Search Results (1,113)

The soil–water retention curve (SWRC) is a fundamental property that governs the hydraulic and mechanical behavior of unsaturated soils. Laboratory SWRC determination remains time-consuming and costly, promoting indirect estimation methods. However, existing methods often oversimplify the pore structure and particle arrangement of soils and neglect the effect of capillary menisci, resulting in discrepancies from natural soil behavior. This study proposes a novel method to estimate the SWRC of coarse-grained soils based on grain size distribution (GSD) and relative density. In the proposed method, soil particles are idealized as spheres in a two-dimensional (2D) plane, and the packing structure is modeled using representative quadrilaterals composed of four poly-disperse particles. The GSD is employed to calculate the probability of different particle sizes occupying the corners of the quadrilateral elements, while the relative density defines their geometric configuration. The water retention behavior is then evaluated using the geometric relationships between the air–water interface and particle radii. The predicted SWRCs are in good agreement with experimental data, indicating that the method can effectively capture the water retention characteristics of coarse-grained soils governed by capillary effects. The method’s applicability is limited to coarse-grained soils and excludes clayey soils where adsorbed water dominates retention mechanisms. Full article

In the article “New Technological Approach to Cable Car Boarding”, the authors attempted to correctly design the curve geometrically along which the rope moves through the station during the deceleration of cabins with attaching platforms in a central position, primarily intended for mass public transport. Since the suspension continuously connects the cabin and the rope during cabin deceleration, the rope moves at a constant speed along a special curve that enables the cabin to stop in the central position. This curve is symmetric with respect to the longitudinal axis of the station. However, the authors found that in the previous article presenting this cable car system, an error was made in the geometric design of the rope path curve, which the original authors were not aware of at the time. They determined that, in the presented example, a suspension length of 8 m was too short for the combination of rope speed of 5 m/s (cable car speed) and cabin deceleration of 0.5 m/s². This article revisits this geometric problem in greater detail. The study shows that not every combination of rope speed, suspension length, and cabin deceleration in the central position functions correctly. First, the boundary conditions and spatial constraints of the rope path curve were defined. Based on the upper bound and lower bound rope path lengths, the optimal or correct shape of the rope path curve was determined geometrically. The study concludes that for a given combination of rope speed (cable car speed) and cabin deceleration, only one suspension length is suitable. In the case of a rope speed of 5 m/s and cabin deceleration of 0.5 m/s², the correct suspension length is 16.85 m. The authors also found that the result depends on the time interval used in constructing the curve. Full article

Accurate and nondestructive monitoring of tomato growth is essential for large-scale greenhouse production; however, it remains challenging for small-fruited cultivars such as cherry tomatoes. Traditional 2D image analysis often fails to capture precise morphological traits, limiting its usefulness in growth modeling and yield estimation. This study proposes an automated phenotyping framework that integrates deep learning-based instance segmentation with high-resolution 3D point cloud reconstruction and ellipsoid fitting to estimate fruit size and ripeness from daily video recordings. These techniques enable accurate camera pose estimation and dense geometric reconstruction (via SfM and MVS), while Nerfacto enhances surface continuity and photorealistic fidelity, resulting in highly precise and visually consistent 3D representations. The reconstructed models are followed by CIELAB color analysis and logistic curve fitting to characterize the growth dynamics. When applied to real greenhouse conditions, the method achieved an average size estimation error of 8.01% compared to manual caliper measurements. During summer, the maximum growth rate (g_max) of size and ripeness were 24.14%, and 95.24% higher than in winter, respectively. Seasonal analysis revealed that winter-grown tomatoes matured approximately 10 days later than summer-grown fruits, highlighting environmental influences on phenological development. By enabling precise, noninvasive tracking of size and ripeness progression, this approach is a novel tool for smart and sustainable agriculture. Full article

Efficient locomotion in autonomous driving and robotics requires clearer visualization and more precise map. This paper presents a high accuracy online mapping including weight matching LiDAR-IMU-GNSS odometry and an object-level highly dynamic point cloud filtering method based on a pseudo-occupancy grid. The odometry integrates IMU pre-integration, ground point segmentation through progressive morphological filtering (PMF), motion compensation, and weight feature point matching. Weight feature point matching enhances alignment accuracy by combining geometric and reflectance intensity similarities. By computing the pseudo-occupancy ratio between the current frame and prior local submaps, the grid probability values are updated to identify the distribution of dynamic grids. Object-level point cloud cluster segmentation is obtained using the curved voxel clustering method, eventually leading to filtering out the object-level highly dynamic point clouds during the online mapping process. Compared to the LIO-SAM and FAST-LIO2 frameworks, the proposed odometry demonstrates superior accuracy in the KITTI, UrbanLoco, and Newer College (NCD) datasets. Meantime, the proposed highly dynamic point cloud filtering algorithm exhibits better detection precision than the performance of Removert and ERASOR. Furthermore, the high-accuracy online mapping is built from a real-time dataset with the comprehensive filtering of driving vehicles, cyclists, and pedestrians. This research contributes to the field of high-accuracy online mapping, especially in filtering highly dynamic objects in an advanced way. Full article

