Modelling

In recent decades, the deployment of quadcopters has significantly expanded, particularly in outdoor applications such as parcel delivery. These missions require highly stable aerial platforms capable of maintaining balance under diverse environmental conditions, ensuring the safe operation of both the drone and its payload. This paper focuses on the stabilization of a quadcopter designed for outdoor use. A detailed dynamic model of a compact vertical takeoff and landing (VTOL) drone forms the basis for a non-linear control strategy targeting stability during the critical takeoff phase. The control law is designed using a quasi-linear parameter-varying (quasi-LPV) model that captures the system’s non-linear dynamics. Lyapunov theory and linear matrix inequalities (LMIs) are employed to validate the stability and design the controller. Numerical simulations demonstrate the controller’s effectiveness, and a comparative study is conducted to benchmark its performance against a reference quadrotor model. Full article

Underground production and injection operations result in mechanical compaction and mineral chemical reactions that alter porosity and permeability. These changes impact the flow and, eventually, the long-term sustainability of reservoirs utilized for CO₂ sequestration and geothermal energy. Even though mechanical and chemical deformations in rocks take place at the pore scale, it is important to investigate their impact at the continuum scale. Rock deformation can be examined using intergranular pressure solution (IPS) models, primarily for uniaxial compaction. Because the reaction rate parameters are estimated using empirical methods and the assumption of constant mineral saturation indices, these models frequently overestimate the rates of compaction and strain by several orders of magnitude. This study presents a new THMC algorithm by combining thermo-mechanical computation with a fractal approach and hydrochemical computations using PHREEQC to evaluate the pressure solution. Thermal stress and strain under axisymmetric conditions are calculated analytically by combining a derived hollow circle mechanical structure with a thermal resistance model. Based on the pore scale, porosity and its impact on the overall excessive stress and strain rate in a domain are estimated by applying the fractal scaling law. Relevant datasets from CO₂ core flooding experiments are used to validate the proposed approach. The comparison is consistent with experimental findings, and the novel analytical method allows for faster inspection compared to numerical simulations. Full article

The nonlocal macro–meso-scale damage (NMMD) model, implemented in the framework of the finite element method, has been demonstrated to be a promising numerical approach in simulating crack initiation and propagation with reliable efficacy and high accuracy. In this study, the NMMD model was further enhanced by employing an identical degradation mechanism for both the tensile and shear components of shear stiffness, thereby overcoming the limitation of equal degradation in shear and tensile stiffness inherent in the original model. Additionally, a more refined and physically sound seepage evolution function was introduced to characterize the variation in permeability in porous media with geometric damage, leading to the development of an improved NMMD model suitable for simulating coupled seepage–stress problems. The reliability of the enhanced NMMD model was verified by the semi-analytical solutions of the classical KGD problem. Finally, based on the modified NMMD model, the effects of preset fracture spacing and natural voids on hydraulic fracture propagation were investigated. Full article

Tight gas wells in Southwest oil and gas fields have significant production and high sand output intensity. The sand out of the wellhead has a certain erosion effect on the downstream pipeline, the equipment, and affects the normal production. This paper models and simulates the desander used at the wellhead according to the real parameters of the tight gas wellhead, and explores the effects of gas production, pressure, temperature, sand particle size, water content, and other factors on the desander’s sand removal efficiency. This paper combines the principle of fluid dynamics to analyze the internal mechanism of the effect trend and according to the simulation results uses the Pearson correlation coefficient quantification of the effect of each operating parameter to explore the optimal boundary condition parameters applicable to the desander. From the simulation results, it can be seen that the separation efficiency of the desander is the highest when the gas production rate is 4 × 10⁴ m³/d, the pressure is 7 MPa, and the lower the working temperature is, the larger is the gravel particle size. Combined with the sand management problems occurring in the field of tight gas wells, suggestions are made for the optimization of the operating parameters and structure of the desander, which will provide a basis for supporting the rapid production and large-scale beneficial development of tight gas fields. Full article

