Search Results (76)

For crop protection, electrostatic spraying technology significantly improves deposition uniformity and pesticide utilization through the “wraparound-adsorption” effect of charged droplets. However, existing electrostatic nozzles using hydraulic atomization suffer from low charge-to-mass ratios due to unclear principles for optimizing electrode parameters. To this end, this study designs and evaluates a novel air-assisted hydraulic-atomization hollow-cone electrostatic nozzle. First, the air-assisted hollow-cone nozzle was designed. High-speed imaging was then employed to obtain morphological parameters of the liquid film (length: 2.14 mm; width: 1.96 mm; and spray angle: 49.25°). Based on these parameters, an electric field simulation model of the electrostatic nozzle was established to analyze the influence of electrode parameters on the charging performance and identify the optimal parameter combination. Finally, feasibility and efficiency evaluation experiments were conducted on the designed electrostatic nozzle. The experimental results demonstrate that cross-sectional dimensions of the electrode exhibit a positive correlation with the surface charge density of the pesticide liquid film. In addition, optimal charging performance is obtained when the electrode plane coincides with the tangent plane of the liquid film leading edge. Based on these charging laws, the optimal electrode parameters were determined as follows: 2.0 × 2.0 mm cross-section with an electrode-to-nozzle tip distance of 3.8 mm. With these parameters, the nozzle achieved a droplet charge-to-mass ratio of 4.9 mC/kg at a charging voltage of 3.0 kV. These charged droplets achieved deposition coverages of 12.19%, 5.72%, and 5.91% on abaxial leaf surfaces in the upper, middle, and lower soybean canopies, respectively, which is a significant improvement in deposition uniformity. This study designed a novel air-assisted hollow-cone electrostatic nozzle, elucidated the optimization principles for annular induction electrodes, and achieved improved spraying performance. The findings contribute to enhanced pesticide application efficiency in crops, providing valuable theoretical guidance and technical references for electrostatic nozzle design and application. Full article

This paper presents a compact monopole wideband antenna based on DGS. The ultimate geometry of the designed antenna is obtained after many design modifications and optimizations. A commercially available Taconic TLY substrate with a dielectric constant (ε_r) = 2.2, loss tangent (tan δ) = 0.0009, and thickness (h) of 1.524 mm is used. The dimension of the substrate is 34 mm × 28 mm. A 50Ω microstrip transmission line of size 12 mm × 3 mm is used to feed the antenna. Simulation results demonstrate a bandwidth from 4.08 to 18.92 GHz, a percentage bandwidth of 129% for S11 < −10 dB, and a peak gain of 7.4 dB. The DGS slots are embedded into the ground plane to enhance the antenna’s bandwidth, impedance matching, gain, and efficiency. For verification, the proposed antenna is fabricated and measured. Good agreement between measured and simulated results is observed. Thus, this antenna is appropriate for various modern wireless communication systems. Full article

In this paper, a global amplitude-controlled discrete hyperchaotic memristive map is designed utilizing the hyperbolic tangent function. This map exhibits fixed points arranged in a line along the y-axis, and the stability distributions of these fixed points are delineated based on variations in both the initial conditions of the map and the parameter plane. The dynamic characteristics of the map were examined through the analysis of its 2D dynamics and the largest Lyapunov exponent (LE) distribution. The existence of multistability was robustly confirmed through a comprehensive analysis of the basin of attraction, the spectra of LE that depend on initial values, bifurcation diagrams, and trajectory plots. Additionally, the amplitude of the map can be adjusted both globally and locally through manipulation of the non-bifurcation parameter. Subsequently, a digital circuit powered by a microcontroller was designed to embody the map. In comparison to recent maps, the newly devised map exhibits superior efficacy in the realm of image encryption applications. Full article

