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At least 289 records · Page 16

Electrically Powered High-Salinity Brine Separation Using Dimethyl Ether

Dewatering highly saline aqueous streams, from mining and geothermal leachates to industrial wastewater, is essential for effective resource recovery and safe disposal. Membraneless water extraction (MWE) uses a low-polarity solvent to separate water from concentrated aqueous solutions. In this study, we design a new MWE that uses dimethyl ether (DME) to selectively extract water from high-salinity brines, leveraging the volatility of DME to achieve rapid solvent recovery. By separating water and dissolved salts at a liquid–liquid interface, MWE minimizes the deleterious effects of scaling on vulnerable membrane and heat exchanger surfaces, reducing the need for extensive pretreatment and expensive materials. We begin by developing a computational framework for a multistage counterflow liquid–liquid contactor, which extracts water into DME, coupled with a multistage solvent regenerator that uses vapor compression to efficiently separate the desalinated water from the DME extractant. Excess Gibbs free energy and equation of state frameworks are used to model fluid phase equilibria in water–DME–sodium chloride (NaCl) mixtures, with interaction parameters estimated from experimental data. Incorporating equilibrium calculations into a system-scale computational model, we examine the performance of MWE using DME for the first time. Our analysis demonstrates that MWE can concentrate seawater desalination brine (>1.0 mol NaCl kg –1 ) to zero-liquid discharge salinities, with an energy consumption of under 50 kW h per m 3 of water extracted with a solvent recovery ratio greater than 99.9%. We highlight the importance of staging the vapor compression process to simultaneously minimize energy consumption while enabling brine concentration and product water solvent contamination. Finally, the thermodynamic framework developed here allows for the robust evaluation of new MWE solvents and systems for critical brine concentration and fractional precipitation applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Individual and Collective Strategies to Limit the Impacts of Large Power Outages of Long Duration

As modern society becomes ever more dependent on the availability of electric power, the costs that could arise from individual and social vulnerability to large outages of long duration (LLD-outages) increases. During such an outage, even a small amount of power would be very valuable. Here, this article compares individual and collective strategies for providing limited amounts of electric power to residential customers in a hypothetical New England community during a large electric power outage of long duration. We develop estimates of the emergency load required for survival and assess the cost of strategies to address outages that last 5, 10, and 20 days in either winter or summer. We find that the cost of collective solutions could be as much as 10 to 40 times less than individual solutions (less than $2 per month per home). However, collective solutions would require community-wide coordination, and if local distribution system lines are destroyed, only individual back-up systems could provide contingency power until those lines are repaired. Costs might be reduced if more robust distributed generation were employed that could be operated continuously with the ability to sell power back to the grid. Our cost-effectiveness analysis only assesses what could be done, developing estimates of preparedness cost. A decision about what should be done would require additional input from a range of stakeholders as well as some form of analytical deliberative process.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Protecting and Defending against Autonomous Control Systems and Digital Twin Cyber Attacks: Response Strategy for Hyperparameter attacks of Digital Twin Machine Learning Models in Nuclear Power Plants (Final)

