Hyperbolic Function Research Articles

Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns

The aim of current work is to establish novel traveling wave solutions of the nonlinear Atangana conformable Klein - Gordon equation using a new extended direct algebraic technique. The Klein - Gordon equation is the relativistic state of the Schrödinger equation with a second - order time derivative and zero spin. Complex wave variable transformation is used to convert Atangana conformable nonlinear differential equation into an ordinary differential equation. Using the proposed technique based on Maple software structure, various types of solutions, such as, generalized trigonometric, generalized hyperbolic, and exponential functions, are established. When special parameteric values are considered for this method, solitary wave solutions can be obtained through other methods, such as the (G′G)-expansion method, the modified Kudryashov method, the sub-equation method, and so forth. A physical explanation is provided for the solutions under consideration to enhance comprehension of the physical phenomena resulting from the obtained solutions, provided that the physical parameters are set appropriately using 3D, 2D, and contour simulations. The results demonstrated that the new extended direct algebraic method provides a more potent mathematical tool for solving numerous more nonlinear partial differential equations with the aid of symbolic computation.

Hyperbolic map unravels eight regions in temperature volatility regionalization of Mainland China

Abstract Abrupt temperature volatility has detrimental effects on daily activities, macroeconomic growth, and human health. Predicting abrupt temperature volatility and thus diminishing its negative impacts can be achieved by exploring homogeneous regions of temperature volatility and analyzing the driving factors. To investigate the regionalization of temperature volatility in Mainland China, a network constructed by the cosine similarity of temperature volatility series from Mainland China was embedded in hyperbolic space. Subsequently, we partitioned the network on the hyperbolic map using the critical gap method and then found eight regions in all. Ultimately, a network of communities was constructed while the interaction among communities was quantified. This yields a perspective of temperature volatility regionalization that can accurately reflect factors including altitude, climate type, and the geographic location of mountains. Further analysis demonstrates that the regionalization in the hyperbolic map is distinct from provinces and has a realistic basis: communities in southwest China show strong correlations due to the temperature sensitivity to altitude, and communities in northern China show a convergence in the area of Dingxi, Gansu, mainly owing to the strong temperature sensitivity to climate types. As a consequence, node distributions and community divisions in the hyperbolic map can offer new insights into the regionalization of temperature volatility in Mainland China. The results demonstrate the potential of hyperbolic embedding of complex networks in forecasting future node associations in real-world data.

Dynamic Docking Anti‐Disturbance Control of Overactuated AUV: System, Method, and Lake Trails

ABSTRACTDynamic docking control technology is crucial for autonomous underwater vehicles (AUV) to perform tasks underwater. To enhance the docking success rate of AUVs during dynamic docking, this paper presents a robust anti‐disturbance control algorithm specifically designed for overactuated AUV dynamic docking scenarios. During a dynamic docking mission, the AUV's depth control is adversely affected by the complex flow field generated by the underwater recovery device. To address this issue, this research proposes an AUV control scheme that combines an extended state observer (ESO) with a combined disturbance rejection method of the elevator‐vertical tunnel controller. First, an ESO is constructed to estimate and compensate for complicated disturbances such as model uncertainty and environmental disturbances. These estimations are then incorporated into the control law to mitigate the effects of the complicated flow field interference experienced during the AUV's dynamic docking process. Second, as turbulence intensifies at the end of the docking stage, the vertical thrust allocation is achieved using a hyperbolic tangent transition function. This ensures the stability of the AUV's attitude and depth, thereby enabling precise docking. Finally, the effectiveness of the proposed control algorithm is verified through lake trials and compared against the classic proportional‐integral‐differential (PID) and active disturbance rejection control (ADRC) methods. The trial results indicate that the proposed control algorithm significantly reduces the pitch and depth errors of the AUV, resulting in a remarkable 91% success rate for dynamic docking (based on 45 tests). The lake trials demonstrate that the proposed control algorithm is highly precise and robust.

Design and implementation of dynamic s-boxes based on non-degenerate discrete chaotic systems

In recent years, digital chaotic systems have received considerable attention in the field of secure communications. However, during the digitalization of the system, the original properties of the chaotic system may change, resulting in the degradation of the dynamics. To address this problem, this paper designs a novel simplicial non-degenerate discrete chaotic system based on the inverse hyperbolic tangent function, and selects a three-dimensional discrete system as the object of analysis. Through the research conducted, it is found that the chaotic system exhibits high Lyapunov exponents under certain conditions. Furthermore, the excellent randomness of the system has been further validated by NIST SP800–22 tests. At the same time, this paper also proposes a dynamic S-box construction method based on the chaotic sequence generated from the three-dimensional chaotic mapping. By performing a series of basic operations and permutation treatment, many dynamic S-boxes can be generated. This paper comprehensively analyses the performance of S-boxes from two perspectives: single S-boxes and multiple S-boxes. The analysis covers issues such as bijective property, nonlinearity, strict avalanche criterion, differential approximation probability and bit independence criteria. The results of the performance analysis show that the dynamically generated S-boxes have excellent cryptographic properties, making them suitable for the design and application of cryptographic algorithms.

Thermo-Mechanical Coupling Load Transfer Method of Energy Pile Based on Hyperbolic Tangent Model

By employing the hyperbolic tangent model of load transfer (LT), this paper establishes the thermo-mechanical (TM) coupling load transfer analysis approach for an energy pile (EP). By incorporating the control condition of the unbalance force at the null point, the method for determining the null point considering the temperature effect is enhanced. The viability of the presented method is validated through the measured outcomes from model experiments of energy piles. A parametric investigation is conducted to explore the impact of the soil shear strength parameters, upper load, temperature variation, head stiffness, and radial expansion on the axial force, strain, and displacement of the energy pile under thermo-mechanical coupling. The results suggest that the locations of the null point and the maximum axial force are dependent on the constraint boundary conditions of the pile side and the two ends. When the stiffness of the pile top increases, axial stress and displacement increase, while strain decreases. An increase in the drained friction angle leads to an increase in axial stress under thermal-load coupling, but strain and displacement decline. The radial expansion has a negligible influence on the thermo-mechanical interaction between the pile and the soil.

Development of an improved mass transfer model for condensation with dynamic feedback regulation

In the field of condensation research, accurate and efficient numerical simulation models are highly desired. One of the widely used phase change mass transfer models is known as the Lee model. However, this model has limitations due to uncertainties in the mass transfer intensity factor, which can lead to simulation failures and impede large-scale engineering applications. This study presents an improved mass transfer model which employs a tuning function to dynamically and accurately modify the mass transfer intensity factor in each two-phase cell via feedback adjustment. This approach enables immediate and customized adjustment of the factor for each grid within the limit of the tuning function, significantly reducing the errors caused by repeated artificial adjustments and related uncertainties. The adjustment capabilities of the hyperbolic tangent and softsign functions are evaluated. The softsign function is superior in both regulation efficiency and accuracy. The model's accuracy is verified by comparing with previous experiments and simulations, as well as by the one-dimensional Stefan problem. The proposed model achieves high prediction accuracy, reduces the risk of simulation dispersion, and significantly enhances computational efficiency with the iteration number reduced by nearly half under certain conditions compared to the Lee model. Furthermore, the new model shows robustness as the prediction accuracy is insensitive to variations in critical parameters. The improved model is expected to provide valuable assistance for future research and applications in flow condensation with outstanding computational accuracy, efficiency, and stability.

