Curvature Of Curve Research Articles

Confined compressive stress–strain model for rectangular geopolymer reinforced concrete members

AbstractIn response to the urgent global challenge of mitigating climate change, sustainable materials have become a focal point across industries, including construction. The construction sector, recognizing its significant contribution to carbon dioxide emissions, has embarked on a relentless pursuit of eco‐friendly practices. Efforts to explore alternatives to cement, notorious for its substantial carbon footprint, have attracted considerable attention. Within this context, the present study delves into an in‐depth analysis of the stress–strain properties exhibited by geopolymer concrete (GC) column members. The primary objective is to develop a comprehensive material model of geopolymer concrete to estimate the flexural capacities of column members. To this end, inspired by the confinement model by Kent and Park, a stress–strain model incorporating the effect of confinement is proposed to accurately estimate the moment capacity of GC columns. The performance of the proposed formulation is checked using 41 different test results obtained from previous research on GC columns. Evaluations on the moment capacity estimations of the proposed model show that the results are promising in reflecting the behavior of geopolymer columns. In addition, moment–curvature curves from six recent experiments are also compared with the moment–curvature curve estimations using the proposed stress–strain model. Results show very close estimations, proving the ability of the model to be a good candidate for the performance‐based design calculations. Besides, the performance of the existing formulations from four prominent international codes (ACI318, BS8110‐97, TS500, and AASHTO) are compared with the proposed model. Notably, the flexural capacity calculated using the code formulations exhibited significant deviations from the experimental results. In contrast, the proposed model demonstrates a strong correlation with the experimental data, substantiating its effectiveness in accurately predicting the flexural capacities of GC columns.

A New Fractional Curvature of Curves and Surfaces in Euclidean Space Using the Caputo’s Fractional Derivative

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 R3, 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.

Adaptive Curve Passing Control in Autonomous Vehicles with Integrated Dynamics and Camera-Based Radius Estimation

Autonomous vehicles frequently encounter performance degradation during high-speed cornering due to excessive speed and lateral acceleration, potentially leading to collisions or rollovers. This paper proposes a novel curve-passing control approach that first estimates the curve radius and then controls the steer and speed for smooth and comfortable handling. In particular, the curve radius is innovatively estimated using a combination of a camera-based lane detection model and a steering wheel dynamic model. The curve-passing control approach is validated on high-speed ramps and curves, demonstrating its robustness and intelligence to adapt to dynamic changes in curve curvature. The model effectively prevents vehicles from entering curves at dangerously high speeds from straight roads and mitigates sudden accelerations or decelerations when entering curves. Experimental results indicate that the vehicle speed is reduced to around 50 km/h and the corresponding acceleration is −0.6 m/s2 upon entering curves with a minimum radius of 150 m. This demonstrates that the proposed control model can ensure a comfortable and safe driving experience by autonomously decelerating the vehicle before entering various types of curves.

Car-following model based on artificial potential field with consideration of horizontal curvature in connected vehicles environment

Connected vehicles (CVs) will gradually replace traditional vehicles to become the main components of traffic flow. Studying the car-following behavior characteristics is crucial for improving traffic flow stability and safety in CVs environment. Additionally, the radius of road curvature significantly impacts vehicle driving behavior, making it necessary to consider it for the car-following models of CVs. The artificial potential field (APF) theory can more accurately and comprehensively depict various microscopic driving behaviors, offering a new approach for modeling vehicle microscopic behavior. Firstly, this paper constructs the attractive and repulsive potential fields considering horizontal curve curvature based on a road coordinate transformation model. Secondly, an Artificial Potential Field-Based Car-Following Model Considering Curvature (APFCCM) in connected vehicles environment is proposed. Finally, the model is calibrated and validated using the Hangzhou - Xifu Freeway dataset from the Tongji Road Trajectory Sharing (TJRD TS) platform, and compared with the full velocity difference model(FVDM), the Intelligent Driver Model (IDM) and the Driving Risk Potential Field Model (DRPFM). The results show that the APFCCM performs well in trajectory simulation, model accuracy, and scenario adaptability, and it has the lowest mean absolute error(MAE) and root mean square error(RMSE) in position, speed, and acceleration metrics.

