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Mathematical Modelling for Sustainable Engineering
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Mathematical Modelling for Sustainable Engineering (MMSE)
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ISSN (print): 3104-9885
ISSN (online): 3104-9877
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2025: Vol. 1
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Mathematical Modelling for Sustainable Engineering (MMSE) focuses on the pivotal role of mathematical modelling in advancing sustainability across the engineering spectrum. Unlike traditional journals that emphasize theoretical work or narrow technical scopes, MMSE highlights the real-world application of models in achieving sustainable goals such as resource optimization, carbon reduction, system resilience, and environmental performance. The journal encourages interdisciplinary collaboration and broadly covers diverse engineering domains, including but not limited to energy, environment, manufacturing, and transportation. MMSE aims to support global sustainability efforts through model-driven innovation and decision-making. Published quarterly by Acadlore, the journal releases issues in March, June, September, and December each year.

  • Professional Service - Every article submitted undergoes an intensive yet swift peer review and editing process, adhering to the highest publication standards.

  • Prompt Publication - Thanks to our expertise in orchestrating the peer-review, editing, and production processes, all accepted articles are published rapidly.

  • Open Access - Every published article is instantly accessible to a global readership, allowing for uninhibited sharing across various platforms at any time.

Editor(s)-in-chief(1)
mehmet yavuz
Department of Mathematics and Computer Sciences, Necmettin Erbakan University, Turkey
mehmetyavuz@erbakan.edu.tr | website
Research interests: Fractional Calculus and Applications; Optimal Control; Adaptive and Robust Control; Chaos and Bifurcation Analysis; Dynamical Systems; Biological Models; Financial Mathematics and Numerical Methods

Aims & Scope

Aims

Mathematical Modelling for Sustainable Engineering (MMSE) is a forward-looking international journal that places sustainability at the core of engineering innovation. It aims to become a premier platform for the application of advanced mathematical modelling techniques in addressing critical challenges related to sustainability across all engineering disciplines. From infrastructure and manufacturing to energy, transportation, environment, and beyond, MMSE fosters cross-disciplinary solutions that are grounded in mathematical rigor and practical relevance.

The mission of MMSE is to promote research that uses mathematical, numerical, or computational models to support sustainable development goals (SDGs), drive carbon neutrality, optimize resource use, and enhance system resilience. The journal invites cutting-edge contributions that bridge theory and real-world applications, offering transformative insights into sustainable engineering design, operation, and decision-making.

MMSE differentiates itself through its comprehensive coverage of engineering sectors, its interdisciplinary vision, and its emphasis on modelling as a vehicle for environmental and societal impact.

Features that set MMSE apart include:

  • Every publication benefits from prominent indexing, ensuring widespread recognition.

  • A distinguished editorial team upholds unparalleled quality and broad appeal.

  • Seamless online discoverability of each article maximizes its global reach.

  • An author-centric and transparent publication process enhances the submission experience.

Scope

MMSE's scope is broad and interdisciplinary, covering a wide array of topics including, but not limited to:

Mathematical Modelling for Sustainable Engineering Systems:

  • Multi-scale modelling and simulation of complex engineering systems

  • Resilience modelling for infrastructure systems under climate change

  • Low-carbon, net-zero energy systems and decarbonization pathways

  • Integrated modelling for water, energy, and environmental systems

  • Mathematical approaches for circular economy and resource reuse

Mathematical and Computational Methodologies:

  • Advanced differential equations, fractional calculus, and dynamical systems

  • Multi-objective, stochastic, and robust optimization methods

  • Data-driven and physics-informed hybrid modelling frameworks

  • Machine learning, neural networks, and AI for sustainable applications

  • Probabilistic modelling, uncertainty quantification, and risk analysis

Sustainable Sector Applications:

