Parabolic Profile Research Articles

Investigating the dynamics of speed and acceleration at merging and diverging sections using UAV based trajectory data

The present study evaluates the speed and acceleration characteristics at the merging and diverging sections near two toll plazas located on National Highway under mixed traffic conditions using trajectory data obtained from video recorded using unmanned aerial vehicles (UAVs). The whole study section of 280 m is divided into zones of 20 m each, and the speed-distance and acceleration-distance relations are studied. The study analyzes the speed variations among vehicle classes in merging and diverging sections. The study shows that due to heterogeneous traffic and weak lane discipline, the speed distribution deviates from the normal distribution and follows the generalized extreme value (GEV) distribution in merging and diverging sections. The average maximum lateral speed is 3.0 km/h in the diverging section and 8.0 km/h in the diverging section (2.6 times higher than in the diverging section). The overall lane selection and lane changes are only prominent in the range from 40 m to 160 m in the merging section and the range from 100 m to 200 m in the diverging section. The results of acceleration modeling indicate that most vehicle classes follow a parabolic profile, except two-wheelers (2Ws) and light commercial vehicles (LCVs), whereas cars follow a dual-regime model in the diverging section, which is consistent with previous literature. The study also identified critical speeds for each vehicle class in both the merging and diverging sections, which can be useful in designing toll plaza facilities and informing safety measures.

Dynamics of a wall-mounted cantilever plate under low Reynolds number transverse flow in a two-dimensional channel

The present work numerically investigates the dynamics of an elastic two-dimensional cantilever plate fixed at the bottom wall of a channel carrying flow using an open-source multi-physics computational fluid dynamics solver, SU2. Chief non-dimensional parameters, viz., Cauchy number (Ca), channel height, and mass ratio, are explored to predict the structural response of the plate interacting with the laminar parabolic profile in the channel at relatively low Reynolds numbers (Re=20−120). For a steady inflow, we show the existence of two distinctive modes of plate flexural oscillations, namely, F1 and F2, where the plate attains self-sustained periodic oscillations close to its first and second natural frequencies, respectively, for discrete ranges of Ca and three static modes, namely, S1, S2, and S3 for the other ranges of Ca in which steady-state configuration is obtained. The physical reasons underpinning the flow-induced oscillations and static shapes are examined using scaling arguments. F1 oscillations are shown to be vortex-induced oscillations, which get suppressed at low enough channel height, owing to higher viscous dissipation. Additionally, the window of F1 zone was found to shift to lower Ca with an increase in the mass ratio. Increasing the Reynolds number was found to cause the F1 zone to diminish in size, and beyond a critical Reynolds number, F1 was completely suppressed. On the other hand, F2 oscillations, which are shown to be induced by an unsteady drag force, are found to exist throughout the range of Re considered in the study.

Apparatus for calibration of fine-wire sensors at stratospheric conditions

A small-scale, open-circuit wind tunnel was developed to calibrate balloon-born fine-wire anemometers for conditions in the stratosphere. The system enables calibration of hotwire anemometers to test gases at flow velocities between 1 and 5 m/s and pressures between 550 and 5475 Pa. Using a metered inflow of test gas into a long circular cross-section pipe, a parabolic velocity profile is expected at the measurement plane for the fully-developed flow as described by Poiseuille flow theory. Traversal of a commercially available hotwire anemometer within the test section confirms the parabolic profile predicted for Poiseuille flow, with only minor deviations. In conjunction with the experimental testing, numerical simulations are performed to quantify probe support blockage effects on the velocity profile measurements. Test results validate the procedure for calibration of hotwire anemometers and development of forced convection heat transfer relations at stratospheric pressure conditions.

Assessment of the Severity of Left Anterior Descending Coronary Artery Stenoses by Enhanced Transthoracic Doppler Echocardiography: Validation of a Method Based on the Continuity Equation.

