Numerical Simulations Research Articles

Improved numerical schemes to solve general fractional diabetes models

In this article, we propose a new class of nonlinear fractional differential equations of diabetes disease based on the concept of Caputo fractional derivative. Two numerical techniques are introduced to analyse the solution of the general fractional diabetes model, that describes glucose homeostasis. The first method, which constructed using the nonstandard finite difference technique involves an asymptotically stable difference scheme. This method maintains important properties of the solutions of the studied system, such as the positivity and boundedness. The second method is the Jacobi-Gauss–Lobatto spectral collocation approach, known for its exponential accuracy. By employing this collocation method, the problem is transformed into a set of algebraic nonlinear equations, simplifying the overall task. Numerical simulations were conducted to compare the performance of these two techniques with other standard methods and the analytic solution in specific cases. Our findings show that the Jacobi-Gauss–Lobatto spectral collocation technique provides higher accuracy in solving the fractional diabetes model system, while the nonstandard finite difference approach requires lower computational duration.

Maximizing the Absorbing Performance of Rectangular Sonic Black Holes

This study examines the absorption performance of rectangular sonic black holes (SBHs), which are designed to provide broadband anechoic termination for rectangular waveguides. The SBHs explored in this work consist of a series of opposing rib pairs embedded within the waveguide, where the distance between the ribs in each pair decreases towards the end of the structure according to a specific profile. A computationally efficient mathematical model, combined with an evolutionary optimization algorithm, is employed to determine the optimal geometrical parameters, including the SBH profile, which maximize absorption performance over a broad frequency range. As the optimal geometries feature very fine internal structures, which pose challenges for practical implementation, micro-perforated plates are incorporated to introduce additional losses. Numerical simulations and optimizations are again utilized to identify the geometrical and physical parameters that maximize the absorption performance of these modified structures. The results demonstrate superior absorption performance, even with internal structures compatible with contemporary manufacturing processes. The results of the numerical simulations are validated via a comparison with detailed and accurate mathematical model.

Seismic Behavior of Cluster-Connected Prefabricated Shear Walls under Different Axial Compression Ratios

This study analyzes the nonlinear seismic behavior of cluster-connected prefabricated shear walls under varying axial compression ratios. The investigation focuses on the connectivity of shear wall segments assembled using cluster connections rather than separate walls connected by beams. Using the finite element software ABAQUS, this study simulates monotonic horizontal displacement loading to evaluate the yield strength, peak strength, and deformation capacity of the shear walls. The results demonstrate that the horizontal load-bearing capacity of the shear wall significantly improves with an increase in axial compression ratio, while the axial compression ratio also influences ductility. The numerical simulations are validated against experimental data, confirming the accuracy of the model. These findings provide essential insights for optimizing the seismic design of precast shear walls.

Free vibration analyses of 3D printed plates with different geometric fillings: experimental testing and numerical simulations

Abstract In this article, the numerical and experimental free vibration analyses of PLA-based composite plates with different filling geometries were carried out. Firstly, the natural frequencies and modal shapes were obtained from finite element (FE) methods to characterize the vibration behavior of the plates. The obtained results were compared with experimental testing of the three-dimensional (3D) produced plates. In the comparison, it was seen that the finite element analysis and the experimental results were quite close to each other. It was also observed that the highest frequencies are measured by a triangle, then the grid and honeycomb. Moreover, higher frequencies and lower weights are possible with the triangle pattern fill. On the other hand, it is noted that the types of filling structures do not affect the modal shapes of the 3D plates. Thus, the results of this paper are of utmost importance for getting light structure and high frequencies.

Emergence of economic and social disparities through competitive gift-giving

Several tiers of social organization with varying economic and social disparities have been observed. However, a quantitative characterization of the types and the causal mechanisms for the transitions have hardly been explained. While anthropologists have emphasized that gift exchange, rather than market exchange, prevails in traditional societies and shapes social relations, few mathematical studies have explored its consequences for social organizations. In this study, we present a simple model of competitive gift-giving that describes how gifts bring goods to the recipient and honor to the donor, and simulate social change. Numerical simulations and an analysis of the corresponding mean-field theory demonstrate the transitions between the following four phases with different distribution shapes of wealth and social reputation: the band, without economic or social disparities; the tribe, with economic but without social disparities; the chiefdom, with both; and the kingdom, with economic disparity and weak social disparity except for an outlier, namely, the “monarch”. The emergence of strong disparities is characterized by power law distributions and is attributed to the “rich get richer” process. In contrast, the absence of such a process leads to exponential distributions due to random fluctuations. The phases depend on the parameters characterizing the frequency and scale of gift interactions. Our findings provide quantitative criteria for classifying social organizations based on economic and social disparities, consistent with both anthropological theory and empirical observations. Thus, we propose empirically measurable explanatory variables and characteristic indices for the evolution of social organizations. The constructive model, guided by social scientific theory, can provide the basic mechanistic explanation of social evolution and integrate theories of the social sciences.

