Numerical Results Research Articles

Numerical analysis of soil reinforced by sand columns using different installation methods

This study involves a finite element numerical simulation of laboratory tests conducted on small-scale models. The tests involved the installation of columns using different techniques: without soil displacement and without column compaction (WR-NC), and without soil displacement but with column compaction (WR-WC). The reinforced soil masses were then subjected to a uniform 150 kPa load. A comparison between the numerical and experimental results showed excellent agreement, validating the simulation. Following this validation, a parametric analysis was carried out to examine the effects of the various parameters on the behavior of the reinforced soil masses. In the first method, three different column diameters were analyzed, focusing on the effects of diameter (area replacement ratio), column length, and geogrid containment benefits. In the second method, three levels of compaction pressure were applied during the column installation. The study evaluated the impact of column installation techniques on the behavior of the reinforced masses. The findings indicate that settlement reduction is proportional to the increase in area replacement ratio and column length. Additionally, confining the columns with geogrid was shown to be effective in further reducing settlements. The results also revealed that increasing compaction stress leads to greater radial expansion of the columns, which densifies and stiffens the surrounding soil, thereby reducing settlement. Overall, the study concludes that column installation techniques significantly influence the behavior of reinforced soil masses.

Performance Analysis and Operation Parameter Optimization of Shaker-Type Harvesting for Camellia Fruits

This study aims to address the challenges of achieving a high harvesting rate and low flower bud damage rate during the harvesting of camellia fruits. To this end, a dynamic model of the camellia osmantha tree and a self-developed shaker-type harvesting machine were used as research subjects. The first 24 natural frequencies and mode shapes of the camellia tree were solved using the finite element method, and the effects of vibration frequency, excitation position, and vibration duration on the harvesting rate and flower bud damage rate were quantitatively analyzed through an orthogonal experiment. The numerical analysis results indicate that the camellia tree exhibits good response characteristics at vibration frequencies of 10–15.5 Hz and 38.5 Hz. The three-factors orthogonal experiment figured out that the optimal operational parameters for shaker-type harvesting were determined to be a vibration duration of 30 s, a motor output frequency of 12.5 Hz, and a gripping position height of 50 to 60 cm above the ground. Meanwhile, under these operational parameters, the harvesting efficiency reached 96.97%, while the flower bud damage rate was only 6%.

Stopping criteria for nonlinear variational problems: iterative approach

AbstractIn this paper, we present and study a stopping criteria based on a priori error estimate for nonlinear variational problems. We show that for nonlinear variational problems, the a priori error estimate is divided into two sub errors namely: the discretization error and the linearization error. We then used that representation to devise a stopping criteria that help to reduce the computational time. The methodology is applied to three problems and the numerical results demonstrate the superiority of the new approach.

A Design of NLOS Communication Scheme Based on SC-FDE with Cyclic Suffix for UAV Payload Communication

Non-line-of-sight (NLOS) communication with severe loss always leads to performance degradation in unmanned aerial vehicle (UAV) payload communication. In this paper, a UAV NLOS communication scheme based on single-carrier frequency domain equalization with cyclic prefix and cyclic suffix (CP/CS-SC-FDE) is designed. First, the reasons behind the generation of later intersymbol interference (LISI) in UAV NLOS communication are investigated. Then, the frame structure of conventional single-carrier frequency domain equalization with cyclic prefix (CP-SC-FDE) is improved, and the UAV NLOS communication frame structure based on cyclic prefix (CP) and cyclic suffix (CS) is designed. Furthermore, a channel estimation algorithm applicable to this scheme is proposed. The numerical results show that this UAV communication scheme can eliminate intersymbol interference (ISI) in NLOS communication. Compared with the conventional CP-SC-FDE system, this scheme can achieve excellent performance in the Rayleigh channel and other standard NLOS channels. In the CP/CS-SC-FDE system, the BER result is similar to that under ideal synchronization.

Numerical optimisation of Dirac eigenvalues

Abstract Motivated by relativistic materials, we develop a numerical scheme to support existing or state new conjectures in the spectral optimisation of eigenvalues of the Dirac operator, subject to infinite-mass boundary conditions. We numerically study the optimality of the regular polygon (respectively, disk) among all polygons of a given number of sides (respectively, arbitrary sets), subject to area or perimeter constraints. We consider the three lowest positive eigenvalues and their ratios. Roughly, we find results analogous to known or expected for the Dirichlet Laplacian, except for the third eigenvalue which does not need to be minimised by the regular polygon (respectively, the disk) for all masses. In addition to the numerical results, a new, mass-dependent upper bound to the lowest eigenvalue in rectangles is proved and its extension to arbitrary quadrilaterals is conjectured.

