications with the underlying electronic structure of the material under investigation. Experimentalists collect data of derived and integrated physical quantities, from which they estimate properties and parameters, e.g., nature of the conduction mechanisms and effective mass. The interpretation is based on simplistic models that rarely represent the complexity of the band structure. The code ▪ improves the current state of the art and facilitates the estimation of effective masses and energies from experimental measurements of electrical conductivity, Seebeck coefficients, and carrier concentration using a multi-valley anisotropic parabolic band structure as a model for the unknown real band structure. Experimental data can be imported and visualized to facilitate the comparison with theoretical analysis.Solution method: The Boltzmann equation within the relaxation-time approximation is used to compute the electronic transport tensors from the electronic density of states characterized in terms of a set of effective masses tensors mi⁎ and critical energies ϵi. Numerical and analytical techniques are adopted to integrate the Boltzmann equation efficiently. By tuning the features of the density of states, temperature, Fermi level, and the functional expression for the relaxation time, the software streamlines the reconstruction of the underlying electronic properties from experimental data.Additional comments including restrictions and unusual features: The software is designed with a server-client architecture to enhance performance and scalability. The server is implemented in the Julia programming language as a stand-alone library. It performs all the numerical operations to compute the transport tensors from a set of multi-valley parabolic band structures. The client is implemented either as a command-line user interface (CLI) or a graphical user interface (GUI) written in the Python programming language. The communications between the server and clients are handled by a REST API, where the data are exchanged using JSON payloads.

Parabolic MMI Coupler for 2 × 2 Silicon Optical Switch With Robustly High Extinction Ratio for Four Paths

We propose and experimentally demonstrate a Mach-Zehnder silicon thermo-optic switch based on a parabolic multi-mode interference coupler. By judiciously designing the parabolic structure, the 2×2 MMI can exhibit extremely small imbalance of output power around 0.1 dB over the C band with good fabrication tolerance according to simulation. As such, for all four possible switching paths, high average extinction ratios over 35 dB can be achieved from 1520 nm to 1580 nm in experiment, with maximum values concurrently over 40 dB. The proposed parabolic MMI occupies a small area of merely 2.4 μm × 9.5 μm.

Low-loss 3-dimensional waveguide crossing with a parabolic taper interlayer coupler based on a SiN-SiN-Si three-layer platform.

We demonstrated a SiN-SiN-Si three-layer silicon waveguide crossing with low-loss crossings and interlayer couplers. The underpass and overpass crossings exhibited ultralow loss (<0.82/1.16 mdB) and cross talk (<-56/-48 dB) in the wavelength range of 1260-1340 nm. To reduce the loss and length of the interlayer coupler, a parabolic interlayer coupling structure was adopted. The measured interlayer coupling loss was less than 0.11 dB from 1260 to 1340 nm, which is, to the best of our knowledge, the lowest loss reported for an interlayer coupler based on a SiN-SiN-Si three-layer platform. The total interlayer coupler length was only 120 µm.