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Hierarchical Epoxy Structures via Tunable Polymerization-Induced Phase Separation Combined with Additive Manufacturing

Polymerization-induced phase separation (PIPS) allows for the control of thermoset morphologies and properties, enabling the tuning of domain sizes and thermomechanical response. However, its use in generating substructural features in additively manufactured materials has been limited. In this work, we combine epoxy PIPS with UV curable acrylate and rheological modifiers to print nano- to macro-phase separating materials via a two-step, dual-cure approach. This method enables direct ink write printing of hierarchical structures with both controlled morphologies through phase separation and macroscale architecture through print design. We find that formulations for phase-separating materials require judicious incorporation of additives to enable printability and to provide sufficient green strength. Atomic force microscopy-nano infrared mapping reveals tunable, reticulated nano- to micron-scale domains of the resultant multiphase materials and their morphology changes due to additives, resulting in alterations to thermomechanical and tensile properties. Shape memory behavior is also demonstrated through multimaterial additive manufacturing of epoxies with functionally graded internal morphology using active mixing techniques, highlighting this method’s ability to fabricate complex architectures with controlled morphologies and thermomechanical response.

Van Meter, Kylie E [Organic Materials Science, San

The Canadian Galactic Emission Mapper: A New 8-10 GHz Telescope To Map the Polarization of the Northern Sky

The Canadian Galactic Emission Mapper (CGEM) radio telescope is mapping polarized Galactic foregrounds from 8-10 GHz to aid in the search for B-modes in the Cosmic Microwave Background (CMB). Here we describe the design and early on-sky characterization of the CGEM optics. CGEM employs an on-axis, hat feed optical design that is a body of revolution (BOR) and exhibits excellent intrinsic polarization purity. We describe how we have optimized the optics with a novel framework that can directly minimize simulated intensity to polarized intensity (T → P) leakage in angular power spectrum space. The optimized optics exhibit simulated T → P leakage that is orders of magnitude below anticipated CℓBB for r = 10 −3 when scaled from 8-10 GHz to the CMB observing window near 95 GHz. We go on to describe the mechanical design of the optics, including a novel secondary mirror support made from Astroquartz composite that has low loss, low dielectric constant, and preserves the BOR symmetry of the optics. We then showcase the early on-sky performance of the optics with observations of the Sun and satellites, which probe the beam to 40dB down from the peak. A beam model for the deployed CGEM optics based on electromagnetic simulations is in excellent agreement with the on-sky data.

cosmic microwave background

Activation dynamics of a water-soluble human mu-opioid receptor

The mu-opioid receptor (MOR), a class A G protein-coupled receptor mediates opioid analgesia and remains a central target for pain therapeutics. While crystal structures of MOR exist, they provide limited insight into the receptor’s dynamic conformational landscape underlying function. Here, we engineered a thermostable water-soluble MOR variant (wsMOR) that retains native-like ligand-binding and activation dynamics. This variant enables high-yield production and detailed solution-phase structural studies that are challenging with membrane-embedded MOR, providing a valuable tool for studying receptor activation and aqueous-phase drug screening. Using a combined computational and experimental approach, we performed long-timescale all-atom molecular dynamics simulations together with neutron scattering and single-molecule FRET, revealing a structurally stable receptor with a diverse ensemble of conformations at different temporal resolutions. In the ligand-free state, wsMOR displayed high conformational flexibility, which decreased upon agonist binding, particularly in transmembrane helix 6, a hallmark of G protein-coupled receptor activation. Positive allosteric modulation and G protein binding further stabilized active-like states. These findings highlight wsMOR’s conformational plasticity across picosecond to millisecond timescales and provide a foundation for structure-guided development of next-generation opioid ligands with improved efficacy and safety.

