Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 3.0% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions for multi-dimensional vectorial lattice Boltzmann schemes tackling systems of hyperbolic conservation laws. In the scalar case, we prove convergence for schemes with monotone relaxation to the weak entropy solution by Bardos, Leroux, and Nédelec [Comm. Partial Differential Equations 4 (1979), pp. 1017–1034], following the path by Crandall and Majda [Math. Comp. 34, (1980), pp. 1–21]. Numerical experiments are conducted both for scalar and vectorial problems, and demonstrate the effectiveness of equilibrium boundary conditions in capturing significant physical phenomena.
Vegetated coastal ecosystems such as seagrass meadows are increasingly recognized as key contributors to climate regulation. Acting as blue carbon sinks, they exhibit carbon burial rates up to 30–50 times higher than those of terrestrial forest soils, thereby storing large amounts of organic carbon in their sediments. However, these benefits may be partly offset by the release of greenhouse gases (GHG), particularly methane (CH₄) and nitrous oxide (N₂O), which possess a much higher global warming potential than CO₂. Comparing seagrass meadows to bare sediments helps identify their specific role as blue carbon ecosystems. In this study, we assessed carbon accumulation rates (CAR) together with in situ fluxes of CH₄ and N₂O in Zostera noltii seagrass meadows and adjacent bare sediments within Arcachon Bay, France, which hosts Europe’s largest Z. noltii meadows. Our results demonstrate that seagrass areas exhibit CAR values that are 2.5 times higher, highlighting their superior carbon burial capacity. However, GHG emissions from seagrass meadows were 3.5 times higher than those from bare sediments, offsetting 28.7 ± 0.3 This graphical abstract provides a concise and visually engaging summary of the study assessing the net climate benefits of seagrass meadows in Arcachon Bay, France. The comparison between seagrass meadows with adjacent bare sediments at seven study sites with six replicates for each sediment type, highlighting the dual processes of carbon burial and greenhouse gas (GHG) fluxes (CH₄ and N₂O). Downward green arrows represent the burial of organic carbon in sediments, while upward red arrows illustrate gaseous emissions to the atmosphere. The balance between these opposing fluxes is central to understanding the overall climate impact of coastal ecosystems. The bar plots emphasizes that, although seagrass meadows bury carbon at rates 2.5 times higher than bare sediments, they also release 3.5 times more GHG, offsetting part of their climate benefit. Importantly, the net climate contribution of seagrass meadows remains 2.2 times greater than that of bare sediments. By distilling the study into a clear and intuitive image, this graphical abstract provides readers with a rapid understanding of the research without reading the full manuscript. It underscores the importance of integrating both carbon burial and GHG fluxes into blue carbon assessments and highlights the value of conserving and restoring seagrass meadows to mitigate climate change, providing actionable insights for their restoration and management. Quantification of blue carbon components: carbon burial and greenhouse gas (CH₄, N₂O) fluxes in seagrass meadows. Direct comparison between seagrass meadows (Zostera noltii) and bare sediments. Seagrass meadows bury 2.5 times more organic carbon but emit 3.5 times more GHG than bare sediments. Net climate benefit in seagrass meadows remains 2.2 times higher than in bare sediments. Strong spatial variability in carbon balances driven by hydrodynamic conditions. Findings provide actionable insights for targeted restoration and coastal ecosystem management.
We study classes of graphs with bounded clique-width that are well-quasi-ordered by the induced subgraph relation, in the presence of labels on the vertices. We prove that, given a finite presentation of a class of graphs, one can decide whether the class is labelled-well-quasi-ordered. This solves an open problem raised by Daligault, Rao and Thomassé in 2010, and answers positively to two conjectures of Pouzet in the restricted case of bounded clique-width classes. Namely, we prove that being labelled-well-quasi-ordered by a set of size 2 or by a well-quasi-ordered infinite set are equivalent conditions, and that in such cases, one can freely assume that the graphs are equipped with a total ordering on their vertices. Finally, we provide a structural characterization of those classes as those that are of bounded clique-width and do not existentially transduce the class of all finite paths.
Polymer based microfluidics, using polydimethylsiloxane (PDMS), are highly adaptable platforms for electrochemical studies commonly used for numerous applications. Deformations of these PDMS devices due to the flow pressure drop in microchannels have been widely documented in literature but cannot be prevented in all applications even though it is critical to measure quantitative data. In this work, we show that in electrochemical microfluidic devices used in energy conversion systems, the velocity profiles and channel deformations can be quantitatively measured based on spectro-electrochemistry and numerical simulations of Hagen-Poiseuille flows. PDMS deformations are found amplified in the case of large channel aspect ratios (i.e. close to 100), with deformation Delta h/h(0)>100% at 50 kPa, and start to be non-negligible >10% for channel internal pressure above 5 kPa. Finally, by considering these channel deformations in the Beer-Lambert law, we show that accurate absorbance and concentration measurements can be obtained using visible spectroscopy regardless the channel internal pressure.
