Search Results (98)

In this work, we provide a promising way to alleviate the Hubble tension within the framework of Myrzakulov $f(R,T)$ gravity. The latter incorporates both curvature and torsion under a non-special connection. We consider the $f(R,T)=R+\alpha R^2$ class, which leads to modified Friedmann equations and an effective dark energy sector. Within this class, we make specific connection choices in order to obtain a Hubble function that coincides with that of $\Lambda$CDM at early times while yielding higher $H_0$ values at late times. The reason behind this behavior is that the dark energy equation of state exhibits phantom behavior, which is known to be a sufficient mechanism for alleviating the $H_0$ tension. A full observational comparison with various datasets, including the Cosmic Microwave Background (CMB), is required to test the viability of this scenario. Strictly speaking, the present work does not provide a complete solution to the Hubble tension but rather proposes a promising way to alleviate it. Full article

A concentric double-flange butterfly valve (DN-500, PN-10) was analyzed to examine its dynamic behavior and internal fluid flow across multiple opening angles. Finite Element Analysis (FEA) was employed to determine natural frequencies, mode shapes, and effective mass participation factors (EMPFs) for valve positions at 30°, 60°, and 90°. The valve geometry was discretized using a curvature-based mesh with linear elastic isotropic properties for 1023 carbon steel. Lower-order vibration modes produced global deformations primarily along the valve disk, while higher-order modes showed localized displacement near the shaft–bearing interface, indicating coupled torsional and translational dynamics. The highest EMPF in the X-direction occurred at 1153.1 Hz with 0.2631 kg, while the Y-direction showed moderate contributions peaking at 0.1239 kg at 392.06 Hz. The Z-direction demonstrated lower influence, with a maximum EMPF of 0.1218 kg. Modes 3 and 4 were critical for potential resonance zones due to significant mass contributions and directional sensitivity. Computational Fluid Dynamics (CFD) simulation analyzed flow behavior, pressure drops, and turbulence under varying valve openings. At a lower opening angle, significant flow separation, recirculation zones, and high turbulence were observed. At 90°, the flow became more streamlined, resulting in a reduction in pressure losses and stabilizing velocity profiles. Full article

In this study, We explore for Minkowski 3-space ${\mathbb{E}}_1^3$ harmonic surfaces’ geometric features by employing a common tangent vector field along a curve situated on the surface. Our analysis is grounded in the rotation minimizing (RM) Darboux frame, which offers a robust alternative to the classical Frenet frame particularly valuable in the Lorentzian setting, where singularities frequently arise. The RM Darboux frame, tailored to curves lying on surfaces, enables the expression of fundamental invariants such as geodesic curvature, normal curvature, and geodesic torsion. We derive specific conditions that characterize harmonic surfaces based on these invariants. We also clarify the connection between the components of the RM Darboux frame and thesurface’s mean curvature vector. This formulation provides fresh perspectives on the classification and intrinsic structure of harmonic surfaces within Minkowski geometry. To support our findings, we present several illustrative examples that demonstrate the applicability and strength of the RM Darboux approach in Lorentzian differential geometry. Full article

This study explores the dynamics of particle motion in pseudo-Galilean $3-$space $G_3^1$ by considering actions that incorporate both curvature and torsion of trajectories. We consider a general energy functional and formulate Euler–Lagrange equations corresponding to this functional under some boundary conditions in $G_3^1$. By adapting the geometric tools of the Frenet frame to this setting, we analyze the resulting variational equations and provide illustrative solutions that highlight their structural properties. In particular, we examine examples derived from natural Hamiltonian trajectories in $G_3^1$ and extend them to reflect the distinctive geometric features of pseudo-Galilean spaces, offering insight into their foundational behavior and theoretical implications. Full article

This systematic review, registered in PROSPERO (CRD42025101243), aimed to evaluate how specific badminton shoe design features influence lower-limb biomechanics, injury risk, and sport-specific performance. A comprehensive search in six databases yielded 445 studies, from which 10 met inclusion criteria after duplicate removal and eligibility screening. The reviewed studies focused on modifications involving forefoot bending stiffness, torsional stiffness, lateral-wedge hardness, insole and midsole hardness, sole structure, and heel curvature. The most consistent biomechanical benefits were associated with moderate levels of forefoot and torsional stiffness (e.g., 60D) and rounded heel designs. Increased forefoot bending stiffness was associated with reduced foot torsion and knee loading during forward lunges. Torsional stiffness around 60D provided favorable ankle support and reduced knee abduction, suggesting potential protection against ligament strain. Rounded heels reduced vertical impact forces and promoted smoother knee–ankle coordination, especially in experienced athletes. Lateral-wedge designs improved movement efficiency by reducing contact time and enhancing joint stiffness. Harder midsoles, however, resulted in increased impact forces upon landing. Excessive stiffness in any component may restrict joint mobility and responsiveness. Studies included 127 male-dominated (aged 18–28) competitive athletes, assessing kinematics, impact forces, and coordination during sport-specific tasks. The reviewed studies predominantly involved male participants, with little attention to sex-specific biomechanical differences such as joint alignment and foot structure. Differences in testing methods and movement tasks further limited direct comparisons. Future research should explore real-game biomechanics, include diverse athlete populations, and investigate long-term adaptations. These efforts will contribute to the development of performance-enhancing, injury-reducing badminton shoes tailored to the unique demands of the sport. Full article

