Search Results (515)

Surface reconstruction from 3D point clouds has a wide range of applications. In this paper, we focus on the reconstruction from raw, sparse point clouds. Although some existing methods work on this topic, the results often suffer from geometric defects. To solve this problem, we propose a novel method that optimizes a neural network (referred to as signed distance function) to fit the Signed Distance Field (SDF) from sparse point clouds. The signed distance function is optimized by projecting query points to its iso-surface accordingly. Our key idea is to encourage both the direction and distance of projection to be correct through the supervision provided by a nearest neighbor prior. In addition, we mitigate the error propagated from the prior function by augmenting the low-frequency components in the input. In our implementation, the nearest neighbor prior is trained with a large-scale local geometry dataset, and the positional encoding with a specified spectrum is used as a regularization for the optimization process. Experiments on the ShapeNetCore dataset demonstrate that our method achieves better accuracy than SDF-based methods while preserving smoothness. Full article

In Building Information Modeling (BIM) of bridge piers, persistent limitations have been observed in the modeling of spiral hoop rebar with variable pitch and diameter. Taking Revit as an example, its built-in family files can only generate spirals with constant geometry. When dealing with non-uniform rebar, designers often have to rely on segmented modeling or manual operations, which is not only time-consuming but also prone to deviations. To solve this problem, this paper proposes a parameterized modeling method based on the secondary development of Revit. By combining the Revit API with the C# programming language, the spiral equation is embedded into the Non-Uniform Rational B-Spline (NURBS) curve reconstruction framework, realizing the continuous modeling of spiral hoop rebar in a unified model. This method also allows users to flexibly input parameters such as cover thickness, rebar diameter, and segment length through a graphical user interface. Through comparative experiments, the proposed method and the traditional family file modeling method were verified respectively in the modeling of a single column and an entire bridge pier. The results indicate that the proposed method reduces the average modeling time of a single bridge pier by 66.5% and that of the entire project by 48.7%. While maintaining high geometric accuracy, this method significantly shortens modeling time and reduces workload, especially demonstrating higher consistency in pitch transition sections and conical sections. Beyond technical performance, this study also demonstrates that the secondary development of Revit provides a practical and feasible solution for the efficient, precise, and generalizable modeling of complex reinforcing bar components in terms of expanding BIM functions, which holds significant practical implications. Full article

This paper introduces novel subfamilies of analytic and bi-univalent functions in $\mathrm{\Omega }=\left\{\varsigma \in \mathbb{C}:\left|\varsigma \right|<1\right\}$, defined by applying a linear operator associated with the Mittag–Leffler function and requiring subordination to domains related to generalized bivariate Fibonacci polynomials. The proposed framework provides a unified treatment that generalizes numerous earlier studies by incorporating parameters controlling both the operator’s fractional calculus features and the domain’s combinatorial geometry. For these subfamilies, we establish initial coefficient bounds ($\left|d_2\right|$, $\left|d_3\right|$) and solve the Fekete–Szegö problem ($\left|d_3-\xi d_2^2\right|$). The derived inequalities are interesting, and their proofs leverage the intricate interplay between the series expansions of the Mittag–Leffler function and the generating function of the Fibonacci polynomials. By specializing the parameters governing the operator and the polynomial domain, we show how our main theorems systematically recover and extend a wide range of known results from the literature, thereby demonstrating the generality and unifying power of our approach. Full article

“Experiments were conducted at DIMEG, University of Calabria, located in the main campus in Arcavacata di Rende, Italy.” This article focuses on the study of the geometry, direct and inverse kinematics, workspace, and singularity of a novel 3-PRRS parallel manipulator (PM) with a redundantly actuated architecture. The PM consists of three active revolute joints and three passive prismatic redundant input joints, all located on a fixed platform. The constant and variable parameters characterizing the PM’s geometry and kinematics are determined. The direct kinematics problem is formulated as a 16th-degree polynomial, while the inverse kinematics problem is solved in closed form. A comparison of the direct and inverse kinematics is provided, and the correctness of the solutions is validated through numerical examples. The equations of motion for the moving platform are derived, and the PM’s workspace is defined based on the inverse kinematics. This work demonstrates how the passive prismatic input joints, specifically included in the design, contribute to an enlarged workspace—particularly in the vertical direction—compared to traditional 3-RRS PM architecture. Full article

