Elliptical Profile Research Articles

Gravitational lensing by an ellipsoidal Navarro–Frenk–White dark-matter halo: An analytic solution and its properties

Context. The analysis of gravitational lensing by galaxies and galaxy clusters typically relies on ellipsoidal lens models to describe the deflection of light by the involved dark-matter halos. These models are most often based on the isothermal density profile – not an optimal description of the halo, but easy to use because it leads to an analytic deflection-angle formula. Aims. Dark-matter halos are better described by the Navarro–Frenk–White (hereafter NFW) density profile. We set out to study lensing by a general triaxial ellipsoidal NFW halo, with the aim of providing an analytic model that would be more consistent with the current understanding of dark-matter halos. Methods. We computed the conversion between the properties of a triaxial ellipsoidal lens model and its elliptical surface-density profile. In the case of the NFW lens model, its angular scale is defined by the projected scale semi-major axis of the halo, while its lensing regime depends on two parameters: the projected eccentricity e and the convergence parameter κs. We employed the Bourassa & Kantowski formalism to compute the complex scattering function of the model, which yields the deflection-angle components when separated into its real and imaginary parts. Results. We present the obtained closed-form expressions for the deflection-angle components, valid for an arbitrary eccentricity of the surface-density profile. We use them to compute and describe the lensing properties of the model, including: the shear, its components, and the phase; the critical curves, caustics, and the parameter-space mapping of their different geometries; the deformations and orientations of images. Conclusions. The analytically solved ellipsoidal NFW lens model is available for implementation in gravitational lensing software. The techniques introduced here such as the image-plane analysis can prove to be useful for understanding the properties of other lens models as well.

Influence of Printing Interval on the Imbibition Behavior of 3D-Printed Foam Concrete for Sustainable and Green Building Applications

Foam concrete is highly valued as a sustainable cement-based material, but the development of 3D-printed foam concrete (3DPFC) has remained constrained. This study investigated the influence of printing interval on the microstructure and imbibition behavior of 3DPFC. The results revealed that horizontal interlayers are broader compared to vertical interlayers, leading to more significant imbibition. For X-oriented 3DPFC, the vertical interlayer was rapidly occupied by water after imbibition, forming an elliptical moisture profile. For Y-oriented 3DPFC, the moisture profile appeared more convoluted, mainly surrounding the horizontal interlayers but shifting at intersections with the vertical interlayers. In Z-oriented 3DPFC, where only tight horizontal interlayers were present, interlayer imbibition was almost negligible. Additionally, when the printing interval was less than 15 min, imbibition was primarily restricted to the top filament since the bottom filament was compacted by the filament above. Conversely, with a printing interval longer than 15 min, the bottom filament hardened before the setting of the top filament. This allowed the surface of the bottom filament to be compacted by the top filament, resulting in a dense interlayer that offers better resistance against imbibition compared to the matrix of 3DPFC. This work contributes to the advancement of green building technologies by providing insights into optimizing the 3D printing process for foam concrete, thereby enhancing its structural performance without compromising the designated air content and consistency of the foam concrete, facilitating a more efficient utilization of materials and a reduction in overall material consumption.

Variable-sagittal-radii elliptical x-ray crystal spectrometers for high-neutron-yield plasma diagnostics.

Sagittally focusing x-ray crystal spectrometers with elliptical profiles in the meridional (x-ray dispersion) plane are proposed for plasma diagnostics in experiments accompanied by high neutron yields. The spectrometers feature a variable sagittal radius of curvature to ensure the sagittal focusing of rays for each photon energy in a chosen detection plane. The detector is placed after the ray crossing point at the second ellipse focus, and the source-to-detector distance is maximized to reduce the neutron-induced background. The elliptical shape imposes a limitation on the spectrometer geometry such that the influence of the source size on the spectral resolution can be avoided only for a demagnifying spectrometer (the source-to-crystal distance is larger than that of crystal-to-detector). Hence, two designs are proposed. The first design, featuring high magnification and limited spectral resolution can be suitable for x-ray continuum spectroscopy. The second design of high demagnification is optimized for spectral resolution, and can be used for time-resolved spectroscopy of plasma's characteristic emission lines using streak cameras. The key performance characteristics of the two designs are verified using ray tracing.

