A Flux-Form Semi-Lagrangian advection scheme for tracer transport on arbitrary meshes
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54 ENVIRONMENTAL SCIENCES↗
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Results for “mathematical model”
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.
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Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets
We present a model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structures. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents, followed by (b) pruning of the shells according to their contributions to the 2- body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-ζ quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree−Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 μE h per electron, respectively.
Approximation↗
Nonlinear Sigma model amplitudes to all loop orders are contained in the Tr ( Φ 3 ) theory
Scattering amplitudes for the simplest theory of colored scalar particles—the Tr ( Φ 3 ) theory—have recently been the subject of active investigations. In this work we describe an unanticipated wider implication of this work: the Tr ( Φ 3 ) theory secretly contains nonlinear sigma model (NLSM) amplitudes to all loop orders. The NLSM amplitudes are obtained from Tr ( Φ 3 ) amplitudes by a unique shift of kinematic variables. We show that this shifted kinematics produces amplitudes for a cubic theory with a linear term in the potential, with extrema spontaneously breaking U ( N ) → U ( N − k ) × U ( k ) . The Goldstone amplitudes for this theory coincide with those of pions in the U ( N ) × U ( N ) → U ( N ) chiral Lagrangian to all orders in the planar limit. We also give a purely on-shell understanding of this correspondence, showing that integrands defined by the kinematic shifts have the correct residues on poles and appropriately produce the Adler zero. Finally, we discuss how similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr ( Φ 3 ) scalars, most of which are not interpretable from the Lagrangian description. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The Scientific Impact of the Exascale Computing Project
The recent arrival of the Frontier Supercomputer at Oak Ridge National Laboratory officially marked the dawn of the exascale computing era. Its successful deployment coincided with the culmination of the U.S. Department of Energy Exascale Computing Project (ECP), an ambitious, complex, and risky research and development effort that integrated contributions from a broad and diverse subset of the high-performance computing community. The success of ECP will ultimately be judged by the scientific and engineering advances that it enabled. In conclusion, this Special Issue is focused on showcasing early successes in the use of exascale resources to enable breakthroughs in key areas of science in engineering.
97 MATHEMATICS AND COMPUTING↗
ChatGPT and Other Large Language Models for Cybersecurity of Smart Grid Applications
Cybersecurity breaches targeting electrical substations constitute a significant threat to the integrity of the power grid, necessitating comprehensive defense and mitigation strategies. Any anomaly in information and communication technology (ICT) should be detected for secure communications between devices in digital substations. This paper proposes large language models (LLMs), e.g., ChatGPT, for the cybersecurity of IEC 61850-based communications. Multi-cast messages such as generic object oriented system events (GOOSE) and sampled values (SV) are used for case studies. The proposed LLM-based cybersecurity framework includes, for the first time, data pre-processing of communication systems and human-in-the-loop (HITL) training (considering the cybersecurity guidelines recommended by humans). The results show a comparative analysis of detected anomaly data carried out based on the performance evaluation metrics for different LLMs. A hardware-in-the-loop (HIL) testbed is used to generate and extract a dataset of IEC 61850 communications.
ChatGPT↗
Investigating Application of LiDAR for Nuclear Power Plants
Many evaluation, assessment, and modeling tasks at nuclear power plants require spatial in-formation; this often requires physical visits to locations within the facility because the 2D or 3D schematics and current models do not contain enough detail or do not capture as-built and real-world conditions. These visits require extensive manual labor for not only the requesting party, but also support groups, such as security. Light Detection and Ranging (LiDAR) mapping is trying to solve that problem by providing very detailed 3D models for low costs. However, the use of these models can be very limited because either component reference information is missing and too costly to add or there is no way to extract specific spatial data needed for other tools. This report outlines two main efforts. First, to reduce the effort of “Tagging” data in large 3D models, a general Application Programming Interface (API) was developed to import a variety of existing plant database information into a 3D-visualization engine. Filters allow the user to have only zone-specific items listed; then, they can simply click and assign the information to a specific spot or component in the 3D model. The second part of the work is the development of an interface for importing pieces from the3D-LiDAR model into other systems needed for modeling and simulation, outlined around fire modeling. This interface allows for the retrieval of item location and boundaries, enabling the auto generation of models for varying tools.
