Sine Research Articles

Effects of Leading-Edge Blowing Control and Reduced Frequency on Airfoil Aerodynamic Performances

Abstract Airfoil leading-edge fluid-blowing control is computationally studied to improve aerodynamic efficiency. The fluid injection momentum coefficient Cμ (the ratio of injection to incoming square velocities times the slot's width to airfoil's half chord length) varies from 0.5% to 5.4%. Both static and dynamic conditions are investigated for a NACA0018 airfoil at low speed and Reynolds number of 250 k based on the airfoil's chord length. The airfoil is dynamically pitched at a reduced frequency (the pitching tangential speed to the freestream speed ratio), varying between 0.0078 and 0.2. Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) is used in the simulations as based on the Transition SST and Spalart–Allmaras models, generally achieving good agreement with experimental results in lift and drag coefficients and in the pressure coefficient distributions along the airfoil. It is found that oscillating the airfoil can delay stall, as expected, in dynamic stall (DS). Leading-edge blowing control can also significantly delay stall both in static and dynamic conditions as long as sufficient momentum is applied to the control. On the other hand, for a small Cμ such as 0.5%, the leading-edge control worsens the performance and hastens the appearance of stall in both static and dynamic conditions. The airfoil's oscillation reduces the differences between pitch-up and pitch-down aerodynamic performances. Detailed analysis of vorticity, pressure, velocity, and streamline contours is given to provide plausible explanations and insight to the flow.

Determining the tectonic velocity of some continuously operating reference stations (CORS) in Vietnam 2019-2022 using precise point positioning method

We use precise point positioning (PPP) technique to process the Global Navigation Satellite Systems (GNSS) data of 10 continuously operating reference stations (CORS) in Vietnam during the period 2019-2022. PPP processing results show that the time series of the North, East and Up components of CORS fluctuate with a period of approximately 1 year. After modelling this variation using a sine function with a fixed period of 351.6 days, we calculate the mean displacement velocity of the CORSs according to the North, East and Up components as follows: (-9.2, +29.5, -4.6) mm/year. The general movement direction of all CORSs is East-Southeast. In which the North, East and Up components of 3 big cities Ha Noi, Da Nang and Ho Chi Minh city are (-9.1, +32.7, +1.0) mm/year, (-9.1, +30.5, -6.0) mm/year and (-7.9, +28.4, -1.9) mm/year, respectively. Compared with the period 2016-2018, the velocities of the tectonic plate change less than 4 mm/year in the horizontal component, and 8 mm/year in the Up component. We have processed three more International GNSS Service (IGS) stations in Thailand (CUSV) and China (HKSL and KMNM) for testing. Our results are consistent with JPL at 1 mm/year in the horizontal and 2 mm/year in the Up component.

A Modified Sine Cosine Algorithm for Numerical Optimization

Sine cosine algorithm (SCA) is a recently developed meta-heuristic method based on the characteristics of sine and cosine functions. However, SCA algorithm may suffer premature convergence in solving complex optimization problems. To mitigate this limitation, a modified SCA (MSCA) is developed to achieve an effective balance between exploration and exploitation. Specifically, the conversion parameter can be configured adaptively by using the individual fitness information in the evolution process to guide the individual search behavior. After that, an inertia weight is embedded in the position updating equation to further improve the search accuracy and accelerate the convergence speed. The performance of MSCA algorithm is investigated on 13 benchmark functions and the chaotic time series prediction problem. Experimental results demonstrate that MSCA algorithm is more effective than the other optimization methods.

Chaotic opposition Golden Sinus Algorithm for global optimization problems

Optimization techniques are required to find the best solutions to challenging problems in many engineering disciplines. Metaheuristic algorithms that effectively increase search performance using various evolutionary strategies have become increasingly popular in recent years. The Golden Sinus Algorithm (GoldSa) is a population-based optimization algorithm that uses the sine function and the golden ratio. In this study, a chaotically enhanced opposition-based Golden Sinus Algorithm (Co-GoldSa) has been proposed to improve the efficiency of the exploitation and exploration ability of the GoldSa method. While designing this approach, it is first necessary to analyze the chaotic behavior of the GoldSa parameters. For this purpose, three chaotic GoldSa methods have been developed using eight chaotic maps to determine the effect of the chaotic maps on the parameters with different behaviors. Secondly, the opposition-based learning strategy is adjusted to the cGoldSa to enhance the searching ability. To investigate the proficiency of the proposed Co-GoldSa method, it has been examined with well-known and newly introduced metaheuristic approaches on benchmark functions and classical engineering design problems. Besides, an efficient framework of the multilevel thresholding image segmentation has been presented based on the Co-GoldSa method since the efficient processing of pathological images is quite important in medical diagnostics. The experimental outcomes reveal the superiority of the proposed method in solving global optimization problems, image segmentation, and engineering problems. Thus, the outcomes of the benchmark functions, image segmentation, and classical engineering problems support that the proposed Co-GoldSa approach can be considered a promising method for resolving challenging optimization problems.

Classification feature selection and dimensionality reduction based on logical binary sine-cosine function arithmetic optimization algorithm

Arithmetic optimization algorithm (AOA) is a meta-heuristic algorithm inspired by mathematical operations. AOA has been diffusely used for optimization issues on continuous domains, but few scholars have studied discrete optimization problems. In this paper, we proposed Binary AOA (BAOA) based on two strategies to handle the feature selection problem. The first strategy used S-shaped and V-shaped shift functions to map continuous variables to discrete variables. The second strategy was to combine four logical operations (AND, OR, XOR, XNOR) on the basis of the transfer function, and constructed a parameter model based on the sine and cosine function. An enhanced logic binary sine–cosine function arithmetic optimization algorithm (LBSCAOA) was proposed to realize the position update of variables. Its purpose was to improve the algorithm's global search capabilities and local exploitation capabilities. In the simulation experiments, 20 datasets were selected to testify the capability of the proposed algorithm. Since KNN had the advantages of easy understanding and low training time complexity, this classifier was selected for evaluation. The performance of the improved algorithm was comprehensively evaluated by comparing the average classification accuracy, the average number of selected features, the average fitness value and the average running time. Simulation results showed LBSCAOA with V-Shaped “V4” stood out among many improved algorithms. On the other hand, LBSCAOA with V-Shaped “V4” was used as a representative to compare with other typical feature selection algorithms to verify its competitivenes.

The puzzling orbital residuals of XTE J1710–281: Is a Jovian planet orbiting the binary system?

is a transient eclipsing binary system with a period close to 3.28 hours that hosts a neutron star. The average eclipse duration is 420 seconds, and eclipse arrival times reported in the literature span from 1999 to 2017. A previous analysis of the eclipse arrival times using the eclipse timing technique revealed a complex pattern of delays, indicating the presence of three orbital glitches. These glitches correspond to sudden variations in the orbital period and allow for the identification of four distinct epochs, during which the orbital period derivative was estimated to be $-1.8 $ s s$^ $ s s$^ $ s s$^ $, and $0.09 $ s s$^ $, respectively. We reanalyzed the 78 eclipse arrival times spanning 18 years utilizing the eclipse timing technique to derive the corresponding delays as a function of time. We find that the observed delays align well with a fitting model that employs an eccentric sine function characterized by an amplitude of $6.1 0.5$ s, an eccentricity of $0.38 0.17$, and a period of $17.1 1.5$ years. Additionally, we identified the orbital period to be 3.28106345(13) hours, with a reference epoch of $T_0=54112.83200(2)$ MJD. We obtained an upper limit to the orbital period derivative of $3.6 $ s s$^ From the average value of the eclipse duration, we estimate that the companion star has a mass of 0.22 for a neutron star mass of 1.4 and that the inclination of the source is $ degrees. The companion star is in thermal equilibrium. The orbital period derivative is consistent with a conservative mass transfer scenario, where the angular momentum loss due to magnetic braking dominates over gravitational radiation angular momentum loss if the former is present. The eccentric modulation can be explained by a third body with a mass of 2.7 Jovian masses, orbiting with a revolution period close to 17 years and an eccentricity of 0.38.