Experimental Verification of a Modified Cylindrical Focused Laser Differential Interferometer

A modification to cylindrical focused laser differential interferometry (CFLDI) that, without beam intersection, can achieve smaller stand-off distances from flat geometries than conventional FLDI is presented. The modified system uses a cylindrical lens pair to expand and collimate the beam in a single direction, parallel to the model surface, forming a long, flat, elliptical profile. Subsequently, a spherical lens focuses the beam. Mach 7.3 hypersonic flow, produced by the T4 Stalker Reflected Shock Tunnel, was used for an experimental comparison between the responses of the modified CFLDI and a similar FLDI system in the freestream and just above the boundary-layer edge. Good agreement between the modified CFLDI and FLDI among all measured frequencies was observed when probing near the boundary-layer edge. The comparison in the freestream had good agreement up to 1500 kHz, and higher frequencies saw the modified CFLDI response attenuated at a shallower angle than the FLDI. A combination of different system parameters and base noise levels between the experiments is believed to account for this difference. The modified CFLDI system was used to probe inside the boundary layer, achieving a y/δ of approximately 0.4, where broadband turbulence is detected.

Tailored laser beam shapes for welding of copper using green laser radiation

AbstractThe rapid development of laser beam sources and adapted welding technologies in recent years lead to an increased use of laser welding techniques in automated production nowadays. Especially its precision and local energy input are key features for joining applications in electric vehicle components, where joints have to meet both mechanical and electrical requirements as current-carrying connections. However, the copper materials used are difficult to weld due to their physical properties, making a stable process with fewest seam imperfections only feasible within a limited process window. Recently available beam sources emitting visible laser radiation have proven to overcome the low absorptivity at process start, but spattering is still a prone defect significantly affecting process efficiency and quality. Literature approaches for modifying the energy input point to laser beam shaping as a method for reducing process imperfections, which, however, has not been extensively researched in copper processing using green laser radiation.Thus, this study investigates the influence of a shaped intensity profile for visible laser radiation created with a reflective diffractive optical element in laser beam welding with laser powers up to 3 kW. A characterization of the process dynamics is performed by use of high-speed imaging, and metallographic analysis is used to elaborate benefits of the applied beam shapes. With beam shaping, an enlarged heat conduction welding regime and an advantageous seam shape are found. Furthermore, a decrease in spatter formation during deep penetration welding is detected for the elliptical beam profile, which correlates with an oscillation movement of the capillary.

Manipulating melt pool thermofluidic transport in directed energy deposition driven by a laser intensity spatial shaping strategy

ABSTRACT A three-dimensional thermofluidic coupling transport model is proposed to investigate the influences of different spatial laser intensity profiles (SLIPs), including circular super-Gaussian profile (C-SGP), transverse elliptical Gaussian profile (TE-GP) and longitudinal elliptical Gaussian profile (LE-GP), on the thermofluidic transport characteristics within the melt pool. The results demonstrate that the SLIPs dramatically influence the melt pool geometries, temperature gradient (both in magnitude and direction) at the solidification interface, and fluid flow dynamics. Under the TE-GP strategy, the highest average temperature gradients are observed at the solidification interface. The LE-GP strategy yields the smallest magnitudes and narrowest variation range of the temperature gradient direction angles. The heat transport of the melt pool under the C-SGP and TE-GP strategies are jointly dominated by convective and conductive heat transfer, while those under the LE-GP strategy are dominated by convective heat transfer. Marangoni convection is strongest in the LE-GP strategy and weakest in the TE-GP strategy.

