Biquadratic Research Articles

The rotating solutions beyond the spontaneous scalarization in Einstein-Maxwell-scalar theory

The Einstein-Maxwell-scalar (EMS) theory with a quartic coupling function features three branches of fundamental black hole (BH) solutions, labeled as cold, hot, and bald black holes. The static bald black holes (the Reissner-Nordström BH) exhibit an intriguing nonlinear instability beyond the spontaneous scalarization. We study the rotating scalarized black hole solutions in the EMS model with a quartic coupling function through the spectral method numerically. The domain of existence for the scalarized BHs is presented in the spin-charge region. We found that the rotating solutions for both the two scalarized branches possess similar thermodynamic behavior compared to the static case while varying the electric charge. The BH spin enlarges the thermodynamic differences between the cold and hot branches. The profile of the metric function and the scalar field for the scalarized BHs is depicted, which demonstrates that the scalar field concentrates more on the equatorial plane in contrast to the axisymmetric region as the spin increases.

Spatiotemporal evolution of ecosystem health and its driving factors in the southwestern karst regions of China

As one of the most typical karst landscapes globally, the karst regions in southwestern China are characterized by prominent rocky desertification and fragile ecological conditions. Consequently, exploring the spatiotemporal evolution and driving influences on ecosystem health (EH) in this region is of great significance for the improvement of ecosystems and green development. This study focuses on assessing EH in these regions from 2000 to 2020 using the “vitality-organization-recovery-service” (VORS) framework. Spatiotemporal changes in EH are analyzed through hotspot analysis, and the functional relationship between driving factors and EH is quantified using XGBoost and SHAP models. Key findings include: (1) Over the past two decades, the proportion of cities experiencing enhanced EH has generally improved in 73% of cities compared to 27% experiencing deterioration. (2) Spatial analysis reveals EH clustering in three regions. One cold spot cluster in the central north and two hot spot clusters in the southwest and southeast. (3) Urbanization level exhibits an inverse logarithmic relationship with EH. Precipitation affects EH in a cubic polynomial pattern—initial decrease, subsequent increase, and final decrease. Temperature impacts EH through a quartic polynomial function with fluctuating increases and decreases. PM2.5 shows a monotonically decreasing relationship with EH, while the normalized difference vegetation index demonstrates a monotonically increasing association. This research contributes to understanding EH dynamics in southwestern China’s karst landscapes, crucial for advancing ecosystem management and sustainable development efforts.

The Impact of the Radius of the Cutting Blade during the Processing of C 60 ± 2 HRC (DIN) Steel

This study investigates the thermal dynamics of the turning process for C60 steel, focusing on the influence of various machining parameters on temperature rise. Integrating experimental methods and statistical analysis, the research examines the effects of cutting speed (v), feed rate (f), depth of cut (a), and cutting insert tip radius (r) on the average temperature in the cutting zone. Experiments were conducted on heat-treated C60 steel rings, using a custom fixture and a modified Kennametal insert holder to ensure precise temperature measurements, collected via a natural thermocouple method. The findings reveal that cutting speed is the most significant factor influencing temperature rise, followed by feed rate, while depth of cut has a minor impact. Notably, the radius of the cutting insert tip is inversely proportional to the temperature, with an increase in the tip radius resulting in a decrease in average temperature. This inverse relationship underscores the potential for optimizing tool design to enhance heat dissipation and reduce thermal stress on the cutting tool. A fourth-degree polynomial model was developed through regression analysis to correlate thermovoltage (V) with temperature (T), providing a quantitative framework for predicting thermal behavior. The model highlights that cutting speed has the greatest effect on temperature rise, with the highest recorded temperature being 795.09°C. Conversely, larger radius of the cutting insert tip corresponds to lower average temperatures, stabilizing around 757.22°C. These insights offer actionable strategies for optimizing machining processes. By strategically adjusting cutting parameters, particularly cutting speed and feed rate, manufacturers can achieve significant improvements in tool life and product quality. The developed mathematical model serves as a predictive tool for fine-tuning machining conditions, ensuring a balance between productivity and tool longevity. This research contributes substantially to the understanding of thermal dynamics in machining processes. It provides a comprehensive analysis and robust modeling of the effects of cutting parameters on temperature rise, supported by rigorous experimental data and statistical validation. The study underscores the importance of considering thermal effects in machining to optimize efficiency, tool life, and product quality, offering valuable insights for both academic research and practical applications in the field of machining and process optimization.

