Correction Term Research Articles

A theoretical derivation of slip boundary conditions based on the Cercignani–Lampis–Lord scattering model

To characterize fluid flow in the slip regime, the use of Navier–Stokes–Fourier (NSF) equations with slip boundary conditions is prevalent. This trend underscores the necessity of developing reliable and accurate slip boundary conditions. According to kinetic theory, slip behaviours are intrinsically linked to the gas scattering processes at the surface. The widely used Maxwell scattering model, which employs a single accommodation coefficient to describe gas scattering processes, reveals its limitations when the difference between accommodation coefficients in the tangential and normal directions becomes significant. In this work, we provide a derivation of velocity slip and temperature jump boundary conditions based on the Cercignani–Lampis–Lord scattering model, which applies two independent accommodation coefficients to describe the gas scattering process. A Knudsen layer correction term is introduced to account for the impact of the surface on the velocity distribution function, which is associated with the scattering model. The governing equation of the correction term is established based on the linearized Boltzmann equation. Additionally, two moments are derived to capture the collision effect in the Knudsen layer: a conserving moment of collision invariants, and an approximate higher-order conserving moment. These moments are then employed to determine the coefficients in the correction term. We demonstrate that the derived slip coefficients align closely with numerical results obtained by solving the Boltzmann equation in the Knudsen layer. Besides, we apply the derived slip boundary conditions within the framework of the NSF equations, yielding numerical results that exhibit excellent consistency with those obtained through molecular-level simulations.

A consistent diffuse-interface model for two-phase flow problems with rapid evaporation

AbstractWe present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several orders of magnitude, leading to high velocity and pressure jumps across the liquid–vapor interface, along with dynamically changing interface topologies. To this end, we integrate an incompressible Navier–Stokes solver combined with a conservative level-set formulation and a regularized, i.e., diffuse, representation of discontinuities into a matrix-free adaptive finite element framework. The achievements are three-fold: First, we propose mathematically consistent definitions for the level-set transport velocity in the diffuse interface region by extrapolating the velocity from the liquid or gas phase. They exhibit superior prediction accuracy for the evaporated mass and the resulting interface dynamics compared to a local velocity evaluation, especially for strongly curved interfaces.Second, we show that accurate prediction of the evaporation-induced pressure jump requires a consistent, namely a reciprocal, density interpolation across the interface, which satisfies local mass conservation. Third, the combination of diffuse interface models for evaporation with standard Stokes-type constitutive relations for viscous flows leads to significant pressure artifacts in the diffuse interface region. To mitigate these, we propose to introduce a correction term for such constitutive model types. Through selected analytical and numerical examples, the aforementioned properties are validated. The presented model promises new insights in simulation-based prediction of melt–vapor interactions in thermal multiphase flows such as in laser-based powder bed fusion of metals.

Nonideal Incompressible Lattice-Boltzmann Method for Multicomponent Phase Separating Systems

Understanding and predicting the dynamics of complex fluid systems including liquid–liquid phase separation, relevant to both biological and engineered applications, typically uses a nonideal free energy. Introducing such a thermodynamic constraint into the Lattice-Boltzmann Method can be accomplished by altering either the equilibrium distribution function or the external force. The former requires a lengthy parameterization for a free energy of multiple independent variables which becomes cumbersome for more than three components. The latter has been done for a multicomponent compressible system, but a correction term for the force is required to recover the expected conservation equations. This work builds upon the incompressible single component forcing method from He et al. (Journal of Computational Physics, Vol. 152, No. 2, 1999) by deriving and implementing the required force needed to successfully recover the expected mass conservation from a nonideal free energy with an arbitrary number of components. This allows the simulation of more realistic phase separating fluid systems by including many interacting components, which is demonstrated here for up to five components and phases.

A momentum-conserving wake superposition method for wind-farm flows under pressure gradient