EXPERIMENTAL STUDY ON FLASH BOILING SPRAY OF HIGH-PRESSURE LIQUID AMMONIA JET WITH ROUND AND ELLIPTICAL HOLE NOZZLES

Ammonia is an ideal alternative fuel for mitigating carbon emissions. High-pressure direct injection of liquid ammonia (LNH<sub>3</sub>) offers significant advantages in enhancing energy efficiency and minimizing emissions. Due to the high saturation vapor pressure, the injection of LNH<sub>3</sub> is susceptible to flash boiling. In this study, we used high-speed micro-imaging technology with backlight lighting to establish a high-pressure common-rail LNH<sub>3</sub> jet experimental platform and investigate the flash boiling spray characteristics of nozzles with round and elliptical holes. The results demonstrated that under non-flash boiling conditions, the residual LNH<sub>3</sub> in the sac chamber and nozzle can rapidly corrode the acrylic material of the nozzle, leading to deformation and failure of the nozzle structure. Under flash boiling conditions, LNH<sub>3</sub> ejected from the hole will produce spherical macroscopic spray morphology. Then, the spray gradually transitions from an elliptical profile to a conical profile as the back pressure increases. Compared to nozzles with round holes, nozzles with elliptical holes exhibit higher flow velocity, which enhances oil-gas mixing and promotes more pronounced flash boiling phenomena. Flash boiling occurs at an earlier stage with an increase in the spray cone angle, thereby improving the atomization characteristics under both flash and non-flash boiling conditions. The tail jet of nozzles with elliptical holes terminates earlier while exhibiting a higher decrease rate in the average gray value, which improves the atomization quality in the tail spray stage and meets the requirements of timing, quantification, and precise control of the fuel injection system.

Bar properties as a function of wavelength: a local baseline with S4G for high-redshift studies

ABSTRACT The redshift evolution of bars is an important signpost of the dynamic maturity of disc galaxies. To characterize the intrinsic evolution safe from band-shifting effects, it is necessary to gauge how bar properties vary locally as a function of wavelength. We investigate bar properties in 16 nearby galaxies from the Spitzer Survey of Stellar Structure in Galaxies (S4G) at ultraviolet, optical, and mid-infrared wavebands. Based on the ellipticity and position angle profiles from fitting elliptical isophotes to the two-dimensional light distribution, we find that both bar length and ellipticity – the latter often used as a proxy for bar strength – increase at bluer wavebands. Bars are 9 per cent longer in the B band than at 3.6 μm. Their ellipticity increases typically by 8 per cent in the B band, with a significant fraction (>40 per cent) displaying an increase up to 35 per cent. We attribute the increase in bar length to the presence of star-forming knots at the end of bars: these regions are brighter in bluer bands, stretching the bar signature further out. The increase in bar ellipticity could be driven by the apparent bulge size: the bulge is less prominent at bluer bands, allowing for thinner ellipses within the bar region. Alternatively, it could be due to younger stellar populations associated with the bar. The resulting effect is that bars appear longer and thinner at bluer wavebands. This indicates that band-shifting effects are significant and need to be corrected for high-redshift studies to reliably gauge any intrinsic evolution of the bar properties with redshift.

Phenomenological emergent dark energy versus the ΛCDM: ellipticity of cosmic voids

ABSTRACT We disclose the influences of the phenomenological emergent dark energy (PEDE) and its generalization (GEDE) on the distribution of tidal ellipticity of the cosmic voids. We also compare our results with that of the standard ΛCDM cosmology. The underlying models consist with recent observations (specially in favour of H0 tension) and may impact the cosmic voids geometry. We employ the analytic approach based on statistics of the tidal tensor eigenvalues. We confirm a significant sensitivity of the ellipticity distribution function for PEDE and GEDE cosmology. We observe the largest deviation from the standard cosmology for GEDE in the range ($z\gt 0, R_{\mathrm{L}}\ge 4\, h^{-1}\, \mathrm{Mpc}$). Working on these distribution functions we reveal that the mean ellipticity (〈ε〉) profile of GEDE versus redshift lies below than that of PEDE and ΛCDM indicating that GEDE leads to a less elongated society of voids with respect to other models. We also identify a tight correlation between σ8 and the mean ellipticity evolution. Finally, we explore the mean ellipticity versus RL and estimate that in this case GEDE leads to a different ellipticity curve (up to 11 ${{\ \rm per\ cent}}$ smaller than that of ΛCDM).