Predicting and Analyzing Electric Bicycle Adoption to Enhance Urban Mobility in Belgrade Using ANN Models

The development of alternative environmentally friendly modes of transportation is becoming an increasingly promising solution in traffic-congested and polluted urban areas. E-bikes, as one of them, are recognized as an ecologically sustainable means of transportation that has significant potential to replace motorized modes of transportation that can improve urban mobility. Relying on artificial intelligence and considering an ecological approach when considering the acceptability of e-bikes by setting a direct question for users influences the development of an innovative way of understanding and evaluating the use of more sustainable modes of transportation. In this regard, this study aims to elucidate the main variables influencing the acceptability of e-bike use using artificial neural network (ANN) models—multilayer perceptron (MLP) and radial basis function (RBF). For training and testing the models, data from a random sample obtained through an online questionnaire, which was answered by 626 residents of Belgrade (Serbia), were used. A multilayer perceptron with nine and seven neurons in two hidden layers, respectively, hyperbolic tangent activation function in the hidden layer and identity function in the output layer, gave better results than the radial basis function model. With an accuracy of 89%, a precision of 83%, a recall of 79%, and an area under the receiver operating characteristic (ROC) curve of 0.927, the multilayer perceptron model recognized the influential variables in predicting acceptability. The results of the model indicate that the mileage traveled, the frequency of motorcycle use, the respondents’ awareness of the pollution in Belgrade, and the age of the respondents have the greatest influence on the acceptability of using e-bikes. In addition to majority acceptability (69.8%), the results obtained by the model can represent a useful basis for decision-makers when defining strategies for the development and application of e-bikes while reducing traffic congestion and environmental pollution in Belgrade.

Predicting and analysis of urban wastewater quantity to be treated by using Neural Network and ODE model: A case study

Wastewater data, including Population of the Municipality Served by the Wastewater Treatment Plants (WWTPs), Capacity, Number of WWTPs, Amount of Daily Wastewater Discharged per Person and Wastewater Treated in WWTPs (y(t)) obtained from Turkish Statistical Institute (TUIK) for Kayseri province for 2003-2020 were mathematically modelled and analysed with Artificial Neural Network (ANN) and Differential equations. Firstly, the data were augmented through ARIMA since TUIK data numbers are insufficient to ANN training and later the data were normalized. The augmented normalized data was trained with ANN twice, thus the effect of other variables on the y(t) variable was shown and mathematical ANN activation functions in the form of a tangent hyperbolic function was proposed for this variable. Then, arbitrary parameters used for a linear system consisting of differential equations representing the five variables mentioned above were estimated using normalized original data and thus the ODE (ordinary differential equation) model was proposed. Two ANN models and ODE model were evaluated on normalized real TUIK data and the performances of these three models were compared. Among these mathematical models, the model that gave the minimum MSE (mean squared error) has been determined as the ODE model. Finally, future predictions were made for the y(t) variable with the ODE model.

Satellite observations and modeling of the plasmapause structure and dynamics

We investigated the structure and dynamics of the plasmapause using electron density data from the Arase (ERG) satellite between 2017 and 2019. By fitting the electron density profile to a hyperbolic function using the least-squares method, 1891 plasmapause events were identified. The hyperbolic function’s fitting parameters were used to estimate the plasmapause’s location and thickness. The plasmapause location and thickness were mapped onto the geomagnetic equator plane. We examined the dependence of the plasmapause location and thickness on the geomagnetic disturbance. The median plasmapause location on the geomagnetic equator plane was 32,089 km from Earth’s center. Plasmapause locations depend on geomagnetic disturbances that vary between four and six radii of the Earth.In contrast, the median plasmapause thickness obtained by fitting a hyperbolic function on the geomagnetic equator plane was 2472 km. The thickness changed from ∼1500 km at night to ∼ 3000 km during the daytime. The thickness was several times larger than the ring current H+ Larmor radius, suggesting an association with plasma instability in the plasmapause due to the penetration of magnetospheric electric fields.Additionally, we developed a three-dimensional empirical electron density model with historical effects associated with refilling the plasmasphere, plasmapause, and magnetosphere. The International Reference Ionosphere (IRI) model can be enhanced to incorporate the electron density model of the plasmasphere and estimate the total electron content (TECp) in the plasmasphere using the empirical model. Our analysis provides valuable insights into plasmapause and contributes to a better understanding of the inner magnetosphere.