E, Agyemang [University of Tennessee Knoxville]

Adaptation of virtual synchronous generators to dynamic conditions in power grids

Virtual synchronous generators (VSGs) are widely adopted as grid-forming controls for inverter-based resources. However, when grid conditions vary significantly as characterized by changes in short-circuit ratio (SCR) and the reactance-to-resistance (X/R) ratio, fixed-gain designs and the commonly used P–Q decoupling assumption can become inaccurate. Such conditions can degrade transient power performance, leading to oscillations, prolonged settling, and overshoot, particularly in stiff-grid operating points. This paper quantifies how grid strength and impedance-dependent coupling affect the active–reactive power dynamics of a conventional VSG over a broad range of SCR and X/R values. An adaptive VSG tuning framework is then developed by combining (i) a coupling-explicit, impedance-parameterized state-space model to enable systematic controller synthesis, (ii) a full-state-feedback law designed via pole placement to meet prescribed damping and settling-time specifications, and (iii) a physics-informed neural network (PINN)–based online grid-impedance estimator that updates controller gains in real time as grid conditions vary. Offline simulations in MATLAB/Simulink and real-time validation on an OPAL-RT platform show that the proposed method preserves consistent damping and settling behavior with reduced overshoot across wide SCR and X/R ranges, compared with fixed-gain VSG baselines.

Adaptive control

Carbon in GaN as a nonradiative recombination center

Trap-assisted nonradiative recombination has been shown to limit the efficiency of optoelectronic devices. While substitutional carbon (⁠C N ) has been suggested to be a nonradiative recombination center in GaN devices, a complete recombination cycle including the two charge-state transition levels has not been previously described. In this work, we investigate the trap-assisted recombination process due to C N in GaN, including multiphonon emission, radiative recombination, trap-assisted Auger–Meitner (TAAM) recombination as well as thermal emission of holes. Our study shows the key role of TAAM processes at the high carrier densities relevant for devices. We also reveal the carrier-density regimes where thermal emission and radiative recombination are expected to play an observable role. Our results highlight that carbon concentrations exceeding ~10 17 cm −3 can have a noticeable impact on device efficiency, not just in GaN active layers but also in InGaN and AlGaN. Furthermore, our comprehensive formalism not only offers detailed results for carbon but also provides a general framework for assessing the multiple processes that participate in trap-assisted recombination in semiconductors.

36 MATERIALS SCIENCE

Crystal Growth Scale-Up and Stability of RbSr 2 X 5 :Eu Scintillators

The discovery and development of new scintillation materials support national security needs. In these applications, large volumes of scintillator crystals are needed to achieve efficient screening for contraband. Therefore, one important step in the discovery of new scintillator compositions is testing their feasibility for scale-up and their stability. In this work, high-quality Ø22 mm crystals of two new scintillators RbSr 2 Br 5 :Eu and RbSr 2 I 5 :Eu were grown via the Vertical Bridgman method, and their scintillation properties were characterized. Here, the Ø22 mm RbSr 2 I 5 :Eu crystals could be grown with fast translation rates up to 3.5 mm/h. Both RbSr 2 Br 5 :Eu and RbSr 2 I 5 :Eu had high scintillation performance, including light yields of 46,000 and 61,000 ph/MeV, respectively, for Ø22 × 35 mm crystals. Additionally, properties related to physical stability were investigated, including the coefficients of thermal expansion via high-temperature X-ray diffraction (HTXRD) as well as moisture sensitivity. HTXRD confirmed the absence of solid–solid phase transitions and showed that RbSr 2 Br 5 had minimal thermal expansion anisotropy compared to RbSr 2 I 5 and some other inorganic metal halide scintillators, which favors the growth of large-sized crystals.

36 MATERIALS SCIENCE

A holistic platform for accelerating sorbent-based carbon capture

Abstract Reducing carbon dioxide (CO 2 ) emissions urgently requires the large-scale deployment of carbon-capture technologies. These technologies must separate CO 2 from various sources and deliver it to different sinks 1,2 . The quest for optimal solutions for specific source–sink pairs is a complex, multi-objective challenge involving multiple stakeholders and depends on social, economic and regional contexts. Currently, research follows a sequential approach: chemists focus on materials design 3 and engineers on optimizing processes 4,5 , which are then operated at a scale that impacts the economy and the environment. Assessing these impacts, such as the greenhouse gas emissions over the plant’s lifetime, is typically one of the final steps 6 . Here we introduce the PrISMa (Process-Informed design of tailor-made Sorbent Materials) platform, which integrates materials, process design, techno-economics and life-cycle assessment. We compare more than 60 case studies capturing CO 2 from various sources in 5 global regions using different technologies. The platform simultaneously informs various stakeholders about the cost-effectiveness of technologies, process configurations and locations, reveals the molecular characteristics of the top-performing sorbents, and provides insights on environmental impacts, co-benefits and trade-offs. By uniting stakeholders at an early research stage, PrISMa accelerates carbon-capture technology development during this critical period as we aim for a net-zero world.

