Convergence Tests Research Articles

Monolayer MoS2 with S vacancy defects doped with Group V non-metallic elements (N, P, As): a first-principles study.

This study systematically investigated the effects of single S-atom vacancy defects and composite defects (vacancy combined with doping) on the properties of MoS2 using density functional theory. The results revealed that N-doped S-vacancy MoS2 has the smallest composite defect formation energy, indicating its highest stability. Doping maintained the direct band gap characteristic, with shifts in the valence band top. The Fermi level slightly shifted down in N- and P-doped systems, with N-doped MoS2 showing a larger increase in valence band top energy. Doping also significantly altered the density of states at the Fermi level and weakened the dielectric properties of MoS2. The maximum dielectric peaks of doped systems appeared near 2.7 eV with reduced intensities and red-shifted energies. Optical properties were significantly changed, with decreased reflectance, narrower reflectance spectra, and blue-shifted absorption spectra. These findings suggest that introducing composite defects can effectively reduce the forbidden bandwidth of MoS2, enhancing electrical conductivity. This research provides theoretical guidance for novel material design and offers insights into composite defect behavior in other two-dimensional materials. The Materials-Studio CASTEP module was used to calculate density functional theory (DFT). A plane wave ultrasoft pseudopotential is used to optimize the crystal structure, and the generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof (PBE) is used to characterize the exchange correlation energy. After the convergence test, the truncation energy and dot settings were finally selected to be 450 eV and 3 × 3 × 1, respectively, the convergence accuracy was set to 1.0e-5eV/atom, and the convergence criterion for the interatomic interaction force was 0.02 eV/Å. The parameters were all at or better than the accuracy settings. The vacuum layer between the layers wasset to 18 Å to avoid interactions caused by the periodic calculation method.

Buckling Analysis of Functionally Graded GPL-Reinforced Composite Plates Under Combined Thermal and Mechanical Loads

The buckling-like mechanical behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) structures is increasingly attracting research attention. However, buckling behavior has previously been studied separately as thermal buckling and mechanical buckling. In this context, this study investigates the buckling behavior of FG-GPLRC plates under combined thermal and mechanical loads. The coupled buckling problem is formulated according to the minimum potential energy theorem using first-order shear deformation theory (FSDT). In addition, the problem is approximated by the 2-D natural element method (NEM), and the resulting coupled eigen matrix equations are derived to compute the critical buckling temperature rise (CBTR) and the mechanical buckling load. The developed numerical method can solve thermal, mechanical, and coupled thermo-mechanical buckling problems, and its reliability is examined through convergence and benchmark tests. Using the developed numerical method, the buckling behavior of FG-GPLRC plates under thermal and mechanical buckling loads is examined in depth with respect to the key parameters. In addition, a comparison with functionally graded CNT-reinforced composite (FG-CNTRC) plates is also presented.

Scalar Auxiliary Variable (SAV) Stabilization of Implicit‐Explicit (IMEX) Time Integration Schemes for Non‐Linear Structural Dynamics

ABSTRACTImplicit‐explicit (IMEX) time integration schemes are well suited for non‐linear structural dynamics because of their low computational cost and high accuracy. However, the stability of IMEX schemes cannot be guaranteed for general non‐linear problems. In this article, we present a scalar auxiliary variable (SAV) stabilization of high‐order IMEX time integration schemes that leads to unconditional stability. The proposed IMEX‐BDFk‐SAV schemes treat linear terms implicitly using kth‐order backward difference formulas (BDFk) and non‐linear terms explicitly. This eliminates the need for iterations in non‐linear problems and leads to low computational costs. Truncation error analysis of the proposed IMEX‐BDFk‐SAV schemes confirms that up to kth‐order accuracy can be achieved and this is verified through a series of convergence tests. Unlike existing SAV schemes for first‐order ordinary differential equations (ODEs), we introduce a novel SAV for the proposed schemes that allows direct solution of the second‐order ODEs without transforming them into a system of first‐order ODEs. Finally, we demonstrate the performance of the proposed schemes by solving several non‐linear problems in structural dynamics and show that the proposed schemes can achieve high accuracy at a low computational cost while maintaining unconditional stability.

Quick-and-Easy Validation of Protein-Ligand Binding Models Using Fragment-Based Semiempirical Quantum Chemistry.

Electronic structure calculations in enzymes converge very slowly with respect to the size of the model region that is described using quantum mechanics (QM), requiring hundreds of atoms to obtain converged results and exhibiting substantial sensitivity (at least in smaller models) to which amino acids are included in the QM region. As such, there is considerable interest in developing automated procedures to construct a QM model region based on well-defined criteria. However, testing such procedures is burdensome due to the cost of large-scale electronic structure calculations. Here, we show that semiempirical methods can be used as alternatives to density functional theory (DFT) to assess convergence in sequences of models generated by various automated protocols. The cost of these convergence tests is reduced even further by means of a many-body expansion. We use this approach to examine convergence (with respect to model size) of protein-ligand binding energies. Fragment-based semiempirical calculations afford well-converged interaction energies in a tiny fraction of the cost required for DFT calculations. Two-body interactions between the ligand and single-residue amino acid fragments afford a low-cost way to construct a "QM-informed" enzyme model of reduced size, furnishing an automatable active-site model-building procedure. This provides a streamlined, user-friendly approach for constructing ligand binding-site models that requires neither a priori information nor manual adjustments. Extension to model-building for thermochemical calculations should be straightforward.

Convergent Protocols for Computing Protein-Ligand Interaction Energies Using Fragment-Based Quantum Chemistry.

Fragment-based quantum chemistry methods offer a means to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein-ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

Significance of variable electrical conductivity on unsteady EMHD flow of nanofluid over a moving wedge with time-dependent chemical reaction

A model based on physical concepts studied the unsteady flow of viscous nanofluid over a wedge with variable electrical conductivity. Electric and magnetic fields are applied at right angles to each other and in the direction of the flow. The electrical conductivity of the medium is considered a power law function. The flow incorporates Brownian diffusion and thermophoresis. The model partial differential equations are transformed into associated nonlinear ordinary differential equations, and these equations are then numerically solved using a boundary value solver. The results of physical interest, like combined electric field and magnetic field, power law index of electrical conductivity, and Brownian motion parameter, are depicted graphically. The results obtained are validated with previous publications, and it was found an excellent agreement between these results. A grid convergence test is performed to find the optimum grid size, which helps to achieve accurate results with minimum computational time. It is observed from the simulation result that the maximum drop in surface friction under the action of Lorentz force occurs when the power law index is zero. Further nanoparticle concentration layer thickness builds up during a generative chemical reaction in the presence of a time-dependent chemical reaction with thermophoresis particle deposition.

All-Electron BSE@GW Method with Numeric Atom-Centered Orbitals for Extended Periodic Systems.

Green's function theory has emerged as a powerful many-body approach not only in condensed matter physics but also in quantum chemistry in recent years. We have developed a new all-electron implementation of the BSE@GW formalism using numeric atom-centered orbital basis sets (Liu, C. J. Chem. Phys. 2020, 152, 044105). We present our recent developments in implementing this formalism for extended periodic systems. We discuss its numerical implementation and various convergence tests pertaining to numerical atom-centered orbitals, auxiliary basis sets for the resolution-of-identity formalism, and Brillouin zone sampling. Several proof-of-principle examples are presented to compare with other formalisms, illustrating the new all-electron BSE@GW method for extended periodic systems.