Trigonometric functions are widely used to express relationships between the sides and angles of triangles, being fundamental in a wide variety of fields in science and engineering. Previous research indicates that the Gudermann function connects hyperbolic and trigonometric functions without requiring complex numbers, while the Mercator projection maps the Earth’s spherical surface onto a cylindrical plane. This article presents four key contributions derived from hyperbolic functions, with the main proof applying Newton’s first law in the static case of cables. First, a new method relates right triangle formulas to the sides of a right triangle, facilitating vector decomposition along the X and Y axes. Second, a right triangle function with a hyperbolic angle is proposed, relating the three sides of a right triangle and the hyperbolic angle, offering an alternative to the Pythagorean theorem. Third, the law of hyperbolic cosines and the law of hyperbolic tangents is applied to trigonometric problems. Fourth, the hyperbolic Mollweide’s formula is used to solve oblique triangles. These results demonstrate the potential of hyperbolic transformations in engineering and mathematical contexts, for both education and research. Future investigations should include experimental and analytical tests to further extend the applications to all branches based on mathematics. Full article

This article presents a new design for a dual-band circular polarization microstrip patch antenna that can be used in unmanned aerial vehicle (UAV) applications. The proposed antenna consists of an etched circular shape on the radiator side of the antenna with multiple slots and stubs. The bottom side comprises a partial ground plane with multiple horizonal, vertical and square slots. These shapes on the front and bottom sides of the antenna are used to keep the resonant frequencies, impedance bandwidth and axial ratio (AR) at the desired values. The antenna operation is within the WiFi frequency bands, achieving maximum gains of 5.01 and 5.27 dBi at 2.4 and 5 GHz, respectively. Circular polarization (CP) is effectively realized through the implementation of opposite truncated corners and intentionally located stubs. The 3 dB axial ratio bandwidth (ARBW) is significantly enhanced, while a defected ground structure (DGS) is utilized to further improve the bandwidth and gain. The optimized antenna has overall dimensions of 40 × 40 × 1.6 mm³ and demonstrates a wide −10 dB reflection bandwidth of 5.38% (2.396–2.525 GHz) and 9.26% (4.91–5.38 GHz), along with a broad 3 dB axial ratio bandwidth (ARBW) of 380 MHz (2.29–2.67 GHz) and 80 MHz (5–5.08 GHz). The proposed antenna is fabricated using a low-cost FR-4 substrate with a dielectric constant of 4.4 and a loss tangent of 0.02. The fabricated antenna is experimentally characterized to verify the design concept as well as to validate the simulation results. It is found that the experimental measurements correlate very well with the simulation results. A comparison with comparable designs in the literature shows that the proposed antenna provides a higher gain with a relatively reduced size. Full article

In this article, we study how a linear polarized wave that is going along an optical fiber works, which is known not only as a curve on a Lie group but also as a rotation of the polarization plane. What we are trying to show in this article is that linear polarized light waves ($\mathcal{PLW}$s) are related to the Berry phase. Moreover, we give magnetic curves created by $\mathfrak{N}$ traveling in the electromagnetic trajectories and the optical fiber generated by the electric field $\mathfrak{N}$ of the $\mathcal{PLW}$ moving through the optical fiber. With this described method, we present a mathematical model to conveniently generate the relationships between an optical fiber and the optical angular momentum in a three-dimensional Lie group. The conjugate frame we used in this article removes unnecessary bending around the tangent and enables a more dynamic characterization, which can still be applied even when the second derivative of the curve is zero. Full article

This study introduces a technique for determining surface orientations by projecting a monochrome, spatial pixel-encoded pattern and calculating the surface normals from single-shot measurement. Our method differs from traditional methods, such as shape from shading and shape from texture, in that it does not require relating the local surface orientations of adjacent points. We propose a multi-resolution system incorporating symbols varying in sizes from 8 × 8, 10 × 10, 12 × 12, 14 × 14, and 16 × 16 pixels. Compared to previous methods, we have achieved a denser reconstruction and obtained a 5.2 mm resolution using an 8 × 8 pattern at a depth of 110 cm. Unlike previous methods, which used local point orientations of grid intersection and multiple colors, we have used the monochrome pattern and deterministic centroid positions to compute the unit vector or direction vector between the neighboring symbols. The light plane intersections are used to calculate the tangent vectors on the surface. Surface normals are determined by the cross-product of two tangent vectors on the surface. A real experiment was conducted to measure simple plane surfaces, circular surfaces, and complex sculptures. The results show that the process of calculating surface normals is fast and reliable, and we have computed 1654 surface normals in 29.4 milliseconds for complex surfaces such as sculptures. Full article

