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 u, this approach relies on establishing that a well-chosen fixed point map is contracting on a neighborhood u. For this matter, we construct an approximate inverse of the linearization around u, 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 u, and control the linearization around u. 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 selective separation of chalcopyrite and molybdenite presents a critical challenge in copper-molybdenum ores. Conventional inorganic depressants such as sodium hydrosulfide (NaHS), sodium sulfide (Na2S), and Nokes reagent (P2S5 + NaOH) are effective but highly toxic, corrosive, and environmentally hazardous. Their instability and tendency to release hydrogen sulfide gas cause serious operational and safety issues. Consequently, there is increasing interest in developing organic depressants that are safer, more stable, and capable of achieving comparable or superior selectivity in Cu–Mo separation. This study investigates the application of disodium carboxymethyl trithiocarbonate (Orfom D8) in selectively depressing chalcopyrite in chalcopyrite–molybdenite flotation. Microflotation experiments were conducted to evaluate the depressant’s selectivity. The interaction mechanisms between Orfom D8 and the mineral surfaces were investigated using zeta potential measurements, Fourier-transform infrared spectroscopy (FTIR), and X-ray photoelectron spectroscopy (XPS).

Unlike gaseous fuels, which are fully characterized by chemical composition, metal fuels also vary in particle size. This paper investigates the effect of particle size on laminar flame propagation in iron particle suspensions with oxygen-argon and oxygen-helium carrier gases. Using a McGill Bunsen-type metal-fuel burner, pure iron flames are stabilized across a broad range of fuel concentrations. Particle size significantly influences the laminar burning velocity, flame temperature, and their sensitivity to fuel concentration. Evidence consistent with a transition from a diffusion-limited to a predominantly kinetically controlled combustion regime is observed as the mean particle size decreases. This transition is hypothesized to be governed by the diffusion resistance across a molten FeO surface layer, leading to arrested ignition in fine particles.

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.