Lot sizing and cutting stock problems are critical for manufacturing companies seeking to optimize resource utilization and minimize waste. This paper addresses the interconnected nature of these problems, often occurring sequentially in industries involving cut items or packaging. We propose a novel mixed integer linear programming (MILP) model that integrates the capacitated lot sizing problem with the one-dimensional cutting stock problem within a multi-level manufacturing framework. The cutting stock problem is addressed using an arc flow formulation. Our model aims to minimize setup, production, holding, and waste material costs while incorporating capacity constraints, setup requirements, inventory balance, and the use of various cutting machines. The effectiveness of our model is demonstrated through numerical experiments using a commercial optimization package. While the model efficiently generates optimal solutions for most scenarios, larger instances pose challenges within the specified time limits. Sensitivity analysis is conducted to evaluate the effect of changing essential parameters of the integrated problem on model performance and to provide managerial insights for real-life applications. Full article

This study presents a high-order shear deformation theory (HSDT)-based model for evaluating the energy harvesting performance of functionally graded material (FGM) beams integrated with a piezoelectric layer and subjected to a moving concentrated load at constant velocity. The governing equations are derived using Hamilton’s principle, and the dynamic response is obtained through the State Function Method with trigonometric mode shapes. The output voltage and harvested power are calculated based on piezoelectric constitutive relations. A comparative analysis with homogeneous isotropic beams demonstrates that HSDT yields more accurate predictions than the Classical Beam Theory (CBT), especially for thick beams; for instance, at a span-to-thickness ratio of h/L = 12.5, HSDT predicts increases of approximately 6%, 7%, and 12% in displacement, voltage, and harvested power, respectively, compared to CBT. Parametric studies further reveal that increasing the load velocity significantly enhances the strain rate in the piezoelectric layer, resulting in higher voltage and power output, with the latter exhibiting quadratic growth. Moreover, increasing the material gradation index n reduces the beam’s effective stiffness, which amplifies vibration amplitudes and improves energy conversion efficiency. These findings underscore the importance of incorporating shear deformation and material gradation effects in the design and optimization of piezoelectric energy harvesting systems using FGM beams subjected to dynamic loading. Full article

The accuracy of the blade pitch angle (BPA) motion in controllable pitch propellers (CPPs) is considered crucial for the efficacy and reliability of marine propulsion systems. The pitch adjustment process of CPPs is highly complex and influenced by various uncertain factors. A parametric kinematic model for the pitch adjustment process for CPPs was established, incorporating the geometric dimensions and material surface friction coefficients caused during workpiece production as uncertainty parameters. The aim was to establish the correspondence between these uncertainty parameters and the BPA of CPPs. A large dataset was generated by batch calling on Adams. Based on the collected dataset, five surrogate models (e.g., deep neural network (DNN), Kriging, support vector regression (SVR), random forest (RF), and polynomial chaos expansion Kriging (PCK)) were constructed to predict the BPA. Among these, the DNN approach demonstrated the highest prediction accuracy. Accordingly, the influence of uncertainties on the BPA was investigated using the DNN model, focusing on variations in the slider width, crank pin diameter, crank disc diameter, piston rod–slider friction coefficient, crank pin–slider friction coefficient, and hub bearing–crank disc friction coefficient. The high-fidelity model established in this study can replace the kinematic model of the CPP pitch adjustment process, significantly improving computational efficiency. The research findings also provide important references for the design optimization of CPPs. Full article

The rapid growth in scientific knowledge has created a critical need for advanced systems capable of managing mathematical knowledge at scale. This study presents a novel approach that integrates ontology-based knowledge representation with large language models (LLMs) to automate the extraction, organization, and reasoning of mathematical knowledge from LaTeX documents. The proposed system enhances Mathematical Knowledge Management (MKM) by enabling structured storage, semantic querying, and logical validation of mathematical statements. The key innovations include a lightweight ontology for modeling hypotheses, conclusions, and proofs, and algorithms for optimizing assumptions and generating pseudo-demonstrations. A user-friendly web interface supports visualization and interaction with the knowledge graph, facilitating tasks such as curriculum validation and intelligent tutoring. The results demonstrate high accuracy in mathematical statement extraction and ontology population, with potential scalability for handling large datasets. This work bridges the gap between symbolic knowledge and data-driven reasoning, offering a robust solution for scalable, interpretable, and precise MKM. Full article

This study addresses the limitations of existing maintenance decision-making approaches that predominantly rely on single-objective strategies for leased production systems with complex series–parallel configurations. An integrated opportunity-based adaptive maintenance strategy is proposed, and a multi-objective optimization model incorporating multiple maintenance alternatives is developed. First, a proportional hazards model to characterize the degradation-dependent failure rates of key components is used to characterize equipment failure rates, which inform the selection of maintenance actions. Second, the effects of virtual age and maintenance strategies on the residual value of leased equipment are analyzed, leading to the formulation of a net residual value model from the lessor’s perspective. Simultaneously, a customer cost model is established by considering both product quality loss and downtime loss. Finally, the NSGA II algorithm is employed to solve the proposed multi-objective optimization model, yielding optimal preventive maintenance intervals, opportunistic maintenance thresholds, preventive maintenance thresholds, and the corresponding Pareto front. A case study illustrates the strategy’s superior flexibility and practical applicability, with its effectiveness further validated through comparative analysis against traditional maintenance strategies. Full article

The initiation condition of the shear band in gas hydrate-bearing sediment (GHBS) was analyzed in this study. First, the mathematical model considering the pore diffusion and stress conservation equations was constructed. The shear stress is assumed to be related to the porosity, shear strain, and shear strain ratio. The expansion of pores causes sediment softening, while the shear strain causes the stiffening of the sediment. The perturbation method was used to analyze the initiation condition of the shear band under porosity softening and strain stiffening based on the presented mathematical model. A numerical simulation was also performed. The development of the strain, stress, and porosity was analyzed. It is shown that the parameters of the sediment change with the strain and porosity. When the parameters are satisfied under certain conditions, the shear band will initiate and develop. The critical condition is when the porosity-softening effects overcome the strain-stiffening effects. In some special cases, the critical condition may be related to other factors, such as when strain softening induces other kinds of initiation of the shear band. Full article

Probabilistic models are used to describe random processes and quantify prediction uncertainties in a principled way. Examples include geotechnical and geological investigations that seek to model subsurface hydrostratigraphic properties or mineral deposits. In mining geology, model validation efforts have generally lagged behind the development and deployment of computational models. One problem is the lack of industry guidelines for evaluating the uncertainty and predictive performance of probabilistic ore grade models. This paper aims to bridge this gap by developing a holistic approach that is autonomous, scalable and transferable across domains. The proposed model assessment targets three objectives. First, we aim to ensure that the predictions are reasonably calibrated with probabilities. Second, statistics are viewed as images to help facilitate large-scale simultaneous comparisons for multiple models across space and time, spanning multiple regions and inference periods. Third, variogram ratios are used to objectively measure the spatial fidelity of models. In this study, we examine models created by ordinary kriging and the Gaussian process in conjunction with sequential or random field simulations. The assessments are underpinned by statistics that evaluate the model’s predictive distributions relative to the ground truth. These statistics are standardised, interpretable and amenable to significance testing. The proposed methods are demonstrated using extensive data from a real copper mine in a grade estimation task and are accompanied by an open-source implementation. The experiments are designed to emphasise data diversity and convey insights, such as the increased difficulty of future-bench prediction (extrapolation) relative to in situ regression (interpolation). This work enables competing models to be evaluated consistently and the robustness and validity of probabilistic predictions to be tested, and it makes cross-study comparison possible irrespective of site conditions. Full article