Navigating through the complex tapestry of technological advancements, "Response Strategy for Hyperparameter attacks of Digital Twin Machine Learning Model in Nuclear Power Plants" stands at the intersection of cybersecurity and nuclear power plant operations, embarking on a journey through the intricacies of securing digital twins against malicious cyber activities. As nuclear power plants progressively integrate digital twin technology and machine learning models to optimize operations and ensure system reliability, they inadvertently expose themselves to a new spectrum of vulnerabilities, notably in the realm of hyperparameter attacks. Hyperparameters, integral in machine learning model tuning and optimal performance of digital twins, have emerged as a target for adversaries aiming to destabilize the predictive capabilities and therefore, the operational accuracy of these digital entities within critical infrastructures like nuclear plants. This paper, therefore, meticulously threads the needle through the development of a robust response strategy, poised to shield these digital reflections against calculated hyperparameter manipulations, ensuring that the digital twin can effectively and securely function as a reliable proxy for its physical counterpart. The ensuing sections delve into the orchestrated maelstrom of multi-rate time-changing intelligent coordinated hyperparameter attacks and the implementation of event-triggered predictive control, laying down a structured, predictive, and responsive framework that safeguards the nexus where the digital and physical realms of nuclear power plants coalesce. The operational integrity of digital twins in nuclear power plants depends critically on the security of machine learning hyperparameters. This study makes two different contributions. First, a decision-based idea known as a multi-rate time changing intelligent coordinated hyperparameter attack is put forth. In this attack, many hyperparameters are repeatedly changed using both random and intelligent optimal techniques by the attacker. These assaults introduce varied rates at different attack steps, compromise various amounts of hyperparameters, and improve stealth and flexibility. Second, a technique is developed for event triggered predictive control to rapidly respond to potential hyperparameter attacks. This control integrates a sliding window framework, retaining a history of previous data points and employing linear regression to predict the next data point from the current dataset. The control gain K is determined using the Lyapunov-Krasovskii method, and subsequently, an action is developed. Finally, the outcome of the simulation demonstrates the viability of the proposed method for defending nuclear power plant digital twins from hyperparameter attacks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Direct Geologic Constraints on the Timing of Late Holocene Ice Thickening in the Amundsen Sea Embayment, Antarctica

Abstract Constraining past West Antarctic Ice Sheet (WAIS) change helps validate numerical models simulating future ice sheet dynamics. Following rapid deglaciation during the mid‐Holocene, ice near Thwaites Glacier was ∼35 m thinner than present; however, the timing of ice regrowth to its present configuration remains unknown. To fill this knowledge gap, we present cosmogenic nuclide exposure ages of cobbles from the surface of a moraine situated between Thwaites and Pope glaciers. We infer that the moraine formed and stabilized in the Late Holocene (∼1.4 ka) when a small glacier thickened. We also present a novel reconstruction of WAIS volume constrained by sea‐level data, which demonstrates that moraine formation coincided with a large‐scale WAIS readvance. Our new geologic constraints will help inform models of the solid Earth response to surface mass loading, improving our understanding of ice sheet dynamics in a vulnerable part of WAIS.

Nichols, Keir A. [Imperial College London London U↗

Artificial Intelligence for Digital Security and Protections

Proper functioning of nuclear power plants relies on a mix of well-regulated human and machine-driven workflows. This regulation supports nuclear safety through a series of processes and many of the tasks that support these processes have a repetitive nature that make artificial intelligence (AI) informed by machine learning (ML) a potential aid in a variety of tasks. AI is being evaluated for activities that include inspections, fuel processing, monitoring, and other activities. The introduction of any new technology presents a potential new attack vector. In the case of AI/ML, there are many attacks that have already been discovered and over time the attacks can be expected to follow the growth pattern observed in cyber security. While future planning is necessary, current efforts need to be established now to predict the threat emergence over the next year 10 years and mitigate potential threats. Based on these observations, AI/ML will need to become trustworthy, which corresponds to techniques and procedures that emphasize AI explainability along with resilience techniques to data, algorithms, models, and systems. This kind of system robustness is the foundation for defenses against AI/ML-specific attacks. Attempting to look forward and take a broad view of capabilities provides input to research roadmaps and the ability to distill vulnerabilities into specific use cases may provide greater assistance in understanding the technology benefits while introducing new risks. The impact of current and future AI in three areas—capabilities, challenges, and recovery strategies—represents an initial attempt at balancing both.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Error-Field Penetration Thresholds in Ohmically Heated ITER and SPARC Plasmas

The critical n=1, n=2, and n=3 error-field amplitudes needed to trigger error-field penetration in ITER and SPARC, steady-state, ohmically heated plasmas are calculated using a standard asymptotic matching approach. The calculation incorporates plasma impurities, trapped particles, the bootstrap current, and neoclassical poloidal flow-damping. The energy confinement time is specified by the neo-Alcator scaling law in the low-density linear ohmic confinement (LOC) regime, and by the ITER-89P L-mode scaling law in the high-density saturated ohmic confinement regime (SOC) regime. The response of the plasma in the inner region is calculated using a linearized version of the four-field model. At the normal operating electron number density, diamagnetic levels of rotation are found to be sufficient to protect ITER and SPARC ohmically heated plasmas from m=2/n=1 error-field penetration. On other hand, SPARC, and especially ITER, ohmically heated plasmas may be vulnerable to n>1 error-field penetration. ITER and SPARC ohmically heated plasmas are also slightly more susceptible to error-field penetration when the electron fluid at the rational surface rotates in the ion diamagnetic direction, rather than the electron diamagnetic direction. At electron number densities that are sufficiently low that the plasma lies in the LOC confinement regime, the error-field penetration threshold increases with increasing density. However, as soon as the electron number density becomes large enough that the plasma enters the SOC regime, the increase in the error-field penetration threshold with increasing density levels off.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Robust Power System Stability Assessment Against Adversarial Machine Learning-Based Cyberattacks via Online Purification

The increasing complexity associated with renewable generation brings more challenges to power system stability assessment (SA). Data-driven approaches based on machine learning (ML) techniques for stability assessment have received significant research interest and shown their promising performance. However, ML-based models are recognized to be vulnerable to adversarial disturbances, where a slight perturbation to power system measurements could lead to unacceptable errors. To address this issue, this paper develops a novel lightweight mitigation strategy, i.e., robust online stability assessment (ROSA), to enhance the ML-based assessment model against both white-box and the black-box adversarial disturbances (i.e., purification) in the online implementation. The ROSA involves a supervised learning-based module for the primary stability assessment and a self-supervised learning-based module. Further, the two modules are trained jointly with different objective (loss) functions and implemented in sequence. A suitable purification objective and various time-series data augmentation methods are designed for SA applications to tackle adversarial disturbances adaptively. Case studies are performed, and the comparative results have clearly illustrated the competitive, robust accuracy against various adversarial scenarios and verified the effectiveness of the proposed online purification strategy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Molecular Interaction Regulates the Performance and Longevity of Defect Passivation for Metal Halide Perovskite Solar Cells

Defect passivation constitutes one of the most commonly used strategies to fabricate highly efficient perovskite solar cells (PSCs). However, the durability of the passivation effects under harsh operational conditions has not been extensively studied regardless of the weak and vulnerable secondary bonding between the molecular passivation agents and perovskite crystals. Here, we incorporated strategically designed passivating agents to investigate the effect of their interaction energies on the perovskite crystals and correlated these with the performance and longevity of the passivation effects. We unraveled that the passivation agents with a stronger interaction energy are advantageous not only for effective defect passivation but also to suppress defect migration. The prototypical PSCs treated with the optimal passivation agent exhibited superior performance and operational stability, retaining 81.9 and 85.3% of their initial performance under continuous illumination or nitrogen at 85 °C after 1008 h, respectively, while the reference device completely degraded during that time. Furthermore, this work provides important insights into designing operationally durable defect passivation agents for perovskite optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reducing Deferrals by Integrating Health Homes with Weatherization

The U.S. Department of Energy’s Weatherization Assistance Program (WAP) improves energy efficiency and household health for low-income families, yet a substantial number of otherwise eligible homes are deferred from due to health and safety concerns in their homes, including mold, moisture damage, or structural deficiencies. These deferred homes are often occupied by marginalized or otherwise vulnerable residents who may be exposed to elevated indoor air pollutant concentration. Integrating Healthy Homes (HH) interventions with weatherization has been proposed as a strategy to reduce deferrals, address environmental justice concerns, and improve health outcomes. However, limited data on the health and economic implications of such integration exist. This study aimed to assess the potential health benefits and savings-to-investment ratio (SIR) associated with integrating Healthy Homes interventions into weatherization programs for homes typically deferred from WAP services. We collected indoor air pollutant data from homes undergoing health home renovations, including fine particulate matter (PM 2.5 ), nitrogen dioxide (NO 2 ), carbon monoxide (CO), and formaldehyde, with sampling times up to one month. Except for fomaldehyde, which was measured using passive UMEx badges, the other metrics were measured using the airQ Pro indoor air quality monitor.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Theoretical Analysis and Experimental Validation of Flying-Capacitor Multilevel Converters Under Short-Circuit Fault Conditions

