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At least 1,621 records · Page 90

Precise 2D electric field density simulations for superconducting quantum devices

Dielectric loss due to two-level systems is a limiting factor for superconducting qubit relaxation times. These losses arise mostly from nanometer-scale interfacial defect regions in superconducting devices with planar dimensions of microns to millimeters, thus making it resource intensive to accurately simulate the electric field density in these regions with traditional electromagnetic solvers. In this work, we demonstrate a fast boundary integral equation solver that allows precise simulation of electric field density in these thin regions, showing a speedup of around two orders of magnitude over traditional solvers, with relative errors around $10^{-7}$ for a ten-minute solution runtime. By computing participation ratios through Green's first identity without squaring the electric field, our approach is less susceptible to the field singularities near conductor corners. We apply this solver to a basic untrenched coplanar waveguide cross-section, showing that the common assumption of participation ratio linearity with dielectric constant holds well for some interfaces and not others; in particular, while the metal-air (MA) top and corner follow this linear relationship strongly, the MA sidewall does not. We then compare isotropic and anisotropic etching, showing that the MA sidewall and the metal-air-substrate triple junction are the most strongly affected. We are currently leveraging this solver to explore geometries that will uniquely isolate the participation ratios of the different dielectrics. Finally, we are working to combine this solver framework with a full 3D microwave solver to accurately calculate participation ratios for the thin dielectrics that are known sources of loss in superconducting qubits.

Gimbutas, Z. [NIST, Boulder] (ORCID:00000003320982↗

Luminescent Metal–Organic Framework for the Selective Detection of Aldehydes

The detection of toxic, hazardous chemical species is an important task because they pose serious risks to either the environment or human health. Luminescent metal–organic frameworks (LMOFs) as alternative sensors offer rapid and sensitive detection of chemical species. Interactions between chemical species and LMOFs result in changes in the photoluminescence (PL) profile of the LMOFs which can be readily detected using a simple fluorometer. Herein, we report the use of a robust, Zn-based LMOF, [Zn 5 (μ 3 -OH) 2 (adtb) 2 (H 2 O) 5 ·5 DMA] (Zn-adtb, LMOF-341), for the selective detection of benzaldehyde. Upon exposure to benzaldehyde, Zn-adtb experiences significant luminescent quenching, as characterized through PL experiments. Photoluminescent titration experiments reveal that LMOF-341 has a detection limit of 64 ppm and a Ksv value of 179 M –1 for benzaldehyde. Furthermore, we study the guest–host interactions that occur between LMOF-341 and benzaldehyde through in situ Fourier transform infrared and computational modeling employing density functional theory. The results show that benzaldehyde interacts more strongly with LMOF-341 compared to formaldehyde and propionaldehyde. Furthermore, our combined studies also reveal that the mechanism of luminescence quenching originates from an electron-transfer process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Warm-phase microphysical evolution in large-eddy simulations of tropical cumulus congestus: evaluating drop size distribution evolution using polarimetry retrievals, in situ measurements, and a thermal-based framework

Owing to uncertainties in convective microphysics processes, improving parameterizations in Earth system models (ESMs) can benefit from observationally constrained cases suitable for scaling between cloud-resolving models and ESMs. We propose a benchmark large-eddy simulation (LES) cumulus congestus case study from the NASA Cloud, Aerosol, and Monsoon Processes Philippines Experiment (CAMP 2 Ex) for evaluating and improving ESMs in single-column model (SCM) mode. We seek observational constraints using novel polarimetric retrievals and in situ cloud microphysics measurements. Simulations using bulk and bin microphysics initialized with observed aerosol profiles are compared to cloud-top retrievals of cloud droplet effective radius (R eff ), effective variance (ν eff ), and number concentration (N d ) from the airborne Research Scanning Polarimeter (RSP). Both schemes reproduce characteristics of cloud-top N d and R eff that increase and decrease with altitude, respectively. Cloud-top N d is low-biased relative to RSP retrievals in both schemes, potentially due to limitations in both simulations and retrieval assumptions. Cloud-top R eff is low-biased in the bulk scheme but reasonably reproduced by the bin scheme. Profiles of N d and R eff are sensitive to the collision–coalescence process and the vertical variation in aerosol size distribution. Comparison of simulated and in situ droplet size distributions (DSDs) shows that, to first order, integrated moments are always sensitive to sizes < ~ 30 µm and can also be sensitive to larger sizes if the DSDs are sufficiently broad, with implications for the assumed maximum observed size retrieved by the RSP. The bin scheme captures the observed extended tail of the DSD, while the bulk scheme is unable to due to parametric constraints. Differences in expected relationships between in situ measurements of cloud cores and cloud-top retrievals by RSP demonstrate difficulty in constraining well the case presented herein. Finally, a thermal-tracking framework demonstrates that the dilution of N d throughout a thermal's lifetime is heavily determined by collision–coalescence and the height-varying aerosol distribution and that, in the absence of these, the impact of entrainment on diluting N d is largely offset by secondary activation. Implications for evaluating warm-phase convective microphysics schemes in ESMs and translating results for use on global, space-based polarimetry platforms are discussed.