Pressure gradient over topography will significantly affect wind-farm flow. However, knowledge gaps still exist on how to superpose wind-turbine wakes in the wind-farm flow analytical model to account for this effect, leading to systematic errors in evaluating wind-farm wake effects. To this end, we derive an implicit momentum-conserving wake superposition method under pressure gradient (PG-IMCM) based on the total momentum deficit equation, which is linearised by the convection velocity introduced by Zong & Porté-Agel (J. Fluid Mech., vol. 889, 2020, A8). The PG-IMCM method consists of the linear-weighted sum of individual velocity deficits, the sum of the individual pressure correction terms and the total pressure correction term. Based on a sensitivity analysis, we demonstrate that the last two terms nearly cancel out and, thus, can be neglected, resulting in a simplified form, which has the same form as its counterpart under zero pressure gradient but with the single-wake quantities redefined based on the wake model under pressure gradient. This motivates us to further examine the performance of the combination of five empirical superposition methods and the stand-alone wake model under pressure gradient. Validation results based on large-eddy simulation show that PG-IMCM has an overall satisfactory performance in both the magnitude and shape of the velocity-deficit profiles, provided that the stand-alone turbine wake can be modelled accurately, which is virtually identical with its simplified form. Further comparison with empirical superposition methods shows that local linear and wind product superposition methods based on the updated base flow also have comparable performance, with only discernable differences with the PG-IMCM method in the near-wake region of downstream turbines. Therefore, they are two attractive methods for engineering applications.

"Vulva," Not "Private Part": The Importance of Accurate Genital Terminology.

Effective communication in pediatric dermatology is critical for accurate diagnosis and treatment, particularly in sensitive areas such as the anogenital region. Unfortunately, children and their families often use euphemisms or incorrect terms when referring to this area, and many adults lack knowledge of anogenital terminology. Pediatric dermatologists can play a unique role in educating children and their families on correct anatomical language, which enhances body awareness, empowers young patients, improves safety, and contributes to accurate medical assessments and treatment adherence. By promoting the use of correct anatomical terms, pediatric dermatologists can improve patient outcomes and foster a healthier understanding of body anatomy and health.

Perturbational Analysis of Magnetic Force Theorem for Magnetic Exchange Interactions in Molecules and Solids.

There have been increasing efforts to compute magnetic exchange coupling constants for transition metal complexes and magnetic insulators using the magnetic force theorem and Green's function-based linear response methods. These were originally conceived for magnetic metals, yet it has not been clear how these methods fare conceptually with the conventional models based on electron-correlation interactions among so-called magnetic orbitals. We present a spinor-based theoretical analysis pertinent to the magnetic force theorem and linear response theory using Brillouin-Wigner perturbation method and Green's function perturbation method, and we shed light on the conceptual nature of the Lichtenstein formula in its applications for calculations of the total energy and magnetic exchange coupling constants for both molecules and solids. Derivation of the magnetic force theorem in this perturbational analysis identifies the first-order energy correction terms, which are considered as the ferromagnetic component for the magnetic exchange interactions of transition metal compounds but are not included in the Lichtenstein formula. Detailed perturbational analysis of the energy components involved in the magnetic force theorem identifies the energy components that are missing in the Lichtenstein formula but are critical in the Anderson's model for transition metal complexes and magnetic insulators where magnetic orbitals can overlap.

A New High-Order Fractional Parallel Iterative Scheme for Solving Nonlinear Equations

Solving fractional-order nonlinear equations is crucial in engineering, where precision and accuracy are essential. This study introduces a novel fractional parallel technique for solving nonlinear equations. To enhance convergence, we incorporate a simple root-finding method of order 3γ + 1 as a correction term in the parallel scheme. Theoretical analysis shows that the parallel scheme achieves a convergence order of 6γ + 3. Using a dynamical system approach, we identify optimal parameter values, and the symmetry in the dynamical planes for different fractional parameters demonstrates the method’s stability and consistency in handling nonlinear problems. These parameter values are applied to the parallel scheme, yielding highly consistent results. Several engineering problems are examined to assess the method’s efficiency, stability, and consistency compared to existing methods.

The Sustainable Development Index: An Integration of the Ecological Framework Considering the Governance-development Nexus

This paper aims to enhance the formulation of the Sustainable Development Index (SDI) by introducing a further correction term, governance lack (GL) index, in additional to the ecological impact index (EII). The GL considers a country’s governance lack by calculating a governance index (GI) with the World Governance Indicators (WGIs) starting from 1996. The SDI(g) retains the original formula of the SDI, thus remaining an indicator of strong environmental sustainability but adequately considering in its formulation the differences significant in countries’ governance climate. Finally, graphical relationships between DI and GI, and DI and (EII + GL) are shown, and the existence of these relationships are tested with WLS and nonparametric regressions. Our findings show that significant differences in country ranking were found; the graphical relationships are empirically proven; and countries with a worse GI have been further penalized in the SDI(g) ranking.

Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization

The homogenization procedure developed here is conducted on a laminate with periodic space–time modulation on the fine scale: at the leading order, this modulation creates convection in the low-wavelength regime if both parameters are modulated. However, if only one parameter is modulated, which is more realistic, this convective term disappears and one recovers a standard diffusion equation with effective homogeneous parameters; this does not describe the non-reciprocity and the propagation of the field observed from exact dispersion diagrams. This inconsistency is corrected here by considering second-order homogenization that results in a non-reciprocal propagation term that is proved to be non-zero for any laminate and verified via numerical simulation. The same methodology is also applied to the case when the density is modulated in the heat equation, leading, therefore, to a corrective advective term that cancels out non-reciprocity at the leading order but not at the second order.

FINANCIAL DEEPENING AND ECONOMIC GROWTH: EVIDENCE FROM BANGLADESH

The present study investigated the causal impact of financial deepening on economic growth in Bangladesh for the period of 1990 to 2022 applying cointegration analysis. The ratio of broad money to GDP, private sector credit to GDP and stock market capitalization to GDP used as proxies for financial deepening indicators in this study. Using Johansen co-integration test, the result of the study explored a positive and statistically significant relationship in the long run among the broad money to GDP, private sector credit to GDP, stock market capitalization to GDP and economic growth. Moreover, the error correction term supported the long-run association, and the variables adjust to their long-run equilibrium. The findings suggested that policymakers should promote policies that increase the money supply and market capitalization and ensure the private sector credit is channeled to the more productive sector which would help to support and boost economic growth in Bangladesh.

Evaluation of the off‐axis and on‐axis tensile creep behavior of glass‐fiber reinforced polymer unidirectional lamina

AbstractThe off‐axis creep behavior of glass‐fiber reinforced polymer (GFRP) unidirectional lamina is crucial for engineering structural applications. A unified prediction model for time‐dependent off‐axis and on‐axis tensile creep strain in GFRP lamina is developed. The model, analogous in form to the one‐parameter plasticity model, accounts for off‐axis creep deformation separately for elastic and plastic response stages, incorporating a correction term to describe on‐axis creep deformation. The accuracy of the model is confirmed through tensile creep tests on unidirectional lamina at angles of 0, 15, 30, 45, 60, and 90 degrees. The model successfully predicts of creep deformation in the elastic and plastic response stages, respectively. The effects of creep stress, creep time, and off‐axis angle on the creep behavior are investigated. The optimal test angles for predicting off‐axis creep behavior using only two off‐axis angles' creep tests are analyzed. The dominant factors of creep behavior at various off‐axis angles are evaluated. The findings of the study include recommendations for lay‐up configuration and engineering applications of GFRP composites.Highlights A unified creep strain prediction model for GFRP lamina was developed. Creep strain was calculated separately in elastic and plastic response stages. The link between stress, time, angle and creep behavior was determined. The optimal test angles for predicting off‐axis creep behavior were evaluated.

Accurate Calculation of Interatomic Forces with Neural Networks Based on a Generative Transformer Architecture.

Using neural networks to express electronic wave functions represents a new paradigm for solving the Schrödinger equation in quantum chemistry. For practical quantum chemistry simulations, one needs to know not only energies of molecules, but also accurate forces acting on constituent atoms. In this work, we achieve the accurate calculation of interatomic forces on QiankunNet, a platform that combines transformer-based deep neural networks with efficient batched autoregressive sampling. Our approach permits the application of the Hellmann-Feynman theorem to force calculations without introducing corrective Pulay terms. The results show that the calculated interatomic forces are in close agreement with those derived from the full configuration interaction method, irrespective of whether the system is a simple molecule or a strongly correlated electron system like a linear hydrogen chain. Furthermore, the calculated interatomic forces are employed for atomic relaxation in the torsional rotation process of ethylene, and the energy barrier obtained from the scanned potential energy surface is in excellent agreement with the experiment. Our work contributes to the application of artificial intelligence to broader quantum chemistry simulations, such as modeling challenging chemical transformations where electron correlations are difficult to describe.

