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Elliptic multipoles and the modeling of narrow-gap bend magnets in accelerators

We highlight the virtues of 2D elliptic-multipole field expansions in modeling the magnetic fields of narrow-aperture, straight-axis bending magnets with parallel faces, addressing the limitations of the conventional circular multipole series when the beam-orbit sagitta exceeds the magnet's vertical half-gap. The elliptic multipoles provide a convenient way to represent the field in all aspects of the magnet development (design, particle-tracking simulations, measurements). We propose a numerically robust method of data analysis to determine the elliptic (or circular) multipoles from stretched-wire measurements with the wire moving on an arbitrary path.

Venturini, Marco

Software Validation Work With The ZPPR-15 Data

The analysis activities for fast reactors involve using many different pieces of software that are relied upon for their predictive capabilities. For this software to be considered reliable, documented proof that the predictions of the software are accurate is required. In this manuscript, the validation work that covers some of the Argonne software used in fast reactor design activities is discussed and displayed. This validation work includes neutron and gamma flux distributions, reaction rate distributions, and reactivity worth. In an ideal world, a reactor development program would have access to a comprehensive set of experimental facilities to help inform the design aspects of the reactor itself. While thermal-hydraulics experiments, and to a limited degree mechanical experiments, can be carried out today for validation needs, neutronics related experimental facilities are rather impractical because of the lack of experimental facilities. Given the desired time table for construction of new reactors, the reconstitution or creation of new neutronic experimental facilities is untenable and thus those reactor development programs must rely upon any available experimental measurements that are qualitatively similar to the design. While a methodology has been proposed to assess the similarity between the past experimental measurements and the reactor itself, that aspect is beyond the scope of this manuscript. In this manuscript, the focus is entirely placed on the analysis results for a series of experiments carried out at the ZPPR facility in Idaho in the mid-1980s. In this regard, this manuscript only shows the validation of the stated neutronics software for specific loadings of the ZPPR reactor. Because of the fuel form, its proposed enrichment, and the material content of the reactor core, the ZPPR-15 experiments were identified as potential validation data for the reactor. The ZPPR-15 experiments were intended as mockups of a 330 MWe Integral Fast Reactor program which was a follow on program to the Clinch River Breeder Reactor. In the ZPPR-15 series of experiments, measurements of the neutron spectrum, control rod worth, sodium void worth, foil reaction rate distributions, Doppler worth of heated samples, gamma dose, and axial expansion worth were all carried out and published. In many cases, these reactivity coefficients are good candidates to validate the reactivity coefficient calculation scheme used by the analysis software and included in the safety analysis activities of fast reactor development projects today. This manuscript discusses the modeling methodology and accuracy of the calculated experimental results using the LANL software MCNP and the ANL software package ARC (Argonne Reactor Codes). As will be shown, for many of the experimental measurements, the two software packages are found to be good predictive analysis tools for those experiments. In other cases, problems with the analysis methodology or underlying cross section data are exposed which indicates where predictive analysis is not as reliable. Finally, in some of the measurements the conclusion is reached that the experimental measurement cannot be reproduced with the analysis software as it is simply too difficult.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Software Validation Work With The ZPPR-15 Data