Stanford, McKenna Wallace [Columbia Univ., New Yor↗

An AI-driven framework for evaluating local and state authorities’ permitting processes

The demand for new energy infrastructure is increasing across the United States, but heterogenous permitting processes and embedded requirements across different local jurisdictions can cause project delays, increase “soft costs,” and hinder developer expansion. This study analyzes the variability in local permitting requirements across the U.S. and develops a quantitative approach to describe their clarity and effectiveness in enabling infrastructure project development. By using an Energy Language Model (ELM), a large language model (LLM) for energy technologies, we systematically gathered permitting information from nearly 300 state-, county-, and city-level documents, creating a structured dataset of requirements and procedures on an unprecedented scale and speed. Our analysis revealed that local (city and county) permitting requirement documents are underrepresented compared to state-level guidance documents, which can impede timely and cost-effective installation of new electric infrastructure. Our validation process showed that the final database has an accuracy of approximately 95%. We, further, created a new quantitative method to score permitting requirements for clarity and efficiency, with electric vehicle supply equipment as an initial use case. The average local permitting document scored a 1.8 out of 5, which we interpret as meaning that half of the requirements developers face when installing electric infrastructure are ambiguous, increasing both cost and time. We also created a “Generalized Permit Process”, highlighting common procedural steps and identifying specific opportunities for municipalities to improve their documentation. This research establishes a systematic and scalable framework for evaluating the complexities of local infrastructure permitting processes by combining LLM-powered data collection and quantitative scoring. The framework enables policymakers and developers to identify and mitigate procedural bottlenecks, with the expectation that these improvements can accelerate application review and approval, reduce project costs, and expedite connection to utility distribution grids. As a foundational approach for streamlining local project development processes, this study’s methods are intended to be extended to a wide range of energy applications.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Sea Ice Rheology Experiment (SIREx): 1. Scaling and Statistical Properties of Sea-Ice Deformation Fields

As the sea-ice modeling community is shifting to advanced numerical frameworks, developing new sea-ice rheologies, and increasing model spatial resolution, ubiquitous deformation features in the Arctic sea ice are now being resolved by sea-ice models. Initiated at the Forum for Arctic Modeling and Observational Synthesis, the Sea Ice Rheology Experiment (SIREx) aims at evaluating state-of-the-art sea-ice models using existing and new metrics to understand how the simulated deformation fields are affected by different representations of sea-ice physics (rheology) and by model configuration. Part 1 of the SIREx analysis is concerned with evaluation of the statistical distribution and scaling properties of sea-ice deformation fields from 35 different simulations against those from the RADARSAT Geophysical Processor System (RGPS). For the first time, the viscous-plastic (and the elastic-viscous-plastic variant), elastic-anisotropic-plastic, and Maxwell-elasto-brittle rheologies are compared in a single study. We find that both plastic and brittle sea-ice rheologies have the potential to reproduce the observed RGPS deformation statistics, including multi-fractality. Model configuration (e.g., numerical convergence, atmospheric representation, spatial resolution) and physical parameterizations (e.g., ice strength parameters and ice thickness distribution) both have effects as important as the choice of sea-ice rheology on the deformation statistics. It is therefore not straightforward to attribute model performance to a specific rheological framework using current deformation metrics. In light of these results, we further evaluate the statistical properties of simulated Linear Kinematic Features in a SIREx Part 2 companion paper.

54 ENVIRONMENTAL SCIENCES↗

Error Analysis on Numerical Integration Algorithms in a Hypoelasticity Framework

This report determines local truncation errors for common stress integration algorithms used in explicit finite element codes with hypoelastic material models. The hypoelastic integration algorithms in question utilize an operator splitting procedure in a rotation neutralized configuration, where the stress response is determined from de- coupling the total deformation into rotational and strain dependent components. This document analyzes the error in evolving the stress given a one-step time increment Δt and compares the errors associated with both the rotational and strain components of the operator splitting method. A slight modification to a traditional algorithm is proposed and studied, where the rate of deformation is appropriately rotated from the midstep configuration at t n+1/2 to the end step configuration at t n+1 before the constitutive evaluation. The proposed modification either completely eliminates the error associated with the rotation rate or is of the same order of magnitude as the original algorithm for the three test cases considered in this report. These cases consist of an unaxial stretch with a constant true strain rate with a rigid body rotation, an uniaxial stretch with a constant engineering strain rate with a rigid body rotation, and a simple shear deformation. All three cases are compared to a closed form solution, and in almost every test case the alternative algorithm yields the most accurate one-step local truncation error.

