Electrochemical cells serve as a building block for producing and storing electrical energy from chemical reactions. The analysis of ion transport in these systems forms the foundation for understanding more complex electrochemical systems that are becoming increasingly present in the broader societal energy infrastructure. From a pedagogical perspective, the “balance sheets” introduced in Chapter 4 of Electrochemical Methods: Fundamentals and Applications by Alan J. Bard, Larry R. Faulkner and Henry S. White (hereafter referred to as BFW) provides a first-pass approach to analyze ion transport in electrochemical cells. However, the balance sheet approach lacks first-principles justifications from the underlying equations that describe the transport processes in electrochemical cells. In this work, we compare a first-principles approach via the Poisson-Nernst-Planck equations to describe ion transport in electrochemical cells to that of the balance sheet approach. By re-working the examples presented in BFW, we illustrate that the balance sheet approach is only theoretically valid in limited scenarios. Furthermore, we show that the PNP equations provide a more physically founded route to analyze ion transport in electrochemical systems. We hope the approach outlined here will be adopted by electrochemical engineering researchers and instructors with an emphasis on improving pedagogical practices within the field.
This paper proposes a residual learning framework that bridges the gap between DC and AC Optimal Power Flow (OPF) formulations. While DC-OPF provides a tractable and simplified linear approximation, it neglects nonlinear AC effects such as voltage magnitude, reactive power, and losses, resulting in infeasible operating points. To overcome this limitation, we introduce a topology-aware local-attention Graph Neural Network that learns the residual corrections required to map DC-OPF solutions to their AC-feasible counterparts. The framework integrates DC features at both the local and global levels and employs a physics-aware loss function enforcing AC power-flow feasibility and operational limits. Using the OPFData benchmark across the IEEE 57, 118, and GOC 2000-bus systems, the proposed model achieves up to 25% reduction in MSE, 3 & times; improvement in AC-feasibility distance, and order-of-magnitude runtime gains compared to AC-OPF solvers, while maintaining robustness under N-1 contingencies. The results highlight residual learning as an effective paradigm for accelerating AC-feasible optimal power flow computation and enabling near real time operational decision making.
This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and an inhibitor. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime hotspots in urban areas to shifts in public attitudes during critical events as individuals and control units move through space. We prove local and global existence of solutions under realistic assumptions and showcase the model through scenarios of protest intensity driven by demonstrators joining and mitigated by two different control managements. Numerical simulations highlight the resulting complex spatial patterns and temporal dynamics.
Distribution System State Estimation (DSSE) plays an increasingly-important role in modern power grids due to the integration of distributed energy resources (DERs). The inherent characteristics of distribution systems make classical estimation methods struggle, and recent advancements in data-driven learning methods, although promising, exhibit systematic failure in generalization and scalability that limits their applicability. In this work, we propose MambaDSSE, a model-free data-driven framework that incorporates Koopman-theoretic probabilistic filtering with a selective state-space model that learn to infer the underlying time-varying behavior of the system from data. We evaluate the model across a variety of test systems and scenarios, and demonstrate that the proposed method outperforms machine learning baselines on scalability, resilience to DER penetration levels, and robustness to data sampling rate irregularities. We further highlight the Mamba-based SSM's ability to capture long range dependencies from data, improving performance on the DSSE task.
Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a sparsity-promoting subgrid-scale (SGS) stress closure modeling framework that identifies explicit polynomial model forms using sparse regression. Candidate models are constructed through scaling a minimal tensor basis by a truncated polynomial expansion of invariant scalars, thereby enforcing fundamental invariance properties while regulating the highest order of admissible terms. Arbitrary filter anisotropy is incorporated to enable consistent representation of turbulent structures across computational grids with anisotropic scales and resolutions. We also explicitly constrain SGS energy dissipation during training to improve functional performance and promote numerical stability. The framework is trained on a small dataset of idealized turbulence and evaluated through a series of a priori and a posteriori tests. Sensitivity studies examine the effects of variations in model order and optimization penalties for regularization and dissipation across a range of canonical flow configurations beyond those represented in the training dataset. We also evaluate on a separated flow benchmark to assess generalizability to a more complex turbulent regime. In many cases, the sparse regression closures achieve predictive accuracy comparable to an invariance-preserving neural network while retaining markedly simpler parametric forms. Moreover, we demonstrate that the sparse closures can be trained and evaluated at a fraction of the cost of the neural network model.
