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At least 361 records · Page 20

Baseline Characterization Database Verification Report - PCEA Billet 02S8-5

The purpose of this engineering calculations and analysis report (ECAR) is to present data collected in the Baseline Graphite Characterization Program, which is directly tasked with supporting the Idaho National Laboratory's (INL's) research and development efforts on the Advanced Reactor Technologies (ART) Program. This program populates a comprehensive database that reflects the baseline properties of nuclear-grade graphite regarding individual grade, billet, and position within individual billets. The physical- and mechanical-property information being collected will be transferred to the Nuclear Data Management and Analysis System (NDMAS), and that database will help populate the handbook of property data available to member nations of the Generation-IV International Forum. Transfer of these data from the applicable technical lead to the dissemination databases available to other end users requires a full review of the test procedures and data-collection efforts through an analysis of the multiple summary spreadsheets and values being collected. This report represents the analysis for PCEA Billet 02S8-5 and facilitates release of associated data to the NDMAS custodians.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Baseline Characterization Database Verification Report ? NBG-17 Billet V104

The purpose of this report is to present data collected in the Baseline Graphite Characterization Program, which is directly tasked with supporting the Idaho National Laboratory’s (INL’s) research and development efforts on the Advanced Reactor Technologies (ART) Program. This program populates a comprehensive database that reflects the baseline properties of nuclear-grade graphite regarding individual grade, billet, and position within individual billets. The physical- and mechanical-property information being collected will be transferred to the Nuclear Data Management and Analysis System (NDMAS), and that database will help populate the handbook of property data available to member nations of the Generation-IV International Forum. Transfer of these data from the applicable technical lead to the dissemination databases available to other end users requires a full review of the test procedures and data-collection efforts through an analysis of the multiple summary spreadsheets and values being collected. This report represents the analysis for NBG-17 Billet V104 and facilitates release of associated data to the NDMAS custodians. Millions of raw data points have been collected during testing and quantification analyses for these billets. The summary scalar property values and supplementary traceability data are collected into comprehensive spreadsheets. Data sets are composed of single billets of graphite for any given grade, organized by mechanical test-specimen type, and further subdivided into individual spreadsheet tabs according to the specific test or evaluation being performed. A direct analysis of properties was not conducted, and this report does not provide information on the validity or performance characteristics of the graphite itself. Rather, this report is intended as a verification of the completeness of actual data collected in accordance with PLN-3467, “Baseline Graphite Characterization Plan: Electromechanical Testing,” [1] and PLN-3348 “Graphite Mechanical Testing” [2] and their representation of the measurement and test results with sole regard to the graphite billets under evaluation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

ECAR: Baseline Characterization Database Verification Report – PCEA Billet 01D3-35

The purpose of this engineering calculations and analysis report (ECAR) is to present data collected in the Baseline Graphite Characterization Program, which is directly tasked with supporting the Idaho National Laboratory’s (INL’s) research and development efforts on the Advanced Reactor Technologies (ART) Program. This program populates a comