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Modelling

Modelling is an international, peer-reviewed, open access journal on theory and applications of modelling and simulation in engineering science, published quarterly online by MDPI.

Quartile Ranking JCR - Q2 (Engineering, Multidisciplinary)

All Articles (397)

Growing Top-Down or Bottom-Up Vortices: Effect of Thermal Gradients

  • María Cruz Navarro,
  • Damián Castaño and
  • Henar Herrero

In this study, we numerically investigate the influence of thermal gradients on the growth and intensification of vortices formed within a rotating cylinder subjected to inhomogeneous cooling at the top or inhomogeneous heating at the bottom. The presence of horizontal thermal inhomogeneities at the upper and lower boundaries determines whether the vortex originates near the top or the bottom of the domain. Moreover, the magnitude of both horizontal and vertical thermal gradients plays a critical role in the vortex’s intensification, vertical stretching, and overall development. The observed phenomena are interpreted through a force balance analysis. Increasing the ambient rotation rate leads to the emergence of periodic structures, such as tilted or double vortices, which also undergo intensification and stretching as thermal gradients increase. These findings highlight the importance of thermal boundary conditions in shaping vortical structures and may contribute to a deeper understanding of the genesis, morphology, and intensification mechanisms of thermoconvective vortices.

16 December 2025

Physical setup considered for each configuration. (a) A thermal inhomogeneity is set at the bottom. (b) A thermal inhomogeneity is set at the top.

Graph learning is well suited to modeling relationships among communicating entities in network intrusion detection. However, the resulting models are frequently difficult to interpret, in contrast to many classical approaches that offer more transparent reasoning. This work integrates SHapley Additive exPlanations with temporal, edge-aware GNN based on GraphSAGE architecture to deliver an explainable, inductive intrusion detection model for NetFlow data named TE-G-SAGE. Using the NF-UNSW-NB15-v3 dataset, flow data are transformed into temporal communication graphs where flows are directed edges and endpoints are nodes. The model learns relational patterns across two-hop neighborhoods and achieves strong recall under chronological evaluation, outperforming a GCN baseline and recovering more attacks than a tuned XGBoost model. SHAP is adapted to graph inputs through a feature attribution on the two-hop computational subgraph, producing global and local explanations that align with analyst reasoning. The resulting attributions identify key discriminative features while revealing shared indicators that explain cross-class confusion. The research shows that temporal validation, inductive graph modeling, and Shapley-based attribution can be combined into a transparent, reproducible intrusion detection framework suited for operational use.

12 December 2025

Architecture for the design of an explainer IDS [23].

Eye tracking scanpaths encode the temporal sequence and spatial distribution of eye movements, offering insights into visual attention and aesthetic perception. However, analysing scanpaths still requires substantial manual effort and specialised expertise, which limits scalability and constrains objectivity of eye tracking methods. This paper examines whether and how multimodal large language models (MLLMs) can provide objective, expert-level scanpath interpretations. We used GPT-4o as a case study to develop eye tracking scanpath analysis (ETSA) approach which integrates (1) structural information extraction to parse scanpath events, (2) knowledge base of visual-behaviour expertise, and (3) least-to-most and few-shot chain-of-thought prompt engineering to guide reasoning. We conducted two studies to evaluate the reliability and effectiveness of the approach, as well as an ablation analysis to quantify the contribution of the knowledge base and a cross-model evaluation to assess generalisability across different MLLMs. The results of repeated-measures experiment show high semantic similarity of 0.884, moderate feature-level agreement with expert scanpath interpretations (F1 = 0.476) and no significant differences from expert annotations based on the exact McNemar test (p = 0.545). Together with the ablation and cross-model findings, this study contributes a generalisable and reliable pipeline for MLLM-based scanpath interpretation, supporting efficient analysis of complex eye tracking data.

10 December 2025

Example of (a) an original image and (b) the corresponding eye tracking scanpath, with numbered circles indicate fixation order.
  • Communication
  • Open Access

Titanium alloys such as Ti-6Al-4V are widely used in aerospace and biomedical fields, but their poor wear resistance and high friction coefficient limit service performance. In this study, laser cladding with La2O3 addition was employed to enhance the surface properties of Ti-6Al-4V, and the underlying mechanisms were systematically investigated by combining experimental characterization with multiphysics simulations. XRD and SEM analyses revealed that La2O3 addition refined grains and promoted uniform phase distribution throughout the coating thickness, leading to good metallurgical bonding. The hardness was 2–3 times higher than that of the titanium alloy substrate when the content of 2–3 wt.% was of added La2O3, while the wear loss ratio was reduced to 0.021% and the average friction coefficient decreased to 0.421. These improvements were strongly supported by simulations: temperature field calculations demonstrated steep thermal gradients conducive to rapid solidification; velocity field analysis and recoil-pressure-driven flow revealed vigorous melt pool convection, which homogenized solute distribution and enhanced coating densification; phase evolution simulations confirmed the role of La2O3 in heterogeneous nucleation and dispersion strengthening. In summary, the combined results establish a mechanistic framework where thermal cycling, melt pool dynamics, and La2O3-induced nucleation act synergistically to optimize coating microstructure, hardness, and wear resistance. This integrated experimental–numerical approach provides not only quantitative improvements but also a generalizable strategy for tailoring surface performance in laser-based manufacturing.

8 December 2025

Domain configuration and fixed heat source location. The red dashed line represents the laser spot.

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New Technological Solutions, Research Methods, Simulation and Analytical Models That Support the Development of Modern Transport Systems
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New Technological Solutions, Research Methods, Simulation and Analytical Models That Support the Development of Modern Transport Systems

Editors: Tomasz Nowakowski, Artur Kierzkowski, Agnieszka A. Tubis, Franciszek Restel, Tomasz Kisiel, Anna Jodejko-Pietruczuk, Mateusz Zaja̧c

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Modelling - ISSN 2673-3951