Retrograde orbits associated separatrices in perturbed restricted three-body problem

This study develops single and multivariate nonlinear regression models for predicting Jacobi constant related to separatrix associated with simply symmetric retrograde periodic orbits in the framework of CRTBP with and without perturbations effects. These models are constructed using data from real and hypothetical systems considering that the parameter of mass is independent variable, while the Jacobi constant is displayed as a function of mass and oblateness parameters. Third-degree polynomials from single-variable regression and fourth-degree polynomials from multivariate regression accurately predict the Jacobi constant for given mass and oblateness values, facilitating the identification of separatrices in the PSS without intensive construction efforts. Error analysis confirms the model’s high accuracy across all parameters values. Additionally, chaos detection techniques, including the SALI, GALI, and Lyapunov exponent methods, along with bifurcation analysis, are employed to identify the regions of local and global chaos.

Adaptive deep neural network optimized control for a class of nonlinear strict‐feedback systems with prescribed performance

SummaryIn this article, an adaptive deep neural network (DNN) optimized control strategy is developed for a class of nonlinear strict‐feedback systems with prescribed performance. First, the DNN is applied to approximate the unknown function, and the weight update law is designed to reduce the mathematical challenge based on the first‐order Taylor's series. Second, the optimized backstepping technique is utilized to construct virtual and actual controllers in the backstepping process to achieve the overall control optimization of the system. Next, a control strategy based on the time‐varying switching function and the quartic barrier Lyapunov function is employed to achieve the prescribed performance. Then, the tracking error can converge to the prescribed accuracy within the prescribed time, and every signal within the system has a bound. Finally, the particle swarm optimization algorithm is utilized to search for the designed parameters and simulation examples to verify the effectiveness of the control strategy.

Dynamic analysis of planetary gear transmission based on Lagrange interpolation polynomials

Abstract This paper proposes a novel dynamic model considering manufacturing errors and eccentricity errors to analyze the dynamics of planetary gear transmission (PGT). The dynamic model is established based on the fractional-order calculus (FOC) and solved by an enhanced fourth-order Lagrange interpolation polynomials (LIP) method. Three numerical examples and the vibration experiments of planetary gear transmission are employed for verification. The comparison results indicate that the proposed solution method has higher solution accuracy and efficient than the existing algorithms in solving fractional equations, and the relative errors of the proposed solution method in three examples are 0.32%, 0.78% and 0.16%, respectively. The proposed dynamic model of PGT has better agreement with the experimentally measured signal compared with the integer-order dynamic model, and the maximum error and average error of the characteristic frequency amplitude between the proposed dynamic model and the measured signal are 4.76% and 3.57%, respectively. The proposed method contributes to the theoretical foundation for the signal monitoring of PGT.

Stability, bifurcation, and chaos in a class of scalar quartic polynomial delay systems.

In this paper, a class of scalar quartic polynomial delay systems is investigated. We found rich dynamics in this system through numerical simulation, including chaotic attractors, chaotic saddles, and intermittent chaos. Moreover, this chaotic quartic system may serve as an approximation, through Taylor expansion, for a wide class of scalar delay differential equations. Thus, these nonlinear systems may exhibit chaotic behaviors, and the studies in our paper may provide an insight into the emergence of chaos in other time-delay nonlinear systems. We also conduct a detailed theoretical analysis of the system, including the stability of equilibria and Hopf bifurcation analysis based on the theory of normal form and center manifold. Additionally, a numerical analysis is provided to give numerical evidence for the existence of chaos.

Prediction Model of Spontaneous Combustion of Lignite in Zhalainuoer Mining Area.

A programmed temperature-increase experiment was conducted on coal samples from four coal mines in the Zhalainuoer mining area to improve the accuracy of predicting and forecasting lignite spontaneous combustion. The gases produced during the coal tests were analyzed, and logistic, exponential, Boltzmann, and fourth-degree polynomial functions were selected to develop predictive models for the gas data. Additionally, the Boltzmann function was used to predict the occurrence of fire. The results revealed that the initial appearance temperature of CO was approximately 50 °C, and it exhibited an exponential growth trend with increasing temperature. The initial appearance temperature of C2H4 was approximately 140 °C, which could serve as an indicator of coal entering the accelerated oxidation stage. Applying the selection principle to gas indicators, CO and C2H4 were identified as single gas indicators for lignite spontaneous combustion in the Zhalainuoer mining area, whereas CO/CO2 and C2H4/C2H6 were identified as composite gas indicators. Among the four functions, the Boltzmann function model exhibited the best fitting effect for CO and CO/CO2 within the temperature range of 0-200 °C. The values of the four parameters (A 1, A 2, dx, and x 0) were determined based on their statistical characteristics, and a functional equation describing the relationship between gas concentration and coal temperature was derived. This indicates that the Boltzmann function model can be effectively used to predict the spontaneous combustion of lignite in the Zhalainuoer mining area.

The impact of diffusion tensor imaging tractography settings on muscle fascicle architecture and diffusion parameter estimates: Tract length, completion, and curvature are most sensitive to tractography settings.

Diffusion-tensor (DT)-MRI tractography provides information about properties relevant to muscle health and function, including estimates of architectural properties such as fascicle length, pennation angle, and curvature and diffusion properties such as mean diffusivity (MD) and fractional anisotropy (FA). Tractography settings, including integration algorithms, thresholds for early tract termination, and tract smoothing approaches, impact the accuracy of the muscle property estimates. However, muscle DT-MRI tractography is performed using a variety of these settings, complicating comparisons between different studies. The effects of different tractography settings on muscle architecture estimates have not been fully explored, and optimized settings for muscle tractography have not yet been determined. We examined the influence of integration algorithm and termination check settings combined with a range of step sizes, termination criteria, and smoothing polynomial orders on tract characteristics, completion/reason for termination, and goodness of fit between fiber tracts and smoothing polynomials using 3-T DT-MR images of the lower leg muscles of seven healthy adults. We found that tract length and completion were highly sensitive to strict FA and intersegment angle thresholds (25%-69% reduction in complete fiber tracts from lowest to highest minimum FA threshold and 11%-36% reduction from highest to lowest intersegment angle threshold). Higher order polynomials (third and fourth order vs. second order) better fit the muscle fiber trajectories, but curvature estimates were highly sensitive to smoothing polynomial order (3.9-6.6 m-1 increase for second- vs. fourth-order fitting polynomials). Step size impacted curvature estimates, albeit to a lesser degree. Integration algorithm had little impact, and mean pennation angle, and tract-based FA and MD, were relatively insensitive to all parameters. The results demonstrate which muscle diffusion measures and architectural estimates are most sensitive to varying tractography settings and support the need for consistent reporting of tractography details to aid interpretation and comparison of results between studies.