Video stabilization is a critical technology for enhancing video quality by eliminating or reducing image instability caused by camera shake, thereby improving the visual viewing experience. It has deeply integrated into diverse applications—including handheld recording, UAV aerial photography, and vehicle-mounted surveillance. Propelled by advances in deep learning, data-driven stabilization methods have emerged as prominent solutions, demonstrating superior efficacy in handling jitter while achieving enhanced processing efficiency. This review systematically examines the field of video stabilization. First, this paper delineates the paradigm shift from classical to deep learning-based approaches. Subsequently, it elucidates conventional digital stabilization frameworks and their deep learning counterparts along with establishing standardized assessment metrics and benchmark datasets for comparative analysis. Finally, this review addresses critical challenges such as robustness limitations in complex motion scenarios and latency constraints in real-time processing. By integrating interdisciplinary perspectives, this work provides scholars with academically rigorous and practically relevant insights to advance video stabilization research. Full article

We present a practical numerical model for calculating transmittance and reflectance of multilayer antireflection coatings taking third-order optical nonlinearities into account. Thereby, the impact of different types of discretization of the complex refractive index profile on the predicted system performance is investigated. Additionally, aspects of parallelism of the calculations are discussed. It is shown that the inclusion of nonlinearity is essential when large laser intensities are incident to the coating. The developed method is applied for the design of different antireflective coatings matching various types of targets. Full article

This study introduces a comprehensive physical modeling framework for phototransistors based on quasi-two-dimensional transition metal dichalcogenides, with a particular emphasis on MoS₂. By integrating electromagnetic simulations of optical absorption with semiconductor transport calculations, the model captures both dark and photocurrent behaviors across diverse operating conditions. For 20 nm MoS₂ films, the model reproduces the experimental transfer characteristics with a threshold voltage accuracy better than 0.1 V and achieves quantitative agreement with photocurrent and dark current values across the full range of gate voltages, with the worst-case deviation not exceeding a factor of seven. Additionally, the model captures a three-order-of-magnitude increase in the photocurrent as the MoS₂ thickness varies from 4 nm to 40 nm, reflecting the strong thickness dependence observed experimentally. A key insight from the study is the critical role of defect states, including traps, impurities, and interfacial imperfections, in governing the dark current and photocurrent under channel pinch-off conditions (Vg < −1.0 V). The model successfully replicates the qualitative trends observed in experimental devices, highlighting how small variations in film thickness, doping levels, and contact geometries can significantly influence device performance, in agreement with published experimental data. These findings underscore the importance of precise defect characterization and optimization of material and structural parameters for 2D-material-based phototransistors. The proposed modeling framework serves as a powerful tool for the design and optimization of next-generation phototransistors, facilitating the integration of 2D materials into practical electronic and optoelectronic applications. Full article

The durability of reinforced concrete (RC) structures is strongly influenced by carbonation, a phenomenon governed by material and environmental interactions. This study applied machine learning (ML) techniques—Random Forest (RF), Support Vector Regression (SVR), and Artificial Neural Networks (ANNs)—to predict carbonation depth using a synthetic dataset of 20,000 instances generated from the validated Possan equation. Model performances were evaluated across multiple scenarios, with compressive strength and exposure time identified as the most influential features, while relative humidity and exposure conditions had intermediate effects. SVR consistently captured linear and nonlinear trends, the ANN achieved the highest R² values but showed minor overestimations, and RF exhibited lower adaptability to feature variations. The results highlight the applicability of ML models for durability assessments, particularly under complex conditions where traditional approaches are limited. Moreover, this study reinforces the strategic value of synthetic datasets in developing predictive models when experimental data collection is time-consuming or impractical. The methodologies developed here can be extended beyond carbonation modeling to other deterioration processes, supporting data-driven strategies for maintenance planning and resilience design in RC structures. Full article

