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At least 1,009 records · Page 56

Statistical methods for the forensic analysis of striated tool marks

In forensics, fingerprints can be used to uniquely identify suspects in a crime. Similarly, a tool mark left at a crime scene can be used to identify the tool that was used. However, the current practice of identifying matching tool marks involves visual inspection of marks by forensic experts which can be a very subjective process. As a result, declared matches are often successfully challenged in court, so law enforcement agencies are particularly interested in encouraging research in more objective approaches. Our analysis is based on comparisons of profilometry data, essentially depth contours of a tool mark surface taken along a linear path. In current practice, for stronger support of a match or non-match, multiple marks are made in the lab under the same conditions by the suspect tool. We propose the use of a likelihood ratio test to analyze the difference between a sample of comparisons of lab tool marks to a field tool mark, against a sample of comparisons of two lab tool marks. Chumbley et al. (2010) point out that the angle of incidence between the tool and the marked surface can have a substantial impact on the tool mark and on the effectiveness of both manual and algorithmic matching procedures. To better address this problem, we describe how the analysis can be enhanced to model the effect of tool angle and allow for angle estimation for a tool mark left at a crime scene. With sufficient development, such methods may lead to more defensible forensic analyses.

97 MATHEMATICS AND COMPUTING↗

Systematic approach to verification and validation: High explosive burn models

Most material models used in numerical simulations are based on heuristics and empirically calibrated to experimental data. For a specific model, key questions are determining its domain of applicability and assessing its relative merits compared to other models. Answering these questions should be a part of model verification and validation (V and V). Here, we focus on V and V of high explosive models. Typically, model developers implemented their model in their own hydro code and use different sets of experiments to calibrate model parameters. Rarely can one find in the literature simulation results for different models of the same experiment. Consequently, it is difficult to assess objectively the relative merits of different models. This situation results in part from the fact that experimental data is scattered through the literature (articles in journals and conference proceedings) and that the printed literature does not allow the reader to obtain data from a figure in electronic form needed to make detailed comparisons among experiments and simulations. In addition, it is very time consuming to set up and run simulations to compare different models over sufficiently many experiments to cover the range of phenomena of interest. The first difficulty could be overcome if the research community were to support an online web based database. The second difficulty can be greatly reduced by automating procedures to set up and run simulations of similar types of experiments. Moreover, automated testing would be greatly facilitated if the data files obtained from a database were in a standard format that contained key experimental parameters as meta-data in a header to the data file. To illustrate our approach to V and V, we have developed a high explosive database (HED) at LANL. It now contains a large number of shock initiation experiments. Utilizing the header information in a data file from HED, we have written scripts to generate an input file for a hydro code, run a simulation, and generate a comparison plot showing simulated and experimental velocity gauge data. These scripts are then applied to several series of experiments and to several HE burn models. The same systematic approach is applicable to other types of material models; for example, equations of state models and material strength models.

36 MATERIALS SCIENCE↗

Using probabilistic solar power forecasts to inform flexible ramp product procurement for the California ISO

How can independent system operators (ISOs) take advantage of probabilistic solar forecasts to lower generation costs and improve reliability of power systems? We discuss one three-step approach for doing so, focusing on how such forecasts might help the California Independent System Operator (CAISO) prepare unexpected net load ramps, where net load equals gross demand minus wind and solar production. First, we enhance an existing solar forecasting system to provide well-calibrated hours-ahead probabilistic forecasts. We then relate the degree of uncertainty reflected in the forecasted prediction intervals (independent variables) to error distributions for net load ramp forecasts for the CAISO real-time market (dependent variable) using machine learning and quantile regression. Projected ramp forecast errors conditioned on solar uncertainty are translated into flexible ramp requirements that therefore reflect real-time meteorological and solar conditions, improving on typical ISO procedures. Detailed descriptions are provided on the quantile regression and kth-nearest neighbor categorization methods for accomplishing that translation. Finally, a multiple time-scale look-ahead market simulation model is applied to a 118-bus IEEE Reliability Test System, modified to represent the CAISO generation mix and demand distributions. The model runs quantify how solar-conditioned ramp requirements can, first, decrease operating costs by reducing requirements compared to often conservative unconditional methods and, second, decrease generation scarcity events and consequently improve reliability by increasing flexibility requirements at times when unconditional forecast-based requirements understate actual ramp uncertainty. Solar-conditioned ramp requirements are found to reduce generation operating costs by about 2% for the test system (which would be equivalent to over $\$100$ million per year for a CAISO-size system).

14 SOLAR ENERGY↗

Benchmark problems and results for verifying resonance calculation methodologies

Resonance calculation is one of the most important procedures for the multi-group neutron transport calculation. With the development of nuclear reactor concepts, many new types of fuel assembly are raised. Compared to the traditional designs, most of the new fuel assemblies have different fuel types either with complex isotopes or with complicated geometry. This makes the traditional resonance calculation method invalid. Recently, many advanced resonance calculation methods are proposed. However, there are few benchmark problems for evaluating those methods with a comprehensive comparison. In this paper, we design 5 groups of benchmark problems including 21 typical cases of different geometries and fuel contents. The reference results of the benchmark problems are generated based on the sub-group method, ultra-fine group method, function expanding method and Monte Carlo method. It is shown that those benchmark problems and their results could be helpful to evaluate the validity of the newly developed resonance calculation method in the future work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A cluster expansion model for predicting activation barrier of atomic processes

We introduce a procedure based on cluster expansion models for predicting the activation barrier of atomic processes encountered while studying the dynamics of a material system using the kinetic Monte Carlo (KMC) method. Starting with an interatomic potential description, a mathematical derivation is presented to show that the local environment dependence of the activation barrier can be captured using cluster interaction models. Next, we develop a systematic procedure for training the cluster interaction model on-the-fly, which involves: (i) obtaining activation barriers for handful local environments using nudged elastic band (NEB) calculations, (ii) identifying the local environment by analyzing the NEB results, and (iii) estimating the cluster interaction model parameters from the activation barrier data. Once a cluster expansion model has been trained, it is used to predict activation barriers without requiring any additional NEB calculations. Numerical studies are performed to validate the cluster expansion model by studying hop processes in Ag/Ag(100). We show that the use of cluster expansion model with KMC enables efficient generation of an accurate process rate catalog.

97 MATHEMATICS AND COMPUTING↗

Uncertainty quantification tools for multiphase gas-solid flow simulations using MFIX

Computational fluid dynamics (CFD) has been widely studied and used in the scientific community and in the industry. Various models were proposed to solve problems in different areas. However, all models deviate from reality. Uncertainty quantification (UQ) process evaluates the overall uncertainties associated with the prediction of quantities of interest. In particular it studies the propagation of input uncertainties to the outputs of the models so that confidence intervals can be provided for the simulation results. In the present work, a non-intrusive quadrature-based uncertainty quantification (QBUQ) approach is proposed. The probability distribution function (PDF) of the system response can be then reconstructed using extended quadrature method of moments (EQMOM) and extended conditional quadrature method of moments (ECQMOM). The report first explains the theory of QBUQ approach, including methods to generate samples for problems with single or multiple uncertain input parameters, low order statistics, and required number of samples. Then methods for univariate PDF reconstruction (EQMOM) and multivariate PDF reconstruction (ECQMOM) are explained. The implementation of QBUQ approach into the open-source CFD code MFIX is discussed next. At last, QBUQ approach is demonstrated in several applications. The method is first applied to two examples: a developing flow in a channel with uncertain viscosity, and an oblique shock problem with uncertain upstream Mach number. The error in the prediction of the moment response is studied as a function of the number of samples, and the accuracy of the moments required to reconstruct the PDF of the system response is discussed. The QBUQ approach is then demonstrated by considering a bubbling fluidized bed as example application. The mean particle size is assumed to be the uncertain input parameter. The system is simulated with a standard two-fluid model with kinetic theory closures for the particulate phase implemented into MFIX. The effect of uncertainty on the disperse-phase volume fraction, on the phase velocities and on the pressure drop inside the fluidized bed are examined, and the reconstructed PDFs are provided for the three quantities studied. Then the approach is applied to a bubbling fluidized bed with two uncertain parameters, particle-particle and particle-wall restitution coefficients. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities and gas pressure are provided. The PDFs of the response are reconstructed using EQMOM with appropriate kernel density functions. The simulation results are compared to experimental data provided by the 2013 NETL small-scale challenge problem. Lastly, the proposed procedure is demonstrated by considering a riser of a circulating fluidized bed as an example application. The mean particle size is considered to be the uncertain input parameter. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities, and granular temperature are provided. Mean values and confidence intervals of the quantities of interest are compared to the experiment results. The univariate and bivariate PDF reconstructions of the system response are performed using EQMOM and ECQMOM.

97 MATHEMATICS AND COMPUTING↗

Fully iterative scatter corrected digital breast tomosynthesis using GPU-based fast Monte Carlo simulation and composition ratio update

Purpose: In digital breast tomosynthesis (DBT), scatter correction is highly desirable, as it improves image quality at low doses. Because the DBT detector panel is typically stationary during the source rotation, antiscatter grids are not generally compatible with DBT; thus, a software-based scatter correction is required. This work proposes a fully iterative scatter correction method that uses a novel fast Monte Carlo simulation (MCS) with a tissue-composition ratio estimation technique for DBT imaging. Methods: To apply MCS to scatter estimation, the material composition in each voxel should be known. To overcome the lack of prior accurate knowledge of tissue composition for DBT, a tissue-composition ratio is estimated based on the observation that the breast tissues are principally composed of adipose and glandular tissues. Using this approximation, the composition ratio can be estimated from the reconstructed attenuation coefficients, and the scatter distribution can then be estimated by MCS using the composition ratio. The scatter estimation and image reconstruction procedures can be performed iteratively until an acceptable accuracy is achieved. For practical use, (i) the authors have implemented a fast MCS using a graphics processing unit (GPU), (ii) the MCS is simplified to transport only x-rays in the energy range of 10–50 keV, modeling Rayleigh and Compton scattering and the photoelectric effect using the tissue-composition ratio of adipose and glandular tissues, and (iii) downsampling is used because the scatter distribution varies rather smoothly. Results: The authors have demonstrated that the proposed method can accurately estimate the scatter distribution, and that the contrast-to-noise ratio of the final reconstructed image is significantly improved. The authors validated the performance of the MCS by changing the tissue thickness, composition ratio, and x-ray energy. The authors confirmed that the tissue-composition ratio estimation was quite accurate under a variety of conditions. Our GPU-based fast MCS implementation took approximately 3 s to generate each angular projection for a 6 cm thick breast, which is believed to make this process acceptable for clinical applications. In addition, the clinical preferences of three radiologists were evaluated; the preference for the proposed method compared to the preference for the convolution-based method was statistically meaningful (p < 0.05, McNemar test). Conclusions: The proposed fully iterative scatter correction method and the GPU-based fast MCS using tissue-composition ratio estimation successfully improved the image quality within a reasonable computational time, which may potentially increase the clinical utility of DBT.

60 APPLIED LIFE SCIENCES↗

The Development of Catalysts for Upgrading of Pyrolysis Vapor for Refinery Feedstocks and Intermediates (CRADA Final Report)

Catalytic fast pyrolysis (CFP) is a versatile technology platform to convert biomass into fungible hydrocarbon transportation fuels and chemical co-products. Key technical barriers to reaching this goal include increasing the product yields and achieving the desired fuel properties for gasoline, diesel, and jet range fuels or blendstocks that would be suitable for introduction into existing refinery unit operations. Overcoming these barriers will require durable catalysts that are effective at upgrading and stabilizing biomass pyrolysis vapors. Towards these goals, this CRADA leveraged NREL experience as a leader in biomass pyrolysis research and Johnson Matthey's (JM) experience as a leader in the production of advanced catalytic materials. The scope spanned CFP catalyst development, characterization, multi-scale reaction testing, and computational modeling. CRADA benefits to DOE, Participant, and U.S. Taxpayer: Assists laboratory in achieving programmatic scope, Uses the laboratory’s core competencies. The purpose of this CRADA was to develop and deploy catalysts for biomass CFP to help achieve cost-competitive biofuels and bio-based products. This was accomplished through a close collaboration between biomass conversion researchers at NREL and catalyst development researchers at JM. Summary of Research Results: Focus Area 1. Foundational research on catalytic conversion and deactivation: Key interactions between pyrolysis vapors and heterogeneous catalysts were probed through catalyst characterization, model compound reaction testing, and atomistic-scale computational modeling. Catalyst development focused on multifunctional materials, which include zeolites, oxides, carbides, and nitrides. Computational modeling identified reaction mechanisms and elucidated surface chemistry to test hypotheses regarding mechanisms of deoxygenation, coupling, cracking, dehydration, coke formation, hydrogen transfer, and aromatic ring reactions. This information was used to design multifunctional catalysts to increase product yields, control product selectivity, and reduce deactivation during CFP and downstream processing steps. The results served to increase fundamental understanding of key catalyst attributes and durability features for the upgrading of biomass pyrolysis vapors. Model compound experiments confirmed the importance of metal-acid bifunctionality for the deoxygenation of lignin-derived phenolic species under hydrodeoxygenation conditions. This insight led to the development of catalysts such as Pt/TiO2 and Mo2C, which were confirmed as high-performing materials during subsequent bench-scale experiments using biomass-derived pyrolysis vapors. This focus area also led to the identification of important catalyst deactivation mechanisms associated with the deposition of inorganic contaminants such as potassium. The molecular-level insight from model compound experiments and computational modeling, shown in Figure 1, informed the development of regeneration procedures that have been shown to be effective for restoration of > 90% of initial catalyst activity. This understanding has subsequently been translated to other catalyst systems, including zeolite materials that can be operated without requirements for co-fed hydrogen.

09 BIOMASS FUELS↗

Dimensionality Reduction with Variational Encoders Based on Subsystem Purification

Efficient methods for encoding and compression are likely to pave the way toward the problem of efficient trainability on higher-dimensional Hilbert spaces, overcoming issues of barren plateaus. Here, we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end, we build a variational algorithm-based autoencoder circuit that takes as input a dataset and optimizes the parameters of a Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as a tensor product of two subsystems by minimizing $Tr(ρ^2)$. The output of this circuit is passed through a series of controlled swap gates and measurements to output a state with half the number of qubits while retaining the features of the starting state in the same spirit as any dimension-reduction technique used in classical algorithms. The output obtained is used for supervised learning to guarantee the working of the encoding procedure thus developed. We make use of the Bars and Stripes (BAS) dataset for an 8 × 8 grid to create efficient encoding states and report a classification accuracy of 95% on the same. Thus, the demonstrated example provides proof for the working of the method in reducing states represented in large Hilbert spaces while maintaining the features required for any further machine learning algorithm that follows.

97 MATHEMATICS AND COMPUTING↗

Planck 2018 results: III. High frequency instrument data processing and frequency maps

This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous Planck 2015 release, many of which were used and described already in an intermediate paper dedicated to the Planck polarized data at low multipoles. These improvements enabled the first significant measurement of the reionization optical depth parameter using Planck-HFI data. This paper presents an extensive analysis of systematic effects, including the use of end-to-end simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved, especially the leakage from intensity to polarization. Calibration, based on the cosmic microwave background (CMB) dipole, is now extremely accurate and in the frequency range 100-353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than 0.35 μK, an accuracy of order 10 -4 . This is a major legacy from the Planck HFI for future CMB experiments. The removal of bandpass leakage has been improved for the main high-frequency foregrounds by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of "frequency maps", which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. End-to-end simulations have been shown to reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect (analogue-to-digital convertor non-linearity residuals). Using these simulations, we have been able to measure and correct the small frequency calibration bias induced by this systematic effect at the 10 -4 level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the 10 -3 level.

79 ASTRONOMY AND ASTROPHYSICS↗

Benchmarking of alignment-free sequence comparison methods

Background: Alignment-free (AF) sequence comparison is attracting persistent interest driven by data-intensive applications. Hence, many AF procedures have been proposed in recent years, but a lack of a clearly defined benchmarking consensus hampers their performance assessment. Results: Here, we present a community resource (http://afproject.org) to establish standards for comparing alignment-free approaches across different areas of sequence-based research. We characterize 74 AF methods available in 24 software tools for five research applications, namely, protein sequence classification, gene tree inference, regulatory element detection, genome-based phylogenetic inference, and reconstruction of species trees under horizontal gene transfer and recombination events. Conclusion: The interactive web service allows researchers to explore the performance of alignment-free tools relevant to their data types and analytical goals. It also allows method developers to assess their own algorithms and compare them with current state-of-the-art tools, accelerating the development of new, more accurate AF solutions

59 BASIC BIOLOGICAL SCIENCES↗

Analysis of the Space Propulsion System Problem Using RAVEN

This paper presents the solution of the space propulsion problem using a PRA code currently under development at Idaho National Laboratory (INL). RAVEN (Reactor Analysis and Virtual control ENviroment) is a multi-purpose Probabilistic Risk Assessment (PRA) software framework that allows dispatching different functionalities. It is designed to derive and actuate the control logic required to simulate the plant control system and operator actions (guided procedures) and to perform both Monte- Carlo sampling of random distributed events and Event Tree based analysis. In order to facilitate the input/output handling, a Graphical User Interface (GUI) and a post-processing data-mining module are available. RAVEN allows also to interface with several numerical codes such as RELAP5 and RELAP-7 and ad-hoc system simulators. For the space propulsion system problem, an ad-hoc simulator has been developed and written in python language and then interfaced to RAVEN. Such simulator fully models both deterministic (e.g., system dynamics and interactions between system components) and stochastic behaviors (i.e., failures of components/systems such as distribution lines and thrusters). Stochastic analysis is performed using random sampling based methodologies (i.e., Monte-Carlo). Such analysis is accomplished to determine both the reliability of the space propulsion system and to propagate the uncertainties associated to a specific set of parameters. As also indicated in the scope of the benchmark problem, the results generated by the stochastic analysis are used to generate risk-informed insights such as conditions under witch different strategy can be followed.

97 MATHEMATICS AND COMPUTING↗

Human factor engineering based design and modernization of control rooms with new I and C systems

Instrumentation and Control (I and C) systems of the latest nuclear power plants are based on the use of digital technology, distributed control systems and the integration of information in data networks (Distributed Control and Instrumentation Systems). This has a repercussion on Control Rooms (CRs), where the operations and monitoring interfaces correspond to these systems. These technologies are also used in modernizing I and C systems in currently operative nuclear power plants. The new interfaces provide additional capabilities for operation and supervision, as well as a high degree of flexibility, versatility and reliability. An example of this is the implementation of solutions such as compact stations, high level supervision screens, overview displays, computerized procedures, new operational support systems or intelligent alarms processing systems in the modernized Man-Machine Interface (MMI). These changes in the MMI are accompanied by newly added Software (SW) controls and new solutions in automation. Tecnatom has been leading various projects in this area for several years, both in Asian countries and in the United States, using in all cases international standards from which Tecnatom own methodologies have been developed and optimized. The experience acquired in applying this methodology to the design of new control rooms is to a large extent applicable also to the modernization of current control rooms. An adequate design of the interface between the operator and the systems will facilitate safe operation, contribute to the prompt identification of problems and help in the distribution of tasks and communications between the different members of the operating shift. Based on Tecnatom experience in the field, this article presents the methodological approach used as well as the most relevant aspects of this kind of project. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Characterization of Quantum States Based on Creation Complexity

Abstract The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which is crucial in developing efficient quantum algorithms that can outperform classical algorithms. A major question unanswered so far is what quantum states can be created with a number of elementary gates that scales polynomially with the number of qubits. In this work, it is first shown that for an entirely general quantum state it is exponentially hard (requires a number of steps that scales exponentially with the number of qubits) to determine if the creation complexity is polynomial. Then, it is shown that it is possible for a large class of quantum states with polynomial creation complexity to have common coefficient features such that, given any candidate quantum state, an efficient coefficient sampling procedure can be designed to determine if the state belongs to the class or not with arbitrarily high success probability. Consequently, partial knowledge of a quantum state's creation complexity is obtained, which can be useful for designing quantum circuits and algorithms involving such a state.

74 ATOMIC AND MOLECULAR PHYSICS↗

Vibrational infrared and Raman spectra of polypeptides: Fragments-in-fragments within molecular tailoring approach

The present work reports the calculation of vibrational infrared (IR) and Raman spectra of large molecular systems employing molecular tailoring approach (MTA). Further, it extends the grafting procedure for the accurate evaluation of IR and Raman spectra of large molecular systems, employing a new methodology termed as Fragments-in-Fragments (FIF), within MTA. Unlike the previous MTA-based studies, the accurate estimation of the requisite molecular properties is achieved without performing any full calculations (FC). The basic idea of the grafting procedure is implemented by invoking the nearly basis-set-independent nature of the MTA-based error vis-à-vis the respective FCs. FIF has been tested out for the estimation of the above molecular properties for three isomers, viz., β-strand, 3{sub 10}- and α-helix of acetyl(alanine){sub n}NH{sub 2} (n = 10, 15) polypeptides, three conformers of doubly protonated gramicidin S decapeptide and trpzip2 protein (PDB id: 1LE1), respectively, employing BP86/TZVP, M06/6-311G**, and M05-2X/6-31G** levels of theory. For most of the cases, a maximum difference of 3 cm{sup −1} is achieved between the grafted-MTA frequencies and the corresponding FC values. Further, a comparison of the BP86/TZVP level IR and Raman spectra of α-helical (alanine){sub 20} and its N-deuterated derivative shows an excellent agreement with the existing experimental spectra. In view of the requirement of only MTA-based calculations and the ability of FIF to work at any level of theory, the current methodology provides a cost-effective solution for obtaining accurate spectra of large molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The SCALE Verified, Archived Library of Inputs and Data - VALID

