Search Results (28)

Near-nozzle atomization characteristics in air-assisted spraying were investigated through a novel 3D transient model integrating Volume-of-Fluid and Large Eddy Simulation (VOF-DPM) methods, with experimental validation of droplet distributions (Malvern analyzer) and coating thickness profiles. Key findings reveal that (1) the spray field stabilizes within 30 mm downstream, achieving 80% atomization efficiency (droplets ≤ 100 μm) at 27.5 mm axial distance; (2) radial momentum originates dually from fan-shaped airflow (max 595 m/s) and transverse motion induced by central atomizing air entrainment—a previously unreported mechanism; (3) paint loading delays flow stabilization to 2.5 ms (vs. 0.7 ms for gas-only flow) while reducing peak axial velocity by 18%–22% due to gas–liquid momentum exchange; (4) auxiliary and fan airflows synergistically constrain dispersion, forming elliptical sprays with characteristic cone angles of 61.7° (short axis) and 99.1° (long axis). Significantly, surface tension plays a dual role in inhibiting droplet atomization while promoting ligament pinch-off at 8.1 mm breakup length. These results provide the first quantitative characterization of gas–liquid interactions in near-nozzle regions, enabling precise parameter control for enhanced coating uniformity on complex surfaces. Full article

This paper investigates the three-dimensional target localization problem in satellite–ground bistatic radar. In conventional bistatic radar systems, passive receivers struggle to directly acquire the altitude information of the target, making it difficult to achieve effective three-dimensional target localization. This paper uses the bistatic distance data obtained after signal processing to construct ellipsoidal constraints, thereafter combining azimuth data to compress the position solution space into a three-dimensional elliptical line. Introducing the assumption of short-term linear uniform motion of the target, the target trajectory and elliptical line constraints are projected onto a two-dimensional plane, establishing an optimization model to determine the target trajectory parameters, ultimately yielding the target’s three-dimensional coordinates and completing the positioning process. The simulation results demonstrate the efficacy and performance of the proposed method. Full article

A novel nested structure of hollow-core anti-resonant optical fiber is proposed to achieve low loss, large effective mode area, and wide transmission band simultaneously in the near-infrared range of 1200–2200 nm. It is composed of six elliptical cladding tubes nested with six large circular cladding tubes, and six small circular cladding tubes are introduced in the gap of the elliptical tubes. The transmission characteristics of the hollow-core anti-resonant optical fiber are numerically investigated using the full-vector finite element method. The effects of structural parameters such as the cladding tube thickness and the tube diameters on the fiber transmission characteristics are analyzed in detail. The results indicate that within the wavelength range of 1200–2200 nm, the confinement loss remains below 0.017 dB/km, and the minimum confinement loss can be as low as 1.2 × 10⁻⁴ dB/km at 1500 nm. The effective mode area remains as large as ~1142.5 μm². It should be noted that in the wide wavelength range of 1000 nm, the dispersion exhibits excellent characteristics ranging from 0.7 to 1.4 ps/(nm·km). Our fiber can find potential applications in ultra-long-distance and ultra-high-power transmission systems with a wide operating wavelength band. Full article

During the last 15–20 years, the experimental methods for autonomous navigation and inter-satellite links have been developing rapidly in order to ensure navigation control and data processing without commands from Earth stations. Inter-satellite links are related to relative ranging between the satellites from one constellation or different constellations and measuring the distances between them with the precision of at least 1 $\mathsf{\mu }$m micrometer (=${10}^{-6}$ m), which should account for the bending of the light (radio or laser) signals due to the action of the Earth’s gravitational field. Thus, the theoretical calculation of the propagation time of a signal should be described in the framework of general relativity theory and the s.c. null cone equation. This review paper summarizes the latest achievements in calculating the propagation time of a signal, emitted by a GPS satellite, moving along a plane elliptical orbit or a space-oriented orbit, described by the full set of six Kepler parameters. It has been proved that for the case of plane elliptical orbit, the propagation time is expressed by a sum of elliptic integrals of the first, the second and the third kind, while for the second case (assuming that only the true anomaly angle is the dynamical parameter), the propagation time is expressed by a sum of elliptic integrals of the second and of the fourth order. For both cases, it has been proved that the propagation time represents a real-valued expression and not an imaginary one, as it should be. For the typical parameters of a GPS orbit, numerical calculations for the first case give acceptable values of the propagation time and, especially, the Shapiro delay term of the order of nanoseconds, thus confirming that this is a propagation time for the signal and not for the time of motion of the satellite. Theoretical arguments, related to general relativity and differential geometry have also been presented in favor of this conclusion. A new analytical method has been developed for transforming an elliptic integral in the Legendre form into an integral in the Weierstrass form. Two different representations have been found, one of them based on the method of four-dimensional uniformization, exposed in the monograph of Whittaker and Watson. The result of this approach is a new formulae for the Weierstrass invariants, depending in a complicated manner on the modulus parameter q of the elliptic integral in the Legendre form. Full article