The bedding structure of layered tunnels has a significant impact on the evolution of excavation damage, yet research on the relevant evolution mechanisms is scarce. In view of this, this paper develops a mesh-free numerical method to simulate the progressive damage process of tunnel excavation and proposes a method for applying stress boundaries within the SPH framework. Through this method, simulations of tunnel excavation damage under different bedding dip angles and stress ratios are conducted. The results show that the following: in the simulation of excavation damage of a tunnel without bedding structures, specific areas around the tunnel exhibit characteristics of tensile–shear composite failure and shear failure, verifying the rationality of the algorithm; under different bedding dip angles, a damage zone is first generated around the tunnel, and shear cracks appear at the tangent of the bedding plane and the tunnel, with the damage degree being the largest when α = 30° and the smallest when α = 45°; and under different stress ratios, the damage starts around the tunnel, continuously evolves, and finally forms a failure zone inside the bedding plane joints tangent to the tunnel, and the damage degree increases with the increase in the stress ratio. This study discusses the damage mechanisms under different calculation schemes and provides a reference for understanding the excavation damage mechanisms of layered tunnels. Full article

As a special type of clay, expansive clay is widely distributed in China. Its characteristics of swelling and softening when meeting water and shrinking and cracking when losing water bring many hidden dangers to engineering construction. Expansive clay is known as “engineering cancer”, and in-depth research on the unloading mechanical response characteristics and the unloading constitutive relationships of expansive clay is a prerequisite for conducting geotechnical engineering design and safety analysis in expansive-soil areas. In order to obtain the unloading mechanical response characteristics and the expression of the unloading tangent modulus of expansive clay, typical expansive clay in the Hefei area was taken as the research object, and triaxial unloading stress path tests were conducted. The stress–strain properties, microstructures, macro failure modes, and strength indexes of the expansive clay were analyzed under unloading stress paths. Through an applicability analysis of several classical soil strength criteria, an unloading constitutive model and the unloading tangent modulus expression of the expansive clay were constructed based on the Mohr–Coulomb (hereinafter referred to as “M-C”) criterion, the Drucker–Prager (hereinafter referred to as “D-P”) criterion, and the extended Spatial Mobilized Plane (hereinafter referred to as “SMP”) criterion theoretical frameworks. The following research results were obtained: (1) The stress–strain curves of the three stress paths of the expansive clay were hyperbolic. The expansive clay showed typical strain-hardening characteristics and belonged to work-hardening soil. (2) Under the unloading stress paths, the soil particles were involved in the unloading process of stress release, and the failure samples showed obvious stretching, curling, and slipping phenomena in their soil sheet elements. (3) Under both unloading stress paths, the strength of the expansive clay was significantly weakened and reduced. Under the lateral unloading paths, the cohesive force (c) of the expansive clay was reduced by 32.7% and the internal friction angle (φ) was increased by 19% compared with those under conventional loading, while under the axial unloading path, c was reduced by 63.5% and φ was reduced by 28.7%. (4) For typical expansive clay in Hefei, the conventional triaxial compression (hereinafter referred to as “CTC”) test, the reduced triaxial compression (hereinafter referred to as “RTC”) test, and the reduced triaxial extension (hereinafter referred to as “RTE”) test stress paths were suitable for characterization and deformation prediction using the M-C strength criterion, D-P strength criterion, and extended SMP strength criterion, respectively. (5) The derived unloading constitutive model and the unified tangent modulus formula of the expansive clay could accurately predict the deformation characteristics of the unloading stress path of the expansive clay. These research results will provide an important reference for future engineering construction in expansive-clay areas. Full article