Intelligent adaptive nonlinear autoregressive eXogeneous neuro‐structure for ferromagnetic Powell‐Eyring fluidic involving cubic autocatalysis chemical reaction

AbstractThe scope of artificial intelligence in the field of fluid mechanics has been expanded with the development sophisticated technology to enhance the efficiency, reliability, solve complexities, introduced alternate transformation and enabling more dependable solutions with their analysis. The goal of this study is to investigate the ferromagnetic Powell‐Eyring fluids (FMPEFs) model with non‐Fourier heat flux by using artificial intelligence‐based scheme by exploiting the adaptive nonlinear autoregressive eXogenous (NARX) neuro‐architecture with backpropagation of Levenberg Marquart (LM), that is, NARX‐LM. The developed NARX‐LM methodology applied on synthetic datasets acquired with the help of Adams numerical method for FMPEF system by prudently changing physical quantities that is, material parameters of Eyring Powell, homogeneous reaction, heterogeneous reaction, dimensionless thermal relaxation time, Prandtl number, Schmidt number with fixed values parameter of ferrohydrodynamic interaction, rate of diffusion coefficient. Outcomes of NARX‐LM are regularly overlapping with the numerical results for the FMPEFs system having reasonable small error magnitude for each variant. The proficiency of intelligent computing anticipated on FMPEFs is depicted exhaustively with iterative mean squared error based iconvergence curves, analysis of adaptive controlling factors, error frequency distribution on the histograms, auto‐correlation, and correlation measures.

Design Optimization of a Plate‐Fin Heat Exchanger With Metaheuristic Hybrid Algorithm

ABSTRACTThis paper introduces a novel approach to enhance the heat transfer efficiency of a plate‐fin heat exchanger. The metaheuristic hybrid approach combines particle swarm optimization (PSO) with the genetic algorithm (GA). Seven critical design parameters are used as variables. The research demonstrates the effectiveness of this hybrid method through a case study based on existing literature. The numerical results show the superior performance of the hybrid genetic algorithm particle swarm optimization over conventional GA and PSO techniques. The hybrid method achieves an optimal configuration with increased accuracy in a shorter computational time, offering significant time and cost savings in the design process.

A time-relaxation reduced order model for the turbulent channel flow

Regularized reduced order models (Reg-ROMs) are stabilization strategies that leverage spatial filtering to alleviate the spurious numerical oscillations generally displayed by the classical Galerkin ROM (G-ROM) in under-resolved numerical simulations of turbulent flows. In this paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which filters the marginally resolved scales. We compare the new TR-ROM with the two other Reg-ROMs in current use, i.e., the Leray ROM (L-ROM) and the evolve-filter-relax ROM (EFR-ROM) and one eddy viscosity model, the mixing-length model, in the numerical simulation of the turbulent channel flow at Reτ=180 and Reτ=395 in both the reproduction and the predictive regimes. For each Reg-ROM, we investigate two different filters: (i) the differential filter (DF), and (ii) the higher-order algebraic filter (HOAF). In our numerical investigation, we monitor the Reg-ROM performance with respect to the ROM dimension, N, and the filter order. We also perform sensitivity studies of the three Reg-ROMs with respect to the time interval, relaxation parameter, and filter radius. The numerical results yield the following conclusions: (i) All three Reg-ROMs are significantly more accurate than the G-ROM. (ii) All three Reg-ROMs are more accurate than the ROM projection in terms of Reynolds stresses. (iii) With the optimal parameter values, the new TR-ROM yields more accurate results than the L-ROM and the EFR-ROM in all tests. (iv) The new TR-ROM is more accurate than the mixing-length ROM. (v) For most N values, DF yields the most accurate results for all three Reg-ROMs. (vi) The optimal parameters trained in the reproduction regime are also optimal for the predictive regime for most N values, demonstrating the Reg-ROM predictive capabilities. (vii) All three Reg-ROMs are sensitive to the filter order and the filter radius, and the EFR-ROM and the TR-ROM are sensitive to the relaxation parameter. (viii) The optimal range for the filter radius and the effect of relaxation parameter are similar for the two Reτ values.

The passive recording of the click trains of a beluga whale (Delphinapterus leucas) and the subsequent creation of a bio-inspired echolocation model.