Topology‐preserving phase‐field modeling of elastic bending energy

AbstractIn vesicle membranes, the minimum of the elastic bending energy determines the equilibrium shape. We can reformulate the energy using a phase‐field function and optimize it using the standard gradient flow approach. The method, in its typical formulation, allows topological changes in the membrane; however, in certain events, like in the simulation of blood cells, maintaining the initial topology of the membrane is crucial. In this study, we add a constraint on the phase‐field method to preserve the topology. We note that even if the phase‐field method is formulated using a hyperbolic tangent function, during a change in topology, the membrane's profile deviates from the tanh function. Owing to this idea, the constraint imposes an additional requirement on the profile to maintain the tanh shape, thus preserving the topology. We perform extensive experiments in two‐dimensional and three‐dimensional scenarios to demonstrate that our method preserves the topology during the simulation.

Onset of Darcy–Brinkman convection with thermal anisotropy in an inclined porous layer

In this article, we study the linear instability and the nonlinear stability (through energy functional) analyses of thermal convection in an inclined Darcy–Brinkman porous layer considering uniformly heated horizontal rigid, impermeable walls from below and above. The effects of a uniform internal heat source and anisotropy in effective thermal diffusivity on heat transfer are also considered. Heating the porous layer from below yields the temperature gradient, influencing the buoyancy and making the convection happen. This temperature gradient also impacts the base state. The basic solution for velocity incorporates both hyperbolic and polynomial functions, significantly increasing the complexity of linear and nonlinear analyses. The Chebyshev-tau method, together with the QZ algorithm, is used to solve the linear and nonlinear perturbed system of equations numerically. The region of subcritical instability is obtained by comparing the linear and nonlinear thresholds for the longitudinal and transverse rolls, respectively. We found that perturbations for longitudinal and transverse rolls do not grow after inclination is more than 30.3° and 31.3°, respectively. It has been noted that in transverse roll scenarios, the flow becomes stabilized when the inclination angle, ϕ, is equal to or exceeds 60°, where ϕ plays a leading role in surpassing the impact of internal heating. However, when the inclination angle is ϕ<60°, then internal heating dominates and destabilizes the flow. For the longitudinal rolls, the internal heating dominates the whole range of ϕ, destabilizing the system. Furthermore, it can be seen that the Darcy number (Da) and the anisotropic thermal diffusivity (ξ) delay the onset of convection.

Preferable price to buy an electric two-wheeled vehicle for college students

This research delves into the determinants affecting Taiwanese college students’ purchasing behavior towards two-wheeled electric vehicles (ETWVs) and the financial allocation they are willing to commit. A choice experiment design was utilized, with a sample of approximately 900 college students, regular users of two-wheeled gasoline vehicles (TWGs). The students engaged in one of two choice scenarios, presented with general characteristics, operational efficiency, vehicle cost, and subsidy strategies. Subsequent to the scenarios, respondents indicated their willingness to pay (WTP) for a ETWV. ETWVs, apart from being an emerging transportation alternative, also present potential environmental and health benefits due to reduced air pollution. The dependent inverse hyperbolic sine (IHS) double-hurdle model was employed, facilitating the accommodation of heteroscedasticity and correlated normality. The outcomes suggest that purchasing behavior for ETWVs among college students is shaped by factors such as purchase subsidy, tax breaks, and ETWVs’ capability in supporting students’ external travel requirements. The average WTP for ETWVs among this demographic stands at US$ 1,410. Importantly, the dependent IHS double-hurdle model, considering heteroscedasticity, proved statistically superior to its counterparts. Insights from this research offer crucial information on the price range students are likely to accommodate for ETWVs and provide a foundation for framing incentive-driven policies to amplify ETWV adoption

On a geometric version of the Grothendieck conjecture for configuration spaces of hyperbolic curves

On a geometric version of the Grothendieck conjecture for configuration spaces of hyperbolic curves

