麦吉尔大学

In this paper, we present a general framework for constructively proving the existence of stationary localized solutions, spatially periodic solutions, and branches of spatially periodic solutions in the 1D Thomas model. Specifically, we develop the necessary analysis to compute explicit upper bounds required in a Newton–Kantorovich approach. Given an approximate solution ū, this approach relies on establishing that a well-chosen fixed point map is contracting on a neighborhood ū. For this matter, we construct an approximate inverse of the linearization around ū, and establish sufficient conditions under which the contraction is achieved. This provides a framework for which computer-assisted analysis can be applied to verify the existence and local uniqueness of solutions in a vicinity of ū, and control the linearization around ū. Furthermore, as the Thomas model has a non-polynomial nonlinearity, we will need to use different techniques to handle it during our analysis. Our contributions are to provide a partial answer to how one can approach rigorously verifying results in the Thomas model, to adapt and combine previously developed techniques to apply to the Thomas model, and to perform the computer-assisted analysis to obtain such results. The code to perform the rigorous proofs is available on Github at Blanco (2026).

This study interrogates patterns of interaction through which corporate actors influence environmental knowledge production. I ask 1) How intensive are relationships between corporate actors and knowledge-producing organizations? 2) What types of knowledge-producing organizations are subject to most engagement by corporate actors? and 3) How do these patterns evolve over time? I answer these questions with the landmark case of lead in the United States (1924–2003). I rely on longitudinal network data built from the raw text of Toxic Docs, a database that comprises millions of previously classified corporate documents over eight decades. Using relational event modeling, I find that corporate engagement with scientific organizations is consistently more likely than with other types of actors. In contrast, corporate engagement with regulatory expert organizations is less so. I also find that corporate engagement with scientific organizations is responsive to growing federal interest in the lead problem and anticipates regulatory developments. This suggests that corporate engagement with scientists is best described not simply as reactive but also as preemptive.

The injection of carbon dioxide into depleted oil and gas reservoirs has emerged as a promising method for enhanced oil recovery (EOR) and safe carbon storage. This process significantly influences the density of CO2-hydrocarbon mixtures, a critical property that directly affects EOR efficiency and storage integrity. However, accurately predicting mixture density remains challenging due to the complex and nonlinear behavior of hydrocarbons, and many existing empirical models show limited reliability under varying conditions. This study primarily aims to develop robust tools leveraging advanced algorithms, Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Bayesian Neural Network (BNN), Adaptive Boosting (AdaBoost), and Random Forest (RF) to accurately estimate the density of CO2-hydrocarbon mixtures, utilizing a rich and extensive databank (17,081). The model inputs included temperature (T), pressure (P), molecular weight (Mw), pseudo-critical temperature (Tpc), pseudo-critical pressure (Ppc), and the mole fraction of CO2. The results were evaluated against several equations of state (EoSs), including the Cubic-Plus-Association (CPA) model developed in this study, as well as Peng-Robinson (PR), Soave-Redlich-Kwong (SRK), and Redlich-Kwong (RK) models for representative CO2-hydrocarbon mixtures (n-Butane, Propane, and Hexadecane). For these specific mixtures, the CPA and PR models showed the best performance among the examined EoSs, while the XGBoost model achieved the highest overall accuracy, with an R2 of 0.9968 and an average absolute percent relative error (AAPRE) of 0.7647. High R2 values (0.97-0.99) indicate that LightGBM, BNN, AdaBoost, and RF all achieved strong predictive performance. Furthermore, trend analysis confirmed that the XGBoost model can accurately capture density variations in response to changes in pressure variable. Moreover sensitivity analysis indicated that pressure with relevancy factor of (0.2045) has the most significant effect on the output. The leverage technique showed that over 96% of the dataset is statistically reliable. In the final stage, Shapley additive explanations (SHAP) analysis demonstrated that both Tpc and Ppcpositively influence the output parameter. These results demonstrate that the XGBoost model provides a reliable and accurate alternative to experimental methods for predicting CO2-hydrocarbon density across a wide range of operating conditions.

The Cantor alloy (CoCrFeNiMn) has attracted increasing research interest in coating applications due to its unique deformation response. Most existing studies have focused on thick coatings (millimeter scale), leaving the mechanical and tribological mechanisms less understood when scaled down to the thin-film dimensions (nano- to micrometer). Therefore, in this study, two Cantor thin films were deposited by magnetron sputtering at ambient (HEF-50) and elevated temperatures (HEF-350). Both films exhibit a dual-phase (FCC+HCP) structure due to strain-induced phase transformation during sputtering; in particular, ultrathin nanotwins are found in HEF-350 as a result of elevated thermal effect. For evaluating the mechanical and tribological mechanisms of two thin films, nanoindentation and microscale reciprocating sliding wear tests were employed. The HEF-350 shows a higher nanohardness of ∼8.4 GPa and better wear resistance with a reduction in wear rate. Schiffmann’s friction model reveals that the HEF-350 undergoes elastic-dominated wear as opposed to plastic-dominated wear in HEF-50, indicating less material removal and a smaller permanent deformation zone in the subsurface of HEF-350. This can be explained by the nanotwins observed in HEF-350, which contribute to plastic deformation accommodation. The subsequent formation of a relatively continuous tribofilm on HEF-350 further reduces the wear. Through correlating the as-deposited microstructural features, subsurface deformation mechanisms, and tribological responses, this work provides referable insights into the design and development of wear-resistant high-entropy thin films.

This study presents a coupled modelling approach that integrates soil deformation prediction and bulldozing force estimation during continuous soil cutting. Two soil mass transfer models are developed: a semi-empirical model and a neural network trained on Discrete Element Method (DEM) simulation data. The semi-empirical model provides a physically interpretable formulation in which soil mass transfer depends solely on cutting depth and bulldozing distance. In contrast, the neural network captures complex deformation behaviours by incorporating five input features. Based on the predicted mass transfer, soil deformation at different locations can be estimated. The semi-empirical model is applicable to both cohesive and noncohesive soils, whereas the current neural network is limited to noncohesive soils as an initial test. The influence of several factors on soil mass transfer is thoroughly investigated, including cohesion, bulldozing velocity, internal friction, and others. A coupling method is proposed that integrates the soil mass-transfer prediction models with a semi-empirical bulldozing-force model. Validation against DEM simulation results shows that both proposed models accurately predict soil mass transfer and surface deformation. The coupling framework also provides accurate and consistent predictions of bulldozing force across a wide range of cutting conditions and varying gravity levels.