Quintic Research Articles

Investigations on application of curve fitting in power system inertia estimation

ABSTRACT As the share of renewable energy sources in the power system keeps growing, a new issue with frequency stability – diminishing and changing inertia – has emerged. Estimating power system inertia has received a lot of attention lately in order to market design of synthetic inertia as an additional service and implement timely corrective steps for robust frequency control. Curve fitting technique has emerged as one of the promising techniques for estimation of power system inertia, however, many challenging aspects need to be addressed for its practical applications. This study aims to systematically assess the effectiveness of the curve fitting method under a range of operational parameters and conditions, such as the curve fitting order, the length of data to be used for curve fitting after an event begins, and the length of the moving average filter applied to the frequency data to remove oscillatory and noise from the frequency transient. The simulation studies have been performed on DIgSILENT and MATLAB platforms. The results show that very high and very low order curve fitting results are high errors and the 5th order model with mean error in estimated value of inertia less than 1% has outperformed others. The analysis on various window width of moving average filter found that increasing the window width results in more error. For IEEE-9 bus system, a filter up to 850 ms width has a mean percentage error below 1%. The analysis also revealed that the duration of the data used for curve fitting is not significant. For variation of the duration of the data used for the curve fitting from 50 ms to 500 ms, the estimated inertia values are found to be in a close range of 2.4881 s to 2.5262 s, for the single machine system with H = 2.5 s. The analysis presented in this study will be useful for effective application of curve fitting method in inertia estimation.

Mathematical model of a lightweight three-axle off-road vehicle construction for Arctic zone of Russia

Introduction. The model and results of calculating the smoothness of a light three-axle off-road vehicle for the Arctic zone of Russia are considered. The model on standard approaches and uses a system of assumptions that limits the number of degrees of freedom for the vehicle body to three, as well as one degree of freedom for the unsprung masses is based. The mathematical model is a system of ordinary differential equations and is supplemented with the necessary algebraic equations, as well as initial conditions. The system is integrated using the 4th order RungeKutta method, for which a program was written in C++. The calculations presented in the article demonstrate the possibility of conducting research on the smoothness of a vehicle under conditions of arbitrary terrain, typical for off-road conditions in the winter conditions of the Arctic zone. The dimensions and other parameters of the vehicle were taken from a full-scale model that was used in real expeditions in 2003-2019. Based on the model, suspension characteristics will be developed for a new all-terrain vehicle.Theory. When operating a wheeled vehicle in a wide range of conditions, even in northern regions, transverseangular vibrations are very often insignificant, so only vertical linear and longitudinal-angular vibrations of the frame can be considered. This problem enables to construct a system of equations of vehicle motion using selected degrees of freedom. From a mathematical point of view, these equations are classified as second-order ordinary differential equations with a variable structure of the right-hand sides, which reflects the non-linear nature of the behavior of the suspension in terms of its geometric constraints.Methods. The work uses numerical methods to solve the equations of the constructed model, which enables to gradually weaken the accepted assumptions and build more general calculation algorithms. The main integration method for ensuring the stability of solutions is the multi-step Adams method, which, with the correct choice of step, ensures the necessary stability of the solution over sufficiently long model times. However, in this work, the 4th order Runge-Kutta method was adopted, which turned out to be quite sufficient.Results and conclusions. The paper presents the results of a numerical study of the oscillatory processes of an off-road vehicle during uniform translational motion of the vehicle on a horizontal surface with a given profile of irregularities. The graphs show a transition process of oscillations, which ends with reaching a steady state. The shape of oscillations in a steady state can be irregular and significantly depends on the given speed of the all-terrain vehicle. Analysis of the dependencies presented in the figures shows that the shape of the oscillations of the allterrain vehicle’s frame, as well as the amplitude and frequency, significantly depend on the speed of the vehicle (at a constant road profile). Changing the road profile leads to corresponding changes in the forms and characteristics of forced vibrations of a vehicle on a suspension, which makes it possible to build the necessary amplitude-frequency characteristics, optimize the elastic and dissipative parameters of suspensions, optimize their number and location, and also monitor the movements of arbitrary points at which various units are located.

Spatial shaping of low- and high-order harmonics generated using vortex beams

We demonstrate the generation of the low- and high-order harmonic vortex beams from a single spiral phase plate illuminated by different laser wavelengths. The second harmonic (532 nm) originates from the application of the wavefront-structured 1064 nm femtosecond pulses with fractional orbital angular momentum (OAM) during propagation through a lithium triborate crystal, while the third harmonic (500 nm) originates from the application of the wavefront-structured near-IR (1500 nm) femtosecond pulses with integer OAM during propagation through a 150 μm thick fused silica plate. The topological charges (TCs) of the second and third harmonics are measured and compared. The increase in TC and the peculiarities in OAM variations during modification of the polarisation of the incident radiation are analysed and discussed. The two-colour-pump-driven second-harmonic vortex radiation interacted with an Ar gas jet to generate vortex harmonics up to the 14th order with double-lobe complex spatial profiles in the extreme ultraviolet region.

Exploring gradual material rigidity degradation effects on the nonlinear coupled axial-transversal nonlinear response of a capacitive micro-beam

The accumulation of damage in materials due to crack propagation can lead them to unpredicted failures. This phenomenon is particularly relevant in materials science, engineering, and other fields where structures or components are subjected to repeated loading, cyclic stresses, or environmental factors. In this paper, the mechanical behavior of a microelectromechanical system subjected to cyclic loads has been modeled, when the stiffness of the material gradually is decreased. As a case study the dynamic response of a micro-beam to DC bias voltage as a static load and AC harmonic voltage as a cyclic load has been studied. The nonlinear coupled equations have been formed and converted to time-dependent ones using a spatial discretization method. Due to long-term integration over time, to achieve more accurate results besides direct 4th order Runge-Kutta integration method, a temporal decomposition method has been used to solve the coupled nonlinear ordinary differential equations. To realize this method, a temporal decomposed solution based on the physical nature of the problem is presented in the form of slow-growing terms and fast-altering harmonic terms with gradually-growing amplitudes. To find the coefficient of these terms a least square method has been utilized to minimize a cost function in a given dynamic time-interval, where the independency of the results to this interval has been assessed. Also, the nonlinear frequency behavior of the proposed model has been studied when the system has suffered various damages. Due to considering gradual rigidity degradation of the material interesting dynamic responses have been observed, that can help to expand the insight in the design of structures.

Integrated photonic waveguides for on-chip SBS with OAM modes

Stimulated Brillouin Scattering (SBS) is a nonlinear optical process that can provide significant on-chip gain in various materials and platforms. The utilization of chalcogenide and silicon (Si) waveguides has facilitated the advancement of Brillouin lasers and diverse microwave photonic functionalities. The predominant approach has been centered on interactions between conventional guided modes, specifically TE/TM. This study introduces a novel approach that explores diverse guided-wave configurations capable of sustaining SBS with orbital angular momentum modes (OAM). These configurations include a cross-Si waveguide and a silica/chalcogenide waveguide. The simulations examine the forward and backward SBS utilizing OAM modes up to the 4th order in planar on-chip waveguides. A maximum on-chip SBS gain of up to ∼540W−1m−1 has been observed for pump and Stokes OAM mode numbers satisfying the topological charge conservation law. This OAM multiplexing approach can open new avenues for on-chip integrated nonlinear photonics for various applications, especially where pump and signal beam filtering or separation are critical.

The thermal equation of state of the magma Ocean

As the protolunar disk formed by the giant impact with the incoming asteroid Theia started to cool, the Earth condensed in its center as a molten planet. The outer layer, rich in lithophile oxides, formed the magma ocean, whose dynamical behavior heavily influenced the entire evolution of the early Earth. Here, we employ first-principles molecular dynamics simulations to characterize the magma ocean in its initial stage. We compute the compressibility and the viscosity of the molten pyrolite, which best approximates the bulk silicate Earth composition. With an extensive set of calculations, we span the entire relevant pressure-temperature range. We provide a detailed analysis of the athermal and thermal equations of state in various formulations. We obtain a linear temperature dependence for the bulk modulus using the 4th order Birch-Murnaghan equation of state. We show that the liquid silicate accommodates compression by the collapse of the second Si-O coordination sphere, whose corresponding coordination number passes from about 24 at the surface of the magma ocean to about 40 at its deepest point. We found that pyrolite melts have a very low viscosity, about one order of magnitude lower than that of molten basalt. We also propose a revised position of the critical point of the bulk silicate Earth, which lies around 6000 K and 1.1–1.2 kbars.

Linear Spectral Method for Simulating the Generation of Regular Waves by a Moving Bottom in a 3-dimensional Space

In this study, we introduce a linear spectral method capable of simulating wave generation and transformation caused by a moving bottom in a 3-dimensional space. The governing equations are linear dynamic free-surface boundary conditions and linear kinematic free-surface boundary conditions, which are solved in Fourier space. Solved velocity potential and free-surface displacement should satisfy continuity equation and kinematic bottom boundary condition. For numerical analysis, a 4th order Runge-Kutta method was utilized to analyze the time integral. The results obtained in Fourier space can be converted into velocity potential and free-surface displacement in a real space using inverse Fourier transform. Regular waves generated by various types of moving bottoms were simulated with the linear spectral method. Additionally, obliquely generated regular waves using specified bottom movements were simulated. The results obtained from the spectral method were compared to analytical solutions, showing good agreement between the two.

Harmonic domain-wall dark pulse generation using unpumped thin-core thulium fiber as interferometer

In this work, the harmonic domain-wall dark pulse is experimentally demonstrated in C-band fiber laser. The domain-wall dark pulse was self-started at pump power of 112 mW. The fundamental dark pulse repetition rate was measured as 0.96 MHz, pulse duration of 250 ns and highest average pulse energy of 3.24 nJ. As the power increased, dark pulses up to the 7th harmonic order were visualized and quantified. Pulse temporal width reduced as harmonic order increased, with the minimum pulse width of 60 ns recorded in the 7th order. The harmonic dark pulse fiber laser demonstrated adequate stability, with signal-to-noise ratios above 50 dB throughout all harmonic operations. The endeavor of harmonic dark pulse dark soliton could lay the groundwork for future sustainable industrial growth.

Heat transfer scrutiny in EMHD ternary hybrid nanofluid flow between convergent/divergent channels with stretchable walls

ABSTRACT The main interest of the existing work is the numerical and analytical exploration of heat transference on MHD Jeffery-Hamel flowing of a ternary hybrid nanofluid with an external magnetized force and electrical field (EMHD). The two walls of the system are also taken to be stretchable (shrinkable). Mixture base fluid (ethylene glycol-water 50%–50%) hybrid nanofluid containing MoS2, Al2O3, and TiO2 as the nanoparticles are contemplated. The modeled partial differential equations were converted to nonlinearly ordinary differential equations by applying the similarity transformations and resolved analytically by utilizing the Duan – Rach Approach (DRA). The present results in particular cases are compared to results obtained by the HAM (homotopy analysis methodology)-based Mathematica BVPh 2.0 code and by the Runge-Kutta Fehlberg 4th–5th order (RKF-45) for validation. The effect of varied factors on non-dimensional rapidity, temperature profiles, frictional force factor, and Nusselt quantity has been examined and explained via tabular and graphical outcomes. Certainly, new modeling and reliable analytic treatment via the DRA approach for the ternary hybrid nanofluid is a sizable accomplishment of the current analysis.

Chelyshkov wavelet-based numerical technique for the solution of Darcy–Forchheimer flow of Erying–Powell radiated dusty fluid over a stretching sheet with Cattaneo–Christov heat flux

This article presents the Chelyshkov wavelet-based numerical technique (CWBNT) for the solution of the system of non-linear differential equations arising in the study of Darcy–Forchheimer flow of Erying–Powell radiated dusty fluid over a stretching sheet with Cattaneo–Christov heat flux. Initially, the proposed technique is implemented on the test problem having exact solution. The obtained results are highly accurate in comparison with the solutions obtained by shooting technique based Runge–Kutta Fehlberg 4th–5th order method. The proposed technique is applied to the governing equations of the considered dusty fluid problem. The results obtained for some fixed values of parameters resemble the previously published results. The comparisons validate the method. The flow behavior of dusty fluid is analyzed and the effect of various factors on the velocity and thermal attribute of the dust and fluid phase are studied. It is inferred that the Erying–Powell fluid parameters ε and α have entirely different effects on temperature, velocity profiles, and skin-friction coefficient. The local inertia parameter decreases the velocity and thermal relaxation parameter decreases the temperature. Enhancement in temperature ratio and radiation parameters escalates the temperature and Nusselt number. The proposed technique is simple, reliable, efficient tool to solve the differential equations arising in dusty fluid flow problems.

Dual-polarization MZM-based photonic nonlinear analog self-interference cancellation for in-band full-duplex radios

In this paper, we propose a dual-polarization Mach-Zehnder modulator-based photonic nonlinear analog self-interference cancellation (SIC) technique for in-band full duplex (IBFD) systems. By using the proposed technique, an arbitrary 4th order nonlinear transfer function can be generated, meaning the performance limitation caused by the nonlinearity of the analog SIC circuit can be overcome by imitating the nonlinear transfer function of the analog SIC circuit before cancellation. This paper also presents a performance analysis through simulations and the results of a proof-of-concept demonstration. In the experiment, the proposed nonlinear SIC technique could achieve 29 dB cancellation over 500 MHz bandwidth centered at 1.25 GHz frequency along various degree of distortion caused by nonlinearity. In addition, the performance enhancements achieved by the proposed technique are evaluated in terms of error vector magnitudes (EVMs) and constellations of the signal-of-interest (SOI) in the simulation which is based on the experimental SIC results. More than 3 dB of SOI power gain could be obtained in evaluated EVM performances.

Quasinormal Spectrum of (2+1)$(2+1)$‐Dimensional Asymptotically Flat, dS and AdS Black Holes

AbstractWhile ‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher resembles that in four‐dimensional spacetime with the corresponding asymptotic.

Time-Optimized Robot Trajectory Based on Improved Whale Optimization Algorithm in Intelligent Manufacturing

Abstract To discuss the low convergence accuracy of whale optimization algorithm (WOA) and the problem of converging to local optima, we proposed using nonlinear convergence factors and introducing nonlinear inertia weights in the WOA. The modified WOA was used to optimize the trajectory of a six-degrees-of-freedom (6DOF) industrial robot. To improve the convergence accuracy and the local and global search ability of the WOA, we first replaced the convergence factor with a nonlinear convergence factor and added a nonlinear inertia weight. The algorithm was used along with a quintic polynomial equation to develop a time-optimal trajectory, for the robot, for use in practical application scenarios. Simulation experiment results showed that the duration of a complete loading–unloading process was reduced by 30% after robot motion trajectory optimization compared with that before optimization, indicating the effectiveness of the improved WOA and its suitability for robot trajectory optimization.

Global centres in a class of quintic polynomial differential systems

A centre of a differential system in the plane $ {\mathbb {R}}^2$ is an equilibrium point $p$ having a neighbourhood $U$ such that $U\setminus \{p\}$ is filled with periodic orbits. A centre $p$ is global when $ {\mathbb {R}}^2\setminus \{p\}$ is filled with periodic orbits. In general, it is a difficult problem to distinguish the centres from the foci for a given class of differential systems, and also it is difficult to distinguish the global centres inside the centres. The goal of this paper is to classify the centres and the global centres of the following class of quintic polynomial differential systems \begin{align*} \dot{x}= y,\quad \dot{y}={-}x+a_{05}\,y^5+a_{14}\,x\,y^4+a_{23}\,x^2\,y^3+a_{32}\,x^3\,y^2+a_{41}\,x^4\,y+a_{50}\,x^5, \end{align*} in the plane $ {\mathbb {R}}^2$ .

