Algebraic Model Research Articles

Thermodiffusively-unstable lean premixed hydrogen flames: Length scale effects and turbulent burning regimes

This paper presents direct numerical simulations (DNS) of thermodiffusively-unstable lean premixed hydrogen flames in the canonical turbulent flame-in-a-box configuration. A range of reactant (pressure, temperature, and equivalence ratio) and turbulent (Karlovitz and Damköhler number) conditions are used to explore the effects of the small and large turbulent scales on local and global flame response. Turbulence-flame interactions are confirmed to be independent from integral length scale (or equivalently, from Damköhler number) for a fixed Karlovitz number. Furthermore, a recent model that predicts mean local flame speed as a function of an instability parameter and Karlovitz number is also demonstrated to be independent from integral length scale. This model thereby reduces turbulent flame speed modelling for thermodiffusively-unstable cases to predicting surface area enhancement. Flame surface area wrinkling is found to have good agreement with Damköhler’s small-scale limit. There is some scatter in the data, although this is comparable with similar experimental data, and the freely-propagating flame properties have a greater impact on the turbulent flame speed than the flame surface area. It is demonstrated that domain size can have an effect on flame surface area even if the integral length scale remains unchanged; the larger volume into which flame surface area can develop results in a higher turbulent flame speed. This is not accounted for in conventional algebraic models for turbulent flame speed. To investigate the influence of the fuel Lewis number Lef, an additional study is presented where Lef (alone) is artificially modified to span a range from 0.35 to 2. The results demonstrate that more flame surface area is generated for smaller Lef, but the difference for Lef≲1 is much smaller than that observed for Lef>1. A volume-filling-surface concept is used to argue that there is a limit to how much flame surface can develop in a given volume, and so there is only so much more flame surface can be induced by the thermodiffusive response; whereas the thermodiffusive response at high Lef is to reduce flame surface area. The agreement of the present data (and previous work) with Damköhler’s small-scale limit (even for low-to-moderate Karlovitz numbers) suggests that a distinction should be made between the small-scale limit and the distributed burning regime. Furthermore, it is argued that the distinction between large- and small-scale limits should be made based on Damköhler number. Consequently, the flamelet, thin reaction and distributed regimes should be distinguished by Karlovitz number (as usual), but the two latter regimes both have separate large- and small-scale regimes. Finally, implications for the turbulent premixed regime diagram are discussed, and a modified regime diagram is proposed.Novelty and significanceThis paper: confirms that turbulence-flame interactions at the flame scale are independent of integral length scale (at fixed Karlovitz number), as is the local flame speed model for thermodiffusively-unstable flames (Howarth et al., 2023); demonstrates potential domain size effect not accounted for in turbulent-flame models; flame surface wrinkling agrees with Damköhler’s small-scale limit for thermodiffusively-unstable flames in the thin reaction zone at low Damköhler number; and flame surface wrinkling increases slightly for low fuel Lewis numbers, but decreases significantly at high fuel Lewis numbers. There are significant consequences for the turbulent premixed regime diagram: distinction between Damköhler’s small-scale limit and distributed burning regime; separation of small- and large-scale limit by Damköhler number; application of the λ-flames concept to thin reaction zone; and exclusive use of Karlovitz and Damköhler number for regime classification and diagram axes.

The influence of radiative heat transfer on flame propagation in dense iron-air aerosols