In this paper, we introduce and develop the concept of osculating curve pairs in the three-dimensional Minkowski space. By defining a vector lying in the intersection of osculating planes of two non-lightlike curves, we characterize osculating mates based on their Frenet frames. We then derive the transformation matrix between these frames and investigate the curvature and torsion relations under varying causal characterizations of the curves—timelike and spacelike. Furthermore, we determine the conditions under which these generalized osculating pairs reduce to well-known curve pairs such as Bertrand, Mannheim, and Bäcklund pairs. Our results extend existing theories by unifying several known curve pair classifications under a single geometric framework in Lorentzian space. Full article

Curved-spoke wheels have been proposed as an effective way to overcome stair-like obstacles with smooth, rotation-only motion. However, when the wheel’s contact point shifts, discontinuous changes in its radius of curvature cause abrupt drops in the robot’s linear speed, often leading to reduced payload stability and slip. As a result, maintaining reliable stair climbing becomes more difficult. At higher speeds, these sudden changes become stronger, further reducing dynamic stability. To address these issues, we propose a passive Compliant Spiral Torsional Suspension (C-STS) attached to the wheel’s drive axis. Through camera-based marker tracking, we analyzed wheel trajectories under various stiffness and speed conditions. In particular, we define the deceleration caused by the velocity drop during contact transitions as our dynamic stability metric and demonstrate that the C-STS significantly reduces this deceleration across low-, medium-, and high-speed climbing, based on comparisons both with and without the suspension. It also raises the average velocity, likely due to a brief release of stored elastic energy, and lowers the net torque requirement. Our findings show that the proposed C-STS greatly improves dynamic stability and suggest its potential for enhancing stair-climbing performance in curved-wheel-based robotic systems. Furthermore, our approach may extend to other reconfigurable wheels facing similar instabilities. Full article

To enhance the efficiency and accuracy of detecting insulation faults such as discharge carbon traces in large oil-immersed transformers, this study employs an inspection micro-robot to replace manual inspection for image acquisition and fault identification. While the micro-robot exhibits compactness and agility, its limited battery capacity necessitates the critical optimization of its 3D inspection path within the transformer. To address this challenge, we propose a hybrid algorithmic framework. First, the task of visiting inspection points is formulated as a Constrained Traveling Salesman Problem (CTSP) and solved using the Ant Colony Optimization (ACO) algorithm to generate an initial sequence of inspection nodes. Once the optimal node sequence is determined, detailed path planning between adjacent points is executed through a synergistic combination of the A algorithm*, Rapidly exploring Random Tree (RRT), and Particle Swarm Optimization (PSO). This integrated strategy ensures robust circumvention of complex 3D obstacles while maintaining path efficiency. Simulation results demonstrate that the hybrid algorithm achieves a 52.6% reduction in path length compared to the unoptimized A* algorithm, with the A*-ACO combination exhibiting exceptional stability. Additionally, post-processing via B-spline interpolation yields smooth trajectories, limiting path curvature and torsion to <0.033 and <0.026, respectively. These advancements not only enhance planning efficiency but also provide substantial practical value and robust theoretical support for advancing key technologies in micro-robot inspection systems for oil-immersed transformer maintenance. Full article

In this study, the geometric properties of curves in multiplicative equiaffine space are investigated using multiplicative calculus. Fundamental geometric concepts such as multiplicative arc length, multiplicative equiaffine curvature, and torsion are introduced. This study derives the multiplicative Frenet frame and associated Frenet equations, providing a systematic framework for describing the geometric behavior of multiplicative equiaffine curves. Additionally, curves with constant multiplicative curvature and torsion are characterized and supported with illustrative examples. Full article