Recently, based on light microscopy images, the tubercle structure on the seed surface of 100 Silene species was quantitatively described, including tubercle width, height, and curvature associated with general morphometric data. Curvature measures the rate of change of the tangent vector in a curve and can be calculated by the following methods described for Arabidopsis roots. Here, we apply curvature measurements to the SEM images of 40 Silene species from Türkiye, demonstrating that a quantitative analysis of tubercles can be made based on SEM images with similar results to optical photographs. The association of morphometric tubercle data allows for classification into six groups, five of them corresponding to described shapes: rugose (two groups), echinate, mammillate, and papillose, and a sixth group of tubercles plane on top. The curvature values vary between 20 and 200 mm⁻¹ and differ among the morphological tubercle types described. The correlation of curvature values with other general measurements and morphological seed characteristics is investigated. Tubercle quantification not only is a useful tool for Silene taxonomy, but also provides the basis for the analysis of the genetic control and developmental effects on tubercle structure and shape in the seed surface. Full article

This study introduces a novel method for classifying sets of images, called Riemannian geodesic discriminant analysis–minimum Riemannian mean distance (RGDA-MRMD). This method first converts image data into symmetric positive definite (SPD) matrices, which capture important features related to the variability within the data. These SPD matrices are then mapped onto simpler, flat spaces (tangent spaces) using a mathematical tool called the logarithm operator, which helps to reduce their complexity and dimensionality. Subsequently, regularized local Fisher discriminant analysis (RLFDA) is employed to refine these simplified data points on the tangent plane, focusing on local data structures to optimize the distances between the points and prevent overfitting. The optimized points are then transformed back into a complex, curved space (SPD manifold) using the exponential operator to enhance robustness. Finally, classification is performed using the minimum Riemannian mean distance (MRMD) algorithm, which assigns each data point to the class with the closest mean in the Riemannian space. Through experiments on the ETH-80 (Eidgenössische Technische Hochschule Zürich-80 object category), AFEW (acted facial expressions in the wild), and FPHA (first-person hand action) datasets, the proposed method demonstrates superior performance, with accuracy scores of 97.50%, 37.27%, and 88.47%, respectively. It outperforms all the comparison methods, effectively preserving the unique topological structure of the SPD matrices and significantly boosting image set classification accuracy. Full article

The evaluation of the lumbopelvic region is a crucial point during postural assessment in childhood and adolescence. Photogrammetry (PG) and Spinal Mouse (SM) are two of the most debated tools to properly analyze postural alignment and avoid misleading data. This study aims to find out the best linear regression model that could relate the analytic measurements of the SM with one or more PG parameters in adolescents with kyphotic postures. Thirty-nine adolescents (female = 35.9%) with structural and non-structural kyphosis were analyzed (13.2 ± 1.8 years; 1.59 ± 0.12 m; 47.6 ± 11.8 kg) using the SM and PG on the sagittal plane in a standing and forward-bending position, allowing for the measurement of body vertical inclination, lumbar and pelvic alignment, trunk flexion, sacral inclination during bending, and hip position during bending. Lordosis lumbar angles (SM) were significantly (r = −0.379, r = −0.328) correlated with the SIPS-SIAS angle (PG) during upright standing, while in the bending position, the highest correlation appeared among the sacral–hip (SM) and the sacral tangent (ST_PG; r = −0.72) angles. The stepwise backward procedure was assessed to estimate the SM variability in the bending and standing positions. Only in the bending position did the linear regression model reach high goodness-of-fit values with two regressors (ST_PG ${\eta }^2=0.504$, BMI ${\eta }^2=0.252;$ adjusted- R² =0.558, p < 0.001, CCC = 0.972, r = 0.763). Despite gold-standard methods reducing error evaluation, physicians and kinesiologists may consider photogrammetry as a good method for spinal curve prediction. Full article