To verify whether the severity of coronary stenosis could be non-invasively assessed by enhanced transthoracic coronary echo Doppler in convergent color Doppler mode (E-Doppler TTE) over a wide range of values (from mild to severe). Color-guided pulsed wave Doppler sampling in the left anterior descending coronary artery (LAD) was performed in 103 diseased LAD segments (corresponding to 94 patients examined) as assessed by quantitative coronary angiography (QCA) or intracoronary ultrasound (IVUS). The E-Doppler TTE examinations consisted of measuring the velocity (vel) at the stenosis site and a reference adjacent segment. Then the continuity equation (C-Eq) was applied to calculate the percent cross-sectional area reduction (%CSA) at the stenosis site. The applied formula was: %CSA = 100 × (1 - [TVIref × 0.5]/TVIs). TVI = the time velocity integral at the stenosis [s] and the reference site [ref], respectively); 0.5 = the correcting factor for a parabolic profile was used only when the % accelerated stenotic flow was >122% (AsF = diastolic peak vel at first site - diastolic peak vel at second site/diastolic peak vel at second site × 100). E-Doppler TTE feasibility was 100%. Doppler and QCA/IVUS-derived %CSA stenosis showed very good agreement over a large range of values (from mild to severe), with no significant bias; the maximum difference between QCA/IVUS and transthoracic Doppler %CSA was mostly around 20% with a few patients exceeding this limit (limits of agreement = -27.53 to 23.5%). The scattering was slightly larger for the non-significant stenoses. The correlation was strong (r = 0.89, p < 0.001). E-Doppler TTE is a feasible and reliable method for assessing the severity of LAD stenosis by applying the C-Eq.

Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides

In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in these structures can be described by using a Gross–Pitaevskii equation with a two-dimensional parabolic spatial potential. Our investigations compare variational approaches, based on the Ritz optimization method, with extensive numerical simulations. We found that, with a Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low pulse energies, where our analytical results find a perfect agreement with the numerical simulations. However, with progressively increasing energies, solitons eventually undergo wave collapse: this occurs below the theoretical limit, which is predicted within the variational approach. In a self-defocusing scenario, a similar trend is found, where the good agreement persists for low energies. For large soliton energies, however, complex spatiotemporal dynamics emerge.

Optimization of Multi‐Segment Work Roll Profile for 1340 mm HC Tandem Cold‐Rolling Mills Based on DBSCAN and NSGA‐II Algorithms

To address issues with saturated work roll bending force (WRB), maximum contact pressure between the work roll and intermediate roll (QWI), and challenging flatness lifting in a four‐stand, six‐high tandem cold mill with a 1340 mm width, the density‐based spatial clustering of applications with noise algorithm and the non‐dominated sorting genetic algorithm II are used for optimal design and online application research of a five‐segment work roll profile. When compared to a flat roll and a parabolic roll profile with a maximum crown of 15 μm, the optimized roll profile decreases the secondary crown of the roll gap (CW2) by 5.99 and 1.055 μm, respectively, and the fourth crown of the roll gap (CW4) by 0.21 and 0.39 μm, respectively. Additionally, QWI in the field of roll gap crown adjustment decreases by 1.04 and 0.445 kN mm−1. Industrial testing shows that the average integrated value of flatness in rolling the four extreme specifications of 1340 mm tandem cold‐rolling mills lowers by 2.65 IU following the application of the new roll profile, and the average reduction of WRB in the last stand is 2.215 MPa.

Photoaligned Tunable Liquid Crystal Lenses with Parabolic Phase Profile

We present a theoretical model of a cylindrical tunable liquid crystal lens based on the modulation of anchoring energy. The latter can be easily obtained using photoalignment techniques. The liquid crystal cell we propose exhibits strong anchoring at the top substrate and anchoring energy with a parabolic profile at the bottom substrate. The model describes the dependence of the focal length on the applied voltage and presents a theoretical study of the lens aberrations. The results obtained are of general relevance and can be used to optimize the performances of every type of liquid crystal lens with a parabolic profile.

Influence of Pulsatility and Inflow Waveforms on Tracheal Airflow Dynamics in Healthy Older Adults.