Plasmon chirality has garnered significant interest in sensing application due to its strong electromagnetic field localization and highly tunable optical properties. Understanding the effects of mode coupling in chiral structures on chiral optical activity is particularly important for advancing this field. In this work, we numerically investigate the circular dichroism (CD) of elliptical nanodisk dimers arranged in an up-and-down configuration with a specific rotation angle. By adjusting the inter-particle distance and geometric parameters, we introduce the coupling between dipole and electric hexapole modes, forming an extended Born–Kuhn model that achieves strong CD. Our findings show that the coupling of dipole modes with electric hexapole modes in elliptical nanodisks can also show obvious Fano resonance and a strong CD effect, and the structure with the largest Fano asymmetry factor shows the highest CD. In addition, CD spectroscopy is highly sensitive to changes in the refractive index of the surrounding medium, especially in the visible and near-infrared regions, highlighting its potential for application in high-sensitivity refractive index sensors. Full article

For low-permeability reservoirs, water-flooding development is usually adopted, which leads to induced fractures near the wellbore, increasing reservoir heterogeneity, and making water-flooding development more complex. This paper focuses on low-permeability reservoirs, considering the characteristics of induced fractures and elliptic-flow composite, and the well-test model for injection wells is established. The mathematical model in Laplace space is obtained through dimensionless transformation and Laplace transformation. Subsequently, the Mathieu function is introduced to obtain the bottom hole pressure, and the pressure response curve is drawn. The six flow stages of the curve are defined, and the sensitivity of parameters such as half-length of induced fractures, range of lateral-swept area, permeability in unswept area, and outer boundary distance at constant pressure are analyzed. The results show that the half-length of the fracture mainly affects the linear flow of the fracture, the range of the lateral wave-affected area mainly affects the radial flow of the swept area, the permeability of the unswept area mainly affects the radial flow of the unswept area, and the outer boundary distance at constant pressure mainly affects the boundary flow. Based on the production performance of a certain injection well in J Oilfield, a series of key parameters are obtained through analytical solution model inversion, including the induced-fracture half-length of 10.32 m, the lateral-swept range of elliptic partition flow of 128.95 m, the permeability of the swept area of 6.87 mD, and the mobility ratio of 119.92, which show the superiority of the analytical solution model. Full article

Geometric shape models often help to extract specific contours in digital images (the segmentation process) with major precision. Motivated by this idea, we introduce two models for the representation of prostate shape in the axial plane of magnetic resonance images. In more detail, the models are two parametric closed curves of the plane. The analytic study of the models includes the geometric role of the parameters describing the curves, symmetries, invariants, special cases, elliptic Fourier descriptors, conditions for simple curves and area of the enclosed surfaces. The models were validated for prostate shapes by fitting the curves to prostate contours delineated by a radiologist and measuring the errors with the mean distance, the Hausdorff distance and the Dice similarity coefficient. Validation was also conducted by comparing our models with the deformed superellipse model used in literature. Our models are equivalent in fitting metrics to the deformed superellipse model; however, they have the advantage of a more straightforward formulation and they depend on fewer parameters, implying a reduced computational time for the fitting process. Due to the validation, our models may be applied for developing innovative and performing segmentation methods or improving existing ones. Full article