An analog of the pendulum/rotor system with elementary solutions

Abstract We explore a novel one-dimensional model potential, V(x), which mimics many aspects of the classic pendulum/rotor system, including low- and high-energy limits which are exactly solvable, as well as a divergent period separating the two. Using energy methods, the classical period, T(E), is evaluated in closed form for all values of the energy (0 < E < ∞) in terms of simple logarithmic functions, in contrast to the pendulum/rotor system where the results require elliptic integrals. We find an unexpected duality between the exact expressions for the period on either side of the divergence. Using both energy methods, and a Newton’s law differential equation approach, we present closed form expressions for trajectory solutions, x(t) and p(t) = mv(t) (or the linear momentum), in terms of hyperbolic functions, which explicitly give the same values for T(E).

Chemical shrinkage characteristics and prediction model of desulfurization electrolytic manganese residue-cement composite slurries

To reveal the chemical shrinkage (CS) characteristics of desulphurized electrolytic manganese residue (D-EMR) cement composite slurries, the CS was measured for slurries with different water-cement ratios (0.3 and 0.4) and varying D-EMR content (0 wt%, 5 wt%, 10 %, 15 wt%, 20 wt%, 25 wt%, and 30 wt%) using the expansion method. Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), and backscattered electron (BSE) image analysis were used to investigate the hydration products and pore porosity at different stages. In addition, the correlation between CS and hydration products was simulated using GEMS thermodynamics. The results indicate that as the water-cement ratio increases, the CS of D-EMR cement composite slurries increases significantly. At a water-cement ratio of 0.4, the CS decreases with increasing D-EMR replacement levels before 1829 h of hydration, but this trend reverses after 1829 h. At 8 days, the CS values for replacement levels of 5 wt%, 10 wt%, 15 wt%, 20 wt%, 25 wt%, and 30 wt% were 97.2 %, 94.9 %, 87.3 %, 84.4 %, 81.5 %, and 78.6 % of those of the pure cement pastes, respectively. The corresponding limiting chemical shrinkage values were 0.0712 mL/g, 0.0725 mL/g, 0.0742 mL/g, 0.0756 mL/g, 0.0769 mL/g, and 0.0780 mL/g. Finally, the prediction of long-term CS of D-EMR cement composite slurries is well described by both hyperbolic function prediction and thermodynamic simulations. These findings provide valuable theoretical support for the use of D-EMR as a supplementary cementitious material in construction.

A robust approach to satellite image encryption using chaotic map and circulant matrices

AbstractIn the modern era, where satellite imagery is vital for applications like ecological monitoring and national security, ensuring the safety and integrity of these data repositories is crucial. This study presents an improved satellite image encryption technique that combines the cryptographic strength of the circulant matrix in the Hill cipher with the dynamic characteristics of the hyperbolic tangent tent map, further enhanced by the Kronecker XOR product. The algorithm initiates with computing alterations by a shift amount. After preserving the leftmost pixel in each row, it executes XOR operations between alternating rows, combining the value of the current even or odd row with corresponding pixels in the adjacent rows followed by encryption using the Hill cipher. The resulting image undergoes a diffusion process utilizing a hyperbolic tangent tent map. The Kronecker XOR product operation is then applied to individual pixels to produce a secure image followed by additional diffusion with keys from the hyperbolic tangent tent map to achieve the final encrypted image. We conducted simulations using MATLAB to assess the efficiency of the proposed satellite image encryption from theoretical and statistical perspectives. The results exhibit robust encryption performance as demonstrated by metrics such as an entropy value of 7.9982, a UACI of 33.5333%, and an NPCR of 99.6038%. The experiment results demonstrate the proposed image encryption scheme's reliability, practicability, and efficiency in securing satellite images during data storage and transmission. Comprehensive testing against various attacks including correlation, histogram, chi‐square, NPCR, PSNR, UACI, SSIM, key space and key sensitivity analysis confirms the scheme's robustness, efficiency and speed. These findings verify the scheme's ability to come across the most stringent encryption and decryption standards, making it an effective solution for securing sensitive satellite image data.