This study explores and evaluates different methodologies for designing the edge-of-traveled-way turning paths at right-angle at-grade intersections, with emphasis on low-speed maneuvers involving large design vehicles. Three geometric approaches are examined as follows: the standard AASHTO configuration, the German RAS-K-1 triple-radius method, and a clothoid-based transition curve design. Simulations using representative design vehicles, conducted under speeds ≤ 15 km/h, are used to assess each method’s performance in terms of spatial efficiency, steering continuity, and lateral clearance. The findings suggest that while the AASHTO asymmetric compound curve offers an effective balance between clearance and compactness, clothoid curves may improve transition smoothness and provide an alternative option for designing the edge-of-traveled-way turning paths at right-angle at-grade intersections. Full article

The mandible of domestic dogs represents a key structure in veterinary anatomy. This study tested the hypothesis that mandibular shape variation in adult mesocephalic dogs follows a non-random modular pattern with limited allometric influence. A total of 168 dry mandibles from academic osteological collections were analyzed using geometric morphometrics. Four anatomical landmarks and two curves of sliding semilandmarks were digitized and processed through Generalized Procrustes Analysis. Principal component analysis revealed that 62.7% of total variance was concentrated in the first two axes, associated with the coronoid height, ramus robustness, and curvature of the mandibular body. Cluster and Canonical Variate Analyses identified two overlapping but statistically distinct configurations, reflecting the intrinsic morphological diversity of mesocephalic dogs. Procrustes regression confirmed a significant yet low allometric effect (2.34%), while modularity tests based on RV coefficients supported a structured organization involving the ramus, coronoid, and angular processes (processus angularis mandibulae) as relatively independent modules. These results indicate that mandibular shape variation is hierarchically organized rather than random, highlighting the coexistence of integration and modular independence within the masticatory apparatus. Beyond its morphometric contribution, this study provides a reproducible anatomical baseline for veterinary and comparative research, facilitating future analyses of sexual dimorphism, functional adaptation, and surgical applications. Full article

This study investigates the geometry of osculating type-2 ruled surfaces in Minkowski 3-space ${\mathbf{E}}_1^3$, formulated through the Type-2 Bishop frame associated with a spacelike curve whose principal normal is timelike and binormal is spacelike. Using the hyperbolic transformation linking the Frenet–Serret and Bishop frames, we analyze how the Bishop curvatures ${\zeta }_1$ and ${\zeta }_2$ affect the geometric behavior and formation of such surfaces. Explicit criteria are derived for cylindrical, developable, and minimal configurations, together with analytical expressions for Gaussian and mean curvatures. We also determine the conditions under which the base curve behaves as a geodesic, asymptotic line, or line of curvature. Several illustrative examples in Minkowski 3-space are provided to visualize the geometric influence of ${\zeta }_1$ and ${\zeta }_2$ on flatness, minimality, and developability. Overall, the Type-2 Bishop frame offers a smooth and effective framework for characterizing Lorentzian geometry and symmetry of osculating ruled surfaces, extending classical Euclidean results to the Minkowski setting. Full article

Variability in reclaimed asphalt pavement (RAP) properties, such as aggregate gradation, asphalt content, and moisture content, poses a significant challenge to producing consistent and reliable recycled asphalt mixtures. This study systematically evaluated processing techniques for mitigating variability through a comparative analysis of four fractionation strategies, i.e., unfractionated, two-fraction, four-fraction, and six-fraction processing. Corresponding to the four approaches, four distinct reference RAP mixtures were fabricated by proportionally recombining the obtained RAP fractions towards a target gradation. The gray relational analysis (GRA) was employed to quantify geometric similarity between the gradation curve of reclaimed aggregates from each fraction and the target gradation curve, thereby facilitating efficient determination of blending proportions without resorting to complex optimization algorithms. Statistical variability indicators, including range, standard deviation, and coefficient of variation (COV), were used to assess the effectiveness of each fractionation and recombining method. The results demonstrated that refined fractionation processing significantly reduced variability, particularly in gradation properties. Compared with the COV values from the commonly used two-fraction processing, those from the refined four-fraction and six-fraction processing methods decreased by up to 51.5% and 73.5%, respectively. While increasing the number of fractions generally enhanced homogeneity, the four-fraction approach emerged as the most technically reliable and economically viable strategy, achieving a desirable balance between processing effort and variability control. Furthermore, the GRA proved to be a practical and efficient tool for blend proportioning, reducing reliance on complex numerical methods. These findings reveal the importance of refined fractionated RAP processing in enabling the production of high-RAP recycled mixtures with improved uniformity and performance. Full article