Science & Technology - Other Topics

How Distributed Energy Resources Can Support Resilience in Utility Distribution Networks

The goal of this webinar is to engage with electric utilities in the Midwest, particularly small public utilities, to understand the industry's needs for science tools to plan for winter resilience in the future, designing tools that will benefit electric power resilience in all communities. Michigan Tech leads this project with partners from multiple academic, government, and industry groups and asked NLR to present on DERs and laboratory tools and resources.

24 POWER TRANSMISSION AND DISTRIBUTION

The Slow Demise of the Long-Lived Sn 2005ip

The Type IIn supernova (SN IIn) 2005ip is one of the most well-studied and long-lasting examples of an SN interacting with its circumstellar environment. The optical light curve plateaued at a nearly constant level for more than five years, suggesting ongoing shock interaction with an extended and clumpy circumstellar medium (CSM). Here, we present continued observations of the SN from ∼1000 to 5000 d post-explosion at all wavelengths, including X-ray, ultraviolet, near-infrared (NIR), and mid-infrared. The UV spectra probe the pre-explosion mass loss and show evidence for CNO processing. From the bolometric light curve, we find that the total radiated energy is in excess of 10 50 erg, the progenitor star’s pre-explosion mass-loss rate was >~ 1 × 10 −2 Mꙩ yr −1 , and the total mass lost shortly before explosion was >~1Mꙩ, though the mass lost could have been considerably larger depending on the efficiency for the conversion of kinetic energy to radiation. The ultraviolet through NIR spectrum is characterized by two high-density components, one with narrow high-ionization lines, and one with broader low-ionization H I, He I, [OI], Mg II, and Fe II lines. The rich Fe II spectrum is strongly affected by Lyα fluorescence, consistent with spectral modelling. Both the Balmer and He I lines indicate a decreasing CSM density during the late interaction period. We find similarities to SN 1988Z, which shows a comparable change in spectrum at around the same time during its very slow decline. These results suggest that, at long last, the shock interaction in SN 2005ip may finally be on the decline.

stars

The first high-redshift cavity power measurements of cool-core galaxy clusters with the International LOFAR Telescope

Radio-mode feedback associated with the active galactic nuclei (AGNs) at the cores of galaxy clusters injects a large amount of energy into the intracluster medium (ICM), offsetting radiative losses through X-ray emission. This mechanism prevents the ICM from rapidly cooling down and fueling extreme starburst activity as it accretes onto the central galaxies, and it is therefore a key ingredient in the evolution of galaxy clusters. However, the influence and mode of feedback at high redshifts (z ∼ 1) remains largely unknown. Low-frequency sub-arcsecond-resolution radio observations taken with the International LOFAR Telescope have demonstrated their ability to assist X-ray observations with constraining the energy output from the AGNs (or “cavity power”) in galaxy clusters, thereby enabling research at higher redshifts than before. In this pilot project, we tested this hybrid method on a high-redshift (0.6 < z < 1.3) sample of 13 galaxy clusters for the first time with the aim of verifying the performance of this method at these redshifts and providing the first estimates of the cavity power associated with the central AGN for a sample of distant clusters. We were able to detect clear radio lobes in three out of 13 galaxy clusters at redshifts of 0.7 < z < 0.9, and we used these detections in combination with ICM pressures surrounding the radio lobes obtained from standard profiles to calculate the corresponding cavity powers of the AGNs. Combining our results with the literature, the current data appear to suggest that the average cavity power peaked at a redshift ofz ∼ 0.4 and slowly decreases toward higher redshifts. However, we require more and tighter constraints on the cavity volume and a better understanding of our observational systematics to confirm any deviation of the cavity power trend from a constant level.