Increasingly high-order hybrid multi-resolution WENO schemes in multi-dimensions

In this paper, a new type of increasingly high-order hybrid multi-resolution weighted essentially non-oscillatory (HMR-WENO) schemes is presented in the finite difference framework for solving hyperbolic conservation laws in one, two, and three dimensions. Based on the reconstruction polynomials defined on the one-point, three-point, five-point, seven-point, and nine-point spatial stencils, we reconstruct one zeroth degree reconstruction polynomial, one quadratic reconstruction polynomial, one quartic reconstruction polynomial, one sextic reconstruction polynomial, one octave reconstruction polynomial, and their derivative polynomials together with a new hierarchical bisection method to design a series of new troubled cell indicators which can precisely find all extreme points of associated unequal degree reconstruction polynomials located inside the smallest interval in one dimension. The new troubled cell indicators do not introduce any manual parameters related to different problems. The new hybrid methodology is divided into two parts: if all extreme points of the reconstruction polynomials are nonexistent or outside the smallest interval, the target cell is not a troubled cell and the simple linear upwind schemes are utilized to obtain high-order approximations. Otherwise, the target cell is a troubled cell and the MR-WENO spatial reconstruction procedures with excellent shock-capture ability are adopted. Then a series of HMR-WENO schemes are proposed by using these new troubled cell indicators, which can be easily expanded to arbitrarily high-order accuracies in multi-dimensions. The main benefits of these HMR-WENO schemes are their efficiency, since they could save about 22%-75% CPU time than that of the same order MR-WENO schemes when simulating some benchmark examples in multi-dimensions.

Detecting Reinforced Concrete Rebars Using Ground Penetrating Radars

A new algorithm is developed to automatically detect rebar locations and diameters of reinforced concrete structures using the ground penetrating radar technique. The study uses two-way travel time and biquadratic equations to formulate electromagnetic wave speed in reinforced concrete structures where hyperbolic signatures are approximated. Leveraging an established algorithm, a computer code has been developed to offer automated analysis of ground-penetrating radar data obtained from survey grids. Four reinforced concrete slabs were designed, fabricated, and tested to validate the developed evaluation approach. The proposed methodology demonstrates outstanding signal processing proficiency and reliably and effectively identifies rebar information.

Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code

This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code’s reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode’s methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode’s adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode’s prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns.

Improving the Spatiotemporal Transferability of Hyperspectral Remote Sensing for Estimating Soil Organic Matter by Minimizing the Coupling Effect of Soil Physical Properties on the Spectrum: A Case Study in Northeast China

Soil organic matter (SOM) is important for the global carbon cycle, and hyperspectral remote sensing has proven to be a promising method for fast SOM content estimation. However, because of the neglect of the spectral response of soil physical properties, the accuracy and spatiotemporal transferability of the SOM prediction model are poor. This study aims to improve the spatiotemporal transferability of the SOM prediction model by alleviating the coupling effect of soil physical properties on spectra. Based on satellite hyperspectral images and soil physical variables, including soil moisture (SM), soil surface roughness (root-mean-square height, RMSH), and soil bulk weight (SBW), a soil spectral correction model was established based on the information unmixing method. Two important grain-producing areas in Northeast China were selected as study areas to verify the performance and transferability of the spectral correction model and SOM content prediction model. The results showed that soil spectral corrections based on fourth-order polynomials and the XG-Boost algorithm had excellent accuracy and generalization ability, with residual predictive deviations (RPDs) exceeding 1.4 in almost all the bands. In addition, when the soil spectral correction strategy was adopted, the accuracy of the SOM prediction model and the generalization ability after the model migration were significantly improved. The SOM prediction accuracy based on the XG-Boost-corrected spectrum was the highest, with a coefficient of determination (R2) of 0.76, a root-mean-square error (RMSE) of 5.74 g/kg, and an RPD of 1.68. The prediction accuracy, R2 value, RMSE, and RPD of the model after the migration were 0.72, 6.71 g/kg, and 1.53, respectively. Compared with the direct migration prediction of the model, adopting the soil spectral correction model based on fourth-order polynomials and XG-Boost reduced the RMSE of the SOM prediction results by 57.90% and 60.27%, respectively. This performance comparison highlighted the advantages for considering soil physical properties in regional-scale SOM predictions.