Numerical Simulation Studies on the Design of the Prosthetic Heart Valves Belly Curves

Prosthetic heart valves (PHVs) are employed to replace the diseased native valve as a treatment of severe aortic valve disease. This study aimed to evaluate the effect of curvature of the belly curve on valve performance, so as to support a better comprehension of the relationship between valve design and its performance. Five PHV models with different curvatures of the belly curve were established. Iterative implicit fluid–structure interaction simulations were carried out, analyzing in detail the effect of belly curvature on the geometric orifice area (GOA), coaptation area (CA), regurgitant fraction (RF), leaflet kinematics and stress distribution on the leaflets. Overall, GOA and CA were negatively and positively related to the curvature of the belly curve, respectively. Nevertheless, an excessive increase in curvature can lead to incomplete sealing of free edges of the valve during its closure, which resulted in a decrease in CA and an increase in regurgitation. The moderate curvature of the belly curve contributed to reducing RF and fluttering frequency. Valves with small curvature experienced a significantly higher frequency of fluttering. Furthermore, all stress concentrations intensified with the increase in the curvature of the belly curve. The valve with moderate curvature of the belly curve strikes the best compromise between valve performance parameters, leaflet kinematics and mechanical stress. Considering the different effects of the curvature of belly curve on valve performance parameters, the PHV design with variable curvature of belly curve may be a direction towards valve performance optimization.

A simple predictive three-step chemical model for gaseous stoichiometric hydrogen–oxygen detonation quenching

Two types of three-step chain-branching kinetics for gaseous hydrogen–oxygen detonation quenching are proposed. The reaction rates dependency on density and pressure, as well as the change in molecular weight are included and fitted to results of detailed chemistry not only along the Hugoniot curve but also behind transverse waves. The trend of induction and reaction times and reduced activation energy of zero-dimensional constant pressure combustion process as well as the induction, reaction lengths, and peak thermicity of the ZND model are focused on in the calibration procedure. One model (3SM-I) is designed to model the ideal detonation whereas the other (3SM-N) focuses on the Dn−κ curve during calibration, i.e. the detonation velocity-mean front curvature curves, aiming to capture the non-idealities. The predictive ability using the proposed models is evaluated in a detonation transmission configuration, a layer of ▪ mixture being confined by N2, in determining the critical height, reactive layer height at which detonation transmission is not possible. Both approaches get closer to the critical height from detailed chemistry. With the present set of model parameters, 3SM-I is better than 3SM-N for prediction of critical height. Moreover, borrowing analytical ignition criteria and wave hierarchy approach, the comparison of various chemical models that are able to recover the critical height suggests that the slope of the Dn−κ curve, linked with the chemical response to losses, is the first key parameter for the critical height determination. In addition, the dynamics of the extinction near criticality such as appearance of transverse detonation and quenching distance from 3SM-I are in very good agreement with that of detailed chemistry due to better estimation of the chemical features along the Hugoniot curve and behind transverse waves. The present study provides a guideline to get simplified chemical models from detailed chemistry for predictive simulations.Novelty and significance statementThe novelty of research is two-fold. The first is to provide general guideline to get simplified models from detailed chemistry for the simulation of detonation extinction with improved predictive ability. The tested configuration was that of a stoichiometric hydrogen–oxygen mixture semi-confined by nitrogen. The evolution of the induction, reaction times, and the maximum thermicity were used as fitting targets for our 3-step model. Furthermore, they were evaluated not only at the post-shock states along the Hugoniot curve, but also behind the transverse waves, keystones of the cellular structure. Second, borrowing analytical ignition criteria and wave hierarchy approach, the comparison of different chemical models that were able to recover the critical height suggested that the slope of the normal velocity–curvature curve was the first key parameter for the critical height determination. Moreover, the dynamics of extinction near criticality, and quenching distance depended on the reaction rate dependency on density and pressure.