Energy Poverty and Environmental Quality Nexus: Empirical Evidence from Selected South Asian Countries

South Asian countries are included in the economies of developing Asia. The region of South Asia is predominantly affected by energy poverty issues due to a heavy reliance on conventional energy and unpredictable access to energy services. It has about a quarter of the world's population and is home to three of the world's ten most populated countries: India, Pakistan, and Bangladesh. This study investigates environmental sustainability dynamics in South Asian countries from 2000 to 2021, utilizing the Cross-sectional Autoregressive Distributed Lag (CS-ARDL) and Dumitrescu-Hurlin (D-H) causality methods. The research offers insights into the long-term trends and causal relationships that shape environmental outcomes in South Asian nations. Based on empirical findings, in the long-term, it is revealed that increases in energy poverty, economic growth, income inequality, and capital formation raise greenhouse gas (GHG) emissions, while renewable energy and labor reduce GHG emissions. On the other hand, the error correction term shows the speed of adjustment toward equilibrium at 0.75%. Furthermore, the D-H panel causality reveals a directional link between variables. These findings highlight the urgent need for South Asian countries to implement policies to address energy poverty, promote renewable energy adoption, and reduce income inequality to mitigate GHG emissions and achieve long-term environmental sustainability effectively.

An Improved Fick Model for Predicting Carbonation Depth of Concrete

Concrete carbonation can weaken its strength, cause the corrosion of steel reinforcement, and shorten its service life. Predicting the concrete carbonation depth is a critical aspect of assessing concrete durability. Currently, mathematical models for the concrete carbonation depth, exemplified by the Fick model, suffer from a low fitting accuracy and limited applicability due to the complexity and variability of concrete materials and service environments. In light of this, this work proposes an improved Fick model that incorporates a correction term to effectively enhance the curve fitting accuracy. The correction term in the improved model provides a reasonable adjustment for deviations in the development pattern of the concrete carbonation depth from the Fick model under different conditions, thereby broadening the applicability of the new model compared to the Fick model. Several sets of experimental data on the concrete carbonation depth are used to validate the universality and superiority of the new model. The results of the case studies indicate that the average prediction error and standard deviation of the new model are significantly smaller than those of the Fick model. For the first two examples, in most situations, the average prediction error and standard deviation of the new model are less than 50% of those of the Fick model, with the lowest average prediction error being only 4% and the lowest standard deviation being only 2% of the Fick model’s respective values. For the third example, the new model demonstrates superior predictive capability for the later-stage concrete carbonation depth compared to the Fick model and the ANN model. Specifically, for the carbonation depth of the concrete on the 56th day, the relative error between the predicted value of the new model and the measured value is only 2%, which is much smaller than the 27% of the Fick model and the 12% of the ANN model. These results demonstrate the unique advantage of the proposed model in predicting the carbonation depth, especially when only a limited amount of experimental data are available.

Knot Floer homology and surgery on equivariant knots

AbstractGiven an equivariant knot of order 2, we study the induced action of the symmetry on the knot Floer homology. We relate this action with the induced action of the symmetry on the Heegaard Floer homology of large surgeries on . This surgery formula can be thought of as an equivariant analog of the involutive large surgery formula proved by Hendricks and Manolescu. As a consequence, we obtain that for certain double branched covers of and corks, the induced action of the involution on Heegaard Floer homology can be identified with an action on the knot Floer homology. As an application, we calculate equivariant correction terms which are invariants of a generalized version of the spin rational homology cobordism group, and define two knot concordance invariants. We also compute the action of the symmetry on the knot Floer complex of for several equivariant knots.

Factors Influencing Inflation: Insights from the Nepalese Economy

Inflation is a persistent issue in developing nations such as Nepal, resulting in serious economic and social consequences. This article examines the macroeconomic determinants of inflation in Nepal, considering the variables as government expenditure, exchange rate remittances, real GDP, and the consumer price index of India. Using the time series data from 1975 to 2023. It employs the Engel-Granger two-step cointegration test to examine the short- and long-term causal connections between Nepal's consumer price index (inflation) and all of these variables. The augmented Dickey-Fuller unit root test confirms that the variables are stationary at first difference, suggesting they possess an integrated order of I. The Engel-Granger test established that there is co-integration among the variables. Additionally, the error correction term (ECT) was found to be statistically significant, with a negative coefficient. The causal association between the selected dependent and explanatory variables in Nepal is both significant and persistent. The empirical findings suggest that India's inflation highly affects inflation in Nepal. Furthermore, the enduring effects of broad money supply and government expenditure are also substantial factors. The results indicate an inverse relationship between inflation and real GDP in Nepal, whereas remittances have no significant impact on consumer prices in the nation. So, it is vital to control inflation to be able to deal with poverty and economic growth. Policies are needed to keep the inflation target range around the optimum inflation rate to accelerate the pace of economic growth and ensure that the adverse effect inflation has on economic growth is minimized.