Astronomy & Astrophysics

Preservation of Previously Unsampled Primordial Isotopic Components in Ryugu and Bennu Samples

Ivuna-type (CI) carbonaceous chondrites are primitive meteorites whose relative elemental abundances closely match the solar photosphere 1 , making them critical benchmarks for the bulk chemical and isotopic composition of the planet-forming disk. Recent sample-return missions to Ryugu 2 and Bennu 3 have enabled direct laboratory analysis of these rubble-pile CI-like asteroids 4 , formed from the reaccumulated fragments of once-larger parent bodies. As such, they may retain a broader spectrum of primordial nucleosynthetic components than is preserved in known meteorites. Here, we report the nucleosynthetic compositions of silicon (μ 30 Si), magnesium (μ 26 Mg*), and iron (μ 54 Fe), three of the four most abundant planet-building elements, in samples from Ryugu and Bennu, along with the newly discovered Oued Chebeika 002 CI chondrite 5 . In contrast to the isotopic homogeneity of CI chondrites, Ryugu and Bennu preserve resolvable μ 26 Mg* and μ 30 Si heterogeneity, revealing μ 26 Mg*- and μ 30 Si-rich nucleosynthetic components not sampled in meteorites. These components may reflect the preservation of previously unsampled primordial isotopic signals, prior to thermal processing 6,7 and late infall of primordial molecular cloud material to the outer disk 8,9 . Additionally, Ryugu particle C0002 exhibits a μ 26 Mg*-poor and μ 54 Cr-rich signature, consistent with incorporation of presolar material from massive supernovae 10,11 . Ryugu and Bennu samples define one end of a μ 54 Fe–μ 30 Si array among carbonaceous asteroid materials 9 , suggesting that the isotopic compositions of these asteroidal materials reflect mixing between early disk isotopic components identified in this study and material derived from the outermost disk 9 . This observation demonstrates that materials with solar chemical abundances can nonetheless exhibit markedly distinct nucleosynthetic signatures. Thus, Ryugu and Bennu samples are critical records of nucleosynthetic diversity among carbonaceous asteroids and underscore the value of sample-return missions in accessing primitive isotopic signatures absent from meteorite collections.

Martin Bizzarro

Establishing accretion flares from supermassive black holes as a source of high-energy neutrinos

ABSTRACT The origin of cosmic high-energy neutrinos remains largely unexplained. For high-energy neutrino alerts from IceCube, a coincidence with time-variable emission has been seen for three different types of accreting black holes: (1) a gamma-ray flare from a blazar (TXS 0506+056), (2) an optical transient following a stellar tidal disruption event (TDE; AT2019dsg), and (3) an optical outburst from an active galactic nucleus (AGN; AT2019fdr). For the latter two sources, infrared follow-up observations revealed a powerful reverberation signal due to dust heated by the flare. This discovery motivates a systematic study of neutrino emission from all supermassive black hole with similar dust echoes. Because dust reprocessing is agnostic to the origin of the outburst, our work unifies TDEs and high-amplitude flares from AGN into a population that we dub accretion flares. Besides the two known events, we uncover a third flare that is coincident with a PeV-scale neutrino (AT2019aalc). Based solely on the optical and infrared properties, we estimate a significance of 3.6σ for this association of high-energy neutrinos with three accretion flares. Our results imply that at least ∼10 per cent of the IceCube high-energy neutrino alerts could be due to accretion flares. This is surprising because the sum of the fluence of these flares is at least three orders of magnitude lower compared to the total fluence of normal AGN. It thus appears that the efficiency of high-energy neutrino production in accretion flares is increased compared to non-flaring AGN. We speculate that this can be explained by the high Eddington ratio of the flares.