It is demonstrated that in the (near) zero-gravity experiments conducted by Tang et al. (Combust. Flame; 2009, 2011) iron powder aerosols created using the finest powders are optically thick, implying that radiative heat transfer between particles should not be neglected. To test this concept, an iron particle oxidation model has been implemented in OpenFOAM, including a coupling with the P1-model for radiative heat transfer.For flame simulations in which radiation is not included, obtained flame propagation velocities deviate less than 8% with results obtained using Chem1D-Fe and also show a good correspondance with algebraic models for optically thin aerosols. No significant difference in predicted flame propagation velocity is observed between 1D and 3D simulations: contrary to what is seen in gaseous flames, including the curvature of the flame does not increase predicted flame speeds substantially. However, measured flame propagation velocity values exceed numerically obtained predictions excluding thermal radiation by a factor of three to four. To the authors’ knowledge, this discrepancy is exemplary for the difference between experimentally obtained values for flame propagation velocities, and predictions made using numerical simulation tools neglecting radiative heat transfer.Accounting for radiation increases predicted flame propagation velocities, in the absence of confining boundaries, by approximately a factor of 10 which is in line with algebraic models for optically thick aerosols. In 3D simulations for the two finest iron powders in the experiments, including radiation and accounting for the presence of the confining tube wall results in an error of 11% and 35% with respect to measured flame propagation velocities, significantly smaller than predictions obtained excluding thermal radiation. Although these flames are not purely radiation-driven, inclusion of particle-to-particle radiative heat transfer enhances flame propagation velocities in simulations to values that correspond much better with experimental values than if radiation would not be taken into account.

TorchSISSO: A PyTorch-based implementation of the sure independence screening and sparsifying operator for efficient and interpretable model discovery

Symbolic regression (SR) is a powerful machine learning approach that searches for both the structure and parameters of algebraic models, offering interpretable and compact representations of complex data. Unlike traditional regression methods, SR explores progressively complex feature spaces, which can uncover simple models that generalize well, even from small datasets. Among SR algorithms, the Sure Independence Screening and Sparsifying Operator (SISSO) has proven particularly effective in the natural sciences, helping to rediscover fundamental physical laws as well as discover new interpretable equations for materials property modeling. However, its widespread adoption has been limited by performance inefficiencies and the challenges posed by its FORTRAN-based implementation, especially in modern computing environments. In this work, we introduce TorchSISSO, a native Python implementation built in the PyTorch framework. TorchSISSO leverages GPU acceleration, easy integration, and extensibility, offering a significant speed-up and improved accuracy over the original. We demonstrate that TorchSISSO matches or exceeds the performance of the original SISSO across a range of tasks, while dramatically reducing computational time and improving accessibility for broader scientific applications.

Pembentukan Representasi Adjoin pada Aljabar Lie

Algebra is a branch of mathematics that can provide understanding in solving problems. This research discusses one form of algebra, namely Lie algebra. Where Lie algebra 𝗀 is a vector space over the field 𝔽 equipped with a bilinear mapping equipped by a commutator operation commonly called the Lie bracket operation denoted [−, −] from 𝗀 × 𝗀 to 𝗀 if it satisfies the anti-symmetry axiom and satisfies Jacobi Identity. One model of Lie algebra is the set of all linear operators of a vector space 𝑉 denoted by 𝑔𝑙(𝑉). In addition, one of the discussions related to Lie algebra in this research is representation theory. Lie algebra uses representation theory with the aim of simplifying abstract algebraic problems into linear algebra by presenting each of its members in the form of linear mappings on vector spaces. There are various forms of representation theory in Lie algebra, one of which is adjoin representation. And this adjoin representation is formed from a derivation and Lie homomorphism. The purpose of this research is to find out how the formation of adjoin representation on Lie algebra. This research uses a qualitative method, where the method applies a way to collect data or library materials as a reference in the form of articles, journals, and even books related to Lie algebra.

Peer-to-Peer Transactive Energy Trading of Smart Homes/Buildings Contributed by A Cloud Energy Storage System

This paper presents a model for transactive energy management within microgrids (MGs) that include smart homes and buildings. The model focuses on peer-to-peer (P2P) transactive energy management among these homes, establishing a collaborative use of a cloud energy storage system (CESS) to reduce daily energy costs for both smart homes and MGs. This research assesses how smart homes and buildings can effectively utilize CESS while implementing P2P transactive energy management. Additionally, it explores the potential of a solar rooftop parking lot facility that offers charging and discharging services for plug-in electric vehicles (PEVs) within the MG. Controllable and non-controllable appliances, along with air conditioning (AC) systems, are managed by a home energy management (HEM) system to optimize energy interactions within daily scheduling. A linear mathematical framework is developed across three scenarios and solved using General Algebraic Modeling System (GAMS 24.1.2) software for optimization. The developed model investigates the operational impacts and optimization opportunities of CESS within smart homes and MGs. It also develops a transactive energy framework in a P2P energy trading market embedded with CESS and analyzes the cost-effectiveness and arbitrage driven by CESS integration. The results of the comparative analysis reveal that integrating CESS within the P2P transactive framework not only opens up further technical opportunities but also significantly reduces MG energy costs from $55.01 to $48.64, achieving an 11.57% improvement. Results are further discussed.