The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, $\varphi :X\to S$ and $\psi :Y\to S$, coincide exactly. This condition of strict equality, however, is insufficient for describing many real-world applications, such as the geometric structure of semantic spaces in modern large language models whose foundational architecture is the Transformer neural network: The token spaces of these models are fundamentally approximate, and recent work has revealed complex geometric singularities, challenging the classical manifold hypothesis. This paper develops a new framework to study and quantify the nature of approximate alignment between morphisms in the context of arithmetic geometry, using the tools of étale homotopy theory. We introduce the central object of our work, the étale mismatch torsor, which is a sheaf of torsors over the product scheme $X{\times }_{S}Y$. The structure of this sheaf serves as a rich, intrinsic, and purely algebraic object amenable to both qualitative classification and quantitative analysis of the global relationship between the two morphisms. Our main results are twofold. First, we provide a complete classification of these structures, establishing a bijection between their isomorphism classes and the first étale cohomology group $H_{ét}^1(X{\times }_{S}Y,\underline{{\pi }_1^{ét}(S)})$. Second, we construct a canonical filtration on this classifying cohomology group based on the theory of infinitesimal neighborhoods. This filtration induces a new invariant, which we term the order of mismatch, providing a hierarchical, algebraic measure for the degree of approximation between the morphisms. We apply this framework to the concrete case of generalized Howe curves over finite fields, demonstrating how both the characteristic class and its order reveal subtle arithmetic properties. Full article

Motion planning in robotic systems, particularly in industrial contexts, must balance execution speed, precision, and safety. Excessive accelerations, especially centripetal ones in high, curvature regions, can cause vibrations, reduce tracking accuracy, and increase mechanical wear. This paper presents an off-line motion planning method that integrates curvature-based velocity modulation with jerk- and acceleration-limited S-curve profiles. The approach autonomously adjusts the speed along a predefined path according to local curvature by planning the motion at piecewise constant velocity and ensuring compliance with dynamic constraints on jerk, acceleration, and velocity. A non-linear filter tracks the velocity reference and smooths transitions while maintaining fluid motion, automatically adjusting velocity based on path curvature, ensuring smooth S-curve trajectories without requiring manual intervention. By jointly addressing geometric feasibility and dynamic smoothness, the proposed method reduces execution time while minimizing vibrations in applications involving abrupt curvature variations, as confirmed by its application to planar and spatial trajectories with varying curvature complexity. The method applies to smooth parametric trajectories and is not intended for paths with tangent discontinuities. The simulation results confirm full compliance with the imposed acceleration and jerk limits; nevertheless, future work will include experimental validation on realistic process trajectories and a quantitative performance assessment. Full article

Research on surfaces generated by curves plays a central role in linking differential geometry with physical applications, especially following Hasimoto’s transformation and the development of Hasimoto-inspired surface models. In this work, we introduce a new class of such surfaces, referred to as RM Hasimoto surfaces, constructed by employing the rotation-minimizing (RM) Darboux frame along both timelike and spacelike curves in Minkowski 3-space ${\mathbb{E}}_1^3$. In contrast to the classical Hasimoto surfaces defined via the Frenet or standard Darboux frames, the RM approach eliminates torsional difficulties and reduces redundant rotational effects. This leads to more straightforward expressions for the first and second fundamental forms, as well as for the Gaussian and mean curvatures, and facilitates a clear classification of key parameter curves. Furthermore, we establish the associated evolution equations, analyze the resulting geometric invariants, and present explicit examples based on timelike and spacelike generating curves. The findings show that adopting the RM Darboux frame provides greater transparency in Lorentzian surface geometry, yielding sharper characterizations and offering new perspectives on relativistic vortex filaments, magnetic field structures, and soliton behavior. Thus, the RM framework opens a promising direction for both theoretical studies and practical applications of surface geometry in Minkowski space. Full article

3D hand pose estimation has achieved remarkable progress in human computer interaction and computer vision; however, real-world hand point clouds often suffer from structural distortions such as partial occlusions, sensor noise, and environmental interference, which significantly degrade the performance of conventional point cloud-based methods. To address these challenges, this study proposes a curve fitting-based framework for robust 3D hand pose estimation from corrupted point clouds, integrating an Adaptive Sampling (AS) module and a Hand-Curve Guide Convolution (HCGC) module. The AS module dynamically selects structurally informative key points according to local density and anatomical importance, mitigating sampling bias in distorted regions, while the HCGC module generates guided curves along fingers and employs dynamic momentum encoding and cross-suppression strategies to preserve anatomical continuity and capture fine-grained geometric features. Extensive experiments on the MSRA, ICVL, and NYU datasets demonstrate that our method consistently outperforms state-of-the-art approaches under local point removal across fixed missing-point ratios ranging from 30% to 50% and noise interference, achieving an average Robustness Curve Area (RCA) of 30.8, outperforming advanced methods such as TriHorn-Net. Notably, although optimized for corrupted point clouds, the framework also achieves competitive accuracy on intact datasets, demonstrating that enhanced robustness does not compromise general performance. These results validate that adaptive curve guided local structure modeling provides a reliable and generalizable solution for realistic 3D hand pose estimation and emphasize its potential for deployment in practical applications where point cloud quality cannot be guaranteed. Full article