We derive the analytical expressions for root-mean-square (rms) beam wander (BW) and relative BW of a twisted electromagnetic elliptical vortex (TEEV) beam propagating through non-Kolmogorov atmospheric turbulence with the help of the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF). Our numerical findings demonstrate that the BW of a TEEV beam with a small ellipticity, a large topological charge as well as a small waist width and initial coherent length is less affected by the turbulence. It can be also found that the effect of turbulence with a larger outer scale of turbulence, a generalized exponent parameter, and a generalized structure parameter on BW is more obvious. It is interesting to find that the effect of atmospheric turbulence on BW for a TEEV beam can be effectively reduced by regulating jointly the symbols and sizes of the twisted factor and topological charge. Therefore, modulation of the structure parameters of a TEEV beam provides a new way to mitigate turbulence-induced beam wander. Our work will be useful for free-space optical communications, remote sensing, and lidar distance measurement. Full article

One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the parameters of the so-called shadow ellipse, the characteristics of the oblique ellipse (the cut) and, finally, the projection of the vertex of the cone onto the oblique ellipse. This paper shows that it is possible to compute that volume just by using the information of the shadow ellipse and the height of the cone. Indeed, the finite slant cone has the same volume of an elliptic right cone, with the base being the shadow ellipse of the cut portion and with the height being the distance between the vertex of the cone and the intersection of the height of the original cone with the cutting plane. This is proved by introducing a volume-preserving shear transformation of the elliptical slant cone to a right cone, so that the standard volume formula for a cone can be straightforwardly applied. This implies a simplification in the procedure for computing the volume, since the oblique ellipse—i.e., the difficult part—can be neglected because only the shadow ellipse needs to be determined. Full article

The main feature of elliptical space—the topological identification of its antipodal points—could be fundamental for understanding the nature of the cosmological redshift. The physical interpretation of the mathematical (topological) structure of elliptical space is made by using physical connections in the form of Einstein-Rosen bridges (also called “wormholes”). The Schwarzschild metric of these structures embedded into a dynamic (expanding) spacetime corresponds to McVittie’s solution of Einstein’s field equations. The cosmological redshift of spectral lines of remote sources in this metric is a combination of gravitational redshift and the time-dependent scale factor of the Friedmann-Lemaitre-Robertson-Walker metric. I compare calculated distance moduli of type-Ia supernovae, which are commonly regarded as “standard candles” in cosmology, with the observational data published in the catalogue “Pantheon+”. The constraint based on these accurate data gives a much smaller expansion rate of the Universe than is currently assumed by modern cosmology, the major part of the cosmological redshift being gravitational by its nature. The estimated age of the Universe within the discussed model is $1.48·{10}^{12}$ yr, which is more than two orders of magnitude larger than the age assumed by using the standard cosmological model parameters. Full article

Entrepreneurs carrying out mining works under seismic hazard conditions are obliged to conduct studies in the field of engineering geophysics, including measuring, interpreting and evaluating the effects of rock mass tremors on ground vibration parameters, and thus the occurrence of harmful impacts on surface objects. However, for technical reasons, this is a difficult task to implement at all points subject to the influence of mining activities. Therefore, it becomes expedient to look for solutions that would provide greater accuracy in forecasting the distribution of ground vibration parameters. This paper proposes a method for forecasting the distribution of peak ground accelerations (PGAs) induced by mining activities, taking into account the directionality of vibration attenuation. In many cases, the explanation of the variation in the magnitude of recorded ground surface vibrations after a rock mass tremor cannot always be explained by only the variation of epicentral distances and the value of the vibration amplification factor by quaternary formations. Therefore, it is reasonable to take into account the directionality of vibration attenuation. The authors analyzed and evaluated the accuracy of predicting the distribution of ground vibration accelerations induced by mining activities, taking into account the directionality of vibration attenuation, using three models: the first, a classical model assuming isotropic vibration attenuation; the second, a model taking into account the anisotropy of vibration attenuation with elliptical isolines; the third, a model without assuming the shape of the isolines of vibration intensity parameters. For both models that took into account anisotropy of vibration attenuation, better results (more accurate descriptions of observed ground vibration accelerations) were obtained than for the model assuming isotropy. The most accurate estimates of vibration magnitude were obtained using the latter model. Full article