Coupling effect of dynamic power and oscillation path on butt weld formation and melt flow behavior during aluminum alloys

The influence of the coupling effect between dynamic power and oscillation path on the formation of weld seams and the fluid behavior of the molten pool during laser welding of 5A06 aluminum alloy was investigated through numerical simulation and experimentation. Three power modes were compared in the experiments: equal power (EP), delayed dynamic power (D-DP), and non-delayed dynamic power (ND-DP). The experimental results show that both D-DP and ND-DP modes are favorable to improve the mechanical properties. Among them, the joints formed under the D-DP mode exhibit the best mechanical properties, with an average tensile strength reaching ≈ 99.1% of the base material, which is an increase of ≈ 35.3% and ≈ 5.6% compared to the EP and ND-DP modes, respectively. Numerical simulation results indicate that the D-DP mode effectively mitigates the average flow velocity of the molten pool, reduces the collision effects between liquid flows, suppresses the impact of fluid on the keyhole walls, and improves the stability of the keyhole and the welding process, thereby enhancing the mechanical properties of the joints.

Simulation and prediction of land subsidence in Decheng District under the constraint of InSAR deformation information

Land subsidence, marked by a decline in surface elevation, poses a significant threat to urban infrastructure and safety. Accurate subsidence information and a reliable prediction model are crucial for prevention and control. In this study, we used persistent scatterer interferometric synthetic aperture radar (PS-InSAR) technology to obtain long-term land subsidence data and analyzed subsidence characteristics in Decheng District. By integrating hydrogeological and groundwater data, we developed a three-dimensional groundwater flow and one-dimensional compaction model through numerical simulation. Furthermore, the subsidence data monitored by PS-InSAR were used to further constrain and validate the model. The evolution trend of land subsidence under different groundwater exploitation scenarios was predicted and analyzed. The results showed that from May 2017 to December 2021, the cumulative maximum subsidence in Decheng District reached −173 mm. The subsidence area is mainly concentrated in the northern area, and its subsidence center is near Qiaoyuan Town. According to the Land Subsidence Prevention and Control Plan of Dezhou City, Shandong Province (2018–2025), we set up different groundwater mining scenarios with the goal that the rate of land subsidence in the key prevention and control area is less than 35 mm/yr in 2025.The Fluid-solid coupled model prediction analysis results indicated that a 30% reduction in groundwater exploitation is reasonable.

Simulation and On-Site Monitoring of Deformation Characteristics of Roadway Excavation along Goaf in Soft and Thick Coal Seams in Western Mining Areas

In the western mining region, weakly cemented rock layers above the coal seams often lead to frequent catastrophic accidents during mining due to their instability. To address this, this paper analyzes the movement characteristics of surrounding rock in the recovery roadway and the effectiveness of from nearby large coal pillar roadways. A mechanical model for the failure of weakly cemented roadways was established, and numerical simulations were used to verify the feasibility of leaving small coal pillars along soft, thick coal seams. Additionally, existing measurements were used to evaluate the impact of leaving small coal pillars on the deformation of the surrounding rock in the recovery roadway. The results show that after changing the coal pillar retention to 5 m in the 130,205 working face of the Yangchangwan mining area, the roadway is in a low-stress zone, with minimal surrounding rock deformation, meeting safety requirements for production.

A new hyperchaotic system: circuit realization, nonlinear analysis and synchronization control

This paper presents a novel seven-dimensional nonlinear hyperchaotic system characterized by a minimal number of nonlinear terms and variables, yet exhibiting high complexity. Standard nonlinear analysis is conducted to unveil the system’s intricacies, emphasizing its notable feature of possessing four to five Lyapunov exponents in certain intervals, signifying its volatility and complexity. Hyperchaotic synchronization is explored using a novel nonsingular terminal sliding control design, effectively achieving synchronization between two hyperchaotic master systems and a hyperchaotic slave system within finite time while mitigating the chattering phenomenon. Practical evaluations through orbital analysis, numerical simulations, and practical implementations further substantiate the efficacy and performance of the proposed system. This study contributes to the advancement of chaotic and hyperchaotic systems, particularly those with dimensions exceeding 5D, offering insights into synchronization techniques and practical applications in engineering and other scientific disciplines.