  • Green building design and energy-efficient construction modelling

  • Sustainable manufacturing, lean processes, and supply chain modelling

  • Smart transportation systems, logistics, and mobility modelling

  • Modelling in resource-intensive sectors: mining, oil & gas, agriculture

  • Aerospace, maritime, and defense sustainability modelling

Environmental and Social Modelling:

  • Carbon footprint modelling and lifecycle assessment (LCA)

  • Air and water pollution modelling, remediation and resource recovery

  • Socio-economic system dynamics, sustainability policy modelling

  • ESG metrics integration into engineering models

  • Modelling for environmental justice and community resilience

Implementation, Case Studies, and Applications:

  • Field-tested mathematical models with sustainability impacts

  • Integration into digital twin environments and real-time systems

  • Case studies on engineering interventions and performance tracking

  • Benchmarking sustainability metrics through modelling

  • Cross-disciplinary implementations of sustainable engineering frameworks

MMSE welcomes contributions that transform mathematical insights into tangible advances for sustainable engineering systems and encourages collaborative research at the intersection of modelling, computation, and sustainability science.

Articles
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The application of fiber-reinforced polymer (FRP) for shear strengthening of concrete structures has become increasingly popular. However, the inherent scatter in shear test makes accurate prediction of the shear capacity a significant challenge, as traditional design code often struggle to capture the complex nonlinear interactions among multiple factors. To address this limitation, this study introduces a machine learning (ML) approach to develop a high-accuracy predictive model. A database comprising 552 experimental tests on FRP-strengthened concrete beams in shear was assembled. Three ensemble learning algorithms—Random Forest (RF), Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost)—were systematically compared and evaluated against predictions from three existing design codes: ACI 440.2-23, FIB Bulletin 14, and GB 50608-2020. Results indicate that all ML models significantly outperform the existing code-based calculations. Among them, the XGBoost model demonstrated the best performance, achieving a coefficient of determination ($\mathrm{R}^2$) of 0.94 and a mean absolute percentage error (MAPE) as low as 12.81% on the test set. Interpretability analysis based on shapely additive explanations (SHAP) values further identified and elucidated the physical significance of key influencing features, such as FRP bonded height ($h_f$), beam width ($b$), and stirrup reinforcement ratio ($\rho_{s v}$), and elucidated their physical significance on the shear capacity. This study confirms the superiority and engineering application potential of data-driven approaches for predicting the shear performance of FRP-strengthened members. Moreover, high-accuracy capacity prediction enables more economical and environmentally friendly strengthening designs. This contributes to reducing material overuse, lowering construction energy consumption and carbon emissions, thereby supporting the sustainability goals of structural engineering.

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Reservoir drawdown is a critical loading condition that alters seepage and stress distributions in earth dams, potentially inducing instability and excessive deformation. Understanding the coupled hydraulic-mechanical response during drawdown is therefore essential for ensuring long-term dam safety and performance. The stability and deformation response of earth dams during reservoir drawdown were systematically investigated, with particular emphasis placed on the coupled effects of drawdown rate, core geometry, core permeability, core strength, and shell strength. Two-dimensional finite element analyses were performed using PLAXIS 2D to evaluate the factor of safety against instability and the associated crest settlement under a range of representative conditions. The numerical results indicate that an increase in the reservoir drawdown rate leads to a noticeable increase in the factor of safety against horizontal instability, whereas the corresponding influence on crest settlement is negligible. Variations in core geometry were found to exert a pronounced effect on dam performance: an increase in undrained core width results in larger crest settlement while simultaneously reducing the factor of safety. In contrast, higher core permeability slightly improves the factor of safety, although its influence on crest settlement remains marginal. The mechanical properties of dam materials were shown to play a dominant role in both stability and deformation behavior. In particular, increases in core and shell strength parameters significantly enhance the factor of safety while substantially reducing crest settlement. These results provide valuable insight for the design, assessment, and risk-informed management of earth dams subjected to rapid or controlled reservoir drawdown conditions.

