Numerical Verification Research Articles

Optimisation of gyrokinetic microstability using adjoint methods

Microinstabilities drive turbulent fluctuations in inhomogeneous, magnetised plasmas. In the context of magnetic confinement fusion devices, this leads to an enhanced transport of particles, momentum and energy, thereby degrading confinement. In this work, we describe an application of the adjoint method to efficiently determine variations of gyrokinetic linear growth rates on a general set of external parameters in the local $\delta f$ -gyrokinetic model. We then offer numerical verification of this approach. When coupled with gradient-based techniques, this methodology can facilitate the optimisation process for the microstability of the confined plasmas across a high-dimensional parameter space. We present a numerical demonstration wherein the ion-temperature-gradient instability growth rate in a tokamak plasma is minimised with respect to flux surface shaping parameters. The adjoint method approach demonstrates a significant computational speed-up compared with a finite-difference gradient calculation.

Structural damage identification by using physics-guided residual neural networks

In recent years, vibration-based structural damage identification has made significant progress by exploiting data-driven deep learning techniques, which can efficiently extract damage-sensitive features from a large amount of data. However, in some practical engineering applications, large volumes of measurement data are not readily available. This paper proposes a novel physics-guided residual neural network (PhyResNet) framework to improve the robustness and accuracy of structural damage identification under data-scarce conditions. In contrast to the state-of-the-art purely data-driven ResNet, the proposed method embedded available physics knowledge (e.g., governing equations of dynamics) of structures into the feature learning process via a novel physics-based loss function. The input-output relationship of the network is constrained to retain its physical meaning implicitly while the demand for large amounts of labeled training data is reduced. Notably, even with only 5 % of the dataset used for training, PhyResNet achieves a 13.1 % improvement in R-Value. The performance of the proposed approach is evaluated through both numerical and experimental verifications. Results demonstrate that damage localization and quantification are achieved with high accuracies and good robustness.

Kinematics of nonlinear waves over variable bathymetry. Part I: Numerical modelling, verification and validation

Fluid particle kinematics due to wave motion (i.e. orbital velocities and accelerations) at and beneath the free surface is involved in many coastal and ocean engineering applications, e.g. estimation of wave-induced forces on structures, sediment transport, etc. This work presents the formulations of these kinematics fields within a fully nonlinear potential flow (FNPF) approach. In this model, the velocity potential is approximated with a high-order polynomial expansion over the water column using an orthogonal basis of Chebyshev polynomials of the first kind. Using the same basis, original analytical expressions of the components of velocity and acceleration are derived in this work. The estimation of particle accelerations in the course of the simulation involves the time derivatives of the decomposition coefficients, which are computed with a high-order backward finite-difference scheme in time. The capability of the numerical model in computing the particle kinematics is first validated for regular nonlinear waves propagating over a flat bottom. The model is shown to be able to predict both the velocity and acceleration of highly nonlinear and nearly breaking waves with negligible error compared to the corresponding stream function wave solution. Then, for regular waves propagating over an uneven bottom (bar-type bottom profile), the simulated results are confronted with existing experimental data, and very good agreement is achieved up to the sixth-order harmonics for free surface elevation, velocity and acceleration.

Safety analysis of temporary anchorage system for immersed tube in Shenzhen–Zhongshan Link

In the construction of the Shenzhen–Zhongshan Link, a temporary anchorage system, distributed uniformly along the pipe wall, has been employed. To assess the safety and reliability of this system, a combined method utilizing numerical analysis and model experiments was applied to study the safety of the temporary anchorage system and the reliability of the tension rods. Firstly, an overall model of the caisson segment based on GINA rebound force was established to analyze the stress state of the entire system. Secondly, a comprehensive numerical analysis and model experiment verification were conducted for the single tensioning system, revealing its failure mode and safety margin. The results indicate that the tension rod systems are uniformly stressed at an average of 444 kN during underwater jointing, with a safety factor of 1.94. At this point, the maximum von Mises stresses appearing at the front plate corners and the lower edge of the U-groove, with stress values of 181.8 MPa and 172.4 MPa, and safety factors of 1.54 and 1.71, respectively. When the tension rod force reaches 940 kN, the tensioning system reaches its bearing limit, with initial yielding occurring at the front plate corners. Model experiments were conducted to verify the theoretical analysis results, under a test load of 444 kN, the stresses at the front plate corners and the lower edge of the U-groove were 159.6 and 195.9 MPa, respectively. As the test load increased to 940 kN, these stresses reached 390 and 389 MPa, exhibiting good agreement with the numerical analysis. Considering the uncertainty of loads and materials, a reliability analysis of the tension rods was conducted, yielding a reliability index of 4.34, meeting the secondary safety standard. Based on the comprehensive analysis, it can be concluded that the temporary anchorage system in the caisson segments of the Shenzhen–Zhongshan Link exhibits excellent safety margins.