The analysis activities for fast reactors involve using many different pieces of software that are relied upon for their predictive capabilities. For this software to be considered reliable, documented proof that the predictions of the software are accurate is required. In this manuscript, the validation work that covers some of the Argonne software used in fast reactor design activities is discussed and displayed. This validation work includes neutron and gamma flux distributions, reaction rate distributions, and reactivity worth. In an ideal world, a reactor development program would have access to a comprehensive set of experimental facilities to help inform the design aspects of the reactor itself. While thermal-hydraulics experiments, and to a limited degree mechanical experiments, can be carried out today for validation needs, neutronics related experimental facilities are rather impractical because of the lack of experimental facilities. Given the desired time table for construction of new reactors, the reconstitution or creation of new neutronic experimental facilities is untenable and thus those reactor development programs must rely upon any available experimental measurements that are qualitatively similar to the design. While a methodology has been proposed to assess the similarity between the past experimental measurements and the reactor itself, that aspect is beyond the scope of this manuscript. In this manuscript, the focus is entirely placed on the analysis results for a series of experiments carried out at the ZPPR facility in Idaho in the mid-1980s. In this regard, this manuscript only shows the validation of the stated neutronics software for specific loadings of the ZPPR reactor. Because of the fuel form, its proposed enrichment, and the material content of the reactor core, the ZPPR-15 experiments were identified as potential validation data for the reactor. The ZPPR-15 experiments were intended as mockups of a 330 MWe Integral Fast Reactor program which was a follow on program to the Clinch River Breeder Reactor. In the ZPPR-15 series of experiments, measurements of the neutron spectrum, control rod worth, sodium void worth, foil reaction rate distributions, Doppler worth of heated samples, gamma dose, and axial expansion worth were all carried out and published. In many cases, these reactivity coefficients are good candidates to validate the reactivity coefficient calculation scheme used by the analysis software and included in the safety analysis activities of fast reactor development projects today. This manuscript discusses the modeling methodology and accuracy of the calculated experimental results using the LANL software MCNP and the ANL software package ARC (Argonne Reactor Codes). As will be shown, for many of the experimental measurements, the two software packages are found to be good predictive analysis tools for those experiments. In other cases, problems with the analysis methodology or underlying cross section data are exposed which indicates where predictive analysis is not as reliable. Finally, in some of the measurements the conclusion is reached that the experimental measurement cannot be reproduced with the analysis software as it is simply too difficult.

Aliberti, Gerardo

Learning from Arctic Microgrids: Cost and Resiliency Projections for Renewable Energy Expansion with Hydrogen and Battery Storage

Electricity in rural Alaska is provided by more than 200 standalone microgrid systems powered predominantly by diesel generators. Incorporating renewable energy generation and storage to these systems can reduce their reliance on costly imported fuel and improve sustainability; however, uncertainty remains about optimal grid architectures to minimize cost, including how and when to incorporate long-duration energy storage. This study implements a novel, multi-pronged approach to assess the techno-economic feasibility of future energy pathways in the community of Kotzebue, which has already successfully deployed solar photovoltaics, wind turbines, and battery storage systems. Using real community load, resource, and generation data, we develop a series of comparison models using the HOMER Pro software tool to evaluate microgrid architectures to meet over 90% of the annual community electricity demand with renewable generation, considering both battery and hydrogen energy storage. We find that near-term planned capacity expansions in the community could enable over 50% renewable generation and reduce the total cost of energy. Additional build-outs to reach 75% renewable generation are shown to be competitive with current costs, but further capacity expansion is not currently economical. We additionally include a cost sensitivity analysis and a storage capacity sizing assessment that suggest hydrogen storage may be economically viable if battery costs increase, but large-scale seasonal storage via hydrogen is currently unlikely to be cost-effective nor practical for the region considered. While these findings are based on data and community priorities in Kotzebue, we expect this approach to be relevant to many communities in the Arctic and Sub-Arctic regions working to improve energy reliability, sustainability, and security.

25 ENERGY STORAGE

MnRhBi 3 : A Cleavable Antiferromagnetic Metal

Cleavable metallic antiferromagnets may be of use for low-dissipation spintronic devices; however, few are currently known. Here, in this study, we present orthorhombic MnRhBi 3 as one such compound and present a thorough study of its physical properties. Exfoliation is demonstrated experimentally, and the cleavage energy and electronic structure are examined by density functional theory calculations. It is concluded that MnRhBi 3 is a van der Waals-layered material that cleaves easily between neighboring Bi layers and that the Bi atoms have lone pairs extending into the van der Waals gaps. A series of four phase transitions are observed below room temperature, and neutron diffraction shows that at least two of the transitions involve the formation of antiferromagnetic order. Anomalous thermal expansion points to a crystallographic phase transition and/or strong magnetoelastic coupling. This work reveals a complex phase evolution in MnRhBi 3 and establishes this cleavable antiferromagnetic metal as an interesting material for studying the interplay of structure, magnetism, and transport in the bulk and ultrathin limits, as well as the role of lone pair electrons in interface chemistry and proximity effects in van der Waals heterostructures.

36 MATERIALS SCIENCE

Hierarchical Truncations for Many-Body Expansion Potentials

In this work, a new strategy to truncate high-order terms in the many-body expansion (MBE) is proposed. This new approach, which we call a hierarchical many-body expansion (HMBE), is based on a hierarchical partition of the system into multitier fragments and can in principle be applied to any large molecular system. Numerical tests on a series of (H 2 O) 64 structures are presented, demonstrating satisfactory relative energies between the clusters and binding energies of individual clusters compared with full-cluster calculations, with significantly fewer high-order terms computed than conventional MBE. The hierarchical truncation can be augmented by certain many-body terms for fragments at the interface between the partitions (called “Schengen terms”) to further improve accuracy. This work establishes the HMBE scheme as a promising framework to model very large systems (e.g., proteins), which are naturally built on a hierarchical structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

MnRhBi3: A Cleavable Antiferromagnetic Metal

This dataset contains DFT input and output files supporting the theoretical modeling in the associated publication (Chem. Mater. 2024, 36, 11306-11316). The calculations characterize MnRhBi3, an orthorhombic (Cmmm) van der Waals-layered intermetallic compound that cleaves easily between neighboring Bi layers. The dataset is organized into three calculation types: (i) Bulk: Structural relaxations of the periodic MnRhBi3 crystal in antiferromagnetic (AFM) and ferromagnetic (FM) configurations, using the vdW-DF-optB86b functional. These provide the equilibrium lattice constants, magnetic energy differences (AFM is 0.5 meV/f.u. lower than FM), and magnetic moments (4.4 µB/Mn, 0.17 µB/Rh, 0.18 µB/Bi) reported in Table 1 of the main text. (ii) Slab: Same magnetic configurations computed with an 18 Ang vacuum layer introduced between Bi layers, used to calculate the cleavage energy Ec = 0.56 J/m2 (AFM) and 0.57 J/m2 (FM), establishing MnRhBi3 as a van der Waals-layered material comparable to graphite, MoS2, and CrI3. (iii) ELF: Single-point calculation on the relaxed bulk AFM geometry with LELF=.TRUE., producing the ELFCAR file used to generate electron localization function isosurfaces and contour maps (Fig. 2, main text) showing Bi lone pairs directed into the van der Waals gaps. All folders contain CONTCAR, INCAR, KPOINTS, OUTCAR, and POSCAR. The ELF/ folder additionally contains ELFCAR. Calculations were performed using VASP 6.3.2 with PBE + vdW-DF-optB86b, PAW potentials, and an energy cutoff of 800 eV.

36 MATERIALS SCIENCE

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets

Failure investigation and mitigation after experimental research reactor fuel plate deformation in an irradiation device

Experimental research reactor fuel testing is conducted in the Belgian Reactor 2 (BR2) of the Belgian Nuclear Research Centre (SCK CEN) in dedicated irradiation vehicles or rigs. One such vehicle allows flat full-size fuel plates to be irradiated by inserting them into slotted baskets that captures a narrow portion of the longitudinal edges of the plates. The motion of the fuel plates within the baskets is possible within the narrow slots and thus, the plate is considered to be unattached. The design intentionally omits fixing mechanisms of the fuel plates to the baskets to facilitate the inspection and repositioning of the plates between the irradiation cycles and the accommodation of thermal expansion of the plates in the lateral direction. However, loosely inserted fuel plates have weak structural boundary conditions allowing for larger out-of-plane deflections caused by hydrodynamic loads exerted by the flowing coolant, as compared to those of fixed plates. Unexpected large deformations of plates occurred in several irradiation cycles that further resulted in a loss of cladding integrity. These deformations could not be attributed to a single source. This triggered a series of thermal hydraulic, structural, and fluid-structure interaction analyses aiming at understanding the observed phenomenon. The analyses revealed that, for a certain combination of unfavorable manufacturing and assembly tolerances, fuel plate edges could escape out of the slots in the irradiation basket due to the hydrodynamic load. Subsequently, the plate could become wedged inside the basket coolant channel opening. This resulted in reduced coolant flow and accelerated temperature increase and thermal expansion of the plate while under irradiation. This unfavorable feedback loop could then lead to excessive plate surface temperatures, deformed plates and cladding failure, as was observed in the experiments. These analyses not only provided a probable cause of the fuel plate failures, but also resulted in a new and improved design of the irradiation basket to avoid these issues in the future. In conclusion, a series of recent successful irradiations confirm that the sources of failures were identified correctly, and the implemented mitigations were adequate.

BR2

Asymptotic errors in adiabatic evolution

The adiabatic theorem in quantum mechanics implies that if a system is in a discrete eigenstate of a Hamiltonian and the Hamiltonian evolves in time arbitrarily slowly, the system will remain in the corresponding eigenstate of the evolved Hamiltonian. Understanding corrections to the adiabatic result that arise when the evolution of the Hamiltonian is slow—but not arbitrarily slow—has become increasingly important, especially since adiabatic evolution has been proposed as a method of state preparation in quantum computing. Here, this paper identifies two regimes, an adiabatic regime in which corrections are generically small and can depend on details of the evolution throughout the path, and a hyperadiabatic regime in which the error is given by a form similar to an asymptotic expansion in the inverse of the evolution time with the coefficients depending principally on the behavior at the endpoints. However, the error in this hyperadiabatic regime is neither given by a true asymptotic series nor solely dependent on the endpoints: the coefficients combine the contributions from both endpoints, with relative phase factors that depend on the average spectral gaps along the trajectory, multiplied by the evolution time. The central result of this paper is to identify a quantity, referred to as the typical error, which is obtained by appropriately averaging the error over evolution times that are small compared to the evolution time itself. This typical error is characterized by an asymptotic series and depends solely on the endpoints of the evolution, remaining independent of the details of the intermediate evolution.

adiabatic approximation

Monthly averages of ED2 model simulations initialized with airborne lidar structure, Jan 1981-Dec 2018, Brazilian Amazon

Deforestation and forest degradation (selective logging, fires, fragmentation) have impacted nearly 40% of the original extent of the Brazilian Amazon, and have markedly impacted forest structure across the region. To date, few studies analysed how shifts in forest structure from degradation influence the forest sensitivity to climate extremes, because of the complex interactions between forest structure and micro-environmental conditions. To address this knowledge gap, we carried out a series of simulations across the Brazilian Amazon using the Ecosystem Demography Model (ED2), using observed forest structure derived from 541 airborne lidar transects (375 ha each) and two scenarios representing forest recovery and expansion of degradation to investigate how shifts in forest structure impact ecosystem function under near-average and extreme climate conditions, as part of the manuscript Longo et al 2025 "Degradation and Deforestation Increase the Sensitivity of the Amazon Forest to Climate Extremes". This dataset provides the output results from the ED2 model simulations for the three simulations at monthly time scales, in NetCDF format. For all simulations, we used bias-corrected hourly reanalyses (WFDE5) for most meteorological drivers, except for precipitation, which was obtained from CHIRPS. The meteorological drivers used in the study span 38 years (Jan 1981–Dec 2018). The output results correspond to the last 38 years of simulation (one full cycle of meteorological drivers), in which ED2 simulations used static stand structure (i.e., the forest structure was held constant). The following files are provided:ED2_emean_Global_R004_BrAmaz_s1c0t0l0f0.nc. This corresponds to the Control simulation. The forest structure was obtained from the airborne lidar.ED2_emean_Global_R005_BrAmaz_s1c0t1l1f0.nc. This corresponds to the Degraded simulation. The forest structure was obtained from a spin-up simulation initialized with airborne lidar and a scenario that expanded deforestation and selective logging across the Amazon.ED2_emean_Global_R006_BrAmaz_s1c0t1l0f0.nc. This corresponds to the Recovery simulation. The forest structure was obtained from a spin-up simulation initialized with airborne lidar and a scenario that completely halted deforestation and degradation, allowing degraded forests to recover for 38 years.We also provide file ED2_zones_R004_BrAmaz_s1c0t0l0f0.nc, which classifies each grid cell into zones used in the reference manuscript: 1: Southeast. 2: South. 3: West. 4: Central. 5: Northeast. 6: North. 7: Northwest". Index 0 corresponds to grid cells excluded from sub-region analyses because they were dominated by flooded forests, deforestation, and naturally non-forest vegetation.

54 ENVIRONMENTAL SCIENCES

Model data for infrastructure-aware simulation of compound flooding at Alligator Bayou Watershed, southeast Texas

This dataset supports infrastructure-aware hydrologic modeling and flood scenario analysis for the Alligator Bayou Watershed, a highly managed urban watershed in Southeast Texas. It includes Jupyter notebooks for figure reproduction, model configuration files, simulation outputs, and derived products used to quantify the influence of engineered stormwater infrastructure on flood behavior across multiple spatial scales. The dataset was generated using the Watershed Workflow Python package and the Advanced Terrestrial Simulator (ATS), enabling integrated surface–subsurface hydrologic simulations on a channel-aligned mesh with explicit representations of pump stations, gate structures, detention basins, and impervious surfaces. Outputs include time series of gate and pump flows, stage observations, and water balance components, as well as spatially explicit fields of peak ponded depth and flood duration across multiple infrastructure scenarios spanning a single-location detention basin expansion, distributed drainage limitations, and compound coastal flooding. These data facilitate full reproducibility of the manuscript figures and support further research on urban flood dynamics and the role of stormwater infrastructure in shaping watershed-scale flood response.

EARTH SCIENCE > OCEANS > COASTAL PROCESSES

Conversations and deliberations: Non-standard cosmological epochs and expansion histories

Here, this paper summarizes the discussions which took place during the PITT-PACC Workshop entitled “Non-Standard Cosmological Epochs and Expansion Histories,” held in Pittsburgh, Pennsylvania, Sept. 5–7, 2024. Much like the non-standard cosmological epochs that were the subject of these discussions, the format of this workshop was also non-standard. Rather than consisting of a series of talks from participants, with each person presenting their own work, this workshop was instead organized around free-form discussion blocks, with each centered on a different overall theme and guided by a different set of Discussion Leaders. This document is not intended to serve as a comprehensive review of these topics, but rather as an informal record of the discussions that took place during the workshop, in the hope that the content and free-flowing spirit of these discussions may inspire new ideas and research directions.

cosmology

Inference of response functions with the help of machine-learning algorithms

Response functions are a key quantity to describe the near-equilibrium dynamics of strongly interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these ab initio have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function 𝑆⁡(𝜔) defined over a range in frequencies 𝜔. Here, we represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian integral transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method.

Kurkcuoglu, Doga Murat [Fermi National Accelerator

Business Models for Scaling Demand Flexibility Volume IV – Program life cycle challenges and lessons learned from U.S. programs

Load growth at the grid edge is driving increased attention to the distribution system and its ability to enable customer technology adoption in an affordable and timely manner. Key industry stakeholders, including electric utilities and regulators, can benefit from strategies to manage and balance customer needs with infrastructure investments, such as demand flexibility. This report focuses on demand flexibility—the ability to reduce, shift, shed, generate, or modulate loads in response to building and grid needs—to reduce the need for costly grid upgrades by deferring investment needs and increase system reliability by shifting electricity usage during periods of high risk. Specifically, we focus on the emerging characteristics of business models for demand flexibility as a framework to understand how demand flexibility programs generate value. In this report, we focus on the life cycle of demand flexibility programs, which provides information on value creation and describes the various deployment phases program implementers navigate from initial program conceptualization through to program expansion and replication to new customer segments and regions. This report characterizes the key phases of the demand flexibility program life cycle, identifies existing challenges across the program deployment phases, and describes lessons learned. This report is part of a series that includes reports on customer relationship management strategies, stakeholder ecosystem management, and program life cycle.