Microfinance, Financial Inclusion and Economic Welfare in Africa: A Panel Investigation

This study explores the relationship between microfinance, financial inclusion, and economic welfare in a sample of 23 African countries for the period of 2004 to 2023 using annual time series data. We measured microfinance with the number of Branches of Microfinance banks, Microfinance Borrowers, Microfinance outstanding deposits, Microfinance outstanding loans; financial inclusion number of registered mobile money accounts per 1,000 adults; the number of mobile money agent outlets par 1,000 adults; and digital card ownership; governance and institutional quality with Rule of law, regulatory quality, and government effectiveness; and economic welfare with household consumption; while we controlled for the inflation rate, interest rate and exchange rate. These variables were estimated using Panel Least Squares, Fully Modified OLS (FMOLS), Dynamic OLS (DOLS), and Panel Autoregressive Distributed Lag (ARDL) estimation techniques. The result of the cointegration revealed that cointegration exists between the variables of the model. Findings from the aforesaid estimation techniques show that there is the existence of long-run relationships between microfinance, financial inclusion, and economic welfare since the coefficients of the microfinance and financial inclusion variables are statistically significant. The coefficients of the error correction terms which measure the effects of the short-run dynamics of the model suggest that the speeds of adjustment from the long run to the short run in the models would be 76%, 61%, 83%, 67%, 68%, 34%, and 80% respectively for all the specified models. Following the findings of the study, conclusions were drawn and the study suggests that microfinance institutions should adapt to the digitization of their products and services for wider coverage on one hand; the government should provide digital financial amenities to create a fertile ground for micro-financial institutions to rely on to maximize the welfare of the economy.

Matter bounce cosmology within Finsler-Randers geometry: A comprehensive study of anisotropic influences

In this study, we explore the dynamics of matter bounce cosmology within the framework of Finsler-Randers geometry, focusing on the role of the Finslerian correction term η(t). By integrating Finsler geometry into cosmological models, we introduce anisotropic effects that significantly impact the evolution of the universe, particularly during the bounce phase. The research examines various cosmological parameters, including the deceleration (qη(t)), jerk (jη(t)), and snap (sη(t)) parameters, highlighting the influence of the Finsler correction on these key indicators. Our results demonstrate that the Finslerian framework leads to more complex and abrupt transitions in the universe's expansion dynamics compared to traditional Riemannian models. The study also reveals that the Finslerian correction intensifies the violations of energy conditions, such as the null energy condition (NEC), which are crucial for the occurrence of a successful bounce. Furthermore, the analysis of the squared sound speed vs2 indicates that the model's stability is highly sensitive to the choice of the Finslerian parameters, with certain configurations leading to instability during the bounce. Our findings underscore the unique contributions of Finsler geometry to cosmological models, offering deeper insights into the behavior of the universe under anisotropic influences and providing a potential avenue for addressing longstanding challenges in cosmology.

Corrected Thermodynamics of Black Holes in f(R) Gravity with Electrodynamic Field and Cosmological Constant.

The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models f(R)=R+αR2 and f(R)=R+2γR+8Λ under the f(R) theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter-RN spacetime) with Λ=-1. It is shown that when the BHs' horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking-Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs.

Numerical Analysis of A Two-Phase Turbine: A Comparative Study Between Barotropic and Mixture Models

Abstract Two-phase turbines offer the potential to significantly enhance the performance of power generation and refrigeration systems. However, their development has been hindered by comparatively lower efficiencies resulting from additional loss mechanisms absent in single-phase turbines. To date, most multiphase CFD studies on turbomachinery have focused on condensation in the final stages of steam turbines, and on cavitation in hydraulic pumps and turbines. These applications, however, are not representative of the conditions in two-phase turbines, where a liquid-dominated mixture undergoes a large expansion ratio, leading to a significant increase in the gas phase volume fraction throughout the entire flow. This paper aims to identify a suitable modeling methodology for two-phase turbines. Our evaluation is centered around two models: the mixture model and the barotropic model. The validity and accuracy of these two modeling approaches is assessed using existing experimental data from a single-stage impulse turbine operating with several mixtures of water and nitrogen as working fluid. The results indicate that both the mixture and barotropic models are consistent and accurately predict the nozzle mass flow rate, yet, both models systematically overpredict the nozzle exit velocity and rotor torque. Adding correction terms for windage and unsteady pumping losses significantly improves the torque predictions, bringing them within the uncertainty range of the experimental data. In addition, refining the models to account for the effect of slip presents a promising avenue to enhance the prediction of nozzle exit velocity and overall performance of two-phase turbines.