Tracheal collapsibility is a dynamic process altering local airflow dynamics. Patient-specific simulation is a powerful technique to explore the physiological and pathological characteristics of human airways. One of the key considerations in implementing airway computations is choosing the right inlet boundary conditions that can act as a surrogate model for understanding realistic airflow simulations. To this end, we numerically examine airflow patterns under the influence of different profiles, i.e., flat, parabolic, and Womersley, and compare these with a realistic inlet obtained from experiments. Simulations are performed in ten patient-specific cases with normal and rapid breathing rates during the inhalation phase of the respiration cycle. At normal breathing, velocity and vorticity contours reveal primary flow structures on the sagittal plane that impart strength to cross-plane vortices. Rapid breathing, however, encounters small recirculation zones. Quantitative flow metrics are evaluated using time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI). Overall, the flow metrics encountered in a real velocity profile are in close agreement with parabolic and Womersley profiles for normal conditions, however, the Womersley inlet alone conforms to a realistic profile under rapid breathing conditions.

Effective Governing Equations for Viscoelastic Composites.

We derive the governing equations for the overall behaviour of linear viscoelastic composites comprising two families of elastic inclusions, subphases and/or fibres, and an incompressible Newtonian fluid interacting with the solid phases at the microscale. We assume that the distance between each of the subphases is very small in comparison to the length of the whole material (the macroscale). We can exploit this sharp scale separation and apply the asymptotic (periodic) homogenization method (AHM) which decouples spatial scales and leads to the derivation of the new homogenised model. It does this via upscaling the fluid-structure interaction problem that arises between the multiple elastic phases and the fluid. As we do not assume that the fluid flow is characterised by a parabolic profile, the new macroscale model, which consists of partial differential equations, is of Kelvin-Voigt viscoelastic type (rather than poroelastic). The novel model has coefficients that encode the properties of the microstructure and are to be computed by solving a single local differential fluid-structure interaction (FSI) problem where the solid and the fluid phases are all present and described by the one problem. The model reduces to the case described by Burridge and Keller (1981) when there is only one elastic phase in contact with the fluid. This model is applicable when the distance between adjacent phases is smaller than the average radius of the fluid flowing in the pores, which can be the case for various highly heterogeneous systems encountered in real-world (e.g., biological, or geological) scenarios of interest.

Design and performance investigation of modified Hybrid Parabolic Linear Fresnel Collector

The Parabolic Trough Collector and Linear Fresnel Collector are the two established solar thermal concentrator technologies. While both technologies have their own advantages, current research focus in on alternate designs to improve optical and thermal performance of the collectors. The optical modifications by changing the primary reflector design have been one of the areas of research. One such modifications is the discretization of the parabolic mirror with flat plates. A hybrid collector combing the flat plates and stationary absorber of LFC with the parabolic profile of a PTC is investigated. A Hybrid Parabolic Linea Fresnel Collector (HPLFC) is designed based on optical analysis with ray tracing analysis and the collector tested experimentally. The average yearly energy production of PTC, LFC and modified HPLFC has been studied with optical and thermal modelling. The optical and thermal modelling estimates that HPLFC has an average optical efficiency of 49 % and overall efficiency of 39 %. The HPLFC efficiency is lower than PTC and performs better than LFC during winter. The HPLFC has been investigated experimentally at Coimbatore, India. The efficiency of HPLFC has been found to be 35 ± 2 %. This can be improved with better manufacturing and optimization of operating conditions.