The study focuses on the T-shaped tunnel scenario with protective doors, performs explosion tests using aluminized explosives, and investigates the propagation patterns and loading characteristics of explosion shock waves in the straight tunnel, at the T-shaped junction, and within the semi-enclosed space in front of the protective door. It was observed that, in comparison to TNT explosives, the overpressure curve of aluminized explosives in the near-explosion zone exhibited a two- batch characteristic. The second batch presented the maximum overpressure peak. In contrast, in the far zone, the curve displayed a stable triangular waveform. In the main tunnel of the T-shaped opening with protective doors, it was found that the back blast surface located in front of the entrance to the main tunnel experienced the maximum momentum, which could be as high as 12 times greater than that of the reflection area on the blast-facing surface at the entrance of the main tunnel and the shock-wave pressure wave pattern can be divided into four batch. The regularities of each measurement point in multiple tests show consistency, highlighting the influence laws of the geometric structure on the wave pattern and load distribution. In addition, this paper integrates LS-DYNA numerical simulation with aerodynamics theory to reveal that shock waves generate expansion waves and oblique shock waves as they pass through the T-shaped opening. After two reflections off the main tunnel wall and the door, a stable propagation waveform is established. In addition, through dimensional analysis and in combination with the experimental results, the momentum at key positions was analyzed and predicted. This study offers a reference for the design of relevant engineering protection measures. Full article

The mechanical properties of dental implants are critical for their durability. The purpose of this study was to determine the maximum force required to induce full pull-out of a titanium implant from the bone and to characterize the mechanical behavior during this process. First, pull-out tests were performed on monolithic implants embedded in bovine ribs and foam blocks that mimic the mechanical parameters of human bone, allowing a quantitative evaluation of implant–bone interface strength and a comparison of geometric variants. Second, the extraction process was recreated in a three dimensional finite element model incorporating nonlinear interface contact and parameterization, enabling the reproduction of load–displacement curves; the results obtained showed good agreement with the experiment. Third, the fracture surfaces were observed macroscopically and by scanning electron microscopy/energy dispersive spectroscopy. The results demonstrated significant distinctions in the forces required to extract implants with varying thread geometries, clearly indicating the impact of implant design on their mechanical stability. The presented FEM-based methodology provides a reliable tool to study mechanical interactions at the implant–bone interface. The findings obtained can improve our understanding of implant behavior in biological systems and provide a basis for further optimization of their design. Full article

By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient $G={\mathbb{Z}}_5⋊2I$, where $2I$ is the binary icosahedral group. The Gröbner basis decomposition of its $SL(2,\mathbb{C})$ character variety yields elliptic curves whose L-function derivatives $L^{\prime }(E,1)$ remarkably match fundamental biological structural ratios. Specifically, we demonstrate that the Birch–Swinnerton-Dyer conjecture’s central quantity: the derivative $L^{\prime }(E,1)$ of the L-function at 1 encodes critical cellular geometries: the crystalline B-DNA pitch-to-diameter ratio ($L^{\prime }(E,1)=1.730$ matching $34\AA /20\AA =1.70$), the B-DNA pitch to major groove width ($L^{\prime }=1.58$) and, additionally, the fundamental cytoskeletal scaling relationship where $L^{\prime }(E,1)=3.570\approx 25/7$, precisely matching the microtubule-to-actin diameter ratio. This pattern extends across the hierarchy ${\mathbb{Z}}_5⋊2P$ with $2P\in \{2O,2T,2I\}$ (binary octahedral, tetrahedral, icosahedral groups), where character tables of $2O$ explain genetic code degeneracies while $2T$ yields microtubule ratios. The convergence of multiple independent mathematical pathways on identical biological values suggests that evolutionary optimization operates under deep arithmetic-geometric constraints encoded in elliptic curve L-functions. Our results position the BSD conjecture not merely as abstract number theory, but as encoding fundamental organizational principles governing cellular architecture. The correspondence reveals arithmetic geometry as the mathematical blueprint underlying major biological structural systems, with Gross–Zagier theory providing the theoretical framework connecting quantum topology to the helical geometries that are essential for life. Full article