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Tower crane structural systems are widely used in large-scale construction projects, where foundation performance is critical to structural safety under ultimate loading conditions. In addition to satisfying ultimate bearing capacity, serviceability requirements—particularly total and differential settlements—must be rigorously addressed in foundation design. In this study, the performance of a tower crane foundation subjected to ultimate loads was evaluated using an integrated approach combining field testing, in situ monitoring, and finite element analysis. A tower crane foundation constructed for an industrial project was examined as a representative case. The subsurface profile comprised an uncontrolled fill layer overlying medium-dense sand, very stiff clay, and hard clay. Due to the high uncertainty associated with the fill material, plate load tests were conducted to characterize its deformation behavior. The test results were subsequently used in a back analysis with PLAXIS 2D to determine representative deformation parameters. The analysis indicated that the foundation dimensions recommended in the manufacturer’s technical catalog were inadequate when settlement criteria were explicitly considered. Consequently, revised foundation dimensions of 8 m × 8 m were proposed. Finite element simulations were performed to evaluate the deformation response of the redesigned foundation under ultimate loading conditions. Field settlement measurements obtained at two monitoring points during operation exhibited close agreement with the numerical predictions. The study underscores the importance of integrating experimentally calibrated numerical analysis and field monitoring in the safety assessment of tower crane foundation systems, particularly for foundations resting on heterogeneous or uncontrolled soil deposits.

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The long-term performance and safety of high-speed railway infrastructure are strongly governed by the dynamic interaction between trains and the rail–track system, particularly in the presence of structural irregularities. In this study, the influence of rail and sleeper irregularities on train-induced vertical ballast settlement was systematically investigated using advanced three-dimensional finite element simulations implemented in PLAXIS 3D. Nine representative track configurations were established, encompassing ideal conditions as well as isolated and combined rail and sleeper irregularities. Dynamic train loading was simulated at operating speeds of 100, 200, and 300 km/h, while nonlinear constitutive behavior of ballast and substructure materials, together with realistic contact interactions between track components, was explicitly considered. The numerical results indicate that even minor geometric or support irregularities significantly disrupt load transfer mechanisms, leading to localized stress concentrations and accelerated ballast settlement. With increasing train speed, the sensitivity of the rail–track system to such irregularities was markedly amplified, resulting in pronounced dynamic displacements. Track configurations involving concurrent rail and sleeper irregularities exhibited the most severe settlement responses. These findings demonstrate that ballast degradation is governed not only by train speed but also by the interaction and superposition of track irregularities, which can substantially shorten maintenance cycles if left unaddressed. The study underscores the critical importance of early defect identification, preventive maintenance strategies, and high-fidelity numerical modeling in enhancing the resilience, serviceability, and long-term reliability of modern high-speed railway networks.

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Efficient management of airflow and heat dissipation in data centers is becoming increasingly critical as computing densities increase and thermal loads grow. To address these challenges, this study numerically examines the thermo-fluid behavior of a medium-sized data center containing twelve heat-generating server racks under multiple ventilation strategies. A three-dimensional CFD model was developed using the RANS equations with the SST $k$–$\omega$ turbulence formulation and the Boussinesq approximation to account for buoyancy-driven flow. Eight ventilated configurations were evaluated by combining two louver orientations (20$^{\circ}$ and 50$^{\circ}$), two inlet heights (top or bottom), and two inlet velocity modes (constant or pulsatile), in addition to a no-ventilation control scenario. Both steady and transient simulations were performed to capture the interactions between inlet momentum, recirculation patterns, and thermal stratification over a one-hour operational period. The control case exhibited strong thermal stratification and a stable hot layer beneath the ceiling, demonstrating the inadequacy of natural convection alone. Introducing ventilation significantly modified the airflow topology and improved cooling performance, though with considerable sensitivity to inlet design. Shallower-angle louvers (20$^{\circ}$) enhanced horizontal jet penetration and reduced recirculation pockets, whereas steeper louvers (50$^{\circ}$) generated stronger impingement and more localized hot spots. Inlet height further shaped vertical temperature distribution: bottom inlets effectively cooled lower and mid-rack levels, while top inlets reduced ceiling-layer temperatures by disrupting buoyant plumes. Pulsatile ventilation outperformed constant inflow by periodically increasing momentum, enhancing mixing, and weakening plume formation during peak phases. Mass-flow analysis similarly showed that extraction capacity strongly correlated with inlet velocity amplitude. Overall, the results highlight the importance of coordinated selection of inlet position, louver angle, and temporal forcing. The combined use of shallow-angle louvers and pulsatile ventilation presents a promising pathway for improving cooling uniformity and thermal management in high-density data centers.

Open Access
Research article
Hotspots in Photovoltaic Arrays Based on Multipoint Parabolic Motion
zhikai dai ,
gong chen ,
zhiqi chen ,
chang lu ,
yao zheng ,
xinyi wang ,
jinqiu wang ,
rui min ,
xinyang wu ,
wei wei ,
zhengpeng yang ,
deyi li ,
huachao zhang ,
ziyu yang ,
yeshuai shao
|
Available online: 09-14-2025

Abstract

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With the rapid development of solar power generation technology, the hotspot effect of photovoltaic (PV) arrays poses a key challenge to the efficiency and stability of the system. Conventional PV array models have significant limitations in dealing with complex shadow shading and multi-peak output characteristics, especially when confronted with complex topologies such as the complex-total-cross-tied (CTCT) structures. To address this issue, this paper proposed a mathematical model for PV arrays based on multipoint parabolic motion, which could accurately simulate the output characteristics of PV arrays under localized shading conditions. The model decomposed the current-voltage ($I-V$) characteristic curve of the PV arrays into multiple parabolic trajectories. A shadow shading model for complex structures was successfully constructed by combining with a kinematic model. MATLAB/Simulink simulations and experimental validation showed that the proposed model guaranteed computational accuracy with error less than 5%, while computational efficiency was greatly improved. The proposed model could accurately capture the multi-peak characteristics when compared with the traditional engineering model. Results from the experiment further verified the robustness of the model in dynamic shading scenarios, hence providing an efficient and reliable tool for maximum power tracking and hotspot localization in the PV system.

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The new generation composite materials are widely used in Engineering due to their light weight, high strength, and resistance to corrosion and wear. Two main modeling strategies, the piecewise layered approach and the continuously graded approach were employed in the literature, with the latter offering a more realistic representation. Recent studies have highlighted the importance of analyzing the stability and vibration behavior of exponentially graded cylindrical shells, particularly when embedded in elastic media. Nevertheless, most works were limited to simply supporting boundary conditions and so neglected the foundation effects. To fill this notable gap in the literature, the present study focused on the buckling behavior of exponentially graded cylindrical shells (EGCSs) with clamped edges under external pressure within an elastic medium. A theoretical framework was then established for future design applications in advanced Engineering fields.

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This study investigated the static bending behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) microbeams supported on an elastic foundation. The proposed model was formulated by coupling higher-order shear deformation beam theories (HoSDBTs) with the modified couple stress theory (MCST). Four distinct CNT distribution patterns within the polymer matrix were considered. Using Hamilton’s principle, governing equations and boundary conditions for simply-supported microbeams were derived and solved analytically. This comprehensive parametric study explored the effects of the material length scale, CNT volume fraction, aspect ratio, foundation stiffness (Winkler and Pasternak models), and CNT gradation on bending stiffness. Results revealed that all parameters notably influenced the mechanical response, with key roles played by size-dependent effects and elastic foundation interactions. The proposed MCST-enhanced HoSDBT model effectively captures size-dependent behaviors, rendering it suitable for the design and optimization of FG-CNTRC micro-devices.
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