Addressing the increasing demand for high- efficiency and high-power-density converters, the flying-capacitor multilevel converter has shown itself as a promising topology. A key advantage of this topology is the reduced voltage rating of the switches, though also makes it vulnerable to device failure during short-circuit conditions. Despite large interest in fault-tolerant operation of these converters, alongside detailed descriptions of flying capacitor balancing, little research has focused on the converter short-circuit fault analysis, which may cause a switch failure if not properly designed for. Therefore, this work presents a comprehensive model describing the large- signal short-circuit switching behavior of a general N -level flying- capacitor multilevel converter. Highly simplified models used to predict the evolution of the switch current and voltage stress during the fault are proposed, targeted at practicing engineers for conservative design guidelines. These models are used to determine the critical time for remedial action of the converter before reaching some predefined maximum conditions. A 2-to-10- level fully-configurable flying-capacitor multilevel converter and a fault circuit hardware prototype are used to experimentally perform different short-circuit tests that show a good match to the measured behavior.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Atmospheric Gases as Quantitative Indicators of Urbanization Across Land-Use Gradients

The urban heat island (UHI) effect is a significant phenomenon characterized by higher surface temperatures in cities compared to surrounding rural areas. This change in the Earth's energy balance presents considerable challenges for urban populations, increasing heat exposure, straining energy infrastructure, and exacerbating health vulnerabilities. Quantifying UHI intensity is challenging due to blurred distinctions between urban and rural areas as land-use patterns evolve. To address this challenge, the present study builds on the framework established by Salvador et al. (2025) and investigates the use of atmospheric constituents, specifically volatile organic compounds (VOCs) and inorganic gases, as tracers of urbanization levels. A key improvement in this approach is the inclusion of a designated true rural site for comparison. Field measurements were conducted at two locations in the Southeastern United States during the summer of 2025. Inorganic gases were monitored continuously, while VOC samples were collected biweekly and analyzed using a proton transfer reaction time-of-flight mass spectrometer. The urban site exhibited elevated concentrations of anthropogenic inorganic gases, with carbon monoxide and nitrogen dioxide averaging 878 ppb and 17.99 ppb, respectively. In contrast, the rural site showed lower levels of these pollutants, 796 ppb for carbon monoxide and 12.46 ppb for nitrogen dioxide, while displaying higher concentrations of biogenic VOCs, including isoprene and monoterpenes at 1.24 ppb and 0.08 ppb, respectively. Extended mass spectral analyses revealed distinct chemical differences between the two sites, supporting the observed variability of major gases. Overall, these findings are consistent with our previous research and highlight the value of atmospheric constituents as effective indicators of urbanization, thereby improving our understanding of UHI dynamics.

54 ENVIRONMENTAL SCIENCES↗

Chemical beneficiation of cobaltiferous pyrite: a thermodynamic and parametric study

Despite ongoing efforts to identify substitute materials, cobalt remains indispensable for the production of rechargeable batteries essential to the global energy transition. Currently, most cobalt is sourced as a by-product of nickel and copper extraction from politically and ethically unstable regions. To address this vulnerability, certain primary cobalt deposits—where cobalt occurs within the crystal lattice of pyrite (FeS 2 )—have been identified as potential alternatives. Nonetheless, conventional beneficiation methods have proven largely ineffective for the potential processing of these minerals. This study investigated the thermal decomposition of cobaltiferous pyrite contained in flotation concentrates as a subsequent chemical beneficiation stage aimed at (i) selectively removing sulfur to further increase cobalt grades and (ii) producing a ferromagnetic product suitable for downstream magnetic separation. A thermodynamic analysis was first conducted to evaluate the feasibility of the decomposition reactions and the temperature-dependent evolution of sulfur species. A parametric experimental study then assessed the influence of temperature, residence time, and gas flow rate under N 2 and CO 2 atmospheres. Under the most favorable experimental conditions tested (650 °C, 15 min), cobalt grades increased by up to 15% with negligible cobalt losses and the co-production of high-purity sulfur (>95%). Magnetic separation of the resulting calcine yielded a final concentrate containing 2.09% cobalt at 82.5% recovery, representing a 16–74% improvement over previous baseline studies on similar feedstocks.