The cosmological constant (CC, $\Lambda$) problem stands as one of the most profound puzzles in the theory of gravity, representing a remarkable discrepancy of about 120 orders of magnitude between the observed value of dark energy and its natural expectation from quantum field theory. This paper synthesizes two innovative paradigms—holographic naturalness (HN) and pre-geometric gravity (PGG)—to propose a unified and natural resolution to the problem. The HN framework posits that the stability of the CC is not a matter of radiative corrections but rather of quantum information and entropy. The large entropy $S_{\mathrm{dS}}\sim M_{\mathrm{P}}^2/\Lambda$ of the de Sitter (dS) vacuum (with $M_{\mathrm{P}}$ being the Planck mass) acts as an entropic barrier, exponentially suppressing any quantum transitions that would otherwise destabilize the vacuum. This explains why the universe remains in a state with high entropy and relatively low CC. We then embed this principle within a pre-geometric theory of gravity, where the spacetime geometry and the Einstein–Hilbert action are not fundamental, but emerge dynamically from the spontaneous symmetry breaking of a larger gauge group, SO($1,4$)→SO($1,3$), driven by a Higgs-like field ${\varphi }^A$. In this mechanism, both $M_{\mathrm{P}}$ and $\Lambda$ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the vacuum expectation value (VEV) v of the pre-geometric Higgs field and the de Sitter entropy: $S_{\mathrm{dS}}\sim v$ (or $v^3$). Thus, the field responsible for generating spacetime itself also encodes its information content. The smallness of $\Lambda$ is therefore a direct consequence of the largeness of the entropy $S_{\mathrm{dS}}$, which is itself a manifestation of a large Higgs VEV v. The CC is stable for the same reason a large-entropy state is stable: the decay of such state is exponentially suppressed. Our study shows that new semi-classical quantum gravity effects dynamically generate particles we call “hairons”, whose mass is tied to the CC. These particles interact with Standard Model matter and can form a cold condensate. The instability of the dS space, driven by the time evolution of a quantum condensate, points at a dynamical origin for dark energy. This paper provides a comprehensive framework where the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime are inextricably linked, thereby providing a novel and compelling path toward solving the CC problem. Full article

This study presents a rigorous error analysis of a previously published estimator that determines the single-frame relative pose of two rigid bodies from batches of point and unit vector measurements. The estimator solves a constrained least-squares optimization problem where the pose is represented by a dual quaternion and the properties of pose dual quaternions are exactly satisfied. We develop an eigenvalue-based error analysis and derive analytical expressions for the three-dimensional attitude and translation errors, along with their means and covariance matrices. The closed-form formulas provide significant insights into the distinctive impacts of the point and vector observations’ geometry and noise. They provide valuable tools for performance analysis and prediction. We consider noises both in the body frame and in the reference frame observations. Extensive Monte-Carlo simulations validate the accuracy and consistency of these formulas. Furthermore, we investigate the algorithm’s sensitivity to variations in the number of observations and in the observations’ weight coefficients of the cost function. Full article

This study investigates the thermal performance of a passive vertical aluminum heat sink with plate fins through combined experimental measurements and numerical simulations. Using a custom-made experimental apparatus which used water as the heat source, heat transfer rate was determined, and heat transfer coefficient was compared against established empirical correlations, demonstrating good agreement. A 3D steady-state mathematical model was developed to capture the conjugate heat transfer problem of conduction and natural convection, with buoyancy-driven airflow modeled with the incompressible ideal gas law. The problem was solved numerically using the finite volume method through ANSYS Fluent 18.2 solver and validated against experimental data and analytical correlations, exhibiting good agreement throughout. Parametric analysis followed, investigating the influence of various base (50, 65, 80 °C) and ambient (19, 24, 29 °C) temperatures, resulting in base-to-ambient temperature differences from 21 to 61 °C. Increasing this temperature difference led to a significant increase in heat transfer rate, while heat transfer coefficient increased and overall thermal resistance decreased moderately. Additionally, a Nusselt–Rayleigh (Nu–Ra) number correlation, consistent with ranges reported in the literature, was derived, providing the scaling to predict the thermal performance of similar natural convection-governed heat sinks. The validated computational methodology, combined with obtained experimental and numerical results, presents a foundation for future studies focused on more complex heat sink geometries and physics. Full article

For the purpose of Fitness-For-Service analysis, the effect of a semi-elliptical surface crack on a parallel quarter-circle corner crack in a semi-infinite solid subjected to pure bending is studied using 3D finite element analyses. While keeping the geometry of the quarter-circle corner crack constant, the SIF distributions along its front are studied for various geometrical configurations of the semi-elliptical surface crack and several crack layouts. The problem is solved for a wide range of parameters, e.g., the ellipticity of the semi-elliptical b₁/a₁ = 0.1~1; the relative crack size of the two parallel cracks a₁/a₂ = 1/3~2; the normalized vertical and horizontal gaps between the two cracks, H/a₂ = 0.4 and 1.2, and S/a₂ = −0.5 and 1, respectively. The results indicate that the semi-elliptical surface crack might have a considerable effect on the SIF distribution along the quarter-circle corner crack both in amplifying and reducing the SIF. These effects are highly dependent on the semi-elliptical surface crack geometry and the cracks’ configuration. It is further concluded that it is necessary to perform a full 3D analysis, similar to the present one, in order to quantify the “real” effect of neighbouring cracks, in view of the existing inadequate fitness for service criteria. Full article

