Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Real Numbers”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21

ATLAS toward the High Luminosity era: challenges on electronic systems

To maximize the physics reach, the Large Hadron Collider (LHC) plans to increase its instantaneous luminosity to $7.5×10^{34} cm^{-2} s^{-1}$ and deliver $3 - 4 ab^{-1}$ of data at a center-of-mass energy of 14 TeV. To profit from this high-luminosity LHC operation with a pile-up up to 200 inelastic collisions per bunch crossing, performance of the ATLAS detector needs to be maintained and in many systems, improved. The upgraded detector will have an unprecedented output data rate of up to 200 TB/s. Real-time processing of this large data volume in a short time period is extremely challenging. New sets of both front-end and back-end electronics are required for all sub-detectors. The large number of detector channels, huge volumes of input and output data, short time available to process and transmit data, harsh radiation environment, and the need of low power consumption all impose great challenges on the designs of electronic systems.

43 PARTICLE ACCELERATORS↗

FY2021 Isolated Grids and Grid-Connected Turbine Reference Systems

For individuals, businesses, and communities focused on building resilient electrical grid infrastructure, wind energy can provide an affordable, accessible, and compatible distributed energy resource option that also enhances the capabilities of local grid operations. However, there are technical barriers to realizing the market value and resilience benefits of distributed wind, and there is little to no ability to quantify those benefits so that stakeholders can compare grid investment options. The central aims of this report are: (1) to drive technology transfer of the methods and technologies developed under the Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL) project and (2) increase the number of referenceable case studies available to stakeholders interested in additional value-added capabilities of wind systems beyond bulk energy supply. We achieve this aim by applying three major methods developed under MIRACL to two real-world distributed wind reference systems. The two real-world distributed wind reference systems are the isolated grid of St. Mary’s, Alaska, and the two 10.5-megawatt (MW) front-of-the-meter wind turbine deployments owned and operated by Iowa Lakes Electric Cooperative (ILEC).

17 WIND ENERGY↗

Cyber risk assessment and investment optimization using game theory and ML-based anomaly detection and mitigation for wide-area control in smart grids

The electric power grid is increasingly becoming susceptible to cyber attacks that exploit vulnerabilities in the smart grid control, information, and physical layers. Successful cyber attacks can have catastrophic impacts on the social and economic well-being of any nation all over the globe. It has, thus, become imperative to secure the smart grid against such adversarial actions to ensure stable, secure, and reliable operation of the grid. The existing research and industry practices prove to be inadequate in terms of providing pragmatic and effective defense methodologies and measures for long-term cybersecurity planning and real-time cybersecurity for grid operation. For example, existing works lack models that incorporate uncertain behavior of cyber-attackers and pragmatic defense measures for cyber risk assessment and cybersecurity investment optimization which often provide unreliable and strictly qualitative solutions to these problems. At the same time, with the growing number of cyber incidents in the grid, there still exists a need to develop attack-resilient algorithms for wide-area monitoring, protection, and control (WAMPAC) applications like the wide-area voltage control systems (WAVCS) for Flexible AC Transmissions Systems (FACTS) that lack in scalable and feasible solutions from the cybersecurity perspective. This dissertation proposes novel models and methodologies for: (1) Cybersecurity planning, and (2) Cybersecurity for system operation. The cybersecurity planning is achieved through cyber risk assessment and cybersecurity resource investment optimization for long-term cybersecurity of the grid using game theory and attack-defense trees. Cybersecurity for system operation consists of development of cyber anomaly detection and mitigation algorithms for flexible AC transmission system (FACTS) controller-based wide-area voltage control systems (WAVCS) using machine learning (ML), and software defined networking-based moving target defense network routing for achieving real-time cyber-physical security for grid operations. This is followed by hardware-in-the-loop (HIL) implementation and evaluation of these attack prevention, detection, and mitigation algorithms and methodologies showcasing their feasibility in a close to real-world environment. For cybersecurity planning, a novel approach involving a combination of game theory and attack defense trees (ADT) for optimal cybersecurity resource allocation in the smart grid is proposed. This methodology involves modeling of the cyber-physical smart grid substations as ADTs, defining attacker costs, defense costs, and attack probabilities for attack access points. Using game theoretical formulation, optimal defense strategies for the defender of the system to invest cybersecurity resources in the grid are obtained. Additionally, a game-theoretic framework is developed for quantitative cyber-physical risk assessment of the grid under a dynamically changing cyber threat space and uncertain behavior of cyber attackers which is further used to optimize investments in the smart grid's cybersecurity resources. The attacker, defender, and the smart grid system are modeled while incorporating attacker-stochasticity and federal guidelines for smart grid cybersecurity. This allows quantification of threat, vulnerabilities, and attack impact of the grid for quantitative risk assessment. The defender's budget to invest in the security resources in the grid is optimized based on the strategies leading to minimum system risk. The evaluation of the proposed solutions highlight the feasibility for practical implementation of these methodologies and algorithms in the smart grid, while taking the federal requirements and guidelines for smart grid security into consideration. For achieving cybersecurity for system operation, attack prevention, detection, and mitigation algorithms and methodologies are developed specifically for FACTS-based WAVCS. Anomaly detection and mitigation in the WAVCS are achieved using algorithms based on machine learning which involves offline training and testing of ML models with CPS datasets incorporating physics-based features that allow accurate distinction between system faults and cyber attacks. For attack prevention, a methodology based on software defined network (SDN)-based moving target defense (MTD) network routing is proposed that enables prevention of Denial of Service (DoS) type attacks on the smart grid communication system. Subsequently, these methodologies and algorithms are implemented and evaluated on an HIL testbed that allows for real-time attack prevention, detection, and mitigation of emulated cyber attacks on the WAVCS in a close to real-world environment. The results show highly accurate and efficient performance of the implemented algorithms and methodologies with the smart grid system operating within the NERC's system operation limits even in the presence of DoS and data integrity cyber attacks. This work opens up future research opportunities in other directions such as (1) Expanding cybersecurity planning methodologies to real-time cyber contingency analysis with different game formulations; and (2) Applying the cybersecurity for system operation algorithms to broader categories of wide-area control applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Constrained non-negative matrix factorization enabling real-time insights of in situ and high-throughput experiments

Non-negative matrix factorization (NMF) is an appealing class of methods for performing unsupervised learning on streaming spectral data, particularly in time-sensitive applications such as in situ characterization of materials. These methods seek to decompose a dataset into a small number of components and weights that can compactly represent the underlying signal while effectively reconstructing the observations with minimal error. However, canonical NMF methods have no underlying requirement that the reconstruction uses components or weights that are representative of the true physical processes. In this work, we demonstrate how constraining a subset of the NMF weights or components as rigid priors, provided as known or assumed values, can provide significant improvement in revealing true underlying phenomena. We present a PyTorch-based method for efficiently applying constrained NMF and demonstrate its application to several synthetic examples. Our implementation allows an expert researcher-in-the-loop to provide and dynamically adjust the constraints during a live experiment involving streaming spectral data. Such interactive priors allow researchers to specify known or identified independent components, as well as functional expectations about the mixing or transitions between the components. We further demonstrate the application of this method to measured synchrotron x-ray total scattering data from in situ beamline experiments. In such a context, constrained NMF can result in a more interpretive and scientifically relevant decomposition than canonical NMF or other decomposition techniques. As a result, the details of the method are provided, along with general guidance for employing constrained NMF in the extraction of critical information and insights during time-sensitive experimental applications.

36 MATERIALS SCIENCE↗

In-situ/operando soft x-ray spectroscopy characterization of energy and catalytic materials

The capabilities of soft x-ray absorption (XAS), soft x-ray emission spectroscopy (XES), resonant inelastic soft x-ray scattering (RIXS), and their application to characterization of solar energy materials are presented. In this work, we have discussed some recent developments of in-situ soft x-ray spectroscopy cells, which enable the investigation of critical solid/liquid or solid/gas interfaces in chemical and electrochemical processes under real-world practical conditions. In particular, in-situ soft x-ray spectroscopies can be utilized to probe the formation of intermediate species, charge separation upon illumination of sunlight and electron transfer to the interfacial reactions. A number of examples using soft x-ray spectroscopies to study these solar energy and catalytic materials are discussed to demonstrate how these powerful characterization tools could be helpful to further understand the energy conversion and energy storage systems.

14 SOLAR ENERGY↗

Statistical Analysis of Intertube Tunneling Contacts in the Macroscopic Electrical Conductivity of Carbon Nanotube Fibers

Here, this study investigates the influence of tunneling contact resistances between carbon nanotubes (CNTs) on electron transport and electrical conductivity of macroscopic carbon nanofibers (CNFs), which profoundly impacts the performance of CNT thin film electronics, CNF electron emitters and cathodes, and energy conversion and storage devices. Utilizing a self-consistent electrical contact model coupling a transmission line model with tunneling current, we calculate the contact resistances of a plethora of CNT-CNT contacts within a CNF fiber, which consists of aligned, densely packed CNTs. A statistical analysis is conducted, using Gaussian distributions to account for variations in contact lengths, tunneling gap distances, and single CNT aspect ratios, to calculate the CNT-CNT contact resistance and the overall resistance of CNT fiber. By scaling our model to a macroscopic level, our results are in good agreement with experimental measurements. Our calculation suggests that while increasing the contact overlap length diminishes individual CNT-CNT contact resistance, it could paradoxically increase macroscopic CNT fiber resistance for a given constant CNF mass density, which is due to that fact that a larger overlap length allows more CNTs to pack along an electrical conduction path per unit length, leading to more tunneling contact junctions connected in series and thus less number of parallel conduction paths within the fiber cross section. Increasing tunneling gap distance increases both individual contact and overall fiber resistance. This research provides a simple design tool for tailoring CNT fiber electrical properties to promote real-world applications using CNTs or similar low-dimensional materials.

36 MATERIALS SCIENCE↗

QUANT-NET Control Plane Framework (QNCP) v1.0.0

The QUANT-NET Control Plane (QNCP) provides a software framework for expressing and managing quantum network resources. It may be used to orchestrate a physical quantum testbed with real device driver implementations, or it may be used as a proving ground when developing new protocols and management functions. In practice, both approaches may be useful when undertaking research and development in emerging quantum testbeds. While a number of control systems have been developed for specific quantum platform demonstrations, an openly available and general solution for operating quantum networks has not emerged. QNCP is designed to fill this gap. The framework has been designed to provide extensible, modular capabilities that include scheduling, routing, monitoring, and pluggable protocols. A number of reference implementations in each module category have been included in the installable packages; however, the intent is that each of these modules may be extended or re-implemented to meet the needs of the particular deployment or research need. The software is currently being used in the QUANT-NET testbed project, which spans resources between LBNL and UC Berkeley Physics.

Zhang, Liang [Lawrence Berkeley National Laborator↗

Evaluation of camera-based freehand SPECT in preoperative sentinel lymph node mapping for melanoma patients

Assessment of lymphatic status via sentinel lymph node (SLN) biopsy is an integral and crucial part of melanoma surgical oncology. The most common technique for sentinel node mapping is preoperative planar scintigraphy of an injected gamma-emitting lymphatic tracer followed by intraoperative node localization using a non-imaging gamma probe with auditory feedback. In recent years, intraoperative visualization of SLNs in 3D has become possible by coupling the probe to an external system capable of tracking its location and orientation as it is read out, thereby enabling computation of the 3D distribution of the tracer (freehand SPECT). In this project, the non-imaging probe of the fhSPECT system was replaced by a unique handheld gamma camera containing an array of sodium iodide crystals optically coupled to an array of silicon photomultipliers (SiPMs). A feasibility study was performed in which preoperative SLN mapping was performed using camera fhSPECT and the number of detected nodes was compared to that visualized by lymphoscintigraphy, probe fhSPECT, and to the number ultimately excised under non-imaging probe guidance. Among five subjects, SLNs were detected in nine lymphatic basins, with one to five SLNs detected per basin. A basin-by-basin comparison showed that the number of SLNs detected using camera fhSPECT exceeded that using lymphoscintigraphy and probe fhSPECT in seven of nine basins and five of five basins, respectively. (Probe fhSPECT scans were not performed for four basins.) It exceeded the number excised under non-imaging probe guidance for seven of nine basins and equaled the number excised for the other two basins. Freehand SPECT using a prototype SiPM-based gamma camera demonstrates high sensitivity for detection of SLNs in a preoperative setting. Camera fhSPECT is a potential means for efficiently obtaining real-time 3D activity distribution maps in applications such as image-guided percutaneous biopsy, and surgical SLN biopsy or radioguided tumor excision.

60 APPLIED LIFE SCIENCES↗

Retro-Commissioning Sensor Suitcase for Energy Efficiency

This project will enable Pacific Northwest National Laboratory (PNNL) and Lawrence Berkeley National Laboratory (LBNL) to work with industry partner, GreenPath Energy Solutions, joint developers of the Suitcase, to enhance the capabilities and usability of the Retro-Commissioning Sensor Suitcase (hereinafter the Sensor Suitcase or Suitcase), assisting GreenPath to take the Suitcase to market and rapidly expand their market share. The proposed project will specifically focus on 1) adding sensors types to extend the data collection capability and support more building and equipment performance metrics and identification of even more energy saving opportunities, 2) developing algorithms to identify recommendations for the new energy savings opportunities from item 1 and to prototype software modifications implementing them, 3) validating the use of vibration sensors to detect the operating state of a broader set of packaged HVAC equipment (additional capacities, different numbers of stages, etc.) than tested in initial development and modifying the state algorithm and software code, as needed, 4) improving cost-effectiveness in manufacturing the Sensor Suitcase, and 5) additional field testing of the technology in real buildings to more comprehensively validate Suitcase performance and to guide refinement of its capabilities. Project results will position GreenPath, and potential future licensees, to implement the new capabilities developed in this project in GreenPath’s RCx Building Suitcase, increasing its functionality and the savings resulting from its use. These enhancements will increase the value of the Suitcase to users and increase the potential market for its use and impacts in that impact.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Distributed Grid Control of Flexible Loads and DERs for Optimized Provision of Synthetic Regulating Reserves

Over the course of this project, we have successfully de-risked our distributed microgrid control architecture by tightly integrating its associated control algorithms into a unified software library, installing the software library on several industrial-grade target hardware platforms, and validating the performance of the resulting microgrid controller in a real-life microgrid. Upon completion of the project, we demonstrated that our distributed control architecture is resilient against (i) failures in control devices, (ii) unreliable communication links, (iii) delays in transmitted data, and (iv) imperfect knowledge of the number of (and state of) generation and load assets in the microgrid. In this final report, we present results from all the milestones that were accomplished over the course of this project.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Applications and Techniques for Fast Machine Learning in Science

In this community review report, we discuss applications and techniques for fast machine learning (ML) in science—the concept of integrating powerful ML methods into the real-time experimental data processing loop to accelerate scientific discovery. The material for the report builds on two workshops held by the Fast ML for Science community and covers three main areas: applications for fast ML across a number of scientific domains; techniques for training and implementing performant and resource-efficient ML algorithms; and computing architectures, platforms, and technologies for deploying these algorithms. We also present overlapping challenges across the multiple scientific domains where common solutions can be found. This community report is intended to give plenty of examples and inspiration for scientific discovery through integrated and accelerated ML solutions. This is followed by a high-level overview and organization of technical advances, including an abundance of pointers to source material, which can enable these breakthroughs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Building MCP-native hierarchical AI scientist ecosystems: a perspective on scaling multi-agent scientific discovery

Large language models (LLMs) are evolving from chatbots with limited tool-using capabilities to agentic AI systems that can perform deep research, assist in proposing hypotheses, help design experiments, automate data analysis, and draft scientific reports. However, there are currently two bottlenecks limiting LLMs' real-world impact on the broader scientific research community beyond academic demonstrations: lack of interoperability (repetitive manual tool-integration is required across scenarios) and the need for scalable coordination (unstructured communication and memory become brittle as the number of agents grows). In this Perspective, we argue that the next phase of agentic scientific discovery requires the development of an ecosystem of protocol-native agents and tools organized through hierarchies inspired by human society, beyond the current paradigm of a single monolithic “AI scientist”. We use Model Context Protocol (MCP) as a concrete example of an emerging interoperability layer for scientific tool and context exchange, and we propose three complementary pathways to increase the scaling capabilities of an MCP-native scientific ecosystem by addressing the composability issues: (1) MCP servers for high-value scientific tools maintained by domain experts, (2) automated transformation of existing code repositories into MCP services, and (3) autonomous invention and evolution of new agents and workflows. Finally, we provide a practical roadmap for scaling AI-driven scientific discovery by expanding tool supply and coordination in MCP-native scientific ecosystems.

97 MATHEMATICS AND COMPUTING↗

A Voltage Inference Framework for Real-Time Observability in Active Distribution Grids

Active distribution grids are gaining traction to meet the growing environmental, socio-economic, and sustainability targets. Various advanced smart grid technologies facilitate the integration of Distributed Energy Resources (DERs) by supporting the bi-directional power flow. The limited observability of distribution grids, primarily related to their location at the very edge of power system infrastructure, brings challenges to optimal grid management. Moreover, only a limited number of measurements at regular intervals are usually available. This paper presents a novel inference framework, referred to as “Voltage Inference”, to overcome the observability issues. The proposed framework employs a prediction step based on the Multivariate Taylor series approximation, followed by a corrector step that minimizes the estimation error to infer the otherwise unknown voltages from the available measurements. Furthermore, numerical results on the IEEE 13-bus test feeder validate the accuracy and computational performance of the proposed framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Co-optimization of repairs and dynamic network reconfiguration for improved distribution system resilience

In this work, a post-disaster distribution system repair and restoration (DSRR) strategy is proposed to improve distribution system resilience. The DSRR strategy is formulated as a two-stage optimization. The first stage is a comprehensive co-optimization of repair crew scheduling, dynamic network reconfiguration, and distributed energy resource (DER) dispatch based on the forecast load profile. The goal is to minimize the accumulative operating cost caused by the load reduction payment as well as DER operating cost. In particular, since the number of available repair crews is usually smaller than the number of faulted lines after a disaster event, the DSRR strategy determines the optimal scheduling for repairing faulted lines. The second stage is a re-dispatch of the DER power output and load shedding based on the real-time load demand of each bus. The proposed algorithm is validated by case studies of the IEEE 33-bus and 123-bus test systems. We consider those scenarios in which faults occur in multiple heavy-loaded feeders. The simulation results demonstrate that the DSRR strategy effectively coordinate the repair scheduling, network reconfiguration and load shedding to minimize the operating cost.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Chemical Imaging of Atmospheric Biomass Burning Particles from North American Wildfires

The effects of biomass burning aerosols (BBA) on radiative forcing and cloud formation depend on chemical composition and the internal structures of individual particles within smoke plumes. To improve our understanding of the chemical and physical properties of BBA emitted at different times of the day and their evolution during atmospheric aging, we conducted a study as a part of the Fire Influence on Regional to Global Environments and Air Quality field campaign. Particle samples were collected onboard a research aircraft from smoke plumes from a wildfire in eastern Oregon during late afternoon and nighttime flights on August 28, 2019. A time-resolved aerosol collector was used to collect samples on substrates for offline spectromicroscopic imaging to investigate the single-particle characteristics of BBA particles. Approximately 20,400 individual particles from 10 selected samples were analyzed using computer-controlled scanning electron microscopy coupled with energy-dispersive X-ray microanalysis, revealing their elemental composition, morphology, and viscosity. Elemental microanalysis indicated that aged potassium is likely found in the form of K 2 SO 4 , KNO 3 , and possible K-organic salts. Further chemical speciation and carbon bonding mapping within individual particles were conducted using synchrotron-based scanning transmission X-ray microscopy (STXM) coupled with near edge X-ray absorption fine structure (NEXAFS) spectroscopy. Real-time, water-soluble light absorption measurements were acquired using a particle-into-liquid sampler instrument coupled to a liquid waveguide capillary cell and total organic analyzer. In the late afternoon samples, 65% of the total particle number population consisted entirely of organic components, compared to 46% in the nighttime particles. These differences were attributed to discrepancies in composition at the time of emission and to the daytime condensation and accumulation of photochemically formed secondary organic material on existing BBA particles, a process that halts at night. Microscopy images indicated that particle viscosity was lower in the nighttime particles (<10 1 Pa·s), likely due to increased relative humidity and a higher contribution from hygroscopic inorganic components. The chemical heterogeneity of individual particles was quantified using STXM-derived mixing state parameters. The nature of carbon bonding within individual particles was inferred from the extent of carbon sp 2 hybridization derived from NEXAFS spectra. Average percentages of sp 2 hybridization range between 40% and 60%, with no noticeable differences between late afternoon and nighttime flights. These findings were compared with the online optical properties of both late afternoon and nighttime smoke plumes, providing valuable insights into the complex relationship between chemical composition and optical properties of BBA particles at different times of the day.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Attack on Grid Event Cause Analysis: An Adversarial Machine Learning Approach

With the ever-increasing reliance on data for data-driven applications in power grids, such as event cause analysis, the authenticity of data streams has become crucially important. The data can be prone to adversarial stealthy attacks aiming to manipulate the data such that residual-based bad data detectors cannot detect them, and the perception of system operators or event classifiers changes about the actual event. This paper investigates the impact of adversarial attacks on convolutional neural network-based event cause analysis frameworks. We have successfully verified the ability of adversaries to maliciously misclassify events through stealthy data manipulations. The vulnerability assessment is studied with respect to the number of compromised measurements. Furthermore, a defense mechanism to robustify the performance of the event cause analysis is proposed. The effectiveness of adversarial attacks on changing the output of the framework is studied using the data generated by real-time digital simulator (RTDS) under different scenarios such as type of attacks and level of access to data.

Niazazari, Iman↗

MCS+: An Efficient Algorithm for Crawling the Community Structure in Multiplex Networks

In this article, we consider the problem of crawling a multiplex network to identify the community structure of a layer-of-interest. A multiplex network is one where there are multiple types of relationships between the nodes. In many multiplex networks, some layers might be easier to explore (in terms of time, money etc.). We propose MCS+, an algorithm that can use the information from the easier to explore layers to help in the exploration of a layer-of-interest that is expensive to explore. We consider the goal of exploration to be generating a sample that is representative of the communities in the complete layer-of-interest. This work has practical applications in areas such as exploration of dark (e.g., criminal) networks, online social networks, biological networks, and so on. For example, in a terrorist network, relationships such as phone records, e-mail records, and so on are easier to collect; in contrast, data on the face-to-face communications are much harder to collect, but also potentially more valuable. We perform extensive experimental evaluations on real-world networks, and we observe that MCS+ consistently outperforms the best baseline—the similarity of the sample that MCS+ generates to the real network is up to three times that of the best baseline in some networks. We also perform theoretical and experimental evaluations on the scalability of MCS+ to network properties, and find that it scales well with the budget, number of layers in the multiplex network, and the average degree in the original network.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