Nonlinear structural strength of steel chain contacted with knuckle-shaped plate under lifting conditions

ABSTRACT The study focuses on evaluating the nonlinear structural strength of steel chains in lifting operations, particularly in contact with knuckle-shaped plates, under various loading conditions. Using finite element analysis (FEA), the research examines how different contact angles (0°, 45°, 90°) and materials (SS400, HT32, HT36, ASTM A356) influence the chain’s performance under tensile loading. The analysis categorises four main loading conditions, referred to as 0 degree through 45 degrees to symmetric direction, each representing different orientations of the chain relative to the lifted object. Among these, lifting at 90 degrees consistently showed the lowest ultimate strength across all materials and chain sizes. The primary cause of this weakness was identified as significant stress concentration at the central link, where the loading angle of 90 degrees led to early yielding. This critical loading condition not only reduced the chain’s load-bearing capacity but also increased the risk of premature failure due to localised stress buildup. The study further highlights that as the yield strength of the material increases, the difference in load capacity between non-symmetric 45 and 90 degrees becomes more pronounced, with 90 degrees lifting exhibiting lower strength across the board. For instance, ASTM A356, although generally stronger than SS400, still demonstrated a notable reduction in load capacity under 90 degrees lifting. Mesh convergence tests were performed to ensure the accuracy of the FEA results, confirming that 12 mesh elements were sufficient to accurately model stress distributions. The results also indicated that increasing the chain diameter could improve load-bearing capacity under most loading conditions, but even larger chains were still vulnerable under 90 degrees lifting. In conclusion, 90 degrees lifting presents a critical design challenge due to its inherent weakness, and mitigating stress concentration at the central link is key to improving chain durability and safety. This study’s findings offer valuable insights for engineers, particularly in the shipbuilding and offshore industries, on how to optimise chain design and improve safety in hoisting operations.

Implementation of a long-wavelength model for parallel magnetic fluctuations in the global GENE code

Abstract A long-wavelength model for the turbulent magnetic fluctuations parallel to the magnetic field (B1,||) has been implemented in the global gyrokinetic code GENE. The model provides a way to include this physical effect with little computational cost, permitting the study of B1,|| on global nonlinear gyrokinetic simulations. The model has been verified through convergence tests and against an arbitrary wavelength solver, resulting in good performance up to moderately high wavelengths (ky ρs ≲ 1). Using this approximation global nonlinear fully electromagnetic simulations were performed with Cyclone Base Case-like parameters to study the impact of B1,|| on different plasma β regimes. A negligible impact for a low beta regime and roughly a doubling of the heat transport when including B1,|| in a high beta KBM regime is found, which is in line with expectations based on linear studies and highlights the impact of B1,|| in KBM driven scenarios.

Convergence Analysis and Predictions for Optimizing Reciprocal Grids: A First-Principles and Machine Learning Study.

When crystalline materials are investigated by performing first-principles density functional theory (DFT) calculations, the reciprocal grid should be fine enough to obtain the converged total energy and electronic structure. Herein, we performed a convergence test of the total energy for the density of reciprocal points to determine fine enough reciprocal grids for high-throughput calculations. Our results show that the nonlinearity of the band structures affects the convergence of the total energy, especially for materials with a finite band gap. We further investigate which physical properties make a finer reciprocal grid necessary based on machine learning (ML) analysis. Our developed models using DFT-based features and elemental properties-based features exhibit R2 of 0.803 and 0.880, respectively. Our ML model quantitatively shows the importance of nonlinearity and band gaps in predicting errors in total energy calculations. Furthermore, our ML model using elemental features can be applied to estimate the appropriate reciprocal grid, facilitating high-throughput calculations.

Convergence tests of self-interacting dark matter simulations

Convergence tests of self-interacting dark matter simulations

Jordan test for the Haar-type systems

We consider Haar-type systems, which are generated by a (generally speaking, unbounded) sequence $ \{ p_n \}_{n=1}^\infty $, and which are defined on the modified segment $ [0, 1]^* $, i.\,e., on the segment [0, 1] whose $ \{ p_n \}$-rational points are calculated two times. The main result of this work is a Jordan-type test for the pointwise and uniform convergence of Fourier series with respect to Haar-type systems. It is shown that the test obtained in the paper can not be improved. An example of a function of bounded variation, whose Fourier series with respect to Haar-type system diverges at some point, is constructed in the case of $ \sup\limits_n p_n = \infty$. Thus for any unbounded sequence $ \{ p_n \}_{n=1}^\infty $ there exists a monotone function whose Fourier series with respect to Haar-type system, generated by the given sequence $ \{ p_n \}_{n=1}^\infty $, diverges at some point. It is found that the Jordan test of convergence of Fourier series with respect to Haar-type systems does not differ from the Dini--Lipschitz condition for those systems. As the Dini--Lipschitz condition was considered earlier, the main value of this work is the construction of a corresponding counterexample, i.\,e., the construction of an example (a model) of a function of bounded variation whose Fourier series with respect to Haar-type Systems diverges at some point. In the counterexamples from the earlier works on the Dini--Lipschitz criterion (as well as for all Dini convergence criteria), the functions were {\it not of bounded variation}. The article's conclusion discusses how the Jordan convergence criterion evolved when transitioning from trigonometric systems of functions to Price systems (and to N.Ya. Vilenkin systems), and from there to generalized Haar systems and Haar-type systems.

Stochastic and club convergence analysis of environmental tax revenues across EU countries.

The European Union (EU) has taken several initiatives over the past two decades to harmonize environmental taxation policies across member countries. The directive on energy taxation (Directive 2003/96/EC) provides the framework for the taxation of energy products within the EU. These harmonization efforts are part of a broader strategy to ensure environmental sustainability and combat climate change. This paper examines whether these efforts have had any impact on the convergence of environmental taxation across EU countries during the period 1995-2021. This paper uses a new panel unit root test that accounts for cross-correlations and structural breaks within the panel since regulations on taxation increase the possibility that EU countries may have commonalities on these issues. The club convergence test is also used to test for the existence of multiple equilibria within groups of countries. The results of the traditional convergence test show that environmental tax revenues are converging across EU countries. Furthermore, the results of the stochastic convergence test indicate that there is a convergence of relative environmental tax revenues. As for the break dates, the results from the tax revenue series show that the first and second break are concentrated in the periods 2002-2007 and 2012-2017, respectively. Finally, the results of the club convergence test reject the full panel convergence and reveal the existence of different convergence clubs. The empirical results of this paper have some implications for environmental taxation in the EU.

Thermal and Computational Analysis of MHD Dissipative Flow of Eyring-Powell Fluid: Non-Similar Approach via Overlapping Grid-Based Spectral Collocation Scheme

The aim of the present study is to numerically investigate the non-similar flow and heat transfer in a dissipative Eyring-Powell fluid (EPF) over a stretching surface. A constant magnetic field is applied perpendicular to the stretched surface to explore the impact of the Lorentz force. Both viscous and magnetic dissipation are considered to comprehensively examine their effects on heat transfer. The problem in hand does not admit self-similar solutions as the non-Newtonian fluid parameter varies with the spatial variable along the stream-wise direction. Consequently, the set of nonlinear partial differential equations, modeling the flow problem is nondimensionalized primarily by employing a pseudo-similarity variable and stream-wise coordinate. The non-dimensional set of nonlinear partial differential equations is solved by a newly developed and efficient “overlapping multi-domain bivariate spectral local linearization method (OMD-BSLLM)”. The current study includes residual error analysis and convergence tests to demonstrate the accuracy of the numerical method applied to the current mathematical model. Graphs show fluid flow and heat transfer results for different flow parameters, while tables display skin friction and Nusselt number values. The results indicate that the non-Newtonian fluid parameter enhances both the velocity profile and temperature distribution. The fluid decelerates with increasing the dimensionless stream wise coordinate and Hartmann number. Viscous dissipation and dimensionless stream-wise coordinate enhances the temperature profile.