Utilizing the considerable cold energy in liquefied natural gas (LNG) through the organic Rankine cycle is a highly important initiative. A multi-stage Rankine-based power generation system using LNG cold energy for waste heat utilization was proposed in this study. Moreover, a comprehensive assessment method was used to select the working fluid for this proposed system. Not only were thermodynamic and economic indicators considered, but also the environmental impact of candidate working fluids was taken into account in the evaluation process. The optimal operating points of the system were determined using non-dominated sorting genetic algorithm II and TOPSIS methods, while employing Gray Relational Analysis was applied to compute the gray relational coefficients of candidate working fluids at the optimal operating points. In addition, four weighting methods were used to calculate the final gray correlation degree of the candidate working fluids by considering the weighting influence. The stability of the calculated gray correlation degree was observed by performing a standard deviation analysis. The results indicate that R245ca was chosen as the optimal working fluid due to its superior performance based on the entropy weighting method, the independent weighting coefficient method, and the mean weighting method. Simultaneously, R245ca exhibits the best specific net power output and levelized cost of energy values of 0.283 USD/kWh and 106.9 kWh/t, respectively, among all candidate working fluids. The gray correlation degree of R1233zd(E) is 0.948, exceeding that of R245ca under the coefficient of variation method. The gray correlation degree under the mean value method is the most stable, with a standard deviation of only 0.162, while the gray correlation degree under the coefficient of variation method exhibits the greatest fluctuation, with a standard deviation of 0.17, in the stability assessment. Full article

The k-nearest- neighbor (kNN) algorithm is crucial in data mining and machine learning, yet its deployment on large-scale datasets within cloud environments presents significant security and efficiency challenges. This paper is dedicated to advancing the resolution of these challenges and presents novel contributions to the development of efficient and secure exact kNN query schemes tailored for spatial datasets in cloud-based location services. Addressing existing limitations, our approach focuses on accelerating query processing while ensuring robust privacy preservation and public verifiability. Key contributions include the establishment of a formal framework underpinned by stringent security definitions, providing a solid groundwork for future advancements. Leveraging Paillier’s homomorphic cryptosystem and public-key signature techniques, our design achieves heightened security by safeguarding databases, query access patterns, and result integrity while enabling public verification. Additionally, our scheme enhances computational efficiency through optimized data-packing techniques and simplified Voronoi diagram-based ciphertext index construction, leading to substantial savings in computational and communication overheads. Rigorous and transparent theoretical analysis substantiates the correctness, security, and efficiency of our design, while comprehensive experimental evaluations confirm the effectiveness of our approach, showcasing its practical applicability and scalability across datasets of varying scales. Full article

Decision-making in complex environments, especially sustainable ones, requires flexible methodologies to handle multiple criteria and stakeholder perspectives. This study introduces the SAPEVO-H² method (Simple Aggregation of Preferences Expressed by Ordinal Vectors—Hybrid and Hierarchical), an extensive model from the SAPEVO family, which offers multi-criteria analysis through a hierarchical structure of variables evaluated by groups partitioned into levels concerning their respective responsibilities. The proposal allows flexible analysis, considering inputs through ordinal and cardinal information. The validation of the methodology is demonstrated through a case study involving an automobile manufacturing company, which focuses on prioritizing sustainability projects based on multiple objectives aimed at minimizing polluting gas emissions. Within a hierarchical structure of five levels, the individual level results are presented. In addition, a sensitivity analysis is applied, exposing the most sensitive variables to changes concerning the highest levels. Then, we discuss the main contributions and limitations concerning the mathematical proposal and the conclusions and proposals for future work. Full article

This study presents an advanced model of thermal Resistances and heat Capacities model approach (RC model), applied to a custom-built skin calorimeter for the in vivo characterization of localized thermal behavior of the skin. The device integrates a heat flux sensor and a programmable thermostat, and is capable of measuring the heat flux, heat capacity, internal thermal resistance, and subcutaneous temperature of the skin, under both resting and exercising conditions. The model, refined through extensive experimental validation, incorporates the skin as part of the system and is adapted to three modes of operation: calibration base, ambient air, and direct skin contact. Simulations are used to analyze heat flux dynamics, optimize control parameters, and validate analytical expressions. Under resting conditions, the model enables the estimation of the skin’s heat capacity and thermal resistance. During exercise, it allows the determination of heat flux and internal temperature variations using simplified expressions. The system demonstrates high sensitivity (195.5 mV/W) and provides a robust, non-invasive method for extracting medically relevant thermal parameters from a 2 × 2 cm² skin area. Full article