Some criminological indicators of land mismanagement

Based on official statistical sources, this article presents a long-term criminological analysis of the situation with land mismanagement in Ukraine spanning the period from 2002 to 2023. The author determines absolute, average and relative indicators, in particular, the rate and dynamics of crimes in this category. The total number of recorded crimes in the category under study (1,240 crimes), their average annual occurrence (56 crimes), and the average growth rate (22.9 %) are calculated. Employing a 5th degree polynomial function, a trend depicting the dynamics of these crimes is constructed. The chosen model aptly captures the development trend of the process with high precision (coefficient of determination R2 = 0.916) and facilitates the identification and characterization of four distinct periods, each reflecting the main trends of land mismanagement in Ukraine.
 A paradoxical situation is revealed by the analysis of the practical application of the criminal law provisions which have supplemented Art. 254 of the Ukrainian Criminal Code « Land Mismanagement» in accordance with Law of Ukraine No. 402-IX of December 19, 2019 « On Amendments to Certain Legislative Acts of Ukraine Regarding Improvement of Legislation on Mining of Amber and Other Minerals». Notably, no crimes were recorded under Part 2 of Article 254 of the Criminal Code of Ukraine (the primary corpus delicti). Conversely, 15 crimes were recorded under Parts 3 and 4 of Article 254 (qualifying elements of the crime). The author concludes that this correlation would be impossible in the case of objective recording of crimes, and it also underscores a noteworthy latent aspect of land mismanagement, in particular, deliberate evasion of mandatory reclamation of lands damaged in the course of pilot commercial development of amber deposits or amber mining under a special subsoil use permit, resulting in considerable damage. The conducted analysis holds an intrinsic value both for scientific research and for law enforcement, ensuring an appropriate information support base for countering land mismanagement, firstly, by providing a clear understanding of the current situation with this phenomenon. Furthermore, it lays the groundwork for the development of the relevant system of criminal preventive measures tailored to address this specific issue.

Experimental use of pig cadavers to locate homicide victim in a large river

The transport of full body human remains in fluvial environments has few published examples to guide recovery efforts. The decomposition stage, flow environment, water temperature and river morphology can all interact to affect the rate and distance deceased human bodies will travel, and case studies or experimental efforts are rare. In this case report, we provide an experimental deployment of pig carcasses to emulate a real homicide event where a body was dropped into a large 7th order Northern Great Plains river to guide recovery of the victims remains. Two pigs were deployed, one wrapped in a tarp to reflect the victim’s circumstances and the other uncovered in a time period and flow condition comparable to what was known of the homicide. The results of the transport are reported, along with the successful recovery of the victim’s remains near one of the pig cadavers. Although small in scope and un-replicated, this case study should be a valuable contribution to knowledge of full body human fluvial taphonomy in the future and help inform future search efforts of comparable systems.

Lane-changing decision and planning under humanized games for intelligent vehicles

Although autonomous driving vehicles have seen rapid development, their decision-making and planning technologies still fall short of meeting human-centric requirements. To address the issue of personalized driving within autonomous vehicles, a human-like autonomous driving framework is proposed. This framework divides the autonomous driving process into task decision-making and path planning. Firstly, during the modeling phase, a combined model of the driver and vehicle is integrated to form an integrated model for designing decision-making algorithms. Subsequently, a decision cost function is constructed during the decision phase to reflect driving safety, passenger comfort, and travel efficiency. Adjustments are made for different driving styles, employing non-cooperative game theory methods to resolve decision cost issues. Finally, an improved algorithm based on quintic polynomials is designed for trajectory planning to meet vehicle safety, comfort, and rapid operation requirements. Test results indicate that different driving styles lead to varying decision outcomes, yet the algorithms employed consistently provide reasonable decisions for autonomous driving vehicles, thereby enhancing road efficiency and safety.