Convergence analysis of exponential time differencing scheme for the nonlocal Cahn–Hilliard equation

In this paper, we provide a rigorous proof of the convergence for both first-order and second-order exponential time differencing (ETD) schemes applied to the nonlocal Cahn–Hilliard (NCH) equation. The spatial discretization is executed through the Fourier spectral collocation method, whereas the temporal discretization is implemented using ETD-based multistep schemes. The absence of a higher-order diffusion term in the NCH equation creates a significant challenge for the convergence analysis of numerical schemes. To address this issue, we introduce novel error decomposition formulas and utilize higher-order consistency analysis. These techniques allow us to establish the ℓ∞ bound of the numerical solution under certain natural constraints. By treating the numerical solution as a perturbation of the exact solution, we derive optimal convergence rates in ℓ∞(0,T;Hh−1)∩ℓ2(0,T;ℓ2). Furthermore, we conduct several numerical experiments to validate the accuracy and efficiency of the proposed schemes. These experiments include convergence tests and the observation of long-term coarsening dynamics, thereby confirming the robustness and reliability of our approach.

Effectiveness of interventions for convergence insufficiency: an observational study evaluating clinical outcomes and health-related quality of life using AS20.

Convergence insufficiency (CI) is a common condition that can impair visual performance and comfort during close visual work. This observational study evaluated the effectiveness of interventions on clinical outcomes and health-related quality-of-life using the Adult Strabismus-20 (AS20) questionnaire in patients with CI. Data was extracted from a database collected at first consultation from 2015 to 2022. Demographics, interventions and outcomes of 75 patients with CI (mean age 47.2 ± 24.7 years) were analysed. Orthoptic exercises were prescribed to 58% of patients, 28% received prisms and 9% received no treatment. At the latest follow-up review, 24% were recommended to continue exercises, 24% had prisms, 1 underwent bimedial resection and 1 had treatment with Botulinum Toxin A (BTXA). The median follow-up was 5.0 (0-55) months, 100% were discharged with 25% following failure-to-attend and 11% died. At the latest follow-up, the attendance failure rate was higher for exercises (36%) than for prisms (10%). Both near-prism cover test and near-point of convergence improved from a median of 12 (95% CI 10-14) prism dioptres (PD) to 8.5 (95% CI 6-12) PD, and 17.5 (95%CI 15-20) cm to 10.0 (95%CI 8.3-12.0) cm respectively (p < 0.05). Near-prism fusion range also improved from 10(95%CI 8-14) PD to 16(95% CI 12-20) PD (p < 0.05). The median AS20 score at presentation were 100/100 (30-100) and 47.5/100 (0-100), and post-intervention were 100/100 (75-100) and 70/100 (12.5-97.5) for psychosocial and functional components, respectively. This cohort offers valuable insights into the real-life clinical management of CI in a tertiary adult strabismus centre. However, the study also found that long-term compliance with treatment is intrinsically challenging, emphasising the importance of disease education.

Primary Visual Pathway Changes in Individuals With Chronic Mild Traumatic Brain Injury

Individuals with mild traumatic brain injury (TBI) often report vision problems despite having normal visual acuity and fundus examinations. Diagnostics are needed for these patients. To determine if a battery of assessments or machine-learning approaches can aid in diagnosing visual dysfunction in patients with mild TBI. This prospective, observational, case-control study was conducted between May 2018 and November 2021. The study setting was at a level 1 trauma research hospital. Participant eligibility included adult males and females with recorded best-corrected visual acuity and normal fundus examination. Individuals in the case group had a history of mild TBI; controls had no history of TBI. Exclusion criteria included a history of ocular, neurological, or psychiatric disease, moderate-severe TBI, recent TBI, metal implants, age younger than 18 years, and pregnancy. Cases and controls were sex- and age-matched. Data analysis was performed from July 2023 to March 2024. History of mild TBI in the case group. The single-session visit included the Neurobehavioral Symptom Inventory and measurements of oculomotor function, optical coherence tomography, contrast sensitivity, visual evoked potentials, visual field testing, and magnetic resonance imaging. A total of 28 participants (mean [SD] age, 35.0 [12.8] years; 15 male [53.6%]) with mild TBI and 28 controls (mean [SD] age, 35.8 [8.5] years; 19 female [67.9%]) were analyzed. Participants with mild TBI showed reduced prism convergence test breakpoint (-8.38; 95% CI, -14.14 to -2.62; P = .008) and recovery point (-8.44; 95% CI, -13.82 to -3.06; P = .004). Participants with mild TBI also had decreased contrast sensitivity (-0.07; 95% CI, -0.13 to -0.01; P = .04) and increased visual evoked potential binocular summation index (0.32; 95% CI, 0.02-0.63; P = .02). A subset of participants exhibited reduced peripapillary retinal nerve fiber layer thickness, increased optic nerve/sheath size, and brain cortical volumes. Machine learning identified subtle differences across the primary visual pathway, including the optic radiations and occipital lobe regions, independent of visual symptoms. Results of this case-control study suggest that the visual system was affected in individuals with mild TBI, even in those who did not self-report vision problems. These findings support the utility of a battery of assessments or machine-learning approaches to accurately diagnose this population.