3D Modelling↗
Theoretical and calculable dependent variables and their covariance in nuclear data libraries [Slides]
This presentation begins by defining observables, including theoretical observable, calculable observable, and measured observable. It also provides definitions and examples of experimental effects. Additionally, uncertainty in evaluated libraries and a metric to probe evaluated uncertainty is presented. In conclusion, being related to theoretical quantities such as resonance parameters, the uncertainty in ENDF libraries (e.g., ENDF/B-VIII.0) can be overestimated because it is usually evaluated under the guidance of experimental uncertainty: lim Δσexp.corr.→0 Δσ = Δσ theoretical model . The presentation states that a clear distinction of the uncertainty between nuclear theoretical models and experimental corrections should be revisited and this is important since (e.g., transport) simulations need theoretical quantities convoluted with specific operational parameters and material configurations. It also states that strong coupling between uncertainty quantification methodologies and optimization procedures exists, and it is necessary to develop methodologies to obtain uncertainty on theoretical models from physical and mathematical constraints.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Editorial: Neuroscience, computing, performance, and benchmarks: Why it matters to neuroscience how fast we can compute
At the turn of the millennium the computational neuroscience community realized that neuroscience was in a software crisis: software development was no longer progressing as expected and reproducibility declined. The International Neuroinformatics Coordinating Facility (INCF) was inaugurated in 2007 as an initiative to improve this situation. The INCF has since pursued its mission to help the development of standards and best practices. In a community paper published this very same year, Brette et al. tried to assess the state of the field and to establish a scientific approach to simulation technology, addressing foundational topics, such as which simulation schemes are best suited for the types of models we see in neuroscience. In 2015, a Frontiers Research Topic “Python in neuroscience” by Muller et al. triggered and documented a revolution in the neuroscience community, namely in the usage of the scripting language Python as a common language for interfacing with simulation codes and connecting between applications. The review by Einevoll et al. documented that simulation tools have since further matured and become reliable research instruments used by many scientific groups for their respective questions. Open source and community standard simulators today allow research groups to focus on their scientific questions and leave the details of the computational work to the community of simulator developers. A parallel development has occurred, which has been barely visible in neuroscientific circles beyond the community of simulator developers: Supercomputers used for large and complex scientific calculations have increased their performance from ~10 TeraFLOPS (10 13 floating point operations per second) in the early 2000s to above 1 ExaFLOPS (10 18 floating point operations per second) in the year 2022. This represents a 100,000-fold increase in our computational capabilities, or almost 17 doublings of computational capability in 22 years. Moore's law (the observation that it is economically viable to double the number of transistors in an integrated circuit every other 18–24 months) explains a part of this; our ability and willingness to build and operate physically larger computers, explains another part. It should be clear, however, that such a technological advancement requires software adaptations and under the hood, simulators had to reinvent themselves and change substantially to embrace this technological opportunity. It actually is quite remarkable that—apart from the change in semantics for the parallelization—this has mostly happened without the users knowing. The current Research Topic was motivated by the wish to assemble an update on the state of neuroscientific software (mostly simulators) in 2022, to assess whether we can see more clearly which scientific questions can (or cannot) be asked due to our increased capability of simulation, and also to anticipate whether and for how long we can expect this increase of computational capabilities to continue.
biophysically detailed models↗
Quantifying Human Behavior and Decision Errors in Security Screening Operations
The potential for human errors in conducting security related screening operations can lead to inadvertent and adverse decision outcomes. This paper overviews an initial mathematical framework designed to model and quantify the various human factors and decision outcomes that may occur in conducting security screening operations, such as U.S. port of entry radiological and nuclear (rad/nuc) security screening. This framework is based on the Human Error Assessment and Reduction (HEART) technique. As applied here, the framework incorporates a set of rules for human engagement, including a prescribed concept of operations (CONOPS) and deviations that may occur from this established CONOPS due to inadvertent personnel decision errors. We also review some of the various factors that may adversely influence such decisions by security screening personnel. Some of these factors include current workload, environmental conditions, training, and various other intangible factors. Using the HEART methodology, we translate each of these factors into error producing conditions, their effects on error, an assessed proportion of effects, and finally the overall probability of human error at each stage of the screening process. We then include a small scale example to demonstrate the methodology and results based on an assumed set of input conditions at a notional port of entry.
Brigantic, Robert T.↗
Mathematical Analysis and Proof of Existence of The Photovoltaic Exponential Model
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Ortiz-Rivera, Eduardo Ivan [Sandia National Labora↗
Analysis of Tempered Fractional Operators
Tempered fractional operators are useful in models for subsurface transport and diffusion due to their ability to capture anomalous diffusion: a behavior which the classical partial differential equation models cannot describe. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators in correspondence of a proper choice of nonlocal kernels. Then, we work towards showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.
97 MATHEMATICS AND COMPUTING↗
Multi-shock design tools in double shell models
The essence of the project was to implement a program in python that demonstrated certain models put forth by fusion physicists. Across the time spent at Los Alamos National Laboratory, much was spent programming. Though fundamentally programmatical in nature, the task contained considerable difficulty hid within mathematically deriving and manipulating the models while maintaining data discretization. The result of solving these complications gave invaluable experience in applied mathematics. The final product, a piece of lengthy code, ended up having the full range of desired capabilities, with plans for more. Given the laser power history from a pulse shot on NIF, Omega, or any other Inertial Confinement Fusion facility, the code maps the terrain of radiation temperature inside the hohlraum throughout the period of the shot. Additionally, shock wave convergence prediction was implemented as additional capability. As the name of the project suggests, this tool acts as a compass of direction for researchers designing laser power profiles. Further development of this tool will undoubtedly assist in the research conducted on single and double-shell indirect ICF, consequently expanding the capabilities of operating stewardship over the national nuclear stockpile.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Bifurcation Analysis Reveals Solution Structures of Phase Field Models
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, in this study, we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models. Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions. To elucidate the idea, we apply this analytical approach to three representative phase field equations: the Allen-Cahn equation, the Cahn-Hilliard equation, and the Allen-Cahn-Ohta-Kawasaki system. The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.
97 MATHEMATICS AND COMPUTING↗
User's Manual for the FE/NETL Onshore CO 2 EOR Cost Model, Version 1
This user's manual describes the conceptual and mathematical basis for the FE/NETL Onshore CO 2 EOR Cost Model (a Fortran program). The model performs a cash flow analysis to estimate the cost of implementing CO 2 EOR using supercritical CO 2 by incorporating oil field performance outputs for a pattern from the FE/NETL CO 2 Prophet Model (available on NETL's website along with its associated user's manuals under the Collection Name: FE/NETL CO 2 Prophet Model) and implementing patterns to develop an oil field for CO 2 EOR. The model calculates capital costs, operation and maintenance costs, and financing costs. The user’s manual also describes how to run the FE/NETL Onshore CO 2 EOR Cost Model, along with the model’s file structure, inputs and outputs. The FE/NETL Onshore CO 2 EOR Cost Model is available on NETL's website under the Collection Name: FE/NETL Onshore CO 2 EOR Cost Model.
54 ENVIRONMENTAL SCIENCES↗
ADAM: A web platform for graph-based modeling and optimization of supply chains
Modeling and optimization are essential tasks that arise in the analysis and design of supply chains (SCs). SC models are essential for understanding emergent behavior such as transactions between participants, inherent value of products exchanged, as well as impact of externalities (e.g., policy and climate) and of constraints. Unfortunately, most users of SC models have limited expertise in mathematical optimization, and this hinders the adoption of advanced decision-making tools. Here, in this work, we present ADAM, a web platform that enables the modeling and optimization of SCs. ADAM facilitates modeling by leveraging intuitive and compact graph-based abstractions that allow the user to express dependencies between locations, products, and participants. ADAM model objects serve as repositories of experimental, technology, and socio-economic data; moreover, the graph abstractions facilitate the organization and exchange of models and provides a natural framework for education and outreach. Here, we discuss the graph abstractions and software design principles behind ADAM, its key functional features and workflows, and application examples.
97 MATHEMATICS AND COMPUTING↗
A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions
Abstract A mathematical framework is provided for a substructuring‐based domain decomposition (DD) approach for nonlocal problems that features interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation (PDE) problems is used in which a computational domain is subdivided into non‐overlapping subdomains. In the nonlocal setting, this approach is substructuring‐based in the sense that those subdomains interact with neighboring domains over interface regions having finite volume, in contrast to the local PDE setting in which interfaces are lower dimensional manifolds separating abutting subdomains. Key results include the equivalence between the global, single‐domain nonlocal problem and its multi‐domain reformulation, both at the continuous and discrete levels. These results provide the rigorous foundation necessary for the development of efficient solution strategies for nonlocal DD methods.
Capodaglio, Giacomo↗
Semi-analytic solutions to the Noh problem with a black box EoS
The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.
97 MATHEMATICS AND COMPUTING↗
A probabilistic graphical model foundation for enabling predictive digital twins at scale
A unifying mathematical formulation is needed to move from one-off digital twins built through custom implementations to robust digital twin implementations at scale. This work proposes a probabilistic graphical model as a formal mathematical representation of a digital twin and its associated physical asset. We create an abstraction of the asset–twin system as a set of coupled dynamical systems, evolving over time through their respective state spaces and interacting via observed data and control inputs. The formal definition of this coupled system as a probabilistic graphical model enables us to draw upon well-established theory and methods from Bayesian statistics, dynamical systems and control theory. The declarative and general nature of the proposed digital twin model make it rigorous yet flexible, enabling its application at scale in a diverse range of application areas. Here, we demonstrate how the model is instantiated to enable a structural digital twin of an unmanned aerial vehicle (UAV). The digital twin is calibrated using experimental data from a physical UAV asset. Its use in dynamic decision-making is then illustrated in a synthetic example where the UAV undergoes an in-flight damage event and the digital twin is dynamically updated using sensor data. The graphical model foundation ensures that the digital twin calibration and updating process is principled, unified and able to scale to an entire fleet of digital twins.
42 ENGINEERING↗