97 MATHEMATICS AND COMPUTING↗

Modeling Monthly Nitrate Concentration in a Karst Spring with and without Discrete Conduit Flow

Understanding the coupled continuum pipe-flow framework for modeling contaminant transport in karst systems is critical for protecting water resources therein. This study simulated point and non-point source nitrate concentration in a karst spring and investigated the results generated from the flow and transport model with and without discrete conduit flow. CFPv2 and CMT3D models were integrated to address the changes in nitrate concentration at a monthly scale in a karst spring, and the results were compared with that from an equivalent porous media (EPM) model with high-hydraulic conductivity (K) zones set in the main karstified area to represent conduits. The results show that the CFPv2+CMT3D model is able to describe well the recession of nitrate concentration in spring discharge, and the relatively larger deviation (slower nitrate recession) from the observed trend for the EPM model is probably a result of the limitation of utilizing high hydraulic conductivity cells to represent conduit. Moreover, simulated hydraulic heads in poorly karstified areas from the two models both show slight differences from the observations (the head RMSE values of calibration/validation for CFPv2 and MODFLOW models are 0.16 m/0.25 m and 0.26 m/0.17 m, respectively), indicating the inclusion of conduits may not affect the simulation considerably, and the lower the proportion of karstic area, the slight effects brought from the inclusion of conduits in the model. For highly karstified areas, the CFPv2+CMT3D model could provide more accurate results (head RMSE of calibration/validation for CFPv2 and MODFLOW are 0.22 m/0.06 and 0.52 m/0.47 m, respectively), showing the coupled continuum pipe-flow framework may be more appropriate for applying to highly and maturely karstified areas where the variations in the behavior of flow and contaminant transport are more affected by turbulent flow regime.

54 ENVIRONMENTAL SCIENCES↗

A Route to Design Novel Functional Peptides by Applying a Denoising Diffusional Model to mRNA Display Libraries

In vitro directed evolution techniques, such as mRNA display, enable peptide ligand discovery and optimization. However, physical libraries that rely on a genetic code can only search a small fraction of sequence space due to inherent biases in the genetic code and experimental limitations. To address this challenge, denoising diffusion implicit models (DDIMs) are applied to generate novel peptide ligands against B‐cell lymphoma extra‐large (Bcl‐x L ), a key cancer target. Starting with high‐throughput sequencing data from previous selections, a DDIM is trained to produce novel sequences with high affinity binding. Experimental validation confirms that most generated sequences are functionally equivalent to the original library members for Bcl‐x L binding and demonstrated comparable binding kinetics and affinity relative to the wildtype and nearest original neighbors. Importantly, this approach generated rare sequences not easily accessible via mutation and directed evolution. These results indicate that DDIMs can complement and expand directed evolution data, efficiently exploring underrepresented regions of sequence space. This approach provides a broadly applicable framework for accelerating ligand discovery and optimizing molecular properties across diverse targets.

Qi, Pearl [Mork Family Department of Chemical Engi↗

Measurement of electroweak $Z\left(\nu \overline{\nu}\right)\gamma jj$ production and limits on anomalous quartic gauge couplings in pp collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

The electroweak production of $Z\left(\nu \overline{\nu}\right)\gamma jj$ in association with two jets is studied in a regime with a photon of high transverse momentum above 150 GeV using proton–proton collisions at a centre-of-mass energy of 13 TeV at the Large Hadron Collider. The analysis uses a data sample with an integrated luminosity of 139 fb –1 collected by the ATLAS detector during the 2015–2018 LHC data-taking period. This process is an important probe of the electroweak symmetry breaking mechanism in the Standard Model and is sensitive to quartic gauge boson couplings via vector-boson scattering. The fiducial $Z\left(\nu \overline{\nu}\right)\gamma jj$ cross section for electroweak production is measured to be ${0.77}_{-0.30}^{+0.34}$ fb and is consistent with the Standard Model prediction. Evidence of electroweak $Z\left(\nu \overline{\nu}\right)\gamma jj$ production is found with an observed significance of 3.2σ for the background-only hypothesis, compared with an expected significance of 3.7σ. The combination of this result with the previously published ATLAS observation of electroweak $Z\left(\nu \overline{\nu}\right)\gamma jj$ production yields an observed (expected) signal significance of 6.3σ (6.6σ). Limits on anomalous quartic gauge boson couplings are obtained in the framework of effective field theory with dimension-8 operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Microstructure Generation via Generative Adversarial Network for Heterogeneous, Topologically Complex 3D Materials