Turbulent flow of a shear-thinning non-Newtonian CMC-based nanofluid in twisted finned tubes with an elliptical profile

In this article, the forced convective turbulent flow of a shear-thinning non-Newtonian nanofluid through twisted tubes with elliptical cross sections is numerically studied and analyzed at various Reynolds numbers. The base fluid of the studied nanofluid is 0.5% carboxymethyl cellulose solution in water (which has non-Newtonian behavior of shear-thinning), and it contains copper oxide nanoparticles. Two types of twisted tubes are considered: finned tubes and unfinned ones. The finite volume method is utilized, and the two-equation model of k-ε has been applied to analyze the flow characteristics of the turbulent problem. The computational results demonstrate an excellent agreement with respect to already published reports, which is a testament to our reasonable and correct procedure. The effects of pipe wall twisting on the average Nusselt number have been investigated. The achievements demonstrate a powerful secondary and rotating flow is formed with the tube surface twisting. This secondary flow causes better mixing and increases the average Nusselt number. The increase is up to 45% for the unfinned case and 62% for the finned case in comparison with the tube without projections. In addition, the coefficient of friction in these pipes increases to 62% and 104% for the unfinned and finned tubes, respectively. It is also observed that by increasing the length of the fin and adding nanoparticles up to 1.5%, the highest value of the performance evaluation criterion (i.e. 1.78) in the twisted finned tube could be achieved, which occurred at the Reynolds number of 4000. The combination of present geometry and the working fluid of shear-thinning non-Newtonian CMC-based nanofluid is the main novelty of this work, and the results can be applicable and reliable in the relevant industries.

Shear Wave Ultrasound Inspection of Flaws in Silicon Wafers using Focused Transducers.

Silicon parts can contain micrometer-sized vertical cracks that are challenging to detect. Inspection using high-frequency focused ultrasound has shown promise for detecting defects of this size and geometry. However, implementing focused ultrasound to inspect anisotropic media can prove challenging, given the directional dependence of wave propagation and subsequent focusing behavior. In this work, back surface-breaking defects at various orientations within silicon wafers (0-, 15-, and 45-degrees relative to the [010] crystallographic axis) are experimentally inspected in an immersion tank setup. Using 100 MHz unfocused and focused shear waves, the impact of medium anisotropy on focusing and defect detection is evaluated. The scattering amplitude and defect detection sensitivity results demonstrate orientation-dependent patterns that strongly rely on the use of focused transducers. The defects along the 45-degree orientation reveal two-lobe scattering patterns with maximum amplitudes less than half that of the defects in the 0-degree orientation, which in contrast show a one-lobe scattering pattern. The experimental results are further explored using Finite Element (FE) modeling and ray tracing to visualize the impact of focusing on wave propagation within the silicon. Ray tracing results show that the focused beam profiles for the 45- and 0-degree orientations form a butterfly wing and elliptical focusing profile, respectively, which correspond directly to experimentally found scattering patterns from defects. Additionally, the FE scattering results from unfocused transducers reveal single lobe scattering for both 0- and 45-degree orientations, proving the varying scattering patterns to be driven by the anisotropic focusing behavior.

Trajectory generation based on power for urban air mobility

A method of generating trajectories based on power is proposed for Urban Air Taxis. The method is simpler and more direct than traditional methods because it does not require a detailed aircraft model or a flight control model. Instead, it allows the user to specify the route, the static longitudinal profile (altitude as a function of distance), and a power model to determine the progress in time along that profile. The power model can be determined from a recorded or simulated trajectory of the same aircraft type. This capability allows a trajectory to be generated or reshaped to avoid conflicts while preserving the basic performance characteristics. Net or excess power is defined as the rate of change of mechanical (kinetic and potential) energy, and it is modeled as a function of airspeed. The time steps between discrete points in space along the trajectory are used to yield a specified power as a function of airspeed, and they are determined by solving a cubic polynomial at each point. An elliptical profile is used to generate an example trajectory. The dependence of trip flight time on various parameters is analyzed and plotted.

Radiation enhancement of a broadband resistively loaded dipole with an overlapping ellipses profile for impulse application

This paper presents a broadband resistively loaded modified dipole (RLMD) with an overlapping ellipses profile for radiation enhancement of impulse systems. Based on the equivalent circuit model, a simple method is introduced and analyzed to improve the impedance matching performance of a printed resistively loaded dipole (RLD) by replacing the metal strip with an elliptical profile metal strip. Following this method, a tapered resistively loaded dipole consisting of several resistors and equally separated metal strips with a profile of three overlapping ellipses is proposed. To further improve the impedance matching performance of the proposed antenna, the normalized Euclid distance (NED) is employed to vary the size and position of each ellipse. To verify the performance, the proposed antenna is fabricated and measured. The measured reflection coefficient of the antenna covers from 390 MHz to 10 GHz, which is consistent with the simulated results. In addition, the transmission performance of the proposed antenna is analyzed in the time domain by measuring it with two identical antennas. The received signal amplitude of RLMD is 5.74 dB higher than that of RLD, which is consistent with the simulated results. Therefore, the proposed antenna is appropriate for enhancing the radiation performance of impulse systems.