Dynamic analysis based on a memristive hyperchaotic system with stable unfixed point and its synchronization application

A novel two-memristor hyperchaotic system is obtained by introducing a cubic magnetic-controlled memristor and a hyperbolic sine function memristor. The dynamics of the new system are analyzed by various techniques such as Lyapunov exponents, complexity, 0–1 test, bifurcation diagram and phase diagram. The results demonstrate that the new system exhibits complex dynamic behaviors, including transient chaos, transient transition, intermittent chaos, and offset-boosting. Notably, a rare phenomenon with stable unfixed point has been discovered in this newly proposed system. The largest Lyapunov exponent of the stable unfixed point fluctuates around 0 and remains predominantly less than or equal to 0. Despite this, the new system still partially exhibits chaotic characteristics, indicating that the stable unfixed point can be regarded as a local chaotic attractor. Furthermore, there are four types of coexisting attractors with period-period, chaos-chaos, chaos-stable unfixed point and stable unfixed point-stable unfixed point in the new system. The circuit design is implemented to validate the accuracy of the memristive chaotic system, and the consistency between numerical calculations and simulation results is confirmed. Finally, the coupling synchronization and tracking synchronization methods are designed, which hold practical applications in the field of secure communication, control systems and signal processing.

Spatial heterogeneity and temporal tendency of channeled snow avalanche activity retrieved from Landsat images in the maritime snow climate of the Parlung Tsangpo catchment, southeastern Tibet

The spatial heterogeneity and temporal tendency of snow avalanche (hereafter called avalanche) activities are responses to variations in the inducing environment under climate warming and epitomize the repercussions of the global cryosphere on climate warming. This paper focuses on channeled avalanches in the marine snow climate region of the Parlung Tsangpo catchment in southeast Tibet as an example. Through field investigations, we identify the spatial extents of avalanche paths, while historical avalanche flow paths from the past 35 years (1986/1987–2021/2022) within these paths are interpreted using Landsat optical images. Statistical analysis is then employed to derive spatial heterogeneity and temporal tendencies within and between years. The results indicate that the runout altitudes of historical avalanches primarily range from 3468 m to 4051 m, with average flow directions predominantly following the northwest, north and northeast directions. Avalanche activity peaks between February and April, with longer runout distances observed during this period. Regarding interannual regularity, the evolution of the runout distance, runout altitude, and height difference of avalanche flow paths over the past 35 years demonstrates a cyclic evolution akin to a sine function. Additionally, a moderate correlation between the interannual variation in historical avalanche activity intensity and the Southern Oscillation Index was observed. These findings strengthen the understanding of the temporal evolutionary pattern of avalanches in response to climate warming, providing valuable insights into the channeled avalanche occurrences in the maritime snow climate of southeastern Tibet.

Prediction of Flow Stress and Characterizing the Deformation Mechanism of As‐Extruded 7005 Aluminum Alloy

This study explores isothermal hot compression of the as‐extruded 7005 aluminum alloy within a temperature range of 573–823 K, with strain rates from 0.001 to 1 s−1 and a strain of 1.2. Three constitutive equations, employing hyperbolic sine, power law, and exponential functions, were formulated and compared to predict rheological peak stress accuracy and applicability. The results indicate that the hyperbolic sine function is suitable across all stress levels, the power law function for low stress (<56 MPa), and the exponential function for high stress (>56 MPa). Introducing a strain compensation function enhances hyperbolic sine function accuracy. The stress exponent (n) and activation energy (Q) decrease with increased deformation, indicating a transition in the deformation mechanism from early‐stage dislocation climb to later‐stage dislocation glide. At 773 K with strain >0.6, the presence of precipitates maintains the n value at approximately 4. Solute atoms (Zn, Mg, and Zr) and precipitates (MgZn2 and Al3Zr) impede diffusion and dislocation motion, resulting in deformation activation energies surpassing pure aluminum. Additionally, kernel average misorientation maps demonstrate that higher deformation temperatures and lower strain rates reduce internal residual stresses.