The Verified, Archived Library of Inputs and Data (VALID) at ORNL contains high quality, independently reviewed models and results that improve confidence in analysis. VALID is developed and maintained according to a procedure of the SCALE quality assurance (QA) plan. This paper reviews the origins of the procedure and its intended purpose, the philosophy of the procedure, some highlights of its implementation, and the future of the procedure and associated VALID library. The original focus of the procedure was the generation of high-quality models that could be archived at ORNL and applied to many studies. The review process associated with model generation minimized the chances of errors in these archived models. Subsequently, the scope of the library and procedure was expanded to provide high quality, reviewed sensitivity data files for deployment through the International Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE). Sensitivity data files for approximately 400 such models are currently available. The VALID procedure and library continue fulfilling these multiple roles. The VALID procedure is based on the quality assurance principles of ISO 9001 and nuclear safety analysis. Some of these key concepts include independent generation and review of information, generation and review by qualified individuals, use of appropriate references for design data and documentation, and retrievability of the models, results, and documentation associated with entries in the library. Some highlights of the detailed procedure are discussed to provide background on its implementation and to indicate limitations of data extracted from VALID for use by the broader community. Specifically, external users of data generated within VALID must take responsibility for ensuring that the files are used within the QA framework of their organization and that use is appropriate. The future plans for the VALID library include expansion to include additional experiments from the IHECSBE, to include experiments from areas beyond criticality safety, such as reactor physics and shielding, and to include application models. In the future, external SCALE users may also obtain qualification under the VALID procedure and be involved in expanding the library. The VALID library provides a pathway for the criticality safety community to leverage modeling and analysis expertise at ORNL.

97 MATHEMATICS AND COMPUTING↗

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

97 MATHEMATICS AND COMPUTING↗

A computational modeling framework for pre-clinical evaluation of cardiac mapping systems

There are a variety of difficulties in evaluating clinical cardiac mapping systems, most notably the inability to record the transmembrane potential throughout the entire heart during patient procedures which prevents the comparison to a relevant “gold standard”. Cardiac mapping systems are comprised of hardware and software elements including sophisticated mathematical algorithms, both of which continue to undergo rapid innovation. The purpose of this study is to develop a computational modeling framework to evaluate the performance of cardiac mapping systems. The framework enables rigorous evaluation of a mapping system’s ability to localize and characterize (i.e., focal or reentrant) arrhythmogenic sources in the heart. The main component of our tool is a library of computer simulations of various dynamic patterns throughout the entire heart in which the type and location of the arrhythmogenic sources are known. Our framework allows for performance evaluation for various electrode configurations, heart geometries, arrhythmias, and electrogram noise levels and involves blind comparison of mapping systems against a “silver standard” comprised of computer simulations in which the precise transmembrane potential patterns throughout the heart are known. A feasibility study was performed using simulations of patterns in the human left atria and three hypothetical virtual catheter electrode arrays. Activation times (AcT) and patterns (AcP) were computed for three virtual electrode arrays: two basket arrays with good and poor contact and one high-resolution grid with uniform spacing. The average root mean squared difference of AcTs of electrograms and those of the nearest endocardial action potential was less than 1 ms and therefore appears to be a poor performance metric. In an effort to standardize performance evaluation of mapping systems a novel performance metric is introduced based on the number of AcPs identified correctly and those considered spurious as well as misclassifications of arrhythmia type; spatial and temporal localization accuracy of correctly identified patterns was also quantified. This approach provides a rigorous quantitative analysis of cardiac mapping system performance. Proof of concept of this computational evaluation framework suggests that it could help safeguard that mapping systems perform as expected as well as provide estimates of system accuracy.

59 BASIC BIOLOGICAL SCIENCES↗