Using a large-scale, experimentally captured 3D microstructure dataset, we implement the generative adversarial network (GAN) framework to learn and generate 3D microstructures of solid oxide fuel cell electrodes. The generated microstructures are visually, statistically, and topologically realistic, with distributions of microstructural parameters, including volume fraction, particle size, surface area, tortuosity, and triple phase boundary density, being highly similar to those of the original microstructure. These results are compared and contrasted with those from an established, grain-based generation algorithm (DREAM.3D). Importantly, simulations of electrochemical performance, using a locally resolved finite element model, demonstrate that the GAN generated microstructures closely match the performance distribution of the original, while DREAM.3D leads to significant differences. Finally, the ability of the generative machine learning model to recreate microstructures with high fidelity suggests that the essence of complex microstructures may be captured and represented in a compact and manipulatable form.

36 MATERIALS SCIENCE↗

B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD

Here, the Deep Operator Network (DeepONet) is a neural network architecture used to approximate operators, including the solution operator of parametric PDEs. DeepONets have shown remarkable approximation ability. However, the performance of DeepONets deteriorates when the training data is polluted with noise, a scenario that occurs in practice. To handle noisy data, we propose a Bayesian DeepONet based on replica exchange Langevin diffusion (reLD). Replica exchange uses two particles. The first particle trains a DeepONet to exploit the loss landscape and make predictions. The other particle trains a different DeepONet to explore the loss landscape and escape local minima via swapping. Compared to DeepONets trained with state-of-the-art gradient-based algorithms (e.g., Adam), the proposed Bayesian DeepONet greatly improves the training convergence for noisy scenarios and accurately estimates the uncertainty. To further reduce the high computational cost of the reLD training of DeepONets, we propose (1) an accelerated training framework that exploits the DeepONet's architecture to reduce its computational cost up to 25% without compromising performance and (2) a transfer learning strategy that accelerates training DeepONets for PDEs with different parameter values. Finally, we illustrate the effectiveness of the proposed Bayesian DeepONet using four parametric PDE problems.

97 MATHEMATICS AND COMPUTING↗

Theoretical power-law relationship between permeability and formation factor

Permeability k and formation factor F are important petrophysical properties that have broad applications to reservoir engineering. Although well-log analysis has advanced reservoir characterizations, direct measurement of k is still not available. Accordingly, resistivity logs and more particularly formation factor have been frequently used to estimate k. In this study, we present a theoretical framework to relate k to F. We use power-law scaling from continuum percolation theory to develop a theoretic relationship between k and F, which is similar in form to a published power-law equation with empirical coefficients. Our result gives a physical interpretation to this empirical relationship. We also compare power-law scaling laws from percolation theory with data derived from experimental measurements and numerical simulations in the literature. Finally, using the Curve Fitting toolbox of MATLAB, the parameters of the power-law equations are determined, and the significance of the non-universal power laws are discussed.

42 ENGINEERING↗

Improving deep learning model performance under parametric constraints for materials informatics applications

Abstract Modern machine learning (ML) and deep learning (DL) techniques using high-dimensional data representations have helped accelerate the materials discovery process by efficiently detecting hidden patterns in existing datasets and linking input representations to output properties for a better understanding of the scientific phenomenon. While a deep neural network comprised of fully connected layers has been widely used for materials property prediction, simply creating a deeper model with a large number of layers often faces with vanishing gradient problem, causing a degradation in the performance, thereby limiting usage. In this paper, we study and propose architectural principles to address the question of improving the performance of model training and inference under fixed parametric constraints. Here, we present a general deep-learning framework based on branched residual learning (BRNet) with fully connected layers that can work with any numerical vector-based representation as input to build accurate models to predict materials properties. We perform model training for materials properties using numerical vectors representing different composition-based attributes of the respective materials and compare the performance of the proposed models against traditional ML and existing DL architectures. We find that the proposed models are significantly more accurate than the ML/DL models for all data sizes by using different composition-based attributes as input. Further, branched learning requires fewer parameters and results in faster model training due to better convergence during the training phase than existing neural networks, thereby efficiently building accurate models for predicting materials properties.