Distinct-positivity-preserving methods for fifth-order finite volume ALW-MR-WENO schemes with a bigger sufficient CFL number for extreme problems

In this paper, the new distinct-positivity-preserving (DPP) methods are proposed for fifth-order finite volume multi-resolution WENO schemes with adaptive linear weights (which are termed as the ALW-MR-WENO schemes) [J. Comput. Phys., 493 (2023), 112471] for solving some extreme problems on structured meshes. Associated WENO spatial reconstruction procedures only require two hierarchical unequal-sized central spatial stencils for achieving fifth-order accuracy in smooth regions and keeping the essentially non-oscillatory property in non-smooth regions. One redefines five cell averages after performing such spatial reconstructions and then designs one quartic polynomial and two cubic reconstruction polynomials based on them in one dimension. After that, a new detective process is used to examine the positivity of the point values of such cubic reconstruction polynomials at some checking points inside the target cell. If the negativity happens, a new over-determined compression limiter is carried out to ensure that the compressed polynomials can achieve the positivity in the whole target cell instead of only at some discrete points inside it. The quartic polynomial could use its four quadrature point values by using a four-point Gauss-Lobatto quadrature formula when performing numerical integrations. Since it is easy to rewrite the point values of one quartic polynomial with the point values of two cubic polynomials timing with associated linear weights, both cubic polynomials could use a four-point Gauss-Lobatto quadrature formula or a three-point Simpson's quadrature formula without losing any algebra precisions. By doing this novelty switching methodology between two quadrature formulas, it is the first time to theoretically prove and increase a sufficient CFL number from 1/12 to 1/7.2 for the fifth-order WENO schemes in one dimension. This methodology can be easily extended to multi-dimensions. Finally, the novelty DPP methods for fifth-order ALW-MR-WENO schemes with a larger practical CFL number of 0.6, instead of the sufficient CFL number of 1/7.2, are also simple and robust enough for some extreme problems without timely halving the CFL number to avoid the appearance of negative density and negative pressure.

Novel patient-specific gingival soft-tissue expander development for large bone defects using silicone 3D-printing technology

The current hydrogel self-inflating expander is limited by its volume and linear expansion rate, making it unsuitable for correcting patient-specific large mandibular bone defects in soft-tissue surgeries. This study devised a novel approach for crafting patient-specific gingival tissue expanders for large mandibular bone defects by employing silicone 3D-printing technology. The biocompatible and swellable polymer tablet was compressed and placed into a 3D-printed silicone membrane to evaluate its expansion capability. Two patient-specific large left and right mandibular bone defects with complex geometries were selected to generate defect expander models in a computer-aided design (CAD) software. The swellable tablets were enveloped in the 3D-printed silicone membranes to form soft-tissue expanders, which were then immersed in phosphate-buffered saline (PBS) for 6 weeks to observe their expansion. Results demonstrated that a slot-shaped silicone soft-tissue tablet attained an expansion volume of 1960 mm³. A fourth-degree polynomial fitting curve illustrated slower expansion rates in the initial 2 weeks and achieved complete expansion in about 6 weeks. Patient-specific silicone expander testing indicated less than 2% error in the average expanded volumes of compared to CAD models. The cross-sectional profile of the soft-tissue expanders closely resembled the CAD model. This study demonstrated that biocompatible polymer could be utilized as swellable tablet material and enveloped within a 3D-printed silicone membrane to generate a novel soft-tissue expander that adhered to clinical standards. Additionally, the study validated the feasibility of expanding patient-specific silicone expanders within 6 weeks for repairing large left and right mandibular bone defects.

Planar quartic G2 Hermite interpolation for curve modeling

We study planar quartic G2 Hermite interpolation, that is, a quartic polynomial curve interpolating two planar data points along with the associated tangent directions and curvatures. When the two specified tangent directions are non-parallel, a quartic Bézier curve interpolating such G2 data is constructed using two geometrically meaningful shape parameters which denote the magnitudes of end tangent vectors. We then determine the two parameters by minimizing a quadratic energy functional or curvature variation energy. When the two specified tangent directions are parallel, a quartic G2 interpolating curve exists only when an additional condition on G2 data is satisfied, and we propose a modified optimization approach. Finally, we demonstrate the achievable quality with a range of examples and the application to curve modeling, and it allows to locally create G2 smooth complex shapes. Compared with the existing quartic interpolation scheme, our method can generate more satisfactory results in terms of approximation accuracy and curvature profiles.