Astronomy & Astrophysics

Block copolymer self-assembly derived mesoporous magnetic materials with three-dimensionally (3D) co-continuous gyroid nanostructure

Magnetic nanomaterials are gaining interest for their many applications in technological areas from information science and computing to next-generation quantum energy materials. While magnetic materials have historically been nanostructured through techniques such as lithography and molecular beam epitaxy, there has recently been growing interest in using soft matter self-assembly. In this work, a triblock terpolymer, poly(isoprene-block-styrene-block-ethylene oxide) (ISO), is used as a structure directing agent for aluminosilicate sol nanoparticles and magnetic material precursors to generate organic–inorganic bulk hybrid films with co-continuous morphology. After thermal processing into mesoporous materials, results from a combination of small angle X-ray scattering (SAXS) and scanning electron microscopy (SEM) are consistent with the double gyroid morphology. Nitrogen sorption measurements reveal a type IV isotherm with H1 hysteresis, and yield a specific surface area of around 200 m 2 g −1 and an average pore size of 23 nm. The magnetization of the mesostructured material as a function of applied field shows magnetic hysteresis and coercivity at 300 K and 10 K. Comparison of magnetic measurements between the mesoporous gyroid and an unstructured bulk magnetic material, derived from the identical inorganic precursors, reveals the structured material exhibits a coercivity of 250 Oe, opposed to 148 Oe for the unstructured at 10 K, and presence of remnant magnetic moment not conventionally found in bulk hematite; both of these properties are attributed to the mesostructure. This scalable route to mesoporous magnetic materials with co-continuous morphologies from block copolymer self-assembly may provide a pathway to advanced magnetic nanomaterials with a range of potential applications.

Chemistry

Toward Tunable Magnetic Dirac Semimetals: Mn Doping of Cd 3 As 2

Magnetic impurities provide a route toward increasing functionality in electronic materials, often enabling new device concepts and architectures. In the case of topological semimetals, dilute magnetic doping presents a particularly attractive approach for inducing a Dirac to Weyl phase change via time reversal symmetry breaking. However, efforts to realize changes in the electronic structure have been limited by challenges in incorporating magnetic impurities into crystals with sufficiently high electron mobilities to detect them via transport or spectroscopic techniques. Here, we demonstrate incorporation of Mn into Cd 3 ⁢As 2 Dirac semimetal thin films grown by molecular beam epitaxy (MBE). Using As-rich growth conditions and [001] oriented thin films, Mn compositions of >10% are achieved. Films contain uniform distributions of Mn with no evidence of secondary phases and exhibit electron mobilities greater than 10 000–30 000 cm 2 /Vs up to 5% Mn. An evolution in the magnetization behavior along with the emergence of a second quantum oscillation frequency at low Mn concentrations provide preliminary evidence of Mn-induced changes in the electronic structure that are consistent with a Weyl phase. This work demonstrates the potential of magnetically doping topological semimetal thin films and a pathway for synthesizing them.

36 MATERIALS SCIENCE

Aliovalent gallium dopants remove Ti 3+ defects and improve photocatalytic and photoelectrochemical water oxidation properties of LaTiO 2 N

LaTiO 2 N is a promising semiconductor for the water splitting reaction due to its 2.1 eV band gap and stability against corrosion. However, its solar energy conversion is limited by Ti 3+ recombination defects introduced during ammonolysis. Here we show for the first time that Ti 3+ defects in LaTiO 2 N can be suppressed with incorporation of 2, 5, and 10% aliovalent gallium (Ga 3+ ) dopants during synthesis via the layered La 2 Ti 2 O 7 intermediate. Electron paramagnetic resonance (EPR) spectroscopy on the solid powders confirms a reduction in the Ti 3+ donor density from 2.97 × 10 17 cm −3 for the non-doped material to ∼6.24 × 10 16 cm −3 for 5% Ga-doped LaTiO 2 N. The remaining Ti 3+ defects are concentrated near the LaTiO 2 N surface, according to X-ray photoelectron spectroscopy. The defect reduction shifts the optical absorption edge from 2.02 to 2.09 eV and eliminates a broad absorption band at 1050 nm from the optical absorption spectra. It also removes a 1.0–1.7 eV sub-band gap photovoltage signal from surface photovoltage spectra. This suggests that empty Ti 3+ d-orbitals are located 1.0–1.7 eV above the LaTiO 2 N valence band edge. Removing these recombination states with increasing Ga 3+ content enhances the photoconversion efficiency of LaTiO 2 N during water oxidation. The optimized 2 wt% CoO x -loaded 5% Ga-doped LaTi O2 N material has a 16% AQE (400 nm) for O 2 production from aqueous silver nitrate solution and a ∼2.1 mA cm −2 water oxidation photocurrent at 1.23 V under 100 mW cm −2 Xe arc lamp illumination. The water oxidation photocurrent is stable during a 50 min test, and the Faraday efficiency for O 2 generation is 97%, confirming short-term corrosion stability of LaTiO 2 N. Altogether, these results provide a better understanding of the distribution, concentration, and impact of Ti 3+ defects on the optical, photovoltage, and photoelectrochemical properties of LaTiO 2 N. In combination with other defect control strategies, aliovalent Ga 3+ doping can help bring the solar energy conversion efficiency of LaTiO 2 N closer to the theoretical limit.