Reduced-order helicopter model identification from closed-loop data

This paper presents the development of an algorithm for open-loop transfer functions identification and reduced-order modelling of a dynamical system, from closed-loop data with highly correlated inputs. Suitable for aeronautical applications (particularly for intrinsically unstable vehicles such as helicopters), it allows the identification of aircraft transfer functions from the knowledge of the time histories of arbitrary external inputs and the corresponding actuated controls and responses. After a numerical verification of the proposed approach considering a simple analytical aircraft dynamical system, it is successfully applied to a realistic engineering problem consisting of identifying the transfer functions of the AW-09 helicopter that relate pilot inputs to vehicle attitude and kinematics. It is shown that helicopter responses to arbitrary pilot inputs predicted by the reduced-order model representation of the helicopter dynamics based on the rational approximation of the identified transfer functions are in good agreement with those determined through the high-fidelity nonlinear flight dynamics solver used to evaluate the closed-loop database.

Optimal multi-segment trajectory of solar sail with analytical approximation

This paper focuses on the optimization of two-dimensional transfer trajectories for solar sails using analytical approximation and modified analytical approximation methods. Instead of assuming circular orbits [29-31,37], the proposed approach allows for the analysis of solar sails launched from general heliocentric elliptical orbits. By employing linear perturbation theory, analytical propelled trajectories with fixed pitch angles are derived, where the perturbation coefficient serves as the reference lightness coefficient. To obtain the optimal transfer orbit between general heliocentric elliptical orbits, the analytical segments corresponding to different pitch angles are spliced together. A nonlinear optimization algorithm is then utilized to optimize the multi-segment trajectory, aiming to achieve the optimal performance index while satisfying boundary and intermediate constraints. Remarkably, this method requires the optimization of only the pitch angle for each segment, resulting in a small number of optimization variables and significantly improved efficiency in transfer orbit optimization. Additionally, the analytical approximation approach offers substantial time savings compared to numerical integration, particularly when repeated calculations are involved. Furthermore, the modified approximate trajectory exhibits high accuracy, with the optimal analytical transfer trajectory closely approximating the optimal actual trajectory acquired through the shooting method. This paper extensively validates and analyzes the precision of the proposed analytical transfer orbit through numerical verification. Additionally, when contrasted with actual transfer orbit, the suggested analytical approach can significantly decrease the computation time for multi-object challenges by a minimum of 80%. This makes the proposed method highly suitable for rapid design of optimal transfer orbits in multi-target mission scenarios for solar sail-based probes.

Structural damage identification based on dual sensitivity analysis from optimal sensor placement

Structural damage identification (SDI) methods using incomplete modal information can avoid the extension for unmeasured degrees of freedom, but the absence of essential damage information often leads to the failure of SDI. To address this problem, a novel SDI method based on dual sensitivity analysis and optimal sensors placement technique is proposed in this study. Firstly, in the optimal sensor placement technique, an improved eigenvector sensitivity method combined with weighted modal kinetic energy is proposed, which enables the acquisition of eigenvector information related to damage sensitivity, and incorporates it into the modal strain energy sensitivity matrix to obtain the dual sensitivity analysis matrix. Then, the sparsity of structural damage is considered, and the L1 sparse regularization is selected and introduced into the dual sensitivity analysis damage equation for better SDI results. Finally, to assess the effectiveness of the proposed method, a series of numerical simulations and experimental verifications were carried out under different structural damage scenarios. The results indicate that the proposed method can efficiently localize and quantify the structural damage with minimal modal information in one single step.

Numerical and experimental verification of column web in transverse compression

This paper focuses on the problem of steel members of open double symmetrical cross-sections in transverse compression. First, the problem is introduced with examples of its application in steel structures of buildings and followed by the overview of selected substantial literature resources and current design codes provisions. The essential part of the paper is a presentation of results of experimental tests and advanced numerical analysis of members subjected to selected cases of transverse compression. Where possible, the results are compared with resistances obtained using provisions in currently valid design codes for steel structures. The influence of selected parameters on the resistance in transverse compression is quantified within the evaluation with specific attention paid to plate buckling of the web. Based on data obtained from the experimental and numerical investigations, the most notable findings are summarized.