Assisting Directional Drilling by Calculating a Safe Operating Envelope

Summary Nowadays, complex 3D trajectories are executed with a succession of circular arcs (CAs). Although they have constant curvature, their tool face is not constant. Consequently, directional drillers must adjust the tool face regularly to reach the target entry within its tolerances. This paper investigates the use of the constant curvature and constant tool face (CTC in short) curve as an alternative to the CA to assist the directional drilling work to reach the target entry within its boundaries. The problem is addressed by calculating a safe operating envelope (SOE) to reach the boundaries of the target entry and provide a tolerance window for the curvature and tool face to support directional drilling decisions. The target entry tolerance is discretized as a polygon. From the current bit position and its direction, the possible choices of curvatures and tool faces are obtained to reach the edges of the target entry shape. The SOE can be calculated with the CA or with the CTC curve. It is, therefore, possible to compare the advantages and disadvantages of both types of curves to attain the target entry and stay within its boundaries. The CA is shorter than the CTC curve. However, it requires adjusting the tool face during the navigation, which is not the case with the CTC curve. As a result, the directional driller can control the bottomhole assembly (BHA) direction such that the well lands within the target entry limits by using set points for tool face and curvature inside the calculated SOE. Furthermore, a new way to represent the SOE is introduced. It makes use of a 3D cylindrical representation where the curvature is mapped as the height of a cylinder, while the tool face corresponds to the azimuth in the cylindrical coordinate system, and the length is linked to the radial distance. This provides a visual aid to understand the SOE. Moreover, this visualization helps to appreciate the relationship between the initial bit location and direction in the construction of the SOE and how the margins increase in a particular manner as the bit approaches the target entry polygon. The CTC curve is the natural one followed by directional positive displacement motors (PDMs) or rotary steerable systems (RSS). Potentially, the CTC curve may be a more straightforward solution to automated directional drilling control because it is easier to be followed by both PDM and RSS.

Gauss–Bonnet Theorem Related to the Semi-Symmetric Metric Connection in the Heisenberg Group

In this paper, we introduce the notion of the semi-symmetric metric connection in the Heisenberg group. Moreover, by using the method of Riemannian approximations, we define the notions of intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on a surface, and the intrinsic Gaussian curvature of the surface away from characteristic points in the Heisenberg group with the semi-symmetric metric connection. Finally, we derive the expressions of those curvatures and prove the Gauss–Bonnet theorem related to the semi-symmetric metric connection in the Heisenberg group.

New insights into folding tape-spring

The tape-spring is widely used in aerospace, mechanical, and civil engineering due to its unique mechanical properties and compact size. This paper aims to establish a new analytical model to more accurately predict the folding behavior of the tape-spring, including the geometric configuration, folding moment versus longitudinal curvature curve, peak moment, and propagation moment. This model comprehensively considers the influence of stretching strain energy and bending strain energy on the total strain energy, and determines the folding behavior of the tape-spring through the minimum energy principle. The proposed analytical model was compared with Wuest’s model, Yee’s model, and Yao’s model. Experiments of tape-springs made from two different materials were utilized for validation. The study shows that the proposed model has the highest prediction accuracy compared with the classical models, with the error of approximately 10%. The reason for the significant difference in the prediction results between the proposed model and Yao’s model was given, and the relationship between stretching strain energy and bending strain energy during the folding process of the tape-spring was analyzed. The proposed model has broader applicability than classical models and provides new insights and solutions for accurate prediction of the folding behavior of the tape-spring.

The curvature quantification of waveI in auditory brainstem responses detects cochlear synaptopathy in human beings.

Patients with age-related hearing loss complain often about reduced speech perception in adverse listening environment. Studies on animals have suggested that cochlear synaptopathy may be one of the primary mechanisms responsible for this phenomenon. A decreased waveI amplitude in supra-threshold auditory brainstem response (ABR) can diagnose this pathology non-invasively. However, the interpretation of the waveI amplitude in humans remains controversial. Recent studies in mice have established a robust and reliable mathematic algorithm, i.e., curve curvature quantification, for detecting cochlear synaptopathy. This study aimed to determine whether the curve curvature has sufficient test-retest reliability to detect cochlear synaptopathy in aging humans. Healthy participants were recruited into this prospective study. All subjects underwent an audiogram examination with standard and extended high frequencies ranging from 0.125 to 16kHz and an ABR with a stimulus of 80dBnHL click. The peak amplitude, peak latency, curvature at the peak, and the area under the curve of waveI were calculated and analyzed. A total of 80 individuals with normal hearing, aged 18 to 61 years, participated in this study, with a mean age of 26.4 years.Pearson correlation analysis showed a significant negative correlation between curvature and age, as well as between curvature and extended high frequency (EHF) threshold (10-16kHz). Additionally, the same correlation was observed between age and area as well as age and EHF threshold. The model comparison demonstrated that the curvature at the peak of waveI is thebest metric to correlate with EHF threshold. The curvature at the peak of wave I is the most sensitive metric for detecting cochlear synaptopathy in humans and may be applied in routine diagnostics to detectearly degenerations of the auditory nerve.