24 POWER TRANSMISSION AND DISTRIBUTION

Validation of the DESI DR2 measurements of baryon acoustic oscillations from galaxies and quasars

The Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) galaxy and quasar clustering data represents a significant expansion of data from Data Release 1 (DR1), providing improved statistical precision in baryon acoustic oscillation (BAO) constraints across multiple tracers, including bright galaxies, luminous red galaxies, emission line galaxies, and quasars. In this paper, we validate the BAO analysis of DR2. We present the results of robustness tests on the blinded DR2 data and, after unblinding, consistency checks on the unblinded DR2 data. All results are compared with those obtained from a suite of mock catalogs that replicate the selection and clustering properties of the DR2 sample. We confirm the consistency of DR2 BAO measurements with DR1 while achieving a reduction in statistical uncertainties due to the increased survey volume and completeness. The combined BAO precision, including both statistical and systematic errors, improves from ∼0.52% in DR1 to 0.30% in DR2—a factor of 1.7 gain. We assess the impact of analysis choices, including different data vectors (correlation function vs power spectrum), modeling approaches and systematics treatments, and an assumption of the Gaussian likelihood, finding that our BAO constraints are stable across these variations and assumptions with a few minor refinements to the baseline setup of the DR1 BAO analysis. We summarize a series of pre-unblinding tests that confirmed the readiness of our analysis pipeline, the final systematic errors, and the DR2 BAO analysis baseline. The successful completion of these tests led to the unblinding of the DR2 BAO measurements, ultimately leading to the DESI DR2 cosmological analysis, with their implications for the expansion history of the Universe and the nature of dark energy presented in the DESI key paper (companion paper).

79 ASTRONOMY AND ASTROPHYSICS

Williston Basin CORE-CM Initiative Final Report

The University of North Dakota Energy & Environmental Research Center (EERC) is leading the Williston Basin Carbon Ore, Rare Earth, and Critical Minerals (CORE-CM) Initiative to drive the expansion and transformation of coal and coal-based resource usage within the Williston Basin to produce rare-earth elements (REEs), CMs, and nonfuel carbon-based products (CBPs). This project is the first phase in a long-term program and set the stage for future work by assessing resource, market, technology, and infrastructure knowledge; identifying knowledge gaps; developing a series of plans to be carried out in future work; and initiating stakeholder engagement. Composed of several tasks, the project sought to identify, characterize, and assess several necessary aspects vital to make this future work a reality. The project’s fundamental task was to characterize the Williston Basin CORE-CM resources. Over 2500 samples from multiple sources were utilized to begin the assessment. Several locations were identified in western North Dakota where sample analysis identified the total REE (TREE) concentration as being over 500 parts per million (ppm), which is at a concentration level that would be suitable to consider for mining and extraction. Current operating coal mines have sufficient concentrations of TREEs for consideration. However, the current data across the basin are still not adequate to fully characterize REE and CM content nor give reliable estimates of the total resource potential. Waste stream reuse was also considered, and several streams were identified which ranged from potential energy sources to chemicals to material wastes. This includes streams that result from oil and gas production. These streams are not fully characterized, and further data are needed before they can be accurately assessed. Infrastructure within the Williston Basin is suitable for expansion of a new industry to mine, extract, and concentrate REEs and CMs. The development of this industry will not only preserve many existing jobs in the coal-mining industry but produce many new jobs. The supply chain for REEs and CMs is currently controlled outside of the United States in nations such as China, but the potential to develop the supply chain within the basin is considered possible. Processing of the mined materials for REEs and CMs needs further research. The technology and knowhow exist outside of the United States, and within the country much of the knowledge has been lost and must be regained. To develop the supply chain and regain lost processing technology, the creation of technology innovation centers (TICs) is crucial. The Williston Basin contains several similar centers and entrepreneurial assistance for other industries that can be applied in the development of REE and CM innovation centers. Education to develop the new skill sets required is also needed. Outreach is important for the development of the REE and CM industry within the basin. Understanding throughout federal and state governments, state agencies, industry, and resource end users is vital for the industry to form and grow. Through this project these groups have been contacted through bulletins, presentations, webinars, and annual symposiums. The report is a summary of the work conducted and throughout refers to a series of appendixes which contain more thorough and specific information about each section.

01 COAL, LIGNITE, AND PEAT

All loop scattering as a counting problem

Abstract This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ’t Hooft expansion. We find novel integral formulas for the amplitudes of this theory, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a radically new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

1/N Expansion