Enhanced through-plane thermal conductivity of graphene membranes by the interlayer microstructure manipulation: Multiscale numerical simulations and experimental verifications

Graphene, with ultrahigh in-plane thermal conductivity (IPTC), has been widely applied in the thermal dissipation of integrated circuits. However, the extremely low through-plane thermal conductivity (TPTC) of graphene limits its further application. In this work, a novel strategy was proposed to enhance the TPTC of graphene membranes (GNMs) by improving the interlayer bonding state through interlayer decoration with metal elements. Molecular dynamics simulations demonstrated that decoration with interlayer elements (Al, Ti, and Ni) enhanced the interfacial thermal conductance. This was attributed to interfacial chemical bonding through strong interfacial interactions (intensive electron localization) formed at the interface between metal and GN sheets as implied by the first principles calculations. Furthermore, the composite GNMs decorated with interlayer metal nanoparticles (Al, Ni, and Co) were prepared through co-reduction using thermal decomposition method. The corresponding TPTC was tested using time-domain thermoreflectance (TDTR) method which was much higher for the composite GNMs (175–400 W/m·K) than for pure GNM (∼140 W/m·K), and this was in consistent with the simulation results. Interlayer decoration, which enhanced the TPTC of GNMs, provides a novel and effective strategy for enhancing the overall thermal management performance of graphene-based materials in both vertical and horizontal directions.

On One Series of the Reciprocals of the Product of two Fibonacci Numbers Whose Indices Differ by an Even Number

This paper is inspired by a very interesting YouTube video by Michael Penn, professor of mathematics at Randolph College in Virginia, USA. He dedicated himself to the popularization of mathematics on his website in addition to his teaching and scientific work at the university and in addition to his scientific work. First, we deal with four specific series of the reciprocals of the product of two Fibonacci numbers whose indices differ by 2, 4, 6, and 8. Then, we generalize these four results to the series of the reciprocals of the product of two Fibonacci numbers whose indices differ by an even number. Finally, we perform a numerical verification of the derived formula using Maple 2020 software. Based on the derived formula, it can be concluded that the series we are dealing with belong to infinite series whose sum can be expressed in closed form.

Numerical analysis and experimental verification of time-dependent heat conduction under the action of ultra-short pulse laser

Numerical analysis and experimental verification of time-dependent heat conduction under the action of ultra-short pulse laser

End-to-End Delay Performance Analysis for Delay-Sensitive Services in Polymorphic Networks

Abstract In the polymorphic network for smart grid, the end-to-end latency performance analysis of delay-sensitive power control services such as differential protection and distributed power regulation is a crucial component in the intelligent control and management of power network slicing. In this paper, based on a detailed analysis of end-to-end delay factors of power control service, the distributed power regulation pilot project is taken as a typical application scenario of power control service, and the end-to-end delay of such service is theoretically derived and analyzed in detail by using network calculus theory. Numerical verification shows that the end-to-end delay performance of the power control service is positively correlated with the number of concurrent data streams and the number of subsystems and negatively correlated with the system service rate. Compared with the burst degree of the current data streams, the burst degree of other data streams significantly impacts the end-to-end delay calculation results of the current data flow.

Influence of the rigid water column assumption on hydrodynamic system stability

When analyzing the hydraulic vibration stability of hydrodynamic systems, a real elastic water column (EWC) is often simplified as a rigid water column (RWC) to derive theoretical stability criteria. This method is believed to yield results that deviate quantitatively from reality without causing qualitative errors. To examine this approach, this study first established a reservoir-pipe-valve-turbine system. Next, a theoretical stability criterion based on the RWC assumption was derived. Finally, the theoretical stability criterion of the real EWC (which was proven using the method of characteristics) was proposed to test the correctness of the RWC assumption, both numerically and theoretically. Results indicated discrepancies between RWC-based predictions and EWC time-domain outcomes, lacking consistent similarities. Specifically, in some cases, the RWC formula indicated instability, while the EWC theoretical criterion and numerical verification suggested stability. In other cases, the RWC formula indicated stability, while the EWC theoretical criterion and numerical verification suggested instability. Meanwhile, there were also cases where both the RWC formula and EWC theoretical criterion yielded consistent results. As the RWC assumption disregards water-hammer wave propagation and hydrodynamic system reflection effects, the validity of its conclusion is uncertain. Hence, when the RWC-based system stability contradicts the EWC theoretical criterion, the latter should guide system design decisions.