Dual solutions of magnetized radiative flow of Casson Nanofluid over a stretching/shrinking cylinder: Stability analysis

The enhanced thermal efficiency exhibited by Casson nanofluids offers significant practical applications across various industrial and engineering sectors. This study focuses on the mathematical investigation of the steady magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid through a stretched/shrinking cylinder, taking into account the effects of suction and thermal radiation. The governing partial differential equations (PDEs) have been subjected to a similarity transformation, resulting in a set of nonlinear ordinary differential equations (ODEs). These ODEs were solved numerically utilizing the code of bvp4c in the software of Matlab which offers high accuracy (4th order). The employed nanofluid model incorporates the effects of Brownian motion and thermophoresis. The present study illustrates the graphical depictions of the impacts of different governing parameters, namely Hartmann (M) number, curvature (γ) parameter, Brownian motion (Nb) parameter, mass suction (S) parameter, thermal radiation (Rd) parameter, and thermophoresis (Nt) parameter, on heat transfer, flow, and mass transfer characteristics. Comprehensive determination and visual presentation of the coefficient of skin friction, local Nusselt number, and local Sherwood number were conducted for a range of estimates of applied parameters. Based on our examination, it has been determined that dual similarity solutions are present within a specific range of mass suction parameters. The relationship between the Casson parameter and various fluid dynamic properties, such as skin friction coefficient, heat transfer rate, and mass transfer rates, has been found to exhibit a decreasing trend. Furthermore, the stability analysis discovered that the first solution exhibits linear stability, whereas the second solution displays linear instability. Additionally, the motivation behind this study is to enhance industrial performance through the optimization of thermal power generation systems, thereby increasing their overall efficiency.

High-order genuinely multidimensional finite volume methods via kernel-based WENO

In this paper a family of fully multidimensional kernel-based reconstruction schemes for use in finite volume methods (FVMs) will be presented. These methods are intended for use in shock dominated problems, and stability is achieved through a suitable adaptation of the Adaptive Order Weighted Essentially Non-Oscillatory (WENO-AO) method to the proposed kernel-based reconstruction schemes. There are a number of key difficulties in the design of high-order finite volume schemes which will be discussed and addressed. High (4th and 6th) order convergence will be demonstrated on smooth exact solutions of the ideal MHD equations. The very same scheme will then be applied to extremely stringent astrophysical benchmark problems.

Viscous dissipation and Joule heating effects of Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk

In this piece of communication, a theoretical investigation of two dimensional boundary layer flow of Magnetohydrodynamics (MHD) Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk is made. The investigation includes the effects of viscous dissipation, Joule heating, thermal radiation, suction/injection, Darcy-Forchheimer porosity model and binary chemical reaction with activation energy, etc. To examine the impacts of the aforementioned effects, the conservation laws are formulated with strongly nonlinear partial differential equations (PDEs), which are then transformed into a system of initial value problems (IVPs) using appropriate similarity transformations and techniques. The 5th order Runge–Kutta with the shooting technique is used to find numerical solutions aided by Python programming with built in program “fsolve”. The method is validated with other published articles under common assumptions and it agrees nicely. The impacts of the pertinent parameters on velocity, temperature, concentration, skin friction coefficient and the rates of mass and heat transfers with in the flow regime are displayed using graphs and tables. The main outcomes include the motivation of local Nusselt and Sherwood numbers for shear thickening (n=1.5) than shear thinning (n=0.5) cases of the Carreau nanofluid. The momentum boundary layer of the Carreau nanofluid gets thinner with an increase in Forchheimer number, unsteady and suction parameters. A dual nature is observed for concentration of the Carreau nanofluid with a rise in Eckert number, i.e increasing in concentration around the wall and decreasing far away from the wall. The rise in destructive and constructive chemical reaction parameters disperse and accumulate the concentration of the system, respectively.