The design of multi-link vehicle suspension systems, such as the 3D double-wishbone, presents a critical challenge in automotive engineering. The process constitutes a high-dimensional, nonlinearly constrained optimization problem where traditional gradient-based methods often fail by converging to suboptimal local minima. This paper introduces a novel two-stage hybrid optimization framework designed to overcome this limitation by intelligently integrating quantum-inspired and classical techniques. The methodology explicitly defines a QUBO (Quadratic Unconstrained Binary Optimization) stage and an SQP (Sequential Quadratic Programming) stage. Stage 1 addresses the complex kinematic constraint problem by formulating it as a QUBO, which is then solved using Simulated Annealing to perform a global search, guaranteeing a physically feasible starting point. Subsequently, Stage 2 takes this feasible solution and employs an SQP algorithm to perform a high-precision local refinement, tuning the geometry to meet specific performance targets for camber and caster curves. The framework successfully converged to a design with a near-zero performance objective of 7.08 × 10⁻¹⁴. The efficacy of this hybrid approach is highlighted by the dramatic improvement from the high-error initial solution found by Simulated Annealing to the final, high-precision result from the SQP refinement. We conclude that this QUBO-SQP framework is a powerful and validated methodology for solving complex, real-world engineering design problems, effectively bridging the gap between global exploration and local precision. Full article

It is well known that the Cahn–Hilliard equation satisfies the energy dissipation law and the mass conservation property. Recently, the radial basis function–finite difference (RBF–FD) approach and its numerous variants have garnered significant attention for the numerical solution of surface-related problems, owing to their intrinsic advantage in handling complex geometries. However, existing RBF–FD schemes generally fail to preserve mass conservation when solving the Cahn–Hilliard equation on smooth closed surfaces. In this paper, based on an $L^2$ projection method, two numerically efficient RBF–FD schemes are proposed to achieve mass-conservative numerical solutions, which are demonstrated to preserve the mass conservation law under relatively mild time-step constraints. Spatial discretization is performed using the RBF–FD method, while based on the convex splitting method and a linear stabilization technique, the first-order backward Euler formula (BDF1) and the second-order Crank–Nicolson (CN) scheme are employed for temporal integration. Extensive numerical experiments not only validate the performance of the proposed numerical schemes but also demonstrate their ability to utilize mild time steps for long-term phase-separation simulations. Full article

Early mathematical learning predicts later academic achievement, and creativity within mathematics plays a central role in higher-order thinking. This study examined the effects of linguistically responsive mathematics enrichment programs for nurturing mathematical creativity. Participants were 250 high-potential kindergarten English Learners across six urban schools in New York, Texas, and California. A linguistically responsive enrichment intervention adapted from the Mentoring Young Mathematicians (M²) math curriculum was implemented for 80 h across seven months. Using the Tangram Creativity Assessment, fluency, flexibility, and originality were measured in students’ tangram problem solving. Additional predictors included Tangram Problem Solving Speed (TPSS), general reasoning (CogAT), and mathematical achievement (NWEA MAP Math). ANCOVA showed significant post-test differences favoring the intervention group across all creativity components. Two-group structural equation modeling analysis supported measurement invariance and explained 55–60% of posttest creativity variance. TPSS emerged as the strongest predictor, with greater effects for the intervention group. These findings highlight the potential of enrichment programs and language-accessible geometry tasks to cultivate creativity in young gifted ELs by strengthening their mathematical foundation while supporting flexible and original problem solving. Full article

The problem of packing multidimensional spheres in a container defined by a hyperbolic surface is introduced. The objective is to minimize the height of the hyperbolic container under non-overlapping and containment conditions for the spheres, considering minimal allowable distances between them. To the best of our knowledge, no mathematical models addressing optimized packing spheres in hyperbolic containers have been proposed before. Our approach is based on a space dimensionality reduction transformation. This transformation relies on projecting a multidimensional hyperboloid into a lower-dimensional space sequentially up to two-dimensional case. Employing the phi-function technique, packing spheres in the hyperbolic container is formulated as a nonlinear programming problem. The latter is solved using a model-based heuristic combined with a decomposition approach. Numerical results are presented for a wide range of parameters, i.e., space dimension, number of spheres, and metric characteristics of the hyperbolic container. The results demonstrate efficiency of the proposed modeling and solution approach highlighting new opportunities for packing problems within non-traditional geometries. Full article