Smooth Solutions of the tt* Equation: A Numerical Aided Case Study

An important special class of the tt* equations are the tt*-Toda equations. Guest et al. have given comprehensive studies on the tt*-Toda equations in a series of papers. The fine asymptotics for a large class of solutions of a special tt*-Toda equation, the case 4a in their classification, have been obtained in the paper [Comm. Math. Phys. 374 (2020), 923-973] in the series. Most of these formulas are obtained with elaborate reasoning and the calculations involved are lengthy. There are concerns about these formulas if they have not been verified by other methods. The first part of this paper is devoted to the numerical verification of these fine asymptotics. In fact, the numerical studies can do more and should do more. A natural question is whether we can find more such beautiful formulas in the tt* equation via numerical study. The second part of this paper is devoted to the numerical study of the fine asymptotics of the solutions in an enlarged class defined from the Stoke data side. All the fine asymptotics of the solutions in the enlarged class are found by the numerical study. The success of the numerical study is largely due to the truncation structures of the tt* equation.

Implementation of tunable frequency-dependent stiffness elements via integrated shunted piezoelectric stacks

Piezoelectric transducers applied on or integrated in structures, combined with appropriate circuits have been extensively investigated as a smart approach to the mitigation of resonant vibrations with high relative amplitudes. A resonant shunt circuit consisting of the capacitive piezoelectric transducer and an inductance can be configured to target specific eigenmodes of a structure, if appropriately placed and tuned. Their effect is expressed in terms of mechanical impedance of the host structure, allowing for the exchange of energy between the mechanical and electrical domain, to dramatically affect the dynamic response of the structure. By re-framing the function of resonant shunted piezoelectric transducers as frequency dependent variable stiffness elements, this paper investigates their capability to realize a frequency dependent structural mechanical connectivity, where the load path within a lattice structure can be interrupted at will for specific frequencies by tunable null-stiffness components. Here, we offer the numerical and experimental verification of this idea, by demonstrating the ability to significantly affect the dynamic response of a unit cell of an adaptive lattice metamaterial, even away from a structural resonance. In the latter case, the null-stiffness shunt leads to an additional resonance peak in the truss’ dynamic response. Its realization as additively manufactured component points to the feasibility of such structures in real life.

A Steady-Pressure Control Method for Emulsion Pump Station Based on Online Updating of Optimal Flow Rate

In order to solve the problem of unstable fluid supply pressure and serious impact caused by the complicated and changeable working condition of a fully mechanized mining face in coal mines and the sluggish response of the fluid supply system to the fluid demand for the hydraulic support, a control method based on online updating generalized regression neural network (GRNN) was proposed. Firstly, the simulated hydraulic support test platform and co-simulation model were built. Secondly, The optimal flow dataset of steady-pressure fluid supply under different working conditions is calculated by simulation. Furthermore, the GRNN prediction model was established by using dataset and online updating learning technology to predict the optimal fluid supply flow according to environmental parameters. Finally, the optimal flow control method of online updating GRNN was established, and numerical research and experimental verification were also carried out in different working conditions. The results indicated that the proposed control method could track the working conditions of the working face in real time and adjusted the fluid supply flow of the emulsion pump station adaptively, which effectively alleviated the pressure fluctuation and pressure shock, and the system pressure was more stable, meeting the demand of steady-pressure fluid supply on the working face.

Numerical Verification of Groundwater Suitability for Irrigation Around the Subsurface Dam Area of Miyako Island, Japan

The sustainable management of water resources is essential for agricultural productivity, especially in areas with scarce water availability. This study focused on assessing groundwater quality for irrigation near the subsurface dam area of Miyako Island, Japan. Water samples from three observation points were tested for various parameters, including electrical conductivity (EC), sodium adsorption ratio (SAR), soluble sodium percentage (SSP), residual sodium bicarbonate (RSBC), permeability index (PI), Kelley's ratio (KR), and magnesium adsorption ratio (MAR). EC values ranged from 270 to 800 µS/cm, suggesting water quality ranging from doubtful to good. SAR values between 0.23 and 1.49 suggested excellent quality. SSP ranged from 7.90% to 31.71%, mostly indicating good to excellent quality. RSBC values fluctuated between -1.57 to 1.45 epm, largely within safe limits. PI values varied from 40.34 to 75.83, indicating good permeability. Total hardness (TH) ranged from 105.50 to 326.45 ppm, classifying the water as hard to very hard. MAR values were below 50, suggesting potential soil issues. A numerical model confirmed observed Ca²⁺ concentrations, showing an increasing trend due to enhanced CO₂ emissions and lower pH. The data analysis revealed strong positive relationships between SSP and KR (r = 0.984), SAR and SSP (r = 0.951), and SAR and KR (r = 0.960). Despite generally acceptable values, continuous monitoring is recommended, especially for hardness, to ensure sustainable crop production. This study underscores the need for regular assessment and management of groundwater quality in subsurface dam areas to mitigate potential adverse effects on soil and agricultural productivity.