Beneficiation↗

Simulating Alpha Particles Incident on MKID Chips for Quantum Sensitivity Analysis

Superconducting quantum devices, such as microwave kinetic inductance detectors (MKIDs), are highly sensitive instruments used in quantum computing and advanced sensing technologies. However, their extreme sensitivity also makes them vulnerable to background noise from natural sources like radiation. One significant contributor to this noise is alpha particles emitted by 210Po, a radon decay daughter that accumulates on surfaces near the detector. This project investigates how alpha particles emitted from 210Po interact with MKID chips. These particles can deposit energy on the detector surface, disrupting its operation and generating false signals. Understanding the energy and behavior of these particles is crucial for improving the design and reliability of quantum devices. To explore this, we first modeled the decay chain starting from 210Pb to 210Po using differential equations. This allowed us to predict how the activity of alpha-emitting isotopes changes over time, reaching a steady state after about two years. Next, we simulated alpha particle interactions with the MKID chip using the Geant4 software toolkit. We built a detailed computer model of the detector housing, including the copper lid where alpha particles originate, the silicon chip, and a thin aluminum sensor layer. Alpha particles were emitted isotropically from just beneath the copper lid’s surface, mimicking natural decay conditions. The simulation tracked how these particles deposit energy on the chip, generating electron-hole pairs and phonons. The results provide insight into the behavior of the resultant electron-hole pairs and phonons, giving us a clear understanding of the energy deposition distribution on the chip. This work supports efforts to mitigate background noise in superconducting sensors, advancing their use in quantum computing and sensitive physics experiments.

Hall, Matthew [Fermilab; UCLA]↗

The impact of plant‐derived fire management prescriptions on fire‐responsive bird species

Abstract In fire‐prone regions, the occurrence of some faunal species is contingent on the presence of resources that arise through post‐fire plant succession. Through planned burning, managers can alter resource availability and aim to provide the conditions required to promote biodiversity. Understanding how species occurrence changes at different spatial and temporal scales after fire is essential to achieve this goal. However, many fire prescriptions are guided primarily by the responses of fire‐sensitive plants when setting tolerable fire intervals. This approach assumes that maintaining floristic diversity will satisfy the requirements of fauna. We surveyed bird species in two semi‐arid vegetation types across an environmental gradient in south‐eastern Australia. We conducted four surveys at each of 253 sites across a 75‐year chronosequence of time since fire and used generalized additive mixed models to examine changes in the occurrence of birds in response to time since fire. Model predictions were compared to plant‐derived fire prescriptions currently guiding fire management in the region. Time since fire was a significant predictor for 18 of 28 species modeled, in at least one vegetation type, over a gradient of 1.3° of latitude. We detected considerable variation in the responses of some species, both between vegetation types and geographically within a vegetation type. Our evaluation of plant‐derived fire prescriptions suggests that the intervals considered acceptable for maintaining floristic diversity may not be sustainable for populations of birds requiring longer unburnt vegetation, with 6 of the 12 species assessed attaining a mean occurrence probability of 20.3% by the minimum tolerable fire interval, and 57.3% by the maximum tolerable fire interval, in their respective vegetation types. Our findings highlight the potential vulnerability of fire‐responsive bird species if fire prescriptions are applied in a manner that fails to account for the slow development of habitat resources needed by some species, and the variation detected within the responses of species. This highlights the need for species‐specific data collected at an appropriate spatial scale to inform management plans.

Makdissi, Rhys↗

Super-Resolution Ptychography with Small Segmented Detectors

To overcome the spatial resolution limit set by aperture-limited diffraction in traditional scanning transmission electron microscopy, microscopists have developed ptychography enabled by iterative phase retrieval algorithms and high-dynamic-range pixel array detectors. Current detector designs are limited by the data rate off chip, so a high-pixel-count detector has a proportionally lower frame rate than the few-segment detectors used for differential phase contrast (DPC) imaging. This slower acquisition speed leads to heightened vulnerability to scan noise, drift, and potential sample damage. This creates opportunities for repurposing fast segmented detectors for ptychography by trading a reduction in reciprocal space pixels for an increase in real space pixels. Here, we explore a strategy of oversampling in real space and instead apply detector pixel upsampling during the reconstruction process. Further, we demonstrate the viability of achieving super-resolution ptychography on thin objects using only 2 × 2 detector pixels, surpassing the resolution of integrated DPC (iDPC) imaging. With optimization using simulated datasets and experiments on MoTe 2 /WSe 2 bilayer moiré superlattices, we achieved super-resolution ptychography reconstructions under rapid acquisition conditions (37.5 pA, 1 μs dwell time), yielding over 50% improvements in contrast and information limit compared to annular dark field and iDPC imaging on the same detectors.