Envelope waves propagation in a one-dimensional tetratomic model of acoustic metamaterial

This paper explores the propagation of modulated waves in systems modelled as one-dimensional network whose elementary cell is constituted of four interacting subsystems. We derive the dispersion relation of its small amplitude plane waves as a quartic polynomial equation in the frequency squared; and numerically show the existence of four frequency bands. These include one acoustic band and three optical bands of which the middle one features the left-handedness. We also use the reductive perturbation method to reduce the discrete equations of motion of the system to the standard nonlinear Schrödinger, thereby predicting the possibility of the propagation modulated waves in the model. This prediction is firmly established through direct numerical simulations in which the analytical solutions of the nonlinear Schrödinger equation are used as input.

Wolfes model aka G2/I6-rational integrable model: g(2), g(3) hidden algebras and quartic polynomial algebra of integrals

One-dimensional 3-body Wolfes model with 2- and 3-body interactions also known as G2/I6-rational integrable model of the Hamiltonian reduction is exactly-solvable and superintegrable. Its Hamiltonian H and two integrals I1,I2, which can be written as algebraic differential operators in two variables (with polynomial coefficients) of the 2nd and 6th orders, respectively, are represented as non-linear combinations of g(2) or g(3) (hidden) algebra generators in a minimal manner. By using a specially designed MAPLE-18 code to deal with algebraic operators it is found that (H,I1,I2,I12≡[I1,I2]) are the four generating elements of the quartic polynomial algebra of integrals. This algebra is embedded into the universal enveloping algebra g(3). In turn, 3-body/A2-rational Calogero model is characterized by cubic polynomial algebra of integrals, it is mentioned briefly.

The law of infrared radiation generation and evolution of coal-rock fracture under load

In order to study the formation mechanism and evolution law of infrared radiation (IR) of coal-rock. A mathematical model of pressure-IR for coal-rock under loading conditions was developed based on theories such as frictional heat generation and heat conduction. The results indicate that: (1) IR and stress exhibit a one-dimensional quartic function relationship, which is consistent with the strong correlation shown by the experimental data curve. As the loading stress increases, the infrared radiation temperature of the coal-rock surface increases. (2) From the simulation results, it can be seen that the increase in surface temperature of coal-rock is essentially influenced by the heat transfer of internal heat sources. The trend of temperature fluctuations is similar for both, with both increasing with ambient temperature and loading rate. And this characteristic change is independent of external loading factors. (3) The IR temperature varies in stages under different loading conditions. In addition, the surface temperature of the coal-rock before fracturing is affected by the frictional heat generation between cracks, resulting in an overall upward trend. When it is about to break, a precursor to the fracture appears. The final IR on the surface of coal-rock increased by 0.04–0.13 °C, which is consistent with the simulation results. It is consistent with the simulation results and reveals the evolution law of IR. The results of this work provide theoretical evidence for the prediction of dynamical disasters in coal and rocks.

Improvement of Commercial Vehicle Seat Suspension Employing a Mechatronic Inerter Element

To further improve the ride comfort of commercial vehicles, a seat ISD (Inerter–Spring–Damper) suspension utilizing a mechatronic inerter is proposed in this paper. Firstly, a five-DOF (degree-of-freedom) commercial vehicle seat ISD model was built. Then, the positive real network constraint conditions of a biquadratic impedance transfer function were determined, and the meta-heuristic intelligent optimization algorithm was used to solve the parameters. According to the solution, the impedance transfer function was obtained and the specific network structure was realized by network synthesis. Lastly, this study compares the vibration isolation performance of the mechatronic ISD suspension of the vehicle seat with that of a passive suspension. In comparison to passive seat suspension, the seat mechatronic ISD suspension reduces seat vibration transmissibility by 16.33% and vertical acceleration by 16.78%. Results indicate that the new suspension system can be an effective improvement in ride comfort.