Radial velocity homogeneous analysis of M dwarfs observed with HARPS. I. Exoplanet detection and candidates

The census of planets around M dwarfs in the solar neighbourhood meets two challenges: detecting the best targets for the future characterisation of planets with ELTs, and studying the statistics of planet occurrence that are crucial to formation scenarios. The radial velocity (RV) method remains the most appropriate for such a census as it is sensitive to the widest ranges of masses and periods. HARPS, mounted on the 3.6 m telescope at La Silla Observatory (ESO, Chile), has been obtaining velocity measurements since 2003, and can therefore be used to analyse a very large and homogeneous dataset. We performed a homogeneous analysis of the RV time series of 200 M dwarfs observed with HARPS from 2003 to 2019 (gathering more than 15000 spectra), with the aim of understanding detectable signals such as stellar and planetary companions and activity signals. The RVs were computed with a template matching method before carrying out the time series analysis. First, we focused on the systematic analysis of the presence of a dominant long-term pattern in the RV time series (linear or quadratic trend and sine function). Then, we analysed higher-frequency perdiodic signals using periodograms of the residual time series and Keplerian function fitting. We found long-term variability in 57 RV time series (28.5<!PCT!>). This led to the revision of the parameters of the massive planet (GJ 9482 b), as well as the detection of four substellar and stellar companions (around GJ 3307, GJ 4001, GJ 4254, and GJ 9588), for which we characterised inclinations and masses by combining RV and astrometry. The periodic analysis allowed us to recover 97<!PCT!> of the planetary systems already published in this sample, but also to propose three new planetary candidates orbiting GJ 300 (7.3M$_ oplus $), GJ 654(5M$_ oplus $), and GJ 739 (39M$_ oplus $), which require additional measurements before they can be confirmed.

On the Basis Property of the System of Exponentials and Trigonometric Systems of Sine and Cosine Functions in Weighted Grand Lebesgue Spaces

On the Basis Property of the System of Exponentials and Trigonometric Systems of Sine and Cosine Functions in Weighted Grand Lebesgue Spaces

Anti-unwinding adaptive robust backstepping attitude maneuver control for rigid spacecraft

In this paper, an anti-unwinding adaptive robust backstepping control law is proposed to solve the attitude control problem of rigid spacecraft with external disturbances and inertia uncertainties. A new variable based on hyperbolic sine functions is designed to prevent the unwinding phenomenon, and then a novel robust backstepping controller is developed. Initially, a nonlinear tracking law is designed to obtain the desired angular velocity and to ensure that the attitude maneuvering system could have two equilibrium points. Subsequently, an adaptive robust control law is devised, which incorporates the adaptive estimation method to update the inertial parameters in real-time. Moreover, the bounded external disturbances are taken into account in the design of the control law, and thus the robustness of the attitude control system is improved. Furthermore, the global asymptotic stability of the attitude control system is verified by the Lyapunov-Krasovskii theorem. Finally, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed control law, as well as the anti-unwinding characteristics are perfectly validated during the attitude maneuver of rigid spacecraft.

On integral theorems and their statistical properties

We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The integral theorems provide natural estimators of density functions via Monte Carlo methods. Assessment of the quality of the density estimators can be used to obtain optimal cyclic functions, alternatives to the sin function, which minimize square integrals. Our proof techniques rely on a variational approach in ordinary differential equations and the Cauchy residue theorem in complex analysis.