A beluga-like model of click train signal is developed by observing beluga's sound recording. To reproduce the feature of the biosonar signal, this paper uses a signal extracting method with a correction factor of inter-click interval to acquire the parameter of click trains. The extracted clicks were analyzed in the time and frequency domain. Furthermore, a joint pulse-frequency representation was undertaken in order to provide a 2D energy distribution for an echolocation click train. The results from joint pulse-frequency representation indicate that click train can be adjusted its energy distribution by using a multi-component signal structure. To evaluate the capability of the click train to inform the whale of relevant target information perception for the click train, a finite element model is built to reproduce target discrimination by the bio-inspired click train. Numerical results indicate that the bio-inspired click train could enhance the echo-response by concentrating energy into the frequency bins for extracting target feature effectively. This proof-of-concept study suggests that the model of click train could be dynamically controlled to match the target properties, and show a promising way to use various types of echolocation click train to interrogate different features of the target by man-made sonar.

Testing the Instanton Approach to the Large Amplification Limit of a Diffraction-Amplification Problem

Abstract The validity of the instanton analysis approach is tested numerically in the case of the diffraction-amplification problem ∂zψ−(i/2m)∂2 x2 ψ=g│S│2 for ln U>>1, where U=│ψ(0,L)│2. Here, S(x,z) is a complex Gaussian random field, z and x respectively are the axial and transverse coordinates, with 0≤z≤L, and both m≠0 and g>0 are real parameters. We consider a class of S, called the `one-max class', for which we devise a specific biased sampling procedure. As an application, p(U), the probability distribution of U, is obtained down to values less than 10-2270 in the far right tail. We find that the agreement of our numerical results with the instanton analysis predictions in Mounaix (2023 J. Phys. A: Math. Theor. 56 305001) is remarkable. Both the predicted algebraic tail of p(U) and concentration of the realizations of S onto the leading instanton are clearly confirmed, which validates the instanton analysis numerically in the large ln U limit for S in the one-max class.

Adaptive Neural Delay Feedback Control of a Typical Robot on a Slope

ABSTRACTIn this article, an adaptive neural delay feedback control strategy is proposed for the motion control of a two‐wheel self‐balancing robot (TWSBR) on a slope with an input delay. Based on the Lagrange equation, the dynamic model of the robot is derived. Given a target trajectory vector, the corresponding error system is obtained. An input delay and uncertainties are considered. First, the system with an input delay is transformed into a delay‐free one. Second, a quadratic performance optimization criterion is defined, and a linear quadratic regulator (LQR) controller is designed to minimize the error between the system's state vector and the target vector. Thirdly, an integral sliding mode controller is added to the LQR controller to enhance the system's robustness. To reduce the “chattering” phenomenon, an adaptive neural delay feedback control scheme is developed based on the adaptive learning of the uncertainties' upper bound by a radial basis function neural network (RBFNN). It is demonstrated that a relaxation process exists at the beginning of the upslope motion. As the input delay increases, the swing range of the center of gravity of the pendulum expands. The angle can converge to the steady state more quickly, but the relaxation time is still 0.031 s which has nothing to do with the input delay. An example of the back‐and‐forth motion of a TWSBR on a slope can verify an excellent agreement between theoretical analysis and numerical results.

On load dependence of detachment rate of kinesin motor

Abstract Kinesin is an archetypal microtubule-based molecular motor that can generate force to transport cargo in cells. The load dependence of the detachment rate is an important factor of the kinesin motor, the determination of which is critically related to the chemomechanical coupling mechanism of the motor. Here, we use three models for the load dependence of the detachment rate of the kinesin motor to study theoretically and numerically the maximal force generated and microtubule-attachment duration of the motor. By comparing the theoretical and numerical results with the available experimental data, we show that only one model can explain well the available experimental data, indicating that only this model can be applicable to the kinesin motor.