Fractional Curvatures of Equiaffine Curves in Three-Dimensional Affine Space

This paper presents a method for computing the curvatures of equiaffine curves in three-dimensional affine space by utilizing local fractional derivatives. First, the concepts of $\alpha$-equiaffine arc length and $\alpha$-equiaffine curvatures are introduced by considering a general local involving conformable derivative, V-derivative, etc. In fractional calculus, equiaffine Frenet formulas and curvatures are reestablished. Then, it presents the relationships between the equiaffine curvatures and $\alpha$-equiaffine curvatures. Furthermore, graphical representations of equiaffine and $\alpha$-equiaffine curvatures illustrate their behavior under various conditions.

A high-precision fusion bathymetry of multi-channel waveform curvature for bathymetric LiDAR systems

Airborne LiDAR bathymetry (ALB) system is an attractive and efficient method for nearshore bathymetry and underwater topography mapping. To ensure and improve the measurement accuracy and reliability in various water environments, different receivers using a segmented field of view (FOV) have been designed and are implemented in ALB. These are used to obtain various echo data of multiple channels and perform bathymetry at various water depths. However, in echo waveform processing, detailed information about the water body described by the different echo waveforms is lacking, making it difficult to overcome severe waveform superposition in extremely shallow areas or to separate the weak echo of the water bottom from the noise in extremely deep areas. Therefore, we employed a novel method of multi-channel waveform fusion bathymetry (MWFB) to achieve information complementarity, gain multi-channel waveforms, and detect the robustness of water and bottom echo signals. This method uses an adaptive signal waveform extraction of a multichannel fusion mechanism to eliminate systematic and random noise, and the waveform curvature is used to reconstruct the energy–waveform curves. Iterative decomposition based on waveform curvature and energy curves was conducted to improve the correctness of waveform decomposition and the reliability of waveform components. Furthermore, the water surface and bottom peaks were detected based on the multichannel waveform curvature, which enabled acquisition of the accurate temporal positions of the peaks and achieve high-accuracy bathymetry. According to the experimental results and a comparison with reference datasets, the highest bathymetric accuracy of the MWFB method reached an RMSE of 0.22. For the different study areas, the bathymetric accuracy of the slope reached 95%, 92%, and 97% at Ganquan Island, Lingyang Reef, and Bei Island, respectively. Furthermore, the bathymetric point numbers were effectively increased and bathymetric accuracy was also improved in shallow and deep water, which illustrates the superior bathymetric performance of the MWFB method and its ability to provide a high-efficiency waveform dataset through multi-channel data fusion. The novel LiDAR bathymetric method proposed in this study can effectively achieve high-accuracy nearshore bathymetry and seafloor topographical mapping.

Curve-Surface Pairs on Embedded Surfaces and Involute D-Scroll of the Curve-Surface Pair in E3

Willmore defined embedded surfaces on f:S→E3, which is the embedding of S into Euclidean 3-space. He investigated the Euclidean metric of E3, inducing a Riemannian structure on f(S). The expression analogous to the left-hand member of the curvature K is replaced by the mean curvature H2 on f(S). Our aim is to observe the Gaussian and mean curvatures of curve–surface pairs using embedded surfaces in different curve–surface pairs and to define some developable operations on their curve–surface pairs. We also investigate the embedded surfaces using the Willmore method. We first recall the Darboux curve–surface and derive the new characterizations. This curve–surface pair is called the osculating Darboux curve–surface if its position vector always lies in the osculating Darboux plane spanned by a Darboux frame. Thus, we observed an osculating Darboux curve–surface pair. We also obtained the D∼-scroll of the curve–surface pair and involute D∼-scroll of the curve–surface pair with some differential geometric elements and found D∼(α,M)(s) and D∗∼(α,M)(s)-scrolls of the curve–surface pair (α,M).