Lump–kink and hybrid solutions of the extended (3+1)-dimensional potential KP equation in fluid mechanics

In this paper, the extended (3+1)-dimensional potential KP equation in fluid mechanics is studied through Hirota bilinear method. Many types of hybrid solutions, such as the lump–kink solution, lump-two kink solution and periodic lump solution are obtained by assuming different functions in the bilinear equation. The interaction solution between lump and triangular periodic wave is also derived by combining sine and cosine functions with quadratic functions. Dynamical structures of these exact solutions are depicted by presenting the corresponding three-dimensional, two-dimensional structures and density graphs. These diverse interaction solutions could be helpful for understanding physical phenomena in fluid mechanics.

Online Collaborative Perception of Full Bridge Deck Driving Visual of Far Blind Area on Suspension Bridge during Vortex-Induced Vibration.

During a vertical vortex-induced vibration (VVIV), an undulating bridge deck will affect drivers' sightlines, causing the phenomenon of drifting and changes in the far blind area, thus presenting a potential threat to driving safety. Consequently, to ensure the safety of driving on a suspension bridge deck under VVIV, it is necessary to perceive the far blind spot caused by the occlusion of the driving sightlines under this condition, and to establish an online perception and evaluation mechanism for driving safety. With a long-span suspension bridge experiencing VVIV as the engineering background, this paper utilizes the acceleration integration algorithm and the sine function fitting method to achieve the online perception of real-time dynamic configurations of the main girder. Then, based on the configurations, the maximum height of the driver's far blind area and effective sight distance are calculated accordingly, and the impact of different driving conditions on them is discussed. The proposed technical framework for driving safety perception in far blind spots is feasible, as it can achieve real-time estimation of the maximum height and effective distance of the far blind area, thereby providing technical support for bridge-vehicle-human collaborative perception and traffic control during vortex-induced vibration.

Experimental and Theoretical Analysis of Bispectrum Characteristics of Phase Coupled Signals

Fourier transform points out that a certain function that meets certain conditions can be decomposed into a linear combination of trigonometric functions (sine or cosine functions). The functions of high-order cumulant include suppressing the Gaussian noise, eliminating independent signal components, and identifying the phase coupling phenomenon of the signal. To prove this hypothesis, this study constructs a cosine signal with the phase coupling phenomenon based on Fourier transform theory which substitutes it into the third-order cumulant expression and performs detailed reasoning. The constructed signal is extended to the complex signal domain and the same conclusion is obtained. The number of coupled signals is expanded from three to a higher value. The results of the study give definite mathematical and physical meaning to the bispectral peaks. The collected mechanical vibration signals are given to demonstrate this conclusion. The demonstrated characteristics of high-order cumulants have made them widely used in many fields.

Mechanical Behavior of Secondary Lining in Super Large-Span Tunnels Considering Temperature Effects

Temperature stress has a significant impact on the structural stress of (super) large-span tunnel lining, which can easily lead to structural fatigue damage and premature cracking. With the increasing scale and quantity of super large-span tunnels, the issue of temperature stress in secondary lining has attracted widespread attention. Previous studies have paid little attention to the influence of temperature stress on the structural internal forces of ordinary small–medium-span tunnels, but this influence cannot be ignored for super large-span tunnels. We take the Letuan Tunnel (a double-hole eight-lane tunnel) of the Binzhou-Laiwu expressway renovation and expansion project in Shandong Province as a case study and analyze the mechanical response of the secondary lining through on-site measurement. Moreover, a numerical simulation was conducted to evaluate the effects of self-weight and temperature stress on the secondary lining of the case tunnel. The results indicate that: the stress of the secondary lining concrete and steel bars is greatly affected by seasonal temperature changes. The compressive stress of the concrete and steel bars is significantly greater in summer than in winter, and the tensile stress is greater in winter than in summer. Furthermore, multiple measurement points have shown a phenomenon of transition between tensile and compressive stress states. The stress of concrete and steel bars fluctuates periodically with a sine function over time, with a fluctuation period of one year. The structural stress increases with the increase of summer temperature and decreases with the decrease of winter temperature. The fluctuation amplitude of stress in the inner side of the lining concrete and steel bars is greater than that on the outer side. Among them, the stress amplitudes of the inner and outer sides of the concrete are between 0.77–1.75 MPa and 0.44–1.07 MPa, respectively, and the stress amplitudes of the inner and outer steel bars are between 5–31 MPa and 7–13 MPa, respectively. The safety factors in summer are lower than those in winter. The minimum safety factors for secondary lining in summer and winter are 3.4 and 4.6, respectively, which can meet the safety requirements for service. The average axial forces of the secondary lining under the coupling effects of self-weight and temperature in winter and summer are 528 MPa and 563 MPa, respectively, which are significantly greater than the combined axial forces under their individual effects. The bending moment distribution of the secondary lining at the tunnel vault, inverted arch, wall spring and other positions under the coupling effect of self-weight and temperature is different from or even opposite to the bending moment superposition result under the two individual actions. The achieved results reveal that the influence of temperature stress on the service performance of the lining structure cannot be ignored, and the research results can provide useful reference for similar tunnels and related studies.