Optimal Allocation of Depots for Electric Bus Charging: Cost Minimization and Power System Impact Mitigation Using Mixed Integer Nonlinear Programming

ABSTRACTThis paper proposes a novel approach for the optimal allocation of a depot for electric buses (EBs) charging in a specific transit service, considering the impact on the power system. The main objective is to minimize the total cost, achieved by minimizing the cost of the new cables connecting the depot station to the distribution system and the upgrade cost of existing lines to meet the additional loads. The outcomes are the optimal location of the depot, the optimal electric node bus in the distribution system to supply it, and the required system upgrades. The optimization problem is formulated as a Mixed Integer Nonlinear Programming (MINLP) model and solved using the General Algebraic Modeling System (GAMS). The methodology is tested on the H16 EB service line in Barcelona, Spain, and a typical electrical distribution system. Three case studies are presented in this paper. In the first case, the impact of a single service on the distribution network is analyzed, and in the second case, three H16 EB services are assumed to serve the network. The third case handles a multi‐route, multi‐terminal bus service to allocate and supply a depot capable of accommodating all the routes. This case will also include sensitivity analysis to test the robustness and reliability of the model. Results show that for a single H16 EB service, no line upgrades were needed, and the total cost per phase was $120,000. For three H16 EB services, three lines required upgrades, and the total cost per phase increased to $718,000. In the third case, the sensitivity analysis revealed that higher demand factors lead to increased costs due to more update requirements and voltage deviations. The results demonstrate that the minimum distance between the depot and node is not always the optimal or feasible solution that would prevent the depot load installation at a weak spot and meet the power flow constraints.

Combinatorial reduction of set functions and matroid permutations through minor invertible product assignment

We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is deformed through a monomial factor in d indeterminates, whose exponents define a Zd-valued set function. By combining the Grassmann-Plücker relations for the two matrices, we derive a family of sparse polynomials, whose factorisation properties in a Laurent polynomial ring are studied and related to information-theoretic notions.Under a given genericity condition, we prove the equivalence between combinatorial reductions and determinantal expansions with invertible minor products; specifically, a deformation returns a determinantal expansion if and only if it is induced by a diagonal matrix of units in C(t) acting as a kernel in the original determinant expression. This characterisation supports the definition of a new method for checking and recovering combinatorial reductions for matroid permutations.

Development of hybrid first principles – Artificial intelligence models for transient modeling of power plant superheaters under load-following operation

This paper develops different approaches for synergistic integration of physics-based models with data-driven models for modeling of high temperature power plant superheaters. Two types of data-driven models are developed, namely all-nonlinear static-dynamic neural network models as well as models obtained using a Bayesian machine learning approach. Series, integrated, and parallel coupling of first-principles models and data-driven models are proposed. Algorithms for solving the training problems for the data-driven models and for simulation of the hybrid models are developed. The developed approach is applied to high temperature power plant superheaters that face considerable modeling and measurement challenges. Measurement challenges arise due to harsh operating conditions that not only make placement of sensors difficult, but life of the placed sensors very limited. Modeling challenges arise due to complex inhomogeneous spatial distribution of flue gas and steam flowrates, especially under load-following operation and uncertainties in heat transfer characteristics because of multiple factors such as stochastic spatio-temporal variation of ash deposits on the superheater tubes in coal-fired power plants, internal oxide scale formation in the tubes, etc. First-principles two-dimensional differential–algebraic equation models of two industrial superheaters, one from a natural gas combined cycle plant and another from a coal-fired power plant, are developed. The results from the models are compared against industrial operational data. For all cases studied in this work, it is observed that both for steady-state and dynamic data, the hybrid models have much higher accuracy than when only the respective first-principles models are used. For example, during prediction of the average outside tube wall temperature of superheater tubes at the combined cycle power plant, the root mean squared error observed for the standalone first-principles model improved from 12.3 °C to 0.5 °C post hybridization with data-driven models. Similarly, while predicting the main steam outlet temperature in the coal-fired plant, the hybrid models resulted in reduction of the root mean squared error value from 19.5 °C to around 2 °C. In addition, the hybrid models yield highly resolved spatio-temporal temperature profiles that can be helpful for developing monitoring approaches of these critical components under load-following operation.

A DATA DRIVEN METHOD FOR THE DERIVATION OF EXPLICIT ALGEBRAIC REYNOLDS STRESS MODELS APPLIED TO THE WAKE LOSSES OF LOW-PRESSURE TURBINE CASCADES

Abstract This paper introduces and validates a data-driven approach to improve the prediction of linear eddy viscosity models (LEVMs). The general approach is adopted in order to improve the wake mixing of low-pressure turbine (LPT) cascades. The approach follows the rationale applied in the derivation of explicit algebraic Reynolds stress models (EARSMs) by including additional second-order tensors in the Boussinesq assumption. The unknown scalar functions that determine the contributions of each second-order tensor to the Reynolds stresses are approximated as polynomials. A metamodel-assisted multi-objective optimization determines the value of each of the polynomial coefficients by minimizing the difference between the result of the EARSM simulation and reference data provided by a high fidelity large eddy simulation (LES). In this study, tailor made EARSMs are calibrated to improve the prediction of the kinetic energy loss distribution in the wake of the T106C LPT cascade. We investigated the influence of each polynomial coefficient of the EARSM on the results. The models generated by the approach reduced the deviations in total kinetic energy loss between the LES reference solution and the baseline model by approximately 70%. The turbulent quantities are analyzed to identify the physical correlations between the model inputs and the improvement. The transferability of the models to unseen test cases was assessed using the MTU-T161 LPT cascade. In summary, the suggested approach was able to generate tailor made EARSM models that reduce the deviations between RANS and LES for the mixing of turbulent wake flows.

Cost minimization of membrane-based separation systems for H2 recovery: A comparison of two optimization approaches

This paper addresses the optimization of membrane-based processes, with a specific focus on H2 recovery in hydrocarbon processing plants. A comparative analysis of two optimization approaches is conducted for designing H2 recovery systems for a multicomponent gas mixture containing H2/N2/CO2/CO. The main objective is to achieve the desired H2 recovery and product purity levels while minimizing costs. The paper compares two approaches for optimization: the first uses a simulation-based optimization technique with Aspen Custom Modeler/ASPEN Plus, while the second employs a simultaneous optimization method using GAMS (General Algebraic Modeling System). The methods are thoroughly compared, evaluating their strengths and weaknesses through qualitative and numerical assessments. To this end, a reference case was selected from the existing literature. The results obtained indicate that both proposed approaches are suitable for optimizing the design of a two-stage membrane configuration, as evidenced by the similarity of the optimal solutions obtained from both approaches. Subsequently, based on the analysis of numerical values for the optimal design problem for the investigated two-stage membrane configuration, a hybrid strategy for the optimal synthesis and design of multi-stage separation processes is proposed.The study fills a gap in the literature by providing a comprehensive analysis of the advantages and disadvantages of optimization approaches in the context of technology of separation of gases. This research provides valuable insights into the field and offers guidance for selecting appropriate approaches to improve the efficiency and cost-effectiveness of gas separation processes in real-world applications.

A Comparative Study on the Prediction of Hydrogen, Nitrogen, and Water Vapor of Regenerative Hydrogen Pump With Different Turbulence Models

Abstract The flow in a regenerative hydrogen pump used in a proton exchange membrane (PEM) fuel cell system is complex, including velocity mixing, streamline distortion, swirling flow, corner flow, and possible boundary separation. Experimental measurement and computational fluid dynamics (CFD) prediction are the main methods used to evaluate such performance. In this work, regenerative hydrogen designed for fuel cell electric vehicles with an impeller diameter of 91 mm and a shaft speed of 22,000 rpm is tested with a mixture of nitrogen, hydrogen, and water vapor. During the test, the flowrate and shaft speed ranges are 151–881 L/min and 8000–22,000 rpm, respectively. The inlet pressure and temperature are 171 kPa and 66 °C, respectively. Then, the flow is predicted by the k − ε model, the renormalization group (RNG) k − ε model, the explicit algebraic Reynolds stress models (EARSM) and the shear-stress transport (SST) detached eddy simulation (DES) model. The differences between the tested and predicted performances are compared. With these results, the velocity distribution in the side channel, the radial force of the impeller and casting, and the changes in the downstream pressure and velocity are analyzed in consideration of the ability of the turbulence models to simulate each characteristic flow. On this basis, the differences and abilities of the turbulence models for predicting the flow in regenerative hydrogen pumps are summarized.

Detection and Signal Processing for Near‐Field Nanoscale Fourier Transform Infrared Spectroscopy

AbstractResearchers from a broad spectrum of scientific and engineering disciplines are increasingly using scattering‐type near‐field infrared spectroscopic techniques to characterize materials non‐destructively with nanoscale spatial resolution. However, a sub‐optimal understanding of a technique's implementation can complicate data interpretation and act as a barrier to entering the field. Here the key detection and processing steps involved in producing scattering‐type near‐field nanoscale Fourier transform infrared spectra (nano‐FTIR) are outlined. The self‐contained mathematical and experimental work derives and explains: i) how normalized complex‐valued nano‐FTIR spectra are generated, ii) why the real and imaginary components of spectra qualitatively relate to dispersion and absorption respectively, iii) a new and generally valid equation for spectra which can be used as a springboard for additional modeling of the scattering processes, and iv) an algebraic expression that can be used to extract an approximation to the sample's local extinction coefficient from nano‐FTIR. The algebraic model for weak oscillators is validated with nano‐FTIR and attenuated total reflectance Fourier transform infrared (ATR‐FTIR) spectra on samples of polystyrene and Kapton and further provides a pedagogical pathway to cementing some of the technique's key qualitative attributes.

Investigation on transition characteristics of hydrofoil boundary layer based on algebraic local-correlation-based transition modeling model

Hydrofoil shapes are used for the marine turbine blades to capture kinetic energy from water currents effectively. Predicting transitions is a critical concern when studying the hydrofoil boundary layer. This paper analyzed the transitional behavior of the boundary layer in the National Advisory Committee of Aeronautics (NACA) hydrofoil, NACA0009, with a blunt trailing edge using the Algebraic Local-Correlation-based Transition Modeling (Algebraic LCTM) model. First, through sensitivity analysis, the effects of the maximum y+ (the dimensionless distance y to the wall), grid expansion ratio, number of normal and streamlined grids, and timescale on transition prediction were studied. The results indicate that finer y+ value and appropriate grid expansion ratios can improve the accuracy of transition prediction, while the influence of timescale on the prediction results is relatively small within the range of Courant number theory values. Second, further analysis was conducted on the transition prediction performance under different Reynolds numbers. It was found that the model predictions were consistent with experimental values at low Reynolds numbers, but the predicted transition position was advanced at high Reynolds numbers, mainly because of the significant disparity in eddy viscosity coefficients within the free flow field. In the study of leading-edge roughness bands' impact on boundary layer transition for hydrofoil, the introduction of roughness significantly expedited the transition process. The Algebraic LCTM model outperformed the gamma (γ) transition model, reducing prediction errors by 5–40% for boundary layer parameters and maintaining errors between 0.005 and 4% for wake vortex shedding frequency, as opposed to the γ model's 0–23%. The results of this study provide a theoretical basis for hydrofoil design.

Simulation of continuous thermally regenerative electrochemical flow cycle and coupled with photovoltaic/thermal system

Thermally regenerative electrochemical cycle (TREC) is an efficient, clean and feasible low-temperature thermoelectric conversion technology. Coupling it with flow battery (FB) can not only achieve continuous operation, but also can be used to realize the heat energy recovery of the photovoltaic/thermal (PV/T) system. In this paper, a continuous TREC-FB system including two charging-free cells is proposed for outputting power at both high and low temperatures. An electrochemical-thermodynamic coupling algebraic model is established to explore the effects of electrolyte flow rate, temperature difference and design parameters of heat exchanger on the power density (PTREC) and thermoelectric efficiency (ηele,TREC) of the TREC-FB. Experimental study on TREC-FB is carried out for model validation. The results show that PTREC is determined by the temperature difference and the electrolyte flow rate, which contribute to enhanced voltage and mass transfer, respectively. For specific heat source scenarios, the ηele,TREC is mainly affected by the flow rate, followed by the heat transfer area AH, and finally is the flow channel height and the thermal conductivity of the heat exchanger. Moreover, for the continuous TREC-FB-PV/T coupled system, the energy conversion efficiency reaches an average of 11 % within one day by optimizing the designed temperature difference.

An Integrated Approach for Ammunition Depot Location Selection and Ammunition Distribution Network Design Based on P-Median and Vehicle Routing Problems

During the war, the safe provision of the required ammunition at the desired place and time can affect the fate of the war and even the country. Determining the number and locations of ammunition depots needed in the war is as important as planning their distribution. Ammunition supply has always been a force multiplier for military units. Although the timely delivery of ammunition to the unit is not sufficient for success on its own, it is an important factor. These two issues are directly related to each other. This study presents a two-stage methodology to solve the problems in question. In the first stage, it was decided which of the 3 different types of depots, whose establishment locations were known with the p-median model, would be opened, and the unit-depot assignments were determined. In the second stage, the distribution network design for the distribution of ammunition from the ammunition depot to the deployed artillery units was realized with the Capacity-Constrained Vehicle Routing Problem (CCVRP) model. This methodology was tested for a fictitious situation where the geographical location and numerical information of the depots and artillery batteries were generated generically. By solving the mathematical model in the General Algebraic Modeling System (GAMS) program, it was determined which depot should distribute how many vehicles to which artillery batteries, and the results were presented visually.

A novel approach for the anomalous collectivity in the neutron-deficient Os isotopes

Abstract An algebraic model with three-body boson interactions is proposed to incorporate the different quadrupole modes in nuclear collectivity. It is shown that the recently observed anomalous collective structure characterized by $B_{4/2}=B(E2;4_1\rightarrow2_1)/B(E2;2_1\rightarrow0_1)<1.0$ and $R_{4/2}= E(4_1)/E(2_1)\geq2.0$, which cannot yet be explained by any other microscopic nuclear models, naturally emerge in the present model due to the inclusion of triaxial rotor modes.
This description is further extended to describe the odd-$A$ nuclei by including the coupling to the Fermion degree of freedom. That allows us to give a unified explanation of the anomalous $B(E2)$ strengths in both even-even and even-odd systems which seemed to indicate different behaviors. As examples, the model is applied to describe the spectroscopy and $E2$ transition properties of $^{168,169,170,171}$Os. All recent measurements of those isotopes can be well reproduced on the same footing which suggests that the anomalous collectivity persists even in the odd-$A$ systems.

Testing the algebraic modeling of competitive impacts from wage premium shocks: a case study from a booming airline market

Labor relations issues such as collective bargaining and strike threat power have recently gained increased attention in the Brazilian air transportation market due to a short-term shortage of qualified workforce, leading stronger pilot unions to demand higher wages and better working conditions. Exacerbated by the notable expansion of the Brazilian economy between 2020 and 2023, where air travel demand surged by 60%, this pressure has driven labor costs to grow more rapidly than other cost categories. This paper examines exogenous flight crew cost shocks, treating these as increases in wage premiums resulting from stronger unionization and higher labor market rents. Using a differentiated duopoly model, we analyze the impact of these wage increases on competition between a major network carrier and a small low-fare carrier, introducing the hypothesis of non-exhausted economies of density. Our findings indicate that smaller airlines are more adversely affected by labor cost shocks, though differentiated wage increase schemes can mitigate these impacts, reducing market concentration and preserving consumer welfare. This study contributes to the literature by incorporating wage premium shocks into existing models and suggesting that labor regulations in Brazil should be liberalized to address the rapid growth in air transportation demand and the resultant workforce shortage.