Metasurface Enabled Multi‐Target and Multi‐Wavelength Diffraction Neural Networks

AbstractBenefiting from low power consumption and high processing speed, there is a growing interest in diffraction neural networks (DNNs), which are typically showcased with 3D printing devices, leading to large volumes, high costs, and low levels of integration. Metasurfaces can desirably manipulate wavefronts of electromagnetic waves, providing a compact platform for mimicking DNNs with novel functions. Although multi‐wavelength and multi‐target recognition provides a richer and more detailed understanding of complex environments, existing architectures are primarily trained to classify a single target at a specific wavelength. A metasurface approach is proposed to design multiplexed DNNs that can classify multiple targets and spatial sequences across various wavelengths in multiple channels. To realize multi‐task processing, the dielectric metasurface is designed based on phase and wavelength multiplexing, which can integrate multi‐target DNNs with different tasks such as operating at distinct wavelengths and classifying diverse targets. The efficacy of this method is exemplified through the numerical simulation and experimental demonstration of recognizing a single target with two wavelengths, two targets at a single wavelength, and two targets at dual wavelengths. This compact metasurface approach enables the design of multi‐target and multi‐wavelength DNNs, opening a new window to develop massively parallel processing and versatile artificial intelligence systems.

Speckle denoising based on Swin-UNet in digital holographic interferometry

Speckle noise, mechano-physical noise, and environmental noise are inevitably introduced in digital holographic coherent imaging, which seriously affects the quality of phase maps, and the removal of non-Gaussian statistical noise represented by speckle noise has been a challenging problem. In the past few years, deep learning methods based on convolutional neural networks (CNNs) have made good progress in removing Gaussian noise. However, they tend to fail when these deep networks designed for Gaussian noise removal are used to remove speckle noise. Recently, numerous studies have employed CNNs to address the issue of degraded speckle images, yielding encouraging results. Nevertheless, the degradation of speckle noise that is simulated in isolation is limited and insufficient to encompass the increasingly complex DHI noise environment. This paper presents what we believe to be a novel approach to simulating complex noise environments by multiplexing simulated Gaussian noise and speckle noise. The noise resulting from aliasing does not adhere to the statistical laws of the noise prior to aliasing, which poses a more challenging task for the noise-reduction algorithms utilized in neural networks. Consequently, in conjunction with the capacity of the Swin Transformer to model multi-scale features, this paper proposes a DHI speckle denoising approach based on Swin-UNet. In this paper, Gaussian, speckle, and blending noise datasets with different noise densities are constructed for training and testing by numerical simulation, and generalizability tests are performed on 1,100 randomly selected open-source holographic tomography (HT) noise images at Warsaw University of Technology and 25 speckle images selected from DATABASE. All test results are quantitatively evaluated by three evaluation metrics: mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). All convolutional neural network (CNN) algorithms are evaluated qualitatively based on the number of parameters, floating point operations, and denoising time. The results of the comparison demonstrate that the denoising algorithm presented in this paper exhibits greater stability, accuracy, and generalizability.

Investigation of Strain Softening Behaviours and Development of Constitutive Model of Red Clays in Guiyang, China

Red clay, characterized by high moisture content, high plasticity, large porosity, high strength, and low compressibility, is widely used in engineering projects. The engineering properties and deformation modeling of red clay in Guiyang differ significantly from those of ordinary soils. Consequently, it is essential to conduct a detailed study of the stress-strain relationship of red clay in order to obtain accurate engineering parameters. Hence, a series of unconsolidated undrained triaxial compression tests (UU) were conducted on red clay in Guiyang under different water contents and confining pressures. The test results show that the stress-strain curve of the clay undergoes three stages: elastic deformation, plastic yielding, and stress reduction after failure. After reaching peak deviatoric stress, the deviatoric stress decreases gradually and stabilizes, showing noticeable strain-softening characteristics. The nonlinear model from Nanjing Hydraulic Research Institute (NHRI) was introduced for fitting and obtaining relevant parameters. Then, based on the FLAC 3D platform, numerical simulation was carried out on a standard soil sample. The research results show that the calculated curve from the nonlinear model fits the experimental curve quite well, and the numerical test curve also agrees with it. This indicates that the nonlinear model from NHRI can effectively reflect the strain-softening behavior of clay and is highly applicable to Guiyang red clay.