2D materials↗

Optimizing Heat Recovery with Storage: Control Validation and Sensitivity Analysis of the Time-Independent Energy Recovery Plant Using Modelica

Heat recovery in large building central plants saves energy but traditionally requires simultaneous heating and cooling. The Time-Independent Energy Recovery (TIER) plant shifts this paradigm by integrating thermal energy storage (TES) to enable heat recovery regardless of concurrent demand, offering a highly efficient, space-saving solution to achieve California’s energy goals. However, its integration of heat recovery chillers, cooling-only chillers, cooling towers, and trim air-source heat pumps (ASHPs) creates growing control and sizing complexity. To overcome this, this study employs high-fidelity Modelica dynamic simulation to validate TIER control sequences and optimize equipment sizing. We translated the written Sequences of Operation into executable Control Description Language (CDL) to test logic against sub-hourly loads. This verification workflow successfully identified and resolved critical vulnerabilities, such as thermal storage freezing and equipment short-cycling, in a virtual environment prior to physical deployment. Then, the study analyzes TIER plant performance across three simulated building types in three locations, and a real building load profile, ensuring variety in heating and cooling loads, and simultaneity factors and explores sizing rules for the TES and ASHP capacity. The analysis shows that the TIER plant operates equipment efficiently leading to a plant SCOP of around 7.5 across all scenarios, higher than a traditional ASHP plant, and a viable pathway to de-risk complex system design and control through simulation to identify optimal designs that maximize energy efficiency, minimize operational costs, and ensure robust operation in varied environmental conditions, thereby facilitating the broader adoption of such a solution for large buildings.

Zanetti, Ettore↗

Automated Adversary-in-the-Loop Cyber-Physical Defense Planning

Security of cyber-physical systems (CPS) continues to pose new challenges due to the tight integration and operational complexity of the cyber and physical components. To address these challenges, this article presents a domain-aware, optimization-based approach to determine an effective defense strategy for CPS in an automated fashion—by emulating a strategic adversary in the loop that exploits system vulnerabilities, interconnection of the CPS, and the dynamics of the physical components. Our approach builds on an adversarial decision-making model based on a Markov Decision Process (MDP) that determines the optimal cyber (discrete) and physical (continuous) attack actions over a CPS attack graph. The defense planning problem is modeled as a non-zero-sum game between the adversary and defender. We use a model-free reinforcement learning method to solve the adversary’s problem as a function of the defense strategy. We then employ Bayesian optimization (BO) to find an approximate best-response for the defender to harden the network against the resulting adversary policy. This process is iterated multiple times to improve the strategy for both players. We demonstrate the effectiveness of our approach on a ransomware-inspired graph with a smart building system as the physical process. Numerical studies show that our method converges to a Nash equilibrium for various defender-specific costs of network hardening.

97 MATHEMATICS AND COMPUTING↗

Spatial Mode Correction of Single Photons Using Machine Learning

Abstract Spatial modes of light constitute valuable resources for a variety of quantum technologies ranging from quantum communication and quantum imaging to remote sensing. Nevertheless, their vulnerabilities to phase distortions, induced by random media, impose significant limitations on the realistic implementation of numerous quantum‐photonic technologies. Unfortunately, this problem is exacerbated at the single‐photon level. Over the last two decades, this challenging problem has been tackled through conventional schemes that utilize optical nonlinearities, quantum correlations, and adaptive optics. In this article, the self‐learning and self‐evolving features of artificial neural networks are exploited to correct the complex spatial profile of distorted Laguerre–Gaussian modes at the single‐photon level. Furthermore, the potential of this technique is used to improve the channel capacity of an optical communication protocol that relies on structured single photons. The results have important implications for real‐time turbulence correction of structured photons and single‐photon images.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