Transmission Expansion Planning (TEP) optimizes power grid upgrades and investments to ensure reliable, efficient, and cost-effective electricity delivery while addressing grid constraints. To support growing demand and renewable energy integration, energy storage is emerging as a pivotal asset that provides temporal flexibility and alleviates congestion. This paper develops a multiperiod, two-stage PTDF formulation that co-optimizes transmission upgrades and storage siting/sizing. To ensure scalability, a trust-region, multicut Benders scheme warm-started from per-representative-day optima is proposed. Applied to a 2,000-bus synthetic Texas system under high-renewable projections, the method attains final optimality gaps below 2% and yields a plan with storage at 167 nodes (32% of peak renewable capacity). These results demonstrate that the proposed PTDF-based methodology efficiently handles large distributed storage fleets, demonstrating scalability at high spatial resolution.
One of the most important classes of even triangle-matroids arises from orientable ribbon graphs, which play a role analogous to that of graphic matroids in matroid theory. Motivated by a natural correspondence between strong triangle-matroids and even triangle- matroids due to Geelen and Murota, we characterize the class of strong triangle-matroids that correspond to orientable ribbon-graphic triangle-matroids. These are precisely the triangle-matroids associated with what we call pseudo-orientable ribbon graphs. Moreover, we present a geometric construction that transforms a pseudoorientable ribbon graph into an orientable ribbon graph, thereby realizing this correspondence. As consequences, we obtain the Matrix-Quasi-tree Theorem, the Hurwitz stability of quasi-tree generating polynomials, and the log-concavity of the sequence counting quasi-trees of size 2i-1 or 2i for pseudo-orientable ribbon graphs. To establish this log-concavity, we generalize Stanley's log-concavity theorem for regular matroids to regular triangle-matroids. Finally, we exhibit an infinite family of non-pseudo-orientable ribbon graphs that fail to satisfy the Matrix-Quasi-tree theorem and Hurwitz stability. (c) 2026 Published by Elsevier Ltd.
In this work, we propose a novel transport model for soluble surfactants in two-phase flows. In a two-phase flow, the soluble surfactants can adsorb/desorb from/into the bulk of any of the phases to the interface and can modify the interface properties. This results in sharp gradients in the surfactant concentration on the interface and also between the two phases in the bulk when there is selective adsorption/desorption, presenting a serious challenge for the numerical simulations.To overcome this challenge, we propose a computational model for the transport of soluble surfactants that can model the adsorption and desorption processes accurately. The model is discretized using a central-difference scheme, which leads to a non-dissipative implementation that is crucial for the simulation of turbulent flows. The model is used with the ACDI diffuse-interface method [1], but can also be used with other algebraic-based interface-capturing methods. Furthermore, the provable strengths of the proposed model are: (a) the model maintains the positivity property of the surfactant concentration field, a physical realizability requirement for the simulation of surfactants, when the proposed criterion is satisfied, (b) the proposed model maintains discrete confinement of the interfacial and bulk surfactants and prevents artificial numerical diffusion of the surfactant between the interface and the bulk and between the two phases in the bulk.Finally, we present numerical simulations using the proposed model for both one-dimensional and multi-dimensional cases and assess: the accuracy and robustness of the model, the validity of the positivity property of the scalar concentration field, and the confinement of the surfactant at the interface. We also study the effect of surfactants on a deforming droplet in a shear flow, an oscillating droplet, and on a complex droplet/bubble-laden turbulent flow.
DC Optimal Power Flow (DCOPF) is widely utilized in power system operations due to its simplicity and computational efficiency. However, its lossless, reactive power-agnostic model often yields dispatches that are infeasible under practical operating scenarios such as the nonlinear AC power flow (ACPF) equations. While theoretical analysis demonstrates that DCOPF solutions are inherently AC-infeasible, their widespread industry adoption suggests substantial practical utility. This paper develops a unified DCOPF -> ACPF pipeline to recover AC feasible solutions from DCOPF-based dispatches. The pipeline uses four DCOPF variants and applies AC feasibility recovery using both distributed slack allocation and PV/PQ switching. The main objective is to identify the most effective pipeline for restoring AC feasibility. Evaluation across over 10,000 dispatch scenarios on various test cases demonstrates that the structured ACPF model yields solutions that satisfy both the ACPF equations, and all engineering inequality constraints. In a 13,659-bus case, the mean absolute error and cost differences between DCOPF and ACOPF are reduced by 75% and 93%, respectively, compared to conventional single slack bus methods. Under extreme loading conditions, the pipeline reduces inequality violations by a factor of 3 to 5.
We study how conditioning context shapes personalization behavior in a teacher-facing educational recommender system. We compare contextual conditioning based on the current student question with memory-based conditioning using persistent learner information. Using deviation correlation and paired statistical tests, we find that contextual recommendations exhibit stronger question-level responsiveness, while memory-based recommendations exhibit history-dependent behaviors, including learner-specific differentiation under identical input. Teacher-facing evaluation signals suggest these recommendations are interpretable and actionable. These results indicate that embedding-based similarity metrics capture responsiveness to the current question but do not characterize personalization grounded in learner history, motivating behavior-level diagnostics for studying conditioning effects.