Mechanical properties study of fiberglass reinforced flexible pipeline in marine applications

ABSTRACT A mechanical properties study of fibereglass reinforced flexible pipe (FGRFP) in marine applications is proposed based on the reinforced layer interface structure design, the anisotropic layer section mechanical performance test, and the structural strength analysis under the laying operation condition. Based on laboratory tests and referencing ASTM and DNV regulations, the technical design indexes of flexible marine pipe that meet strength requirements have been provided. Through tests, the maximum yield tension of FGRFP is 89.8kN, the ultimate curvature is 3.3 rad/m, the bending moment is 2312.2Nm, the torsion angle is 0.32 rad, and the torque is 2610.4Nm. Based on numerical simulation, static analysis can identify weak points in flexible pipelines. Especially, the feasibility of FGRFP structural section design was verified through dynamic analysis under the combined action of waves and currents. Finally, parameter sensitivity studies were conducted, including the effects of wave/flow direction, wave height, and period.

Analysis of Wave Load Characteristics of Hovercraft Based on Model Test

The prediction of the wave load on a hovercraft is essential for the design of the hull structure and safety. However, theoretical methods for the prediction of wave loads are still not mature enough due to the unique and complex nature of the air cushion structure, and numerical modeling and simulation are challenging due to the complexity of the gas-solid-liquid three-phase coupling, so the study of wave loads on hovercrafts still relies on experimentation. In this study, we aim to analyze the wave load response characteristics of a four-chamber hovercraft by conducting a wave load model test under medium/low sea states. The load components and amplitude-frequency response characteristics were thoroughly analyzed based on the acquired data of the cushion pressure, acceleration, and bending moment. The main characteristics of the wave-induced response of the hovercraft were described in detail, and an analytical relationship between the cushion pressure and hull acceleration was derived. The reliability of the experimental results was confirmed through a comparison with the derived results. The relationship between the cushion pressure and cushion volume was investigated in terms of the observed geometric volume of the air chamber, and the relationship between the cushion pressure and flow rate was analyzed to validate the derivation of the theory of wave loads on hovercrafts.

Horseshoes and spiral waves: capturing the 3D flow induced by a low-mass planet analytically

Abstract The key difficulty faced by 2D models for planet-disc interaction is in appropriately accounting for the impact of the disc’s vertical structure on the dynamics. 3D effects are often mimicked via softening of the planet’s potential; however, the planet-induced flow and torques often depend strongly on the choice of softening length. We show that for a linear adiabatic flow perturbing a vertically isothermal disc, there is a particular vertical average of the 3D equations of motion which exactly reproduces 2D fluid equations for arbitrary adiabatic index. There is a strong connection here with the Lubow-Pringle 2D mode of the disc. Correspondingly, we find a simple, general prescription for the consistent treatment of planetary potentials embedded within ‘2D’ discs. The flow induced by a low-mass planet involves large-scale excited spiral density waves which transport angular momentum radially away from the planet, and ‘horseshoe streamlines’ within the co-orbital region. We derive simple linear equations governing the flow which locally capture both effects faithfully simultaneously. We present an accurate co-orbital flow solution allowing for inexpensive future study of corotation torques, and predict the vertical structure of the co-orbital flow and horseshoe region width for different values of adiabatic index, as well as the vertical dependence of the initial shock location. We find strong agreement with the flow computed in 3D numerical simulations, and with 3D one-sided Lindblad torque estimates, which are a factor of 2 to 3 times lower than values from previous 2D simulations.

Enhancing light absorption in ultra-thin perovskite solar cells using plasmonic gold nanoparticle clusters

Perovskite solar cells with ultra-thin absorber layers offer potential cost savings in manufacturing, but their reduced thickness can limit light absorption and efficiency. This work explores using plasmonic gold nanoparticles as a light-trapping strategy to compensate for lower absorption in ultra-thin perovskite devices. Numerical simulations investigate embedding 25 nm radius gold nanoparticles within the 200 nm thick perovskite active layer to boost optical absorption through near-field enhancement and light scattering effects. The solar cell structure incorporating these plasmonic nanoparticles achieves a substantially higher short-circuit current density of 23.10 mA cm−2 compared to 18.70 mA cm−2 for a reference cell without nanoparticles. This study provides design approaches for realizing high-efficiency yet cost-effective ultra-thin perovskite photovoltaics by harnessing plasmonic light-trapping techniques. The results display methodologies to improve photon absorption and power conversion in thin-film perovskite devices through strategic nanoparticle integration.