36 MATERIALS SCIENCE↗

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗

An Optimization-Based Planning Tool for On-Demand Mobility Service Operations

Regions worldwide are adopting and exploring low-speed automated electric shuttle (AES) service as an on-demand shared mobility service in dense geofenced urban areas. Building on this concept, the National Renewable Energy Laboratory (NREL) recently developed the Automated Mobility District (AMD) toolkit. The AMD toolkit—comprising of a travel micro-simulation model and an energy estimation model—estimates the mobility and energy impacts of a given shuttle configuration within an AMD. Early-stage AMD deployments need to find optimal operational configurations that include: (a) passenger capacity of an AES, (b) time-dependent routes, and (c) fleet size (AES units) to satisfy the demand for the region. This research extends the AMD toolkit functionality by developing an optimization-based planning module that will assist in the operations of AES units. We developed a constrained mixed-integer program accounting for passenger waiting time, battery range, and passenger capacity of AES units. For scalability, we demonstrated the Tabu search-based solution technique for a real-world network—a proposed AMD deployment in Greenville, South Carolina, USA. Compared to rule-based operations, our developed solution yields higher travel time and energy savings for the network at different demand levels. The sensitivity analyses for waiting time thresholds indicate nonlinearity in the system performance, underscoring the need to meet shared-use mobility user-level expectations. The developed optimization framework can be adapted and extended to accommodate different categories of shared-use on-demand mobility services.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

Constraints on S 8 from a full-scale and full-shape analysis of redshift-space clustering and galaxy–galaxy lensing in BOSS

ABSTRACT We present a novel simulation-based cosmological analysis of galaxy–galaxy lensing and galaxy redshift-space clustering. Compared to analysis methods based on perturbation theory, our simulation-based approach allows us to probe a much wider range of scales, $0.4 \, h^{-1} \, \mathrm{Mpc}$ to $63 \, h^{-1} \, \mathrm{Mpc}$, including highly non-linear scales, and marginalizes over astrophysical effects such as assembly bias. We apply this framework to data from the Baryon Oscillation Spectroscopic Survey LOWZ sample cross-correlated with state-of-the-art gravitational lensing catalogues from the Kilo Degree Survey and the Dark Energy Survey. We show that gravitational lensing and redshift-space clustering when analysed over a large range of scales place tight constraints on the growth-of-structure parameter $S_8 = \sigma _8 \sqrt{\Omega _{\rm m} / 0.3}$. Overall, we infer S8 = 0.792 ± 0.022 when analysing the combination of galaxy–galaxy lensing and projected galaxy clustering and S8 = 0.771 ± 0.027 for galaxy redshift-space clustering. These findings highlight the potential constraining power of full-scale studies over studies analysing only large scales and also showcase the benefits of analysing multiple large-scale structure surveys jointly. Our inferred values for S8 fall below the value inferred from the CMB, S8 = 0.834 ± 0.016. While this difference is not statistically significant by itself, our results mirror other findings in the literature whereby low-redshift large-scale structure probes infer lower values for S8 than the CMB, the so-called S8-tension.

79 ASTRONOMY AND ASTROPHYSICS↗

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. Further, the method is demonstrated through calculations of the binding energies of nuclei with atomic number A ϵ {2,3,4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and infinite-volume effective field theory calculations of A ϵ {2,3,4,5,6} systems based on this matching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantum Distributed Unit Commitment: An Application in Microgrids

The dawn of quantum computing brings on a revolution in the way combinatorially complex power system problems such as Unit Commitment are solved. The Unit Commitment problem complexity is expected to increase in the future because of the trend toward the increase of penetration of intermittent renewables. Even though quantum computing has proven effective for solving a host of problems, its applications for power systems’ problems have been rather limited. Here, in this paper, a quantum unit commitment is innovatively formulated and the quantum version of the decomposition and coordination alternate direction method of multipliers (ADMM) is established. The above is achieved by devising quantum algorithms and by exploiting the superposition and entanglement of quantum bits (qubits) for solving subproblems, which are then coordinated through ADMM to obtain feasible solutions. The main contributions of this paper include: 1) the innovative development of a quantum model for Unit Commitment; 2) development of decomposition and coordination-supported framework which paves the way for the utilization of limited quantum resources to potentially solve the large-scale discrete optimization problems; 3) devising the novel quantum distributed unit commitment (QDUC) to solve the problem in a larger scale than currently available quantum computers are capable of solving. The QDUC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing.

97 MATHEMATICS AND COMPUTING↗