Robust Constant Curvature Curve Communications with Complex and Quaternion Neural Networks

Robust Constant Curvature Curve Communications with Complex and Quaternion Neural Networks

Analysis on the allocation equality in occupational health technology service resource in Gansu Province

Objective: To investigate and analyze the allocation equality of occupational health technology service resource of Gansu disease control and prevention institutions, providing reference basis for optimizing the allocation of occupational health technology service resources. Methods: Combined with the survey data in September 2021, Gansu Province was divided into five economic regions by geographical location and economic characteristics. Taking the service number of enterprises and workers as the analysis dimensions, the allocation level of occupational health technology service resources in different regions was compared. The allocation equality was analyzed through Lorentz curve, Gini coefficient and Theil index. Results: There were 301 occupational health technicians and 1914 sampling and testing equipments of Gansu Provincial disease control and prevention institutions in 2021. All of the technicians and equipments were used for serving 1952 enterprises and 465800 workers. The curvature of Lorentz curves and Gini coefficient which measured by the service number of enterprises and workers were: occupational health technicians>radioactive factor sampling and testing equipment >physical factor sampling and testing equipment >chemical factor sampling and testing equipment, and chemical factor sampling and testing equipment>physical factor sampling and testing equipment >radioactive factor sampling and testing equipment >occupational health technicians, respectively. Theil index of occupational health technology service resources suggested that differences in regions were the main unfair reason effected the allocation of occupational health technicians and radioactive factor sampling and testing equipment, while the differences between regions were the main unfair reason effected the allocation of chemical and physical factor sampling and testing equipment. Conclusion: The allocation equality in occupational health technology service resources of Gansu Provincial disease control and prevention institutions was not enough, and the differences in regions and between regions should be considered. This study suggests that it is necessary to introduce more occupational health technicians. The allocation of occupational health technology service resources should match with the number of local enterprises and the types of potential hazard factors of enterprises as far as possible.

Coupled effects of temperature and relative humidity on desiccation curling of a clayey soil

Soil curling caused by drying is a common phenomenon in nature, and it can vary depending on different atmospheric effects. To investigate the coupled effects of temperature and relative humidity on soil curling, a sequence of desiccation experiments were performed by using elongated strip soil samples in the laboratory. The soil curling process is divided into five stages: vertical settlement stage, lateral contraction stage, concave-up curling stage, curling recovery stage and convex-up curling stage. In this study, the soil evaporation characteristic and curvature curves are obtained under different temperature and relative humidity conditions. The findings revealed that a lower relative humidity results in a higher evaporation rate and a smaller maximum concave-up curling curvature for soil samples. Additionally, as the temperature increased, the water content associated with concave curling decreased. The maximum concave-up curling curvature was determined by the transition from the appearance of concave-up curling to the maximum curvature of concave-up curling. Under the coupled effect of temperature and relative humidity, all the water content associated with the occurrence of concave-up curling, maximum concave-up and convex-up curling appearance are reduced with increasing temperature and decreasing relative humidity. As the temperature ranged from 20 °C to 40 °C, the maximum concave-up curling curvature initially decreased and then increased. Conversely, the maximum concave-up curling curvature increased within the relative humidity range of 30% to 45%.

Experimental and theoretical study on longitudinal deformation and internal force of shield tunnel under surcharge

The longitudinal behavior of a shield tunnel is essential for analyzing its deformation and internal forces under surcharge. This study involved the design and construction of a reduced-size indoor model of a tunnel to investigate its performance with various initial ovalities when subjected to different surcharges. Furthermore, a model was proposed to investigate the longitudinal deformation of the tunnel caused by rotation and dislocation, which was verified and compared. The results reveal that the longitudinal settlement of the tunnel follows a normal distribution. The maximum settlement occurs at the central ring and increases linearly with the applied load. The zone of strong influence extends approximately 1.6 times the load width, and an additional load of 20 kPa can be employed as a control value for the surcharge. Additionally, the study found that stress concentration typically occurs on the side of the tunnel waist under surcharge. As a result, the horizontal convergence at the central ring increases at a faster rate, leading to transverse elliptical deformation of the entire structure. The longitudinal curves of curvature and dislocation visually reflect that the dangerous sections of the tunnel structure are concentrated at the center and edge of the load. Moreover, the rate of deformation development and final deformation values differ among tunnels with varying initial ovalities, and there is no simple linear relationship between them. The oval shape of the tunnel exacerbates the progression of longitudinal deformation while inducing a three-dimensional coupling effect between adjacent segments. Ultimately, the plausibility of the experimental results is confirmed based on the proposed longitudinal model of the tunnel, thereby establishing a connection with practical engineering applications.

An improved dynamic threshold method for determining the start of the vegetation greening season in remote sensing monitoring: The case of Inner Mongolia

The start of the greening season (SOS) is the beginning of vegetation phenology, and its time of occurrence affects the carbon cycle and organic matter production of the ecosystem. Accurate retrieval of vegetation phenology in remote sensing monitoring is important for sustainable management of vegetation resources. The dynamic threshold method (DTM) is one of the mainstream methods to retrieve vegetation phenology. However, it suffers the following two shortcomings. First, a subjective threshold percentage of the phenology nodes is used based on the user's empirical thresholds, and the determined threshold is not universal. Second, a common threshold is used for identifying the phenology globally with little consideration of the physiological characteristics of different vegetation types, thus blurring the phenology variability among vegetation types. Here, we developed an improved dynamic threshold method (IDTM) for the retrieval of the start of the greening season and tested it using temperate grassland and forest vegetation in Inner Mongolia. The algorithm in the IDTM uses the curvature of the EVI2 time series curves of different vegetation types to determine the threshold for the SOS, thus eliminating the subjectivity of the original DTM. The predicted SOS of the IDTM is in better agreement with the ground observations than the MCD12 Q2 vegetation phenology product or the DTM with different empirical thresholds. In terms of spatial correlations, the SOS of the IDTM was significantly correlated with that of the MCD12 Q2 phenology product (r = 0.72, p < 0.05). Our study indicates the efficacy of the IDTM in predicting the SOS of vegetation and that the average SOS of vegetation in Inner Mongolia is in early May (on Day 126) but has a large variation across vegetation zones.

Ruled surface family with common special curve

In this paper, we investigate the problem of the construction of a ruled surface family passing through the striction curve (c) of a ruled surface φ. We first define ruled surface family with common striction curve (c). Using the geodesic Frenet frame {e,t,g} of the ruled surface φ, we present sufficient conditions for that striction curve to be geodesic, line of curvature and asymptotic curve. Finally, we give some examples to show ruled surfaces with common geodesic, line of curvature and asymptotic curve.

Ultra-thin composites membrane for deployable structures: XCT driven characterization and FE modeling of folding structure

Light-weight, ultra-thin, high performance, origami-inspired deployable folding structures can be fabricated by simulating various designs and material combinations. In this study, an XCT-driven finite element (FE) model of a building block in a typical full-scale origami structure consisting of stiff and fold regions was developed. Following our previous work, the stiff region of the fold sample was fabricated using a hot compression molding technique whereas hand layup was employed for the fold region. XCT-driven FE based homogenization was carried out on an RVE of real microstructure of both ultra-thin composite laminates. The FE homogenization results were found to be in good agreement with the experimentally-measured effective stiffness properties of both the stiff and fold regions, with a maximum error of ∼10%. Folding tests were conducted on a simple fold and the force vs. displacement and moment vs. curvature curves were plotted. The applicability of XCT-driven FE modeling to simulate foldable structures were demonstrated using post-buckling and bending analysis available in the FE software ABAQUS®. A uniform and symmetric fold curvature, along with the corresponding force vs. displacement response were predicted using XCT-driven FE techniques and found to be in good agreement with data from the experimental tests. The peak force predicted by the FE model showed an error of ∼5.2% compared to the experimental fold test.