Effects of thickness profile and inner/outer of localized thin area defects on the remaining strength of pressure equipment

When encountering pressure equipment with a structural defect such as a local thinning defect (LTA), a critical question often arises regarding the safety of continued operation. This is primarily determined by the strength at the LTA zone, as it represents the weakest point of the structure. The remaining strength factor (RSF) is proposed as an indicator to evaluate the remaining strength and life of pressure equipment when a severe LTA is identified. The API 579/ASME FFS standard offers a series of practical engineering approaches for field engineers to follow, which have achieved great success. However, it has been found that the simpler Level 1 and Level 2 approaches sometimes fail to differentiate between LTAs on the inner or outer surface of the pressure equipment, yielding identical numerical processes and results. Moreover, the use of critical thickness profiles to replace the actual thickness profile in analysis can lead to overly optimistic estimation of the RSF, posing a potential danger when the RSF is close to the allowable limit. Key issues investigated in this study include: (a) discrepancies caused by the use of simplified critical thickness profiles or parabolic profiles, as API 579 suggested, on the RSF; (b) differences in RSFs when the same LTA is on the inner and outer wall; and (c) comparisons of membrane stress and bending stress, as well as their influences on the RSF at the cross-section of the vessel wall. It can be concluded with certainty that all simplified geometries (CTP and PTP) tend to underestimate the RSF and should be used with caution. Additionally, the actual remaining strength of the outer LTA was found to be slightly lower than that of the inner LTA of identical size. Therefore, when remaining life and derating for prolonged operation are of interest, finite element analysis on pressure equipment with the LTA is recommended.

Production of pure water and dry salt from NaCl solutions via percrystallisation by supported carbon membranes

Membrane percrystallisation is an alternate crystallisation process where a membrane disperses aqueous salt solution into a thin film on the permeate side. This thin film can be instantaneously vaporised to form pure water vapor and dry, crystallised salt under vacuum conditions. This work demonstrates, for the first time, that supported carbon membranes are a viable configuration for the percrystallisation of saline solutions. Within the work, the carbon materials in powder and supported membrane form were produced from polyvinylpyrrolidone (PVP) by pyrolysis at temperatures ranging from 450 and 800 °C. Porosity analysis identified that the materials do not adsorb gas. This suggests that the materials are non-porous or the pores are not accessible at the analysis conditions. All produced membranes were of supported nature with approximate thickness of 8 μm. The flux measurement revealed that the membranes, despite being similar in thickness, resulted in variable flux exhibiting a parabolic profile, with a maximum flux obtained (18 kg m−2 h−1) when tested for percrystallisation at 50 °C. The membranes maintained structural integrity when operated with 3.5 to 10 wt% NaCl solutions at 50 °C. However, membranes began to degrade when operating with 20 wt% solutions at 70 °C. The solid product analysis showed that the NaCl produced by percrystallisation is crystalline NaCl, with various morphological properties. The analysis also revealed that the particle size and shape depends on the solution flux through the membrane with smaller crystals at higher fluxes. The results of this study are used to propose a mechanism of salt formation for the percrystallisation of aqueous salt solutions.

Photocatalytic degradation of ethylene in tubular microreactor coated with thin-film of TiO2: Mathematical modeling with experimental validation and geometry analysis using computational fluid dynamics simulations

The study aimed to establish a comprehensive understanding of the photocatalytic process and optimize the reactor design for efficient ethylene regulation to improve the shelf-life of fruits and vegetables. For this, it was performed 2D computational fluid dynamics modeling at two different reactor geometry (conventional cylindric reactor and annular cylindric reactor) using the conservation equations combined with Langmuir-Hinshelwood mechanism. A continuous single-phase multicomponent fluid flow with the reactor surface supported with a thin-film catalyst under UV-A light irradiation was simulated for initial ethylene concentration at 0.479–4.234 × 10−3 molC2H4 m−3 and inlet axial velocity at 0.0085–0.1019 m s−1. In the 2D CFD results, it was observed that the difference in ethylene concentration between the microreactor bulk and surface is only significant for high initial concentrations and axial velocities. Furthermore, it was found that the parabolic conversion profile remains unchanged for lengths greater than 10% of the reactor length across all geometries studied. The variation in reactor diameters resulted in a substantial reduction in ethylene conversion; however, the incorporation of an annular cylinder coated with a catalyst led to an enhancement in conversion rates, with improvements of approximately 28%, 17%, and 6% observed for diameters of 5 mm, 10 mm, and 20 mm, respectively. This reduction in improvement as diameter increase can be attributed to the laminar flow dynamics that impede the diffusion of ethylene molecules from the bulk to the catalytic surface. Consequently, the simulated data highlight the potential of employing a catalyst-doped annular cylinder as a promising strategy to increase ethylene conversion and extend the shelf life of fruits. However, it should be noted that the addition of an annular cylinder, while enhancing conversion, also introduces operational complexities and cost implications due to the significant increase in pressure drop associated with lower diameters.