Analysis of the spatio-temporal evolutionary characteristics of myopia among students aged 7-18 years in China: based on panel data analysis.

Myopia is a major important public health concern and has huge burden on health system across the world. This study aimed to explore the spatial and temporal analysis of the prevalence of myopia among students aged 7-18 years to identify the potential clusters and the trends of myopia in China. Spatial autocorrelation analysis, temporal and spatial scan analysis and beta convergence test were performed using ArcGIS10.0 and Stata 15.0. The present study indicated that the prevalence of myopia among students aged 7-18 years in China increased every five years from 1995 to 2019, and there was a certain spatial clustering. The phased spatiotemporal scanning analysis indicated that the gathering area of myopia in students aged 7-18 years in China first shifted from northwest to southeast, and the gradually shifted to Hebei, Shanxi and other northern China regions with Tianjin as the core, and finally spread to the whole of East China, where high-risk areas regarding myopia continue to exist. At the same time, the difference in the level of myopia in each region will gradually shrink over time and will converge. There is a great deal of spatial variations in the pattern of the prevalence of myopia among children and adolescents in China. The spatial cluster analysis provides new evidence for policy-makers to design tailored interventions to reduce the prevalence of myopia and allocate health resource to unmet need areas.

Structure‐Preserving Approximation of the Cahn‐Hilliard‐Biot System

ABSTRACTIn this work, we propose a structure‐preserving discretization for the recently studied Cahn‐Hilliard‐Biot system using conforming finite elements in space and problem‐adapted explicit‐implicit Euler time integration. We prove that the scheme is thermodynamically consistent, that is, the balance of global phase and global volumetric fluid content and the energy dissipation balance. The existence of discrete solutions is established under suitable growth conditions. Furthermore, it is shown that the algorithm can be realized as a splitting method, that is, decoupling the Cahn‐Hilliard subsystem from the poro‐elasticity subsystem, while the first one is nonlinear and the second subsystem is linear. The schemes are illustrated by numerical examples and a convergence test.

Novel Finite‐Volume Complete Flux Approximation Schemes for the Incompressible Navier–Stokes Equations

ABSTRACTWe construct novel flux approximation schemes for the semidiscretized incompressible Navier–Stokes equations by finite‐volume method on a staggered mesh. The calculation of the cell‐face fluxes has been done by solving appropriate local non‐linear boundary value problems (BVP). Consequently, the cell‐face fluxes are represented as the sum of a homogeneous and an inhomogeneous flux; the homogeneous part represents the contribution of convection and viscous‐friction, while the inhomogeneous part represents the contribution of the source terms. We derive three flux approximation schemes to include the impact of the source terms on the numerical fluxes. The first one is based on a homogeneous 1‐D local BVP without source. The second scheme is based on an inhomogeneous 1‐D local BVP considering only the pressure gradient term in the source. Finally, a complete flux scheme is derived which is based on an inhomogeneous 2‐D local BVP. It takes into account both the gradient of the cross‐flux and the pressure gradient in the source term. The numerical validation of the schemes is done for the benchmark lid‐driven cavity flow for considerably high numbers along with a numerical convergence test for the exact solution of the Taylor–Green vortex problem.