A Numerical Investigation on the Sinkage of the Deep-Sea Mining Vehicle Based on a Modified Constitutive Soil Model

Abstract The seabed soil of the polymetallic nodule mining area is relatively thin, soft, and fluid, which will produce large deformation under external disturbance. Its undrained shear strength is related to strain-rate and strain-softening effect. It is an important engineering safety problem for the deep-sea mining vehicle (DSMV) to travel in the soft seabed, and its sinkage is a vital index affecting the traction performance. It is necessary to study the sinkage performance of the DSMV under the characteristics of large soil deformation, but there are only few existing studies. This study established a numerical model of seabed soft soil with Tresca constitutive considering strain-rate and strain-softening effects. First, a numerical simulation study was carried out on the interaction between the DSMV track plate and the seabed soil, and the influence of track plate structures on the pressure–sinkage characteristic was obtained. Then, a simplified three-dimensional model of the “PIONEER-I” DSMV was established. Under the condition of wet weight and initial vertical velocity, the influence of different initial bottoming velocities, weight, and soil parameters on the sinkage of the DSMV was obtained. An empirical prediction model of the DSMV sinkage was established based on the energy method and numerical calculation results.

Online updating Huber robust regression for big data streams

ABSTRACT Big data streams have garnered significant attention in multiple industries. However, the immense volume and the presence of outliers in high-velocity streaming data pose great challenges to its analysis. To address these concerns, this paper introduces a novel Online Updating Huber Robust Regression algorithm. By efficiently capturing the salient features of new data subsets, a computationally efficient online updating estimator is proposed without the need for storing historical data. Furthermore, by incorporating Huber regression into its framework, the estimator exhibits robustness to heavy-tailed, heterogeneous as well as outlier-contaminated data. Theoretically, the proposed online updating estimator is asymptotically equivalent to an Oracle estimator derived from the entire dataset. Extensive numerical simulations and a real-world data analysis have been conducted to demonstrate the effectiveness and practicality of the proposed method.

How Does the Ocean Melt Antarctic Ice Shelves?

The present-day state and future of the Antarctic Ice Sheet depend on the rate at which the ocean melts its fringing ice shelves. Ocean heat must cross many physical and dynamical barriers to melt ice shelves, with the last of these being the ice-ocean boundary layer. This review summarizes the current understanding of ice-ocean boundary-layer dynamics, focusing on recent progress from laboratory experiments, turbulence-resolving numerical simulations, novel observations, and the application to large-scale simulations. The complex interplay between buoyant meltwater and external processes such as current shear leads to the emergence of several melting regimes that we describe, as well as freezing processes. The remaining challenges include developing new parameterizations for large-scale ice-ocean models based on recent advances and understanding the coevolution of melt and basal topography.

Investigation of the Discharge Coefficient for Laidback Fan-Shaped Holes on Turbine Blades Under Internal Crossflow Condition

Abstract The discharge coefficient of laidback fan-shaped holes on turbine blades under internal crossflow conditions is investigated using experimental and numerical simulation methods. The study is conducted on a linear cascade, with single rows of film holes set on both the pressure and suction surfaces of the test blade, coolant supplied by an internal crossflow channel. The internal crossflow Reynolds number ranged from 39,100 to 78,200, and the pressure ratio ranged from 1 to 1.5. This research considered the effects of internal crossflow Reynolds numbers and hole length-to-diameter ratio on the discharge coefficient of laidback fan-shaped holes. The findings are as follows: internal crossflow increases the inlet loss of film holes and flow separation within the holes, leading to a significant reduction in the discharge coefficient of film holes. Meanwhile, film holes on the pressure surface of the blade exhibit greater sensitivity to crossflow. Under different hole length-to-diameter ratio conditions, the length of the cylindrical section is the primary factor affecting the discharge coefficient, and the magnitude of the discharge coefficient depends on the extent of flow separation within the cylindrical section. The sensitivity of the discharge coefficient to variations in the cylindrical section length decreases once the cylindrical section length exceeds 2.8D for the pressure surface and 2.0D for the suction surface, where the inlet separation region reattaches to the wall. Under plenum conditions, there are significant differences in the discharge coefficients of film holes between the suction surface and pressure surface, especially at pressure ratios below 1.05.