Modeling dynamic fragmentation of tempered glass

Understanding why a strengthened glass article will fragment, and to what extent, has long been incomplete. This work addresses this gap for glass plates with parabolic residual stress profiles; this can include tempered glass as well as deep chemically strengthened profiles. Various thicknesses of glass are studied to give credibility to a parameter that defines the onset of fragmentation susceptibility (frangibility limit) and an equation that predicts the number of fragments per sheet area. This equation can then be used to fit experimental data, thus allowing for back calculating the frangibility limit and dynamic toughness. This is beneficial since neither of these values is easily measurable. Future work will seek to understand how differently shaped stress profiles fit into this theoretical framework.

The Therapeutic Frequency Profile of Subthalamic Nucleus Deep Brain Stimulation in Rats Is Shaped by Antidromic Spike Failure.

The therapeutic mechanisms of subthalamic nucleus (STN) deep brain stimulation (DBS) may depend on antidromic activation of cortex via the hyperdirect pathway. However, hyperdirect pathway neurons cannot reliably follow high-stimulation frequencies, and the spike failure rate appears to correlate with symptom relief as a function of stimulation frequency. We hypothesized that antidromic spike failure contributes to the cortical desynchronization caused by DBS. We measured in vivo evoked cortical activity in female Sprague Dawley rats and developed a computational model of cortical activation from STN DBS. We modeled stochastic antidromic spike failure to determine how spike failure affected the desynchronization of pathophysiological oscillatory activity in cortex. We found that high-frequency STN DBS desynchronized pathologic oscillations via the masking of intrinsic spiking through a combination of spike collision, refractoriness, and synaptic depletion. Antidromic spike failure shaped the parabolic relationship between DBS frequency and cortical desynchronization, with maximum desynchronization at ∼130 Hz. These findings reveal that antidromic spike failure plays a critical role in mediating the dependency of symptom relief on stimulation frequency.SIGNIFICANCE STATEMENT Deep brain stimulation (DBS) is a highly effective neuromodulation therapy, yet it remains uncertain why conventionally used stimulation frequencies (e.g., ∼130 Hz) are optimal. In this study, we demonstrate a potential explanation for the stimulation frequency dependency of DBS through a combination of in vivo experimental measurements and computational modeling. We show that high-frequency stimulation can desynchronize pathologic firing patterns in populations of neurons by inducing an informational lesion. However, sporadic spike failure at these high frequencies limits the efficacy of the informational lesion, yielding a parabolic profile with optimal effects at ∼130 Hz. This work provides a potential explanation for the therapeutic mechanism of DBS, and highlights the importance of considering spike failure in mechanistic models of DBS.

Biomimetic moth-eye nanostructures fabricated by nanosphere lithography in ZnSe enhancing transmission in the mid-infrared

ZnSe is a highly regarded material for optical windows in the infrared spectrum, where transmission efficiency is a critical factor. Traditional surface antireflective coatings have limitations that can be overcome with biomimetic moth-eye nanostructures. In this paper, we present a novel method using nanosphere lithography with polystyrene (PS) nanosphere to fabricate moth-eye nanostructures (MENS) on ZnSe surface with an exceptional antireflection effect. The parabolic profile MENS, which is challenging to fabricate through conventional methods, was directly obtained using our dry etch process. This profile outperformed other shapes like circular cones, resulting in better antireflective performance. Our experimental results matched perfectly with the modeling and demonstrated that the MENS had broadband antireflection performance in the 2–5 μm wavelength range. The maximum transmission of MENS was 82.6%, which was a significant improvement over the flat ZnSe with 71.28% transmission, achieving a 17.2% transmittance enhancement that is close to the ZnSe transmission limit. Moreover, the MENS exhibited a highly desirable hydrophobicity with a wetting angle of 114° instead of 71° on flat ZnSe. Our work displays great potential in optoelectronic devices and high-power laser applications.