This study investigates the thermal characteristics of two hybrid nanofluids, single-walled carbon nanotubes with titanium dioxide ($SWCNT-Ti{O}_2$) and multi-walled carbon nanotubes with copper ($MWCNT-Cu$), as they flow over an inclined, porous, and longitudinally stretched cylindrical surface with kerosene as the base fluid. The model takes into consideration all of the consequences of magnetohydrodynamic (MHD) effects, thermal radiation, and Arrhenius-like energy of activation. The outcomes of this investigation hold practical significance for energy storage systems, nuclear reactor heat exchangers, electronic cooling devices, biomedical hyperthermia treatments, oil and gas transport processes, and aerospace thermal protection technologies. The proposed hybrid ANN–numerical framework provides an effective strategy for optimizing the thermal performance of hybrid nanofluids in advanced thermal management and energy systems. A set of coupled ordinary differential equations is created by applying similarity transformations to the governing nonlinear partial differential equations that reflect conservation of mass, momentum, energy, and species concentration. The boundary value problem solver bvp4c, which is based in MATLAB (R2020b), is used to solve these equations numerically. The findings demonstrate that, in comparison to the $MWCNT-Cu/kerosene$ nanofluid, the $SWCNT-Ti{O}_2$/kerosene hybrid nanofluid improves the heat transfer rate (Nusselt number) by up to $23.6\%$. When a magnetic field is applied, velocity magnitudes are reduced by almost $15\%$, and the temperature field is enhanced by around $12\%$ when thermal radiation is applied. The impact of important dimensionless variables, such as the cylindrical surface’s inclination angle, the medium’s porosity, the magnetic field’s strength, the thermal radiation parameter, the curvature ratio, the activation energy, and the volume fraction of nanoparticles, is investigated in detail using a parametric study. According to the comparison findings, at the same flow and thermal boundary conditions, the $SWCNT-Ti{O}_2$/kerosene hybrid nanofluid performs better thermally than its $MWCNT-Cu$/kerosene counterpart. These results offer important new information for maximizing heat transfer in engineering systems with hybrid nanofluids and inclined porous geometries under intricate physical conditions. With its high degree of agreement with numerical results, the ANN model provides a computationally effective stand-in for real-time thermal system optimization. Full article

An analytical method is proposed for determining the stress-strain state in an elastic layer with a cylindrical cavity supported by linear continuous supports perpendicular to the cavity. The need for such a development is due to the fact that in aerospace and mechanical engineering, structural elements are often affected by loads and supports described by infinite functions. This complicates the calculation for spatial bodies with complex geometry and stress concentrators. The methodology is based on the generalized Fourier method within the spatial problem of elasticity theory. The model is considered as a layer with specified stresses at the outer boundaries, where the reactions of the supports are represented as applied loads. A combined approach is used to describe the geometry using a Cartesian coordinate system for the layer and a cylindrical coordinate system for the cavity. The key idea is to decompose the original problem into two simpler ones using the principle of superposition. Auxiliary problem: the stresses in a solid layer (without a cavity) are calculated to determine the stress fields at its nominal location. Main problem: a layer with a cavity is considered, on the surface of which the stresses calculated in the first step are acting but taken with the opposite sign. The complete solution is the sum of the solutions of these two problems. Each of them is reduced to an infinite system of linear algebraic equations, which is solved by the method of reduction. This approach makes it possible to calculate the stress-strain state at any point of the body with high accuracy. Numerical analysis confirmed the correctness of satisfying the boundary conditions and showed the dependence of stresses on the nature of the distributed loads. The cylindrical cavity acts as a stress concentrator, which leads to a local increase in stresses σ_x and σ_z at the upper and lower boundaries of the layer to values that exceed both the applied load by and the calculated resistance of concrete of class C25/30. Full article

This study focuses on the problem of local instability of sandwich panels, which consist of two thin but relatively stiff facings and a thick but shear-deformable core. Such structures are commonly used in civil engineering and in the aerospace, aviation, and automotive industries. A case is presented in which one of the facings is deep-profiled. Due to typical mechanical or thermal interactions, this facing is subjected to compression. The thick core of the sandwich panel plays a stabilizing role. However, at a specific critical load, local stability is lost, representing a typical form of damage that occurs in sandwich panels. In the case of a deep-profiled facing, the geometry of the facing must also be taken into account, specifically the fact that the bends resulting from profiling constitute a significant limitation to its deformation. In this study, expressions are derived that enable the determination of the critical (wrinkling) stress, taking into account the geometry of the compressed facing bands and various boundary conditions defined along their edges. The energy approach is used to solve the problem. The presented solution to the problem of local instability is illustrated using examples. The obtained results indicate that the use of narrow bands is particularly effective while also allowing for determination of the maximum benefits resulting from deep profiling of the facings. This information is essential when considering changes to the geometry of industrially produced sandwich panels or when optimizing the load-bearing capacity of individual sandwich elements. Full article