Generation multi-scroll chaotic attractors using composite sine function and its application in image encryption

In this paper, a composite sine function is proposed and applied in a chaotic system, which is capable of generating definite number of chaotic attractors. The proposed composite sine function possesses infinite breakpoints, but it can produce a fixed number of scrolls by adjusting its parameters. Compared to other chaotic systems with multiple scrolls chaotic attractors, the realization circuit of the chaotic system with compound sine function allows obtaining different numbers of scrolls by adjusting only one resistance value. As a result, the circuit structure remains unchanged despite variations in the number of scrolls. Various analytical methods are applied to study the dynamical behaviors of the proposed chaotic system, including Lyapunov exponent, equilibrium point, bifurcation diagram, phase diagram, spectral entropy and C0-algorithm. Furthermore, based on the analysis of dynamical characteristics, the electronic circuits of the proposed system are given on Multisim circuit simulation software, and the multi-scroll chaotic attractors exhibit consistency with the numerical simulation results. Finally, we incorporated the proposed chaotic system into a Deoxyribonucleic acid coding algorithm for image encryption, and this method exhibits excellent encryption efficiency and high level of security.

Non-polynomial q-Askey Scheme: Integral Representations, Eigenfunction Properties, and Polynomial Limits

AbstractWe construct a non-polynomial generalization of the q-Askey scheme. Whereas the elements of the q-Askey scheme are given by q-hypergeometric series, the elements of the non-polynomial scheme are given by contour integrals, whose integrands are built from Ruijsenaars’ hyperbolic gamma function. Alternatively, the integrands can be expressed in terms of Faddeev’s quantum dilogarithm, Woronowicz’s quantum exponential, or Kurokawa’s double sine function. We present the basic properties of all the elements of the scheme, including their integral representations, joint eigenfunction properties, and polynomial limits.

Exact periodic solution of the undamped Helmholtz oscillator subject to a constant force and arbitrary initial conditions

The Helmholtz oscillator is a nonlinear mixed‐parity oscillator that models the asymmetric vibrations of many engineering and scientific systems. This paper investigated a general and completely integrable form of the Helmholtz oscillator and derived its exact periodic solution from the first integral of the governing differential equation. The considered Helmholtz oscillator has general linear and nonlinear stiffness constants, is subject to a constant force, and has arbitrary initial conditions. Its exact time period was derived in terms of the complete elliptic integral of the first kind, while the exact displacement was derived in terms of the Jacobi elliptic sine function. The validity of the exact solutions was verified for various combinations of the system parameters and initial conditions by comparing with numerical solutions. The exact solutions and numerical solutions were found to match perfectly. Furthermore, the exact solution was applied to analyze the vibration response of real‐world systems that could be modeled as Helmholtz oscillators. The present exact solutions provide benchmark solutions that could be used to determine the accuracy of new and existing approximate solutions for the Helmholtz oscillator.