Loop subdivision is a significant surface scheme with wide applications in fields like computer graphics and wavelet. As a type of stationary scheme, Loop subdivision cannot adjust the limit surface directly. In this paper, we present a new way to solve this problem by proposing a symmetric non-stationary Loop subdivision based on a suitable iteration. This new scheme can be used to adjust the limit surfaces freely and thus can generate surfaces with different shapes. For this new scheme, we show that it is $C^2$ convergent in the regular part of mesh and is at least tangent plane continuous at the limit positions of the extraordinary points. Additionally, we present a non-uniform generalization of this new symmetric non-stationary subdivision so as to locally control the shape of the limit surfaces. More interestingly, we present the limit positions of the initial points, both for the symmetric non-stationary Loop subdivision and its non-uniform generalization. Such limit positions can be used to interpolate the initial points with different valences, generalizing the existing result. Several numerical examples are given to illustrate the performance of the new schemes. Full article

This article explores the evolution of Lorenz trajectories within attractors. Specifically, based on the characteristics of the tangents to trajectories, we derive quantitative standards for determining the spatial position of trajectory lines. The Lorenz trajectory is decomposed into four parts. This standard is objective and quantitative and is independent of the initial field of the Lorenz equation and the calculation scheme; importantly, it is designed based on the inherent dynamic characteristics of the Lorenz equation. Linear fitting of the trajectories in the left and right equilibrium point regions shows that the trajectories lie on planes, indicating the existence of linear features in the nonlinear system. This study identifies the fundamental causes of chaos in the Lorenz equation using the microscopic evolution and local characteristics of the trajectories, and indicating that the spatial position of the initial field is important for their predictability. We theoretically demonstrate that mutation is essentially self-regulation within chaotic systems. This scheme is designed according to the evolution characteristics of Lorenz trajectories, and thus has certain methodological limitations that mean it may not be applicable to other chaotic systems. However, it does depict the causes of chaos and elucidates the sensitivity of differential equations to initial values in terms of trajectory evolution. Full article

A novel quasi-twisted miniaturized wideband branch line coupler (BLC) is proposed. The design is based on bisecting the conventional microstrip line BLC transversely and folding bisected sections on double-layered substrates with a common ground plane in between. The input and output terminals, each with a length of λ_g/4, and the pair of quarter-wavelength horizontal parallel arms are converted into a Z-shaped meandered microstrip line in the designed structure. Conversely, the pair of quarter-wavelength vertical arms are halved into two lines and transformed into a periodically loaded slow-wave structure. The bisected parts of the BLC are placed on the opposite side of the doubled-layer substrate and connected through four vias passing through the common ground plane. This technique enabled a compact BLC size of 6.4 × 18 mm², which corresponds to a surface area miniaturization by ~50% as compared to the classical BLC size of 10 × 23 mm² at 6 GHz. Moreover, the attained relative bandwidth is 73.9% (4.6–10 GHz) for S11, S33, S21, and the phase difference between outputs (∠S21 − ∠S41). However, if a coupling parameter (S41) of up to −7.5 dB is considered, then the relative bandwidth reduces to 53.9% (4.6–10 GHz) for port 1 as the input. Similarly, for port 3 as the input, the obtained bandwidth is 75.8% (4.5–10 GHz) for S33, S11, S43, and the phase difference between outputs (∠S43 − ∠S23). Likewise, this bandwidth reduces to 56% (4.5–8 GHz) when a coupling parameter (S23) of up to −7.5 dB is considered. In contrast, the relative bandwidth for the ordinary BLC is 41% at the same resonant frequency. The circuit is constructed on a double-layered low-cost FR4 substrate with a relative permittivity of 4.3 and a loss tangent of 0.025. An isolation of −13 dB was realized in both S₁₃ and S₃₁ demonstrating an excellent performance. The transmission coefficients between input/output ports S₂₁, S₄₁, S₂₃, and S₄₃ are between −3.1 dB to −3.5 dB at a frequency of 6 GHz. Finally, the proposed BLC provides phase differences between output ports of 90.5° and 94.8° at a frequency of 6 GHz when the input ports 1 and 3 are excited, respectively. The presented design offers the potential of being utilized as a unit cell for building a Butler matrix (BM) for sub-6 GHz 5G beamforming networks. Full article