The differential geometry of space curves is a fascinating area of research for mathematicians and physicists, and this refers to its crucial applications in many areas. In this paper, a new method is derived to study the differential geometry of space curves. More specifically, the position vector of a constant vector in ${\mathbb{R}}^3$ is given in the Frenet apparatus of a space curve, and it is implemented to study the differential geometry of the given space curve. Easy and neat proofs of various well-known results are given using this new method. Also, new results and the properties of space curves are obtained in light of this new method. More specifically, the position vectors of helices are given in simple forms. Moreover, a new frame associated with a smooth curve is obtained, as well as new curvatures associated with the new frame. The new frame and its curvatures are investigated and used to give the position vector of slant helix in a simple and memorable form. Furthermore, some non-trivial examples are given to illustrate some of the results obtained in this article. Full article

Inspired by earthworm peristalsis, a novel modular robot suitable for narrow spaces is proposed, capable of elongation, contraction, deflection and crawling. Unlike motor-driven robots, the earthworm-inspired robot achieves extension and deflection in each module through “on–off” control of the SMA springs, utilizing the cooperation of mechanical skeletons and gears to avoid posture redundancy. The return to the initial posture and the maintenance of the posture are achieved through tension and torsion springs. To study the extension and deflection characteristics, we established a model through kinematic and force analysis to estimate the relationship between the length change and tensile characteristics of the SMA on both sides and the robot’s extension length and deflection angle. Through model verification and experiments, the robot’s extension, deflection and movement characteristics in narrow spaces and varying curvature narrow spaces were comprehensively studied. The results show that the earthworm-inspired robot, as predicted by the model, possesses accurate extension and deflection performance, and can perform inspection tasks in complex and narrow space environments. Additionally, compared to motor-driven robots, the robot designed in this study does not require insulation in low-temperature environments, and the cold conditions can improve its movement efficiency. This new configuration design and the extension and deflection characteristics provide valuable insights for the development of new modular robots and robot drive designs for extremely cold environments. Full article

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities $Q_k^{\left(i\right)}\left(X\right)$ and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

The rotation speed directly influences the vibration and lubrication behaviors of gear pairs, but studying the effects of time-varying rotation speeds during their operation poses substantial challenges. The present work proposed an approach to analyzing the dynamic response and lubrication performance of spur gear pairs under time-varying rotation speeds. A single-degree-of-freedom torsional dynamics model was established to capture the vibration responses and meshing forces of a gear pair, with the meshing stiffness modulated by the time-varying rotation speed. Additionally, a transient elastohydrodynamic lubrication model of the gear system was proposed to obtain the pressure pro-file and film shape, incorporating the effects of time-varying rotation speeds. Three types of time-varying rotation speeds were investigated: acceleration, deceleration, and oscillation. The results reveal that the time-varying rotation speed induces chaotic motion of the gear system, resulting in significant changes in the dynamic meshing force, entrainment velocity, and curvature radius of the gear pair compared to those in constant-speed scenarios. The lubrication performance under time-varying rotation speeds also shows diverse dynamic characteristics, highlighting significant differences from that observed under a constant rotation speed. These insights contribute to a more comprehensive understanding of gear dynamics under realistic operating conditions, enhancing gears’ performance and reliability in practical applications. Full article

In this study, we explore the sweeping surfaces in Euclidean 3-space, utilizing the modified orthogonal frames with non-zero curvature and torsion, which allows us to consider the spine curves even if their second differentiations vanish. If the curvature of the spine curve of a sweeping surface has discrete zero points, the Frenet frame might undergo a discontinuous change in orientation. Therefore, the conventional parametrization with the Frenet frame of such a surface cannot be given. Thus, we introduce two types of modified sweeping surfaces by considering two types of spine curves; the first one’s curvature is not identically zero and the second one’s torsion is not identically zero. Then, we determine the criteria for classifying the coordinate curves of these two types of modified sweeping surfaces as geodesic, asymptotic, or curvature lines. Additionally, we delve into determining criteria for the modified sweeping surfaces to be minimal, developable, or Weingarten. Through our analysis, we aim to clarify the characteristics defining these surfaces. We present graphical representations of sample modified sweeping surfaces to enhance understanding and provide concrete examples that showcase their properties. Full article

In this paper, the authors generalize the fractional curvature of plane curves introduced by Rubio et al. in 2023, to regular curves in the Euclidean space ${\mathbb{R}}^3$, and study the geometric properties of the curve using Caputo’s fractional derivative. Furthermore, we introduce a new definition of fractional curvature and fractional mean curvature of a regular surface, using fractional principal curvatures; and prove that such concepts are invariant under isometries; i.e., they belong to the intrinsic geometry of the regular surface. Also, a geometric interpretation is given to Caputo’s fractional derivative of algebraic polynomials. Full article