In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained using the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion. Full article

At present, a large number of two-degree-of-freedom piezoelectrically driven compliant mechanisms (2-DOF PDCMs) have been widely adopted to construct various elliptical vibration machining (EVM) devices employed in precisely fabricating functional micro-structured surfaces on difficult-to-cut materials, which have broad applications in many significant fields like optical engineering and precision manufacturing. For a higher precision of conventional 2-DOF PDCMs on tracking elliptical trajectories, a novel type of pseudo-decoupling method is proposed based on phase difference compensation (PDC). With finite element analysis (FEA), the dependences of elliptical trajectory tracking precision on PDC angles will then be investigated for optimizing PDC angles under different elliptical parameters. As the modification of the PDC-based method, another type of pseudo-decoupling method will be improved based on elliptical parameter compensation (EPC) for much higher tracking precision, an amplification coefficient and a coupling coefficient will be introduced to mathematically construct the EPC-based model. A series of FEA simulations will also be conducted on a conventional 2-DOF PDCM to calculate the amplification and coupling coefficients as well as optimize the EPC parameters under four series of elliptical parameters. The tracking precision and operational feasibility of these two new pseudo-decoupling methods on four series of elliptical trajectories will be further analyzed and discussed in detail. Meanwhile, a conventional 2-DOF PDCM will be practically adopted to build an experimental system for investigating the pseudo-decoupling performances of an EPC-based method, the input and output displacements will be measured and collected to actually calculate the amplification coefficients and coupling coefficients, further inversely solving the actual input elliptical parameters with EPC. The error distances between the expected and experimental elliptical trajectories will also be calculated and discussed. Finally, several critical conclusions on this study will be briefly summarized. Full article

Simulated raw data have become an essential tool for testing and assessing system parameters and imaging performance due to the high cost and limited availability of real raw data from spaceborne synthetic aperture radar (SAR). However, with increasing resolution and higher orbit altitudes, existing simulation methods fail to generate SAR simulated raw data that closely resemble real raw data. This is due to approximations such as curved orbits, “stop-and-go” assumption, and Earth’s rotation, among other factors. To overcome these challenges, this paper presents an accurate range model with a “nonstop-and-go” configuration for raw data simulation based on existing time-domain simulation methods. We model the SAR echo signal and establish a precise space geometry for spaceborne SAR. Additionally, we precisely identify the target illumination area based on elliptical beams through space coordinate transformation. Finally, the SAR raw data were accurately simulated using high-precision time-domain simulation methods. The accuracy of the proposed model was validated by comparing it with the traditional hyperbolic model and the curved orbit model with “stop-and-go” assumption through image processing of the generated raw data. Through the analysis of point target quality parameters, the errors of various parameters in our distance model compared with the other two models are within 1%. Furthermore, this simulation method can be adapted to simulate raw data of other modes and satellite orbits by adjusting beam control and satellite orbit parameters, respectively. The proposed simulation method demonstrated high accuracy and versatility, thereby providing a valuable contribution to the development of remote sensing technology. Full article

The traditional ship collision risk index model based on the distance at the closest point of approach (DCPA) and the time to the closest point of approach (TCPA) is insufficient for estimating ship collision risk and planning collision avoidance operations. This paper constructs an elliptical, dynamic ship domain that changes with ship speed and maneuverability parameters to overcome subjective human factors. Based on the constructed domain model, the concept of the ship domain proximity factor is introduced to improve the ship collision risk model based on DCPA and TCPA, and a risk calculation function model that considers the safety of ship navigation is constructed. The numerical calculation of the improved collision risk index calculation model confirms that the enhanced model has a higher rate of identification of risk between ships. The model is more compatible with the requirements of ship navigation decision-making and can provide theoretical support and a technical basis for research on ship collision avoidance decision-making. Full article