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.
In this paper, a Hybrid High-Order (HHO) framework is developed for the Helmholtz equation with a spatially varying wave number and mixed Dirichlet–Neumann boundary conditions. A discrete Gårding-type inequality is established, leading to stability under the resolution condition ∥κ2∥L∞h2≲1, which is less restrictive in its dependence on the wave number than the classical κ3 h2 ≲ 1 condition often required in low-order finite element methods. Optimal error estimates are derived in both the energy norm and the L2-norm, achieving convergence rates of order k+1 and k+2, respectively, for sufficiently smooth solutions. The method is implemented on general polygonal meshes and incorporates static condensation for efficiency. Numerical experiments validate the theoretical results and demonstrate the method’s flexibility in handling variable coefficients and mixed boundary conditions, including Robin-type boundaries.
Biogas separation is essential for producing high purity CH4 as a clean fuel while enabling CO2 capture within carbon capture, utilization and storage (CCUS). However, insufficient separation can result in methane losses and incomplete CO2 capture, undermining climate benefits by high impact CH4 emissions with continued CO2 release. Hydrate based gas separation (HBGS) can be a potential solution for this purpose. The successful application of hydrate-based biogas storage depends on resolving the challenge of slow formation kinetics by developing methods that can effectively accelerate hydrate onset and growth. Thermodynamic additives (Tetrahydrofuran (THF), Cyclopentane (CP), 1,3 Dioxolane (DIOX) [forming sII structure] and Tetrabutyl methyl ether(TBME) [forming sH structure] at their stoichiometric concentrations alongside combinations with kinetic additives were employed to separate 24.8 mol% CO2 / 74.2 mol% CH4 (biogas) mixture at 4.7 MPa and 283.2 K. Dimethyl sulfoxide (DMSO) and piperazine were also tested in combination for their effect on formation kinetics and separation efficiency.Highest gas uptake of 102.72 ± 5.12 mmol/mol was obtained using 2.86 mol% TBME with 0.1 wt% l-leucine. Selective separation ability of TBME forming sH hydrate was found to be higher compared to THF, CP and DIOX (structure sII hydrates) as it demonstrated highest separation factor of 2.45 ± 0.1, employing 2.86 mol% TBME with 5 wt% piperazine. DIOX sII mixed hydrate showed better performance compared to THF and CP in terms of gas uptake and rate of hydrate formation specifically in combination with l-methionine. Dissociation study of mixed hydrates with morphological observations show case higher thermodynamic stability of CP compared to THF and DIOX, other sII promoters. Overall, this work provides the systematic comprehensive evaluation of sII and sH promoters integrated with different bio-additives, advancing HBGS as a viable strategy for simultaneous methane enrichment and CO2 capture with reduced environmental impact aligning with United Nations sustainable development goals (SDGs) of 7 and 13.
Cellulose aerogel-based phase change materials (CA-PCMs) combine the latent heat storage capability of phase change materials (PCMs) with the hierarchical porous architecture, low density, and structural stability of cellulose aerogels (CA), providing a promising platform for sustainable thermal energy storage. This review critically examines recent advances in CA-PCMs from a materials-by-design perspective by correlating fabrication strategies, thermophysical properties, and structure-property-performance relationships. A comparative assessment of impregnation, in situ polymerization, encapsulation, and direct mixing establishes the influence of fabrication route on PCM loading, latent heat retention, thermal conductivity, mechanical stability, and cycling durability. Furthermore, graphene-, MXene-, CNT-, polymer-, and other cellulose-based hybrid systems are critically compared, demonstrating that conductive nanofillers can enhance thermal conductivity by 50-200% while introducing important trade-offs between heat transfer, latent heat storage, multifunctionality, and manufacturing scalability. Unlike previous reviews, this work integrates comparative performance analysis, commercialization perspectives, and emerging computational approaches into a unified materials design strategy for rational CA-PCM development. Finally, the review identifies key challenges, including long-term durability, scalable manufacturing, sustainable processing, and multifunctional integration, and proposes a research roadmap to accelerate the industrial translation of next-generation CA-PCMs.
Let D be a quaternion division algebra over a non-Archimedean local field F of characteristic zero, and let Gn=GLn(D). Let H1,n−1 denote the subgroup of Gn consisting of block-diagonal matrices of the form diag(g1,g2), where g1∈G1 and g2∈Gn−1. In this article, we classify all irreducible smooth H1,n−1-distinguished representations of Gn for n=3 and 4. Furthermore, we conjecture that an irreducible smooth representation π of Gn, for n>2, is H1,n−1-distinguished if and only if either π is a trivial representation or it is parabolically induced from the trivial representation of Gn−2 and an infinite-dimensional irreducible H1,1-distinguished representation of G2.