A comprehensive study of beam modal functions in the free vibration analysis of cylindrical shells: Critical examination on the applicability to the clamped-free boundary condition

Over the past few decades, approximate methods that can provide solutions of sufficient accuracy have received considerable attention in the free vibration analysis of cylindrical shells, where a great deal of studies adopted the beam modal functions as the trial functions for the axial mode shapes of cylindrical shells. Nevertheless, most studies were restricted to the application of single term beam modal function and failed to simulate elastic boundary conditions of cylindrical shells, while the accuracy of the corresponding methods has recently sparked significant controversy, especially for cylindrical shells under the clamped-free boundary condition. This paper presents a comparative study of three forms of beam modal functions in the free vibration analysis of cylindrical shells, one of which is proposed for the first time to simulate elastic boundary conditions of cylindrical shells. A unified model is developed using the general Rayleigh–Ritz method, incorporating the breathing modes with circumferential orders being zero, and four types of commonly used thin shell theories, namely the Donnell, Reissner, Love, and Sanders theories. From both perspectives of natural frequencies and mode shapes, numerical results are validated by comparison with those existing in the literature and those calculated from the finite element method (FEM). The results not only clarify the distinction of different forms of beam modal functions used in the Rayleigh-Ritz method, but also provide explanations for the controversy raised in recent studies. Furthermore, the unified formulations can be extended to vibration analysis of various forms of shell structures, and can also be helpful to the vibration analysis of beams and plates with elastic boundary conditions.

Numerical methods and analytic results for one-dimensional strongly interacting spinor gases

Numerical methods and analytic results for one-dimensional strongly interacting spinor gases

Whale Optimization Algorithm with Machine Learning for Microwave Imaging

This paper introduces a novel approach for reconstructing microwave imaging by combining the Whale Optimization Algorithm (WOA) with deep learning techniques. In it, electromagnetic waves are used to illuminate inhomogeneous dielectric objects in free space, and the scattered field is recorded. Due to the highly nonlinear nature of microwave imaging, the WOA is first employed to calculate an initial guess from the measured scattered field of dielectric objects. This step significantly reduces the training complexity for machine learning. Subsequently, the initial guess provided by the WOA is fed into a U-Net to accurately reconstruct the microwave image. Numerical simulation results indicate that the combination of the WOA and machine learning outperforms traditional methods under varying noise levels, enhancing the precision and effectiveness of the reconstruction process. In detail, the RMSE can be reduced 4–10% for dielectric constant distribution from 1 to 2.5 and SSIM can be increased about 30% for most cases.

Rewritable Broadband Lossy Absorber Based on Laser Induction Technology

AbstractThe tunable and reversible fabrication function of stealth metasurfaces has significant application value in complex electromagnetic environments., but the extremely low fault tolerance of the existing fabrication methods limits their further development and utilization. In this manuscript, a design and fabrication method for rewritable broadband stealth metasurfaces with memory function is proposed. The reversible phase transition is achieved by laser induced germanium telluride (GeTe) film, which provides the possibility for metasurface to realize the rewriting function. The process of laser induced GeTe and the simulation model of GeTe are investigated, and the conclusions are verified by rewritable broadband polarization converter (RBPC) and rewritable broadband lossy absorber (RBLA). The experimental results show that the reflectivity of fabricated RBLA is less than −10 dB in the range of 7.8–16.1 GHz, which is in good agreement with the numerical simulation results. Meanwhile, there is a highly consistent performance effect before and after repeated induction. The research has the advantages of high efficiency, region selectivity, non volatility and high fault tolerance, which can provide new manufacturing ideas and good candidates for tunable metamaterials.

Surface Profile Recovery from Electromagnetic Fields with Physics-Informed Neural Networks

Physics-informed neural networks (PINN) have shown their potential in solving both direct and inverse problems of partial differential equations. In this paper, we introduce a PINN-based deep learning approach to reconstruct one-dimensional rough surfaces from field data illuminated by an electromagnetic incident wave. In the proposed algorithm, the rough surface is approximated by a neural network, with which the spatial derivatives of surface function can be obtained via automatic differentiation, and then the scattered field can be calculated using the method of moments. The neural network is trained by minimizing the loss between the calculated and the observed field data. Furthermore, the proposed method is an unsupervised approach, independent of any surface data, where only the field data are used. Both transverse electric (TE) field (Dirichlet boundary condition) and transverse magnetic (TM) field (Neumann boundary condition) are considered. Two types of field data are used here: full-scattered field data and phaseless total field data. The performance of the method is verified by testing with Gaussian-correlated random rough surfaces. Numerical results demonstrate that the PINN-based method can recover rough surfaces with great accuracy and is robust with respect to a wide range of problem regimes.

Device optimization of all-perovskite triple-junction solar cells for realistic irradiation conditions

All-perovskite two-terminal tandem solar cells, comprising two or more junctions, offer high power conversion efficiencies (PCEs) that exceed the limits of single-junction photovoltaics. Realizing high-efficiency SCs requires carefully optimizing the photoactive layer, front electrodes, and functional layers. Here, we first aim to determine the optimal device architecture, i.e., the perovskites bandgaps and optimum layer thicknesses, for standard test conditions (STCs). We then optimize the energy yield (EY) under realistic outdoor conditions (ROCs), i.e., the overall electrical energy to be expected in one year at a specific location. In the first step, we reference our simulation with two terminal all-perovskite triple-junction SCs (2T3J-PSCs) to previously experimentally realized PSC with a PCE of 20.1% as a benchmark to derive the underlying diode parameters and use our in-house energy yield code combined with a hybrid particle swarm optimization and gravitational search algorithm (PSOGSA) to find the optimal bandgap combination and perovskite layer thicknesses. The optimized SCs with the optimal bandgap combination offer a PCE of 25.1% with a current density of 10.1 mA/cm2. Furthermore, the effect of the other functional layers, such as transparent conductive oxide (TCO), hole transport layer (HTL), and recombination junctions (RJs), is also investigated to enhance the cell performance further. The SCs with optimized layers exhibit improved parameters: PCE of 27.1%, with a relative improvement of 34.8% in the PCE compared with the fabricated cell, and a high current matching a of 10.8 mA/cm2. The numerical results showed that the reported cell can potentially achieve a PCE of 36% at an eVoc/EG ratio of 0.72. However, the optimal parameters may vary in real-world operating conditions due to variations in temperature, humidity, and light exposure. As a result, the optimal energy yield (EY) parameters may differ. Therefore, the energy yield optimizing process is also carried out by considering ROCs in Phoenix, AZ, USA, to find the best parameters under these conditions. We found that the optimum top layer bandgap under ROCs is lower than under STCs due to a bluer, more shifted spectrum in ROCs. After that, the optimized cell under ROCs is tested in several locations exhibiting different climatic conditions (Seattle, Honolulu, Los Angeles, Miami, and Milwaukee). The numerical results show that the optimized cell under ROCs offers an increase in energy yield in several locations compared to conventional single-junction crystalline Si-SCs (PCE = 23.6%) with a high energy yield of 648.2 kWh/m2 in Phoenix, with an improvement of 39.9% in the EY compared to the Si-SC counterpart. Our results provide design guidelines for fabricating a highly efficient triple-junction perovskite SC in the lab and outdoor applications and improve the efficiency of 2T3J-PSCs beyond the 30% limit.

Turing Instability and Dynamic Bifurcation for the One‐Dimensional Gray–Scott Model

ABSTRACTWe study the dynamic bifurcation of the one‐dimensional Gray–Scott model by taking the diffusion coefficient of the reactor as a bifurcation parameter. We define a parameter space of for which the Turing instability may happen. Then, we show that it really occurs below the critical number and obtain rigorous formula for the bifurcated stable patterns. When the critical eigenvalue is simple, the bifurcation leads to a continuous (resp. jump) transition for if is negative (resp. positive). We prove that when lies near the Bogdanov–Takens point . When the critical eigenvalue is double, we have a supercritical bifurcation that produces an ‐attractor . We prove that consists of four asymptotically stable static solutions, four saddle static solutions, and orbits connecting them. We also provide numerical results that illustrate the main theorems.

Numerical modeling of the transfer length of 17.8 mm (0.7 in) diameter prestressing strands in pretensioned members

The bond between concrete and reinforcing steel bars in reinforced concrete structures is crucial. Prestressing strands with a diameter of 17.8 mm (0.7 in) transfer higher compression per unit area than smaller strands, improving moment capacity and shear strength and extending the girder span. However, limited research on the bond performance of these 17.8 mm diameter prestressing strands has restricted their widespread use despite their advantages. This study presents a methodology to determine the transfer length of pretensioned members numerically. The influence of pretension force and bond strength on a 17.8 mm diameter strand was assessed through the validation of a finite element model using experimental results from a standardized pretensioned pull-out test. Analytical calculations using different code formulas were also conducted, encompassing strands of varying diameters. Our finite element analysis suggests that a 50.8 mm spacing between adjacent 17.8 mm diameter strands is applicable, ensuring there is no stress overlap in the transfer zones, which can lead to concrete cracking and reduced structural integrity. Existing code formulas, such as ACI 318–19 and AASHTO LRFD 9th edition, require longer transfer lengths when compared with the numerical results. The fib MC 2010 and EC2 formulas offer closer results to numerical results of smaller diameter strands but underestimate the transfer length for the 17.8 mm diameter strand. Therefore, improvements to code formulations may be necessary for more accurate transfer length predictions for this specific strand size.