High-efficiency broad-linewidth widely-tunable mid-infrared OPO based on fan-out PPLT

We reported a high-efficiency, broad-linewidth, wide-tuning-range singly-resonated optical parametric oscillator (OPO) based on a fan-out PPLT crystal. When the PPLT crystal was operated at 120 °C and pumped by Q-switched 1064 nm laser at 14.17 W with a circular pump profile, the overall output power of OPO was 7.22 W (η = 50.4%) for both the signal and idler waves. The central wavelength and linewidth of the mid-infrared (MIR) laser were 3770 nm and ∼40 nm. A wavelength tuning range of 3538–3941 nm was accomplished by adjusting the crystal period through simple mechanical movement. Due to the larger coverage of gratings with an elliptical pump profile, the output linewidth of the MIR laser was further broadened to ∼100 nm, which is ten times more than other non-fan-out PPLT OPOs. Both pumping methods with different profiles were operated at 30 kHz, 49.2 ns for the 1064 nm laser, the power fluctuation of the obtained MIR laser was within 3.5%.

Torsional static and vibration analysis of a non-circular restrained micro/nanowire

This paper aims to study the static and free torsional vibration of non-circular micro/nanowires using the modified couple stress theory with several deformable and non-deformable support conditions. The geometrical properties of the micro/nanowires are considered to have triangular, elliptical and circular profiles. Equation of motion in torsional direction is derived based on torsional equilibrium and systems of linear equations are computed by adopting Fourier sine series with Stokes’ transformation. Moreover, deformable boundary conditions have been taken into account to formulate eigenvalue problem by employing the higher-order force boundary conditions. Material length scale parameter and the shape of cross-section have considerable impacts on torsional vibration frequencies of restrained microwire. The obtained frequency curves of restrained microwires are shown to be dependent on various parameters such as the shape of cross-section, deformable boundaries, material length scale parameter and also warping function.

Application of Elliptic Jerk Motion Profile to Cartesian Space Position Control of a Serial Robot

The paper discusses the application of a motion profile with an elliptic jerk to Cartesian space position control of serial robots. This motion profile is obtained by means of a kinematic approach, starting from the jerk profile and then calculating acceleration, velocity and position by successive integrations. Until now, this profile has been compared to other motion laws (trapezoidal velocity, trapezoidal acceleration, cycloidal, sinusoidal jerk, modified sinusoidal jerk) considering single-input single-output systems. In this work, the comparison is extended to nonlinear multi-input multi-output systems, investigating the application to Cartesian space position control of serial robots. As case study, a 4-DOF SCARA-like architecture with elastic balancing is considered; both an integer-order and a fractional-order controller are applied. Multibody simulation results show that, independently of the controller, the behavior of the robot using the elliptic jerk profile is similar to the case of adopting the sinusoidal jerk and modified sinusoidal jerk laws, but with a slight reduction in the position error (−3.8% with respect to the sinusoidal jerk law and −0.8% with respect to the modified sinusoidal jerk law in terms of Integral Square Error) and of the control effort (−8.2% with respect to the sinusoidal jerk law and −1.3% with respect to the modified sinusoidal jerk law in terms of Integral Control Effort).

Aerodynamic analysis of a 2-stage elliptical-bladed Savonius wind rotor: Numerical simulation and experimental validation

ABSTRACT The Savonius rotor is a type of vertical-axis wind turbine that utilizes drag to generate power. Its design simplicity and ability to self-start at low wind speeds make it an attractive option for small-scale wind energy generation. Previous research has focused on optimizing the geometric configuration of a 1-stage, 2-bladed rotor with semicircular blade profiles to improve its performance and mitigate negative torque. However, limited research has been conducted on 2-stage, 2-bladed Savonius rotors with elliptical blade profiles. The present investigation aims to fill this research gap by evaluating the aerodynamic characteristics of a 2-stage, 2-bladed Savonius rotor with elliptical profiles. 3D unsteady simulations using the SST k-ω turbulence model in ANSYS Fluent are conducted to evaluate the performance coefficients over a range of tip speed ratios. The numerical results are validated through wind tunnel experiments. The results show that the CPmax (maximum power coefficient) for the 1-stage rotor is 0.19 and 0.12 for numerical and experimental analyses, respectively. For the 2-stage rotor, the CPmax is 0.21 and 0.17 for numerical and experimental analyses, respectively. These findings suggest that the 2-stage rotor with elliptical profiles has the potential to efficiently harness wind energy.

Numerical investigation of aerodynamic performance of an axial fan blade equipped with vortex generators

Delay in the onset of static stall via passive vortex generators (VGs) results in more efficient equipment. Nevertheless, most studies of VGs are conducted on wind turbine blades rather than other turbomachinery devices like axial fan blades. This study is feasibility research to see whether the aerodynamic performance of axial fan blades improves in the presence of VGs. Therefore, the VGs' effect of a static blade with an elliptical profile having a maximum thickness of 8% chord length and without a twist angle is investigated. Fully resolved RANS (Reynolds-averaged Navier–Stokes) simulation with the shear stress transport k–ω turbulence model at Re = 1 × 105 is used to discover the blade flow characteristics with VGs for two types of fan, eight and twelve blades. It is shown that, in both fans, not only can implementing VGs improve the aerodynamic performance of the blade effectively but also the separation phenomenon is delayed. Furthermore, it is concluded that installing VGs performed better in the 8-blade fan, with up to a 3° separation delay, a 9.88% increase in the maximum lift coefficient, and a 48.15% decrease in the maximum drag coefficient with respect to the clean blade. Analyzing the aerodynamic performance of real axial fans considering rotary blades with twist angles equipped with VGs will be feasible in future research.

Исследование перетеканий в двухроторном вакуумном насосе типа Рутс с эллиптическим профилем роторов при молекулярном режиме течения газа

A Roots-type two-rotor vacuum pump with the rotors’ elliptical profile was designed, developed and manufactured. Its channels conductivity was measured experimentally at various angles of the rotors’ rotation and pressures. Experimental conductivity of the channels was determined in the flow molecular regime. Using the angle factor method implemented in the COMSOL Multiphysics package calculated values of the channel conductivity were obtained for a two-rotor vacuum pump. Deviations in calculated data from the experimental data were not exceeding 10%. Verification and validation of analytical expressions for conductivity of the non-contact pump slot channels demonstrated possibility of their application in mathematical models of the working process of the two-rotor vacuum pumps.

Precision Modeling of JWST's First Cluster Lens SMACS J0723.3–7327* *Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs GO-11103, GO-12166, GO-12884, GO-1409; and on observations made with the

Exploiting the fundamentally achromatic nature of gravitational lensing, we present a lens model for the massive galaxy cluster SMACS J0723.3−7323 (SMACS J0723; z = 0.388) that significantly improves upon earlier work. Building on strong-lensing constraints identified in prior Hubble Space Telescope (HST) observations, the mass model utilizes 21 multiple-image systems, 17 of which were newly discovered in Early Release Observation data from the JWST. The resulting lens model maps the cluster mass distribution to an rms spatial precision of 0.″32, and is publicly available. Consistent with previous analyses, our study shows SMACS J0723.3 to be well described by a single large-scale component centered on the location of the brightest cluster galaxy. However, satisfying all lensing constraints provided by the JWST data, the model points to the need for the inclusion of an additional, diffuse component west of the cluster. A comparison of the galaxy, mass, and gas distributions in the core of SMACS J0723 based on HST, JWST, and Chandra data reveals a concentrated regular elliptical profile along with tell-tale signs of a recent merger, possibly proceeding almost along our line of sight. The exquisite sensitivity of JWST’s NIRCam reveals in spectacular fashion both the extended intracluster light distribution and numerous star-forming clumps in magnified background galaxies. The high-precision lens model derived here for SMACS J0723 demonstrates the unprecedented power of combining HST and JWST data for studies of structure formation and evolution in the distant universe.