Investigation of reflections of terahertz waves from an inhomogeneous planar layer of a chiral metamaterial with allowance for frequency dispersion

The main purpose of this work is to develop a method for calculating the reflections of linearly polarized waves from an inhomogeneous planar layer of a chiral metamaterial. A mathematical model of a homogeneous inhomogeneous chiral medium is considered taking into account the frequency dispersion of material parameters. The moduli of the reflection coefficients of the main and cross-polarized field components from an inhomogeneous layer with parabolic and linear profiles of changes in the resonant frequency of a chiral metamaterial are calculated. It is shown that inhomogeneous planar structures of chiral metamaterials can significantly reduce the level of reflection of cross-polarized waves in the optical and terahertz ranges.

Semi-analytical formulation for exciton in cuboidal semiconductor quantum dot with parabolic confinement: Hydrostatic pressure and temperature effects

The exciton properties in a cubical quantum dot (CQD), with parabolic confining potential, are theoretically investigated. We have used the two-band model, the effective mass approximation, and the variational method. An analytical formulation to be used for calculating exciton properties in a cubical quantum dot with a parabolic potential profile has been developed. The analytical expressions of the binding energy, the normalized photoluminescence energy transition, the spatial extension, and the oscillator strength of the exciton, in the ground state, have been obtained. The numerical calculations for the typical GaAs/AlxGa1−xAs CQD are presented. The effects of the side length of a cubic quantum dot, the hydrostatic pressure, and the temperature on the exciton properties are discussed. The results of the calculation illuminate that the hydrostatic pressure and the CQD length can make an important impact on the exciton binding energy and the photoluminescence peak energy.

Further Validation of a Simple Mathematical Description of Wear and Contact Pressure Evolution in Sliding Contacts

The present study proposes the further validation of a simple mathematical procedure recently proposed by the authors to describe contact and wear evolution in line and point contacts. The procedure assumed that the maximum contact pressure could be determined using Hertz equations and a parabolic pressure profile. The contact half-width was obtained using the equilibrium equation and the Archard wear law. Several cases were selected from the literature, reporting experimental data or Finite Element simulations, and the results were compared to those obtained with the proposed approach. This paper confirms the reliability and potentialities of the proposed analytical procedure, which is capable of providing accurate solutions in case of frictional contacts and at the borders of the contact area, where the main discrepancies were found in the previous study.

Flow-Induced Forces for a Group of One Large and Several Small Structures in the Sheared Turbulent Flow

Evaluating the hydrodynamic force fluctuations acting on each structure in a group of subsea objects of different cross-section shapes, sizes and relative positions represents a challenge due to the sensitivity of the vortex shedding process, especially for a variety of sheared flows. The present study uses the numerical 2D computational fluid dynamics model to estimate the flow-induced forces on a group of small circular and D-shaped cylinders in the linear and parabolic sheared flow, which are placed in proximity to a larger structure of the squared cross-section. This allows us to evaluate loads, which are affected by the presence of subsea equipment located on the seabed. The average Reynolds number of the considered linear flow profile is 3900, while the parabolic flow profile has the maximum Reynolds number of 3900. The k-ω SST turbulence model is used for simulations. The work demonstrates the effect of the cross-sectional shape of smaller cylinders on hydrodynamic coefficients, explores the effect from the spacing in between the structures and highlights differences between loads in the linearly sheared and parabolic flow. The results obtained show that the presence of the squared cylinder notably influences the mean drag coefficient on the first cylinder, for both circular and D-shaped cylinders. The parabolic sheared flow profile in this series leads to the highest mean drag and the highest amplitudes of the fluctuating drag and lift coefficients.