Electromagnetic and two-photon transition form factors of the pseudoscalar mesons: An algebraic model computation

We compute electromagnetic and two-photon transition form factors of ground-state pseudoscalar mesons: π,K,ηc,ηb. To this end, we employ an algebraic model based upon the coupled formalism of Schwinger-Dyson and Bethe-Salpeter equations. Within this approach, the dressed quark propagator and the relevant Bethe-Salpeter amplitude encode the internal structure of the corresponding meson. Electromagnetic properties of the meson are probed via the quark-photon interaction. The algebraic model employed by us unifies the treatment of all ground-state pseudoscalar mesons. Its parameters are carefully fitted performing a global analysis of existing experimental data including the knowledge of the charge radii of the mesons studied. We then compute and predict electromagnetic and two-photon transition form factors for a wide range of probing photon momentum-squared which is of direct relevance to the experimental observations carried out thus far or planned at different hadron physics facilities such as the Thomas Jefferson National Accelerator Facility (JLab) and the forthcoming Electron-Ion Collider. We also present comparisons with other theoretical models and approaches and lattice quantum chromodynamics. Published by the American Physical Society 2024

The algebraic learning of middle school students’ evolution during a school year: a statistical large-scale study based on results in mathematics didactics

This large-scale study characterizes the algebraic learning of a cohort of nearly 800 French students during the last year of middle school (9th grade, 14–15 years old) and examines their evolution in relation to the composition of the classes to which the students belong. Based on the Anthropological Theory of the Didactic (ATD), the study is founded both on a reference model of elementary algebra and on technological-theoretical levels characterizing the students’ reasoning and their knowledge regarding institutional expectations. These are used to code the data and define the statistical variables on which multivariate descriptive analyses are carried out. Students’ learning is analyzed through Pépite, an algebra test given at the beginning and at the end of the year. A cluster analysis resulted in three distinct clusters of similar classes and of similar students both at the beginning and end of the grade 9 school year. They are interpreted didactically and could be useful for a teacher who has to manage the heterogeneity of learning in a class. Some classes and students move from one cluster to another between the beginning and the end of the year, showing a wide variety of ways in which students’ algebra learning progresses or regresses over a school year.

A latent class analysis of biosecurity attitudes and decision-making strategies of swine producers in the United States

The 2018 African swine fever (ASF) outbreak highlighted the importance of biosecurity in food production systems. Despite the significant economic impacts, the sociopsychological consequences on decision-making have been overlooked. Previous studies have focused on algebraic models and simulation-based models without considering the complex psychological and social factors that influence farmers' biosecurity behaviors and decision-making processes. This study aims to classify livestock producers into distinct subgroups based on their attitudes towards biosecurity. We conducted a survey presenting producers with three scenarios to assess their willingness to report suspected ASF cases, trust in government agencies, risk perception, biosecurity knowledge, willingness to purchase livestock insurance, motivation to invest in biosecurity, readiness to report suspected infections, and intention to contact a veterinarian. Using latent class analysis, we identified three distinct classes: Biosecurity Sceptics, Biosecurity Compliant, and Biosecurity Ultra-Compliant. Our results show that producer characteristics significantly influence biosecurity attitudes and class membership, with small-scale producers less likely to adopt ultra-compliant biosecurity practices. Attending at least one eradication program encouraged biosecurity compliance. This research informs the design of targeted food policy and risk communication strategies that account for attitudes of livestock producers to encourage biosecurity adoption and reduce the likelihood of Tier 1 disease incursion.