Chebyshev polynomial approach to Loschmidt echo: Application to quench dynamics in two-dimensional quasicrystals.

The understanding of quantum phase transitions in disordered or quasicrystal media is a central issue in condensed matter physics. In this paper we investigate localization properties of the two-dimensional Aubry-André model. We find that the system exhibits self-duality for the transformation between position and momentum spaces at a critical quasiperiodic potential, leading to an energy-independent Anderson transition. Most importantly, we present the implementation of an efficient and accurate algorithm based on the Chebyshev polynomial expansion of the Loschmidt echo, which characterizes the nonequilibrium dynamics of quantum quenched quasiperiodic systems. We analytically prove that the system under quench dynamics displays dynamical quantum phase transitions and further provide numerical verification by computing the polynomial expansion of the Loschmidt echo. Our results may provide insight into the realization of electronic transport in experiments.

Fast analysis approach for instability problems of thin shells utilizing ANNs and a Bayesian regularization back-propagation algorithm

Abstract This research develops a data-driven methodology for structural instability problems with highly nonlinear, difficult, noisy, and small data. A fast analysis and prediction (FAP) approach for instability problems of thin shells is first proposed. This approach contains two phases: the fast numerical analysis and the pure prediction utilizing artificial neural networks (ANNs) incorporated with the Bayesian regularization (B-R) algorithm as follows: (1) in Phase 1 (the fast numerical analysis), post-buckling analysis is conducted utilizing a minor amount of load steps. The load–displacement relation achieved from Phase 1 is not exact because of the small number of load steps utilized; (2) in Phase 2 (the prediction), the loads and deflections achieved from Phase 1 were employed as the data for training ANNs. The trained networks, including the load and displacement networks, were employed to fast predict loads and deflections at any step of the post-buckling analysis. After utilizing Phase 2, a smooth, complete and exact load–displacement curve was achieved. In Phase 1, the available formulation for post-buckling analysis of thin shells in the literature was utilized. Five popular types of instabilities chosen to confirm the effectiveness and exactness of the FAP were snap-through, snap-back, softening–hardening, kink instabilities, and delamination buckling and post-buckling of composites. The high exactness and effectiveness of the FAP were confirmed in the numerical verification section. The present approach saves a huge computation compared to the other ones. It was found that ANNs incorporated with the B-R algorithm have notable advantages compared to numerous neural networks. The proposed approach is applicable to simulations or experiments where data are “expensive”, highly nonlinear, difficult, and limited. Utilizing the proposed approach for these fields can dramatically save time and money.

Optical transmission trajectories in single tapered fibers of TOFA by numerical simulation and experimental verification

Tens of millions or billions of single tapered fibers are independent optical transmission elements of tapered optical fiber array (TOFA) for imaging. The optical transmission trajectories of these single tapered fibers, which directly affect imaging qualities of TOFA, are rarely analyzed. This paper provides a method to numerically simulate it for fibers located at different positions along the radial direction of TOFA. The tapered curves of TOFA were firstly simulated by Finite Element Analysis (FEA) software and experimentally verified by the same preparation parameters. It is shown that the slope of tapered curve increases with stretching length. Meanwhile, the taper angle gets greater, and the profile of tapered deformation zone expands outward, while the radius of straight zone remains stable. Based on these, the optical transmission trajectory of single tapered fibers located from center to edge in TOFA was simulated, and then further verified by a self-developed instrument. Both simulation and experiment illustrate that the relative transmittance of single tapered optical fiber is decreased along the radial direction within the same TOFA. In comparison with the transmittance of the central axial fiber, the simulated and experimental unevenness on relative transmittance of peripheral fibers is within 7.11% and 9.74%, respectively. With the relative transmittance at the central position of the optical fiber being identical, the difference of relative transmittance (ΔT) between the simulation and experiment is gradually increased from center to peripheral regions along the radial direction of TOFA, reaching the maximum ΔT of 4.23%. The simulated results are well in agreement with the experimental ones.