Wang, Li [University of California, Davis, CA (Uni

Ammonolysis with N 2 -diluted NH 3 suppresses Ta( IV ) defects in BaTaO 2 N and enhances photocatalytic water oxidation

BaTaO 2 N stands out among oxynitride photocatalysts because of its ability to capture visible light and to drive the photoelectrochemical water oxidation reaction. However, its solar energy conversion performance is limited by electron–hole recombination at Ta( IV ) defects in the material. These defects are formed by overreduction of the Ta(v) oxide precursor by excess ammonia under the high temperature conditions during ammonolysis. Here we show for the first time that Ta( IV ) defect concentrations can be lowered by conducting the ammonolysis reaction in mixed NH 3 /N 2 gas. The obtained BaTaO 2 N samples crystallize in the cubic CaTiO 3 structure type and form 200–300 nm faceted nanocrystals, based on X-ray diffraction, scanning electron microscopy, and HRTEM. Electron paramagnetic resonance spectra observe the Ta( IV ) defects at g = 1.999 and confirm an 11-fold reduction for the product synthesized in mixed (0.13 : 1.0 vol) NH 3 /N 2 gas, equivalent to 1.14 × 10 16 cm −3 Ta( IV ) ions. This optimized BaTaO 2 N has nearly twice the photocatalytic oxygen evolution activity (AQE of 6.78% at 400 nm) of a reference material made with 1.0 atm ammonia and 78% higher photoelectrochemical water oxidation photocurrent (0.9 mA cm −2 at 1.23 V vs. RHE) under simulated sunlight. According to X-ray photoelectron spectroscopy, remaining Ta( IV ) defects are concentrated in the surface region of the BaTaO 2 N particles, where >50% of all Ta ions are found in the +4 oxidation state. This surface Ta( IV ) population can be directly observed in Vibrating Kelvin Probe Surface Photovoltage Spectra (VK-SPV) via its 1.2–1.4 eV photovoltage onset. Here, it suggests that the surface Ta( IV ) ions contribute empty d-states 0.5–0.7 eV below the BaTaO 2 N conduction band edge. These findings highlight how the energetics and concentrations of Ta( IV ) defects influence the photoelectrochemical water oxidation ability of BaTaO 2 N. Additionally, the work establishes ammonolysis with diluted NH 3 as a new tool to minimize defects in BaTaO 2 N and to raise its solar energy conversion efficiency toward its theoretical limit. Because of its simplicity, the reduced ammonia pressure strategy will likely be applicable to other oxynitrides, which generally suffer from overreduction problems during ammonolysis.

Salmanion, Mahya [University of California, Davis,

Shakeup and shakeoff spectra in the electron capture decay of atomic 7 Be

The most stringent laboratory-based experimental limits on the existence of submegaelectronvolt sterile neutrinos are currently set by decay spectroscopy of radioactive 7 Be embedded into superconducting sensors. The systematic uncertainties are dominated by the modeling of the electron shakeup and shakeoff spectra that are not based on state-of-the-art atomic theory and do not include electron correlations or relativistic effects. We have used the multiconfiguration Dirac-Fock formalism to obtain correlated wave functions ab initio and compute all single and double shake processes in the electron capture decay of atomic 7 Be . The simulations can explain some but not all of the observed spectral features, likely because the wave functions are modified by the Ta sensor material that the 7 Be is embedded into. The new models also show that the 𝐿/𝐾 electron capture ratio of 7 Be in Ta has previously been slightly underestimated revising the previous value of 0.070(7) to a new value of 0.0756(20).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil