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At least 307 records · Page 17

FECM/NETL Natural Gas with Hydrogen Pipeline Cost Model (2024): Description and User’s Manual

This is the user’s manual for The FECM/NETL Natural Gas with Hydrogen Pipeline Cost Model (NG-H2_P_COM) that estimates costs for transporting gaseous hydrogen with natural gas in a pipeline from a source, such as a hydrogen production facility, to a final destination which may be a user of the hydrogen and natural gas or a distribution center where hydrogen in the pipeline with natural gas is diverted to multiple end users. This user’s manual provides two main functions. First, the detailed statement describes the equations and algorithms that are used by the model to calculate technical quantities (such as blend hydrogen percentage, reuse percentage of the pipeline and stations, the pipe diameter size and length needed to transport a user-specified hydrogen with natural gas rate in a specified distance) and engineering-economic quantities (such as capital costs, operating costs, and cash flows). Second, the document is a user’s manual for the model that describes the procedures the user must follow to configure and setup the model, run the model, analyze the results, and visualize the outcomes. Such details offer user a quick and handy way to utilize the model for their application and decision making. The model can be accessed at this URL: https://www.netl.doe.gov/energy-analysis/details?id=cf3f6564-3c55-4aa5-b712-7160e558d9f6. The Model Results and Comparative Analysis can be accessed here: https://www.netl.doe.gov/energy-analysis/details?id=83862799-a28c-4944-a809-90b7e23d4af6.

03 NATURAL GAS↗

Mars Global Reference Atmospheric Model 2010 Version: Users Guide

This Technical Memorandum (TM) presents the Mars Global Reference Atmospheric Model 2010 (Mars-GRAM 2010) and its new features. Mars-GRAM is an engineering-level atmospheric model widely used for diverse mission applications. Applications include systems design, performance analysis, and operations planning for aerobraking, entry, descent and landing, and aerocapture. Additionally, this TM includes instructions on obtaining the Mars-GRAM source code and data files as well as running Mars-GRAM. It also contains sample Mars-GRAM input and output files and an example of how to incorporate Mars-GRAM as an atmospheric subroutine in a trajectory code.

Justh, H. L.↗

Final report of activities for the LDRD-express project #223796 titled: “Fluid models of charged species transport: numerical methods with mathematically guaranteed properties”, PI: Ignacio Tomas, Co-PI: John Shadid

This report summarizes the findings and outcomes of the LDRD-express project with title “Fluid models of charged species transport: numerical methods with mathematically guaranteed properties”. The primary motivation of this project was the computational/mathematical exploration of the ideas advanced aiming to improve the state-of-the-art on numerical methods for the one-fluid Euler-Poisson models and gain some understanding on the Euler-Maxwell model. Euler-Poisson and Euler-Maxwell, by themselves are not the most technically relevant PDE plasma-models. However, both of them are elementary building blocks of PDE-models used in actual technical applications and include most (if not all) of their mathematical difficulties. Outside the classical ideal MHD models, rigorous mathematical and numerical understanding of one-fluid models is still a quite undeveloped research area, and the treatment/understanding of boundary conditions is minimal (borderline non-existent) at this point in time. This report focuses primarily on bulk-behaviour of Euler-Poisson’s model, touching boundary conditions only tangentially.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimal gas cooling with minimal aero-opticaldistortion for next generation high-average-power lasers (Progress report, Year 2)

Next-generation lasers that combine high-peak-power ultrashort pulses with high repetition rates have the potential to efficiently deliver the high-average-power outputs required for inertial fusion energy generation, laser-based particle acceleration, and to generate compact secondary x- and 𝛾-ray radiation sources, among others. The combination of long gain length with high surface-to-volume ratio to remove residual heat makes gas-cooled multi-slab amplifier heads an inherently aperture- and average power scalable technology that enables this new class of solid-state lasers, and their thermal management becomes the most pressing technical challenge. As the index-of refraction depends on the gas density, heat removal from the slab surfaces unavoidably entails scattering of propagated light from regions of high temperature fluctuations. The requirement to maximize convective heat extraction from the gain medium under the constraint of minimum optical aberration of the beam renders amplifier slab cooling a technological challenge at the intersection of aero-optics, fluid-mechanics and heat transfer. The goal of this research is to leverage computational fluid dynamics and aero optics simulations of different levels of fidelity to devise a numerical modeling and optimization framework for gas-cooled multi-slab amplifiers. The project will be conducted in close collaboration with the Advanced Photon Technologies Group at Lawrence Livermore National Laboratory, where a gas-cooled test stand for laser materials and thermal management structures will be developed and installed. The final goal of the collaborative effort is to manufacture and benchmark a physical prototype of an numerically optimized amplifier head design. Measurement data on solid-state and thermo-optical distortions will be used for the validation of the numerical models. The key technical challenge in this multi-objective design problem is that of balancing optimal heat removal with minimal optical distortion. To facilitate computationally efficient design optimization and, at the same time, deepen our basic understanding of the interaction of light with turbulence, a complementary study that combines high and low-fidelity flow simulations and aero-optical models is proposed. Along the lines of these two objectives and solution strategies, the project is organized into two thrusts.

42 ENGINEERING↗

Bridging the Gap for Powering Data Centers

The rapid expansion of data centers, primarily driven by artificial intelligence, is outpacing the adaptability of the U.S. electric grid. This report, developed by Idaho National Laboratory (INL) , presents a gap analysis of some of the infrastructure challenges associated with large-scale data center deployment. Drawing from a national workshop hosted by INL in October of 2025, the report synthesizes stakeholder insights, survey data, and technical discussions to identify critical barriers and research needs. Key findings highlight the growing preference for behind-the-meter generation, the perceived inadequacy of legacy interconnection processes, and the urgent need for improved coordination between utilities, regulators, and data center developers. Environmental concerns such as water use and noise pollution, as well as economic constraints like equipment lead times and cost allocation, are also explored. The report outlines national lab capabilities in modeling, simulation, and technical assistance, and proposes targeted R&D priorities to support resilient, scalable, and efficient integration of data centers into the grid.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Collaborative Research: Unveiling the Interplay Between Magnetic Reconnection and Turbulence — Theory and Modeling

This is the final technical report for the project "Collaborative Research: Unveiling the Interplay Between Magnetic Reconnection and Turbulence — Theory and Modeling." This project investigated the interplay between two fundamental plasma processes — turbulence and magnetic reconnection — and the associated heating and particle acceleration. In particular, we focused on a new regime where the plasmoid instability mediates the turbulent energy cascade. In this new regime, reconnecting current sheets are disrupted by the growth of plasmoids/flux ropes on time scales shorter than the typical turnover times of eddies, speeding up the energy cascade and steepening the turbulence energy spectrum. This project addressed the following outstanding open questions: (1) What are the fundamental differences between plasmoid‐mediated turbulence cascade in three dimensions (3D) and two dimensions (2D)? (2) What are the essential features of plasmoid‐mediated turbulence in weakly collisional or collisionless regimes beyond resistive MHD? (3) How does the interplay of turbulence and reconnection regulate the energy release and dissipation in space and astrophysical plasmas? To address these questions, we have carried out three investigations: (1) Three-dimensional plasmoid-mediated turbulence energy cascade; (2) plasmoid-mediated reconnection and turbulence in three-dimensional Hall MHD; (3) reconnection and heating in coronal loops. This technical report summarizes the key findings of these investigations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Productive Use of Energy in African Micro-Grids: Technical and Business Considerations

Demand for electricity from small industry and businesses, which is defined as the productive use of energy (PUE), is a key success factor for micro-grids. Because of the typically low energy usage of residential customers, without linkage to and support for these energy users, micro-grids are likely to struggle to reach the critical revenue needed for financial viability. This report is a resource entrepreneurs and developers can use to understand the technical and business model challenges related to PUE in smaller micro-grids. It focuses on small agricultural processing, and small industrial and commercial loads. This report examines best practices for promoting PUE and the business models used by developers. It starts with background information and a literature review followed by a discussion of key enterprise considerations for productive use (PU) including: value chain and business case analysis, enterprise development and training, appliance financing, and developers running PU businesses. Unlike many other reports on PUE, this report is based on application specific data. The report is also unique in that it provides actual customer demographics and load profiles. This report considers PUE from both business and technical perspectives, and it considers the interests of both the micro-grid operators and the microenterprises and entrepreneurs they serve. It looks at the service levels required by different PUs and the technical characteristics and challenges of different types of PU equipment. The report also includes examples of business cases for some of the most important PU opportunities, including milling, ice making, carpentry, egg incubation, and water treatment. This report is a resource that entrepreneurs, governments, and non-governmental organizations can use to help design programs to meet their individual goals of PUE in micro-grids and economic development in rural Africa. It can also be used by developers, engineers, and other organizations designing micro-grids to inform their technical and business decisions and to improve system design, reduce risk, and increase success with adding PU loads to both new and existing micro-grids.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Using Model-Based Systems Engineering To Provide Artifacts for NASA Project Life-Cycle and Technical Reviews

The ability of systems engineers to use model-based systems engineering (MBSE) to generate self-consistent, up-to-date systems engineering products for project life-cycle and technical reviews is an important aspect for the continued and accelerated acceptance of MBSE. Currently, many review products are generated using labor-intensive, error-prone approaches based on documents, spreadsheets, and chart sets; a promised benefit of MBSE is that users will experience reductions in inconsistencies and errors. This work examines features of SysML that can be used to generate systems engineering products. Model elements, relationships, tables, and diagrams are identified for a large number of the typical systems engineering artifacts. A SysML system model can contain and generate most systems engineering products to a significant extent and this paper provides a guide on how to use MBSE to generate products for project life-cycle and technical reviews. The use of MBSE can reduce the schedule impact usually experienced for review preparation, as in many cases the review products can be auto-generated directly from the system model. These approaches are useful to systems engineers, project managers, review board members, and other key project stakeholders.

SE Product↗

Experiments to validate Thermodynamics and Transport models of Strongly Coupled Dusty Plasma Matter (Final Technical Report for DE-SC0023416)

The goal of this two-year grant is to provide access to the PI to dusty plasma experimental facilities at the DOE-funded Collaborative Research Facility Magnetized Plasma Research Laboratory, Auburn University to become a user of that facility, to obtain experimental data to support another ongoing grant DE-SC0021146 (an Early Career Award to the PI that is focused on modeling of dusty plasma thermodynamics and transport processes), to generate experimental data for funding proposals, and to provide exposure to University of Memphis students to advanced experimental techniques. The following technical accomplishments were made: 1. Development of a novel Bidirectional Electrode Control Arms Assembly (BECAA) for producing perfect 2D grain layers for complex plasma experimentation. BECAA uses movable electrode arms to tilt or move the electrode in a RF discharge from outside the chamber, allowing for the manipulation of grain clouds without needing to change the plasma parameters or gas pressure. This work addresses a longstanding gap in the literature for a method to produce clusters of selectable number of grains and that are perfectly two dimensional as opposed to being only quasi-2D. 2. Experimental investigation of the structural properties of finite-N clusters with N=2 to 50. Individual particle behavior in clusters could vary from grain to grain and this study measured systematically produced clusters for two different grain sizes. Analysis (funded by another grant DE-SC0021146) is currently underway to quantify the differences between grains that are found on the surface vs. the interior of clusters, the shell structure, and the decay of correlations in position, velocity, and kinetic energy. 3. An experimental method to measure the structural entropy of clusters was developed by observing the self-induced structural transitions between various possible arrangements. In a series of heating and cooling cycles, the number of times each possible arrangement was attained was experimentally observed and used to compute the probability of existence of that arrangement, and subsequently the configurational entropy of the cluster. Analysis (funded by another grant DE-SC0021146) is currently underway to produce the entropy of clusters as a function of the number of grains and use the same to compute thermodynamic state variables for 2D complex plasma/grain clusters. 4. A preliminary experimental study of multibody collisions between N grains (N=2 – 10) was conducted. The clusters were produced using the BECAA technique and velocities were imparted to the grains using manipulation laser pulses. Analysis (funded by another grant DE-SC0021146) is currently underway to develop a theoretical framework to describe multibody collisions analogous to classical two-body interactions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

AI Model Benchmarking for Nonproliferation Applications: Steel Thread Benchmarking Task Force Technical Report (Rev. 2)

Steel Thread is a NA-22 venture that seeks to build trustworthy, reliable AI models that can be used in a wide variety of nonproliferation tasks. A key aspect of building these models is developing appropriate benchmarks and evaluation methods, which will enable the venture to identify and adapt models to provide the most value in the nonproliferation domain. Benchmarks must be relevant to key tasks in this domain, such as question answering, information retrieval, document summarization and classification, consensus analysis, and image and data analysis. This report 1) provides an overview of benchmark design, evaluation, and challenges; 2) reviews a variety of open benchmarks, with a focus on language models and tasks; and 3) identifies benchmarks that are most relevant to Steel Thread. This report is intended to serve as a basis for further efforts to classify and evaluate benchmarks and their correlation with success on nonproliferation-specific tasks. The Steel Thread venture has defined benchmarks to be a particular combination of a dataset (or datasets) and a metric (or metrics) conceptualized as representing one or more specific tasks or sets of abilities for a specific modality. It is adopted by a research community as a shared framework for comparing methods.1 It includes 1) Data: Labeled (a designated subset not used for training, which could be all the data), 2) Metric: A way to quantify performance, 3) Task/Ability: What the benchmark is testing, 4) Protocol: A structured and repeatable evaluation process, 5) Baseline/Reference Model: For comparison; could be statistical, rule-based, SME-derived, or another model, and 6) Maintenance Plan: to update with new information over time; important for long-term utility. For further clarity, the definition includes what a benchmark, in this context, is not. It is not a corpus of training data, specific to a model (it is intended to apply to a range of models), a universal evaluation of performance, a guarantee that the ‘top’ model on the leaderboard will be the best fit for every specific use case, an all-encompassing proof of a model’s universal quality, nor is it a one-size-fits-all measure of success. It does not cover every real-world constraint (like operational, ethical, or cost considerations), a systems integration test, or a unit test. This definition was inspired by and resulted from discussions within the Steel Thread Benchmarking Task Force. This group was formed to define what we would mean as a benchmark within Steel Thread but persisted as the need to develop a thorough understanding of the large and expanding existing benchmarking space. This technical report is a result of the group’s divide and conquer approach to exploring this space. The release of benchmarks might not be progressing as quickly as model development, but it is moving very fast, as many benchmarks quickly become saturated, when state-of-the-art models score so close to the benchmark’s ceiling that their results are virtually indistinguishable. At that point, the test no longer differentiates between new systems, so researchers usually stop reporting scores as the benchmark no longer informs about improvements from the next generation of models. In the OpenAI announcement of GPT-5, they reported results on six flagship public benchmarks (AIME 2025, SWE-bench Verified, Aider Polyglot, MMMU, HealthBench Hard, GPQA) but the full system-card covers roughly thirty-five separate evaluations, comprising hundreds of test task items in total. There have been some efforts to summarize benchmarks in specific fields, like for text-to-image generation, but these surveys have had a narrow methodology scope. Therefore, a comprehensive survey of all benchmarks or even all benchmarks that could be relevant to Steel Thread is outside of the scope of this report. We chose some specific benchmarks to investigate in detail.

97 MATHEMATICS AND COMPUTING↗

Complete tank tests of two flying-boat hulls with pointed steps - N.A.C.A. Models 22-A and 35

This note presents the results of complete tank test of N.A.C.A. Models 22-A and 35, two flying-boat hulls of the deep pointed-step type with low dead rise. Model 22-A is a form derived by modification of Model 22, the test results of which are given in N.A.C.A. Technical Note No. 488. Model 35 is a form of the same type but has a higher length-beam ratio than either Model 22 or 22-A. Take-off examples are worked out using data from these tests and a previous test of a conventional model applied to an arbitrary set of design specifications for a 15,000-pound flying boat. The comparison of these examples shows both pointed-step models to be superior to the conventional form, and Model 35 to be the better of the two. Model 35 is applied to a hypothetical 100,000-pound flying boat of the twin-hull type and performance calculations are made both for take-off and range. The results indicate that the high performance of this type of hull will enable the designer to use higher wing and power loadings than are found in current practice, with a resulting increase in range and pay load.

Shoemaker, James M↗

Scenario Development Process at the Vertical Motion Simulator

There has been a significant effort within the simulation community to standardize many aspects of flight simulation. More recently, an effort has begun to develop a formal scenario definition language for aviation. A working group within the AIAA Modeling and Simulation Technical Committee has been created to develop a standard aviation scenario definition language, though much of the initial effort has been tailored to training simulators. Research and development (R&D) simulators, like the Vertical Motion Simulator (VMS), and training simulators have different missions and thus have different scenario requirements. The purpose of this paper is to highlight some of the unique tasks and scenario elements used at the VMS so they may be captured by scenario standardization efforts. The VMS most often performs handling qualities studies and transfer of training studies. Three representative handling qualities simulation studies and two transfer of training simulation studies are described in this paper. Unique scenario elements discussed in this paper included special out-the-window (OTW) targets and environmental conditions, motion system parameters, active inceptor parameters, and configurable vehicle math model parameters.

Vertical Motion Simulator↗

Physical and technical basis of Materials Plasma Exposure eXperiment from modeling and Proto-MPEX results *

Abstract The Materials Plasma Exposure eXperiment (MPEX) is a steady-state linear plasma device that will address plasma-material interaction (PMI) science and enable testing of fusion reactor-relevant divertor plasma-facing materials. The MPEX source concept consists of a helicon plasma source to generate the plasma, electron cyclotron heating (ECH) for electron heating, and ion cyclotron heating (ICH) for ion heating. The MPEX source plasma is then transported axially to the PMI material target region to test material samples in fusion reactor-relevant divertor conditions. This paper will summarize the physical and technical basis of MPEX. The paper will first define the MPEX parameters and scenarios at the target relevant to PMI science for various fusion reactor-relevant divertor conditions and show plasma transport modeling results to set the MPEX source parameters. Recent experimental and modeling results from Proto-MPEX, a short-pulse experiment to develop the plasma production, heating, and transport physics for MPEX, will be shown. From these results, it will be shown that MPEX can reach its desired scenarios. The MPEX physical and technical basis will also determine important functional requirements for magnetic field, radiofrequency (RF) power, RF frequency, and neutral pressure in the helicon, ECH, ICH, and PMI regions that are required to achieve the desired MPEX scenarios. The necessity for key in-vessel components such as skimmers, limiters, and microwave absorbers will also be highlighted.

Lau, C. (ORCID:0000000285765867)↗

Playing a 3-Stringed Violin: Innovation via the Joint Evolution of People, Process, and Knowledge Management System

Users continuously evaluate the value and performance of their Knowledge Management Systems (KMS). As suggested by a punctuated socio-technical system process model, today's success can quickly become tomorrow's failure should the KMS fail to meet evolving needs and expectations. The more deeply a tool is embedded in the actual work process, the more vulnerable it is to emergent changes and perturbations. This paper uses the metaphor of a "3-stringed violin" to explore how differing levels of user knowledge about tools and processes can lead to system perturbations and how the active involvement of other actors can dampen the impact of perturbations, i.e., help the system survive the operational equivalent of a broken string. Recommendations suggest ways to increase system resiliency and contribute to incremental innovation.

Socio-technical systems↗

U.S. Department of Energy-National Lab Equity Summit: Grid Planning and Operations (Workshop Report)

This report summarizes the U.S. DOE and national laboratories equity summit that was held on February 5, 2024, and focused on grid planning and operations. The objectives of the summit were to connect DOE and lab researchers working on grid-related equity issues, share information on current and planned grid-related equity projects and initiatives, and inspire and educate participants by hearing from our panelists about solutions and challenges to integrating equity in grid planning and operations. The summit included two panels of industry leaders. The first was a state and community perspectives panel that included representatives from a state public utility commission (Oregon Public Utility Commission), a state energy office (Washington Department of Commerce), a state utility consumer advocate (Connecticut Consumer Counsel), and industry consultants (Elevated Engagement and ArkSpring Consulting). Panelists shared successes they have seen, critical challenges related to equity and grid planning and operations, and other considerations. The second panel addressed utility perspectives and included representatives from two utilities (Commonwealth Edison and Tacoma Power), the National Rural Electric Cooperative (NRECA), and a former utility employee and legal consultant. Panelists discussed the role of the utility concerning equity, the most significant technical and data modeling needs and opportunities, and the role the labs could help advance equity in grid planning and operations. There was also a session on partner organization presentations. Argonne National Laboratory made a short presentation on the Grid Modernization Laboratory Consortium (GMLC) project they are leading on equity-informed power system planning. NARUC, NASEO, and the Clean Energy States Alliance, as partners of the GMLC project also shared updates on relevant activities and resources. During the summit, there were two rounds of lightning presentations by national labs and DOE highlighting research that addresses equity and grid planning and operations (Tables 5 and 6 and slides in the Appendix). The goal of the lightning rounds was to share information between participants to encourage collaboration and leverage ongoing research at labs and DOE. The summit included two interactive exercises where summit participants shared their perspectives on relevant equity projects and initiatives (Table 2), key challenges regarding equity and grid planning and operations (Table 3), and promising innovations or progress (Table 4). At the end of the session, participants were asked to share essential insights from the event (Table 7) and an action they plan to take as a result of the event. Participants agreed that the event was useful in helping them share and learn from each other. The project team plans to use the information from the summit as a starting point to help inform future research and technical assistance. In 2026, another Equity Summit will be held (virtually or in person) as part of the same project to help raise awareness and disseminate research and resources completed during the project's duration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

First Principles Modeling of Cluster-Based Solid Electrolytes (Final Technical Report)

Given the trend of global warming and the urgent need to transition from fossil fuels to green energy, lithium-ion batteries continue to be an integral part of our lives. Design, development, and understanding of novel solid-state electrolyte materials play the key role for achieving next-generation all-solid-state batteries with high energy and great safety. The current modeling schemes to develop advanced solid electrolytes are focusing on materials in which the building blocks are individual atoms. Our theoretical approach is a paradigm shift in solid-state electrolyte design. Instead of atoms, we focus on clusters as the building blocks and model these solid electrolytes and their interfaces with electrodes, especially Li-metal anode, for their successful implementation in solid-state batteries. The advantage of using the cluster ions to replace elemental ions is that the size, composition, and shape of the former can be tailored to achieve higher ionic conductivity at room temperature, electrochemical stability, and charge transfer across solid-solid interfaces than conventional materials. Specifically, the project includes: (1) Developing cluster-based solid electrolytes, where the halogen components are replaced by cluster ions that mimic the chemistry of halogens but are characterized by additional degrees of freedom, including the size, shape, composition, and motional dynamics under excitation. (2) Providing a fundamental understanding of the ion conduction mechanism in the developed cluster-based solid electrolytes; (3) Modeling the interfacial properties (i.e., structural, chemical, and transport properties) between the cluster-based solid electrolytes and electrodes at the atomic level. For the cluster-based solid electrolytes incompatible with the Li-metal anode or cathode materials, potential candidates for interfacial coatings are identified and studied. (4) Providing a theoretical framework towards optimizing critical parameters of the solid-state electrolytes that guides experimentalists to attain desired cathode-electrode interface for cluster-based solid-state electrolytes.

25 ENERGY STORAGE↗

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.

Bilevel multistage stochastic programming problem↗