Detecting edges of geologic sources from gravity or magnetic anomalies through a novel algorithm based on hyperbolic tangent function

Detecting edges of geologic sources from gravity or magnetic anomalies through a novel algorithm based on hyperbolic tangent function

A novel deep learning‐based technique for driver drowsiness detection

AbstractEvery year, many people lose their lives because of road accidents. It is evident from statistics that drowsiness is one of the main causes of a large number of car accidents. In our research, we wish to solve this major problem by measuring the drowsiness level of the human brain while driving. The study aims to develop a novel technique to detect different alertness levels (i.e., awake, moderately drowsy, and maximally drowsy) of a person while driving. A hybrid model using a stacked autoencoder and hyperbolic tangent Long Short‐Term Memory (TLSTM) network with attention mechanism is designed for this purpose. The designed model uses different biopotential signals, such as electroencephalography (EEG), facial electromyography (EMG), and different biomarkers, such as pulse rate, respiration rate galvanic skin response, and head movement to detect a person's alertness level. Here, the stacked autoencoder model is used for automated feature extraction. TLSTM is used to predict a person's alertness level using stacked autoencoder network‐extracted features. The proposed model can classify awake, moderately drowsy, and maximally drowsy states of a person with accuracies of 99%, 98.3%, and 98.6%, respectively. The novel contributions of the paper includes (i) incorporation of an attention mechanism into the TLSTM network of the proposed hybrid model to focus on the emphatic states to enhance classification accuracy, and (ii) utilization of EEG, facial EMG, pulse rate, respiration rate, galvanic skin reaction, and head movement pattern to assess a person's alertness level.

Hot Torsion Tests of AA6082 Alloy

Materials characterization and the knowledge of their elastic-plastic behavior are of fundamental importance for the design of industrial manufacturing processes. Nowadays, FEM simulation is the main tool used to optimize product quality and minimize scraps, and the numerical codes have evolved over the years to obtain accurate solutions with reduced computational times. Nevertheless, in order to perform reliable simulations, it is necessary to include accurate modeling of the material flow stress. Hot torsion is a powerful method for the characterization of the material flow stress because, tests can be carried out at constant speeds and temperatures, reaching large strain values, and thus getting over the limits of compression and tensile tests. In this paper the hot torsion characterization applied to AA6082 alloy is presented: tests were performed with equivalent strain rates of 0.01, 0.1, 1, and 10 s-1, in the temperature range from 440 to 550 °C (from 713.15 to 823.15 K). The results are presented in terms of equivalent stress vs equivalent strain. Finally, the material flow stress curve was predicted by the Hyperbolic sine model and Hensel-Spittel law, and the material parameters A, m1-9 are provided for the temperature expressed in °C and K.

Validation of a novel effort-discounting assessment and evaluation of the effort-delay confound on effort discounting.

A vast literature highlights the prevalence of impulsive decision making in maladaptive outcomes. Most research has focused on one form-delay discounting. Less research has focused on effort discounting, possibly because of a lack of a standardized task for assessment. In published effort-discounting tasks, effort is conceptualized in many ways, making it difficult to compare findings across studies. Additionally, most effort-discounting tasks do not control for the time inherent in completing the effortful task, which makes it difficult to disentangle effort discounting from delay discounting. The current study evaluated the validity of a novel hypothetical effort-discounting task. The novel task was used to evaluate the influence of the effort-delay confound on rates of effort discounting in humans. Participants were randomly assigned to complete a confounded or a controlled version of the novel effort-discounting task. The effort-discounting data were well described by hyperbolic and exponential functions. When effort and delay were confounded, effort-discounting rates were significantly higher than when effort alone influenced discounting. The results suggest that data that are produced by effort-discounting tasks that do not control the effort-delay confound should be interpreted cautiously because they are also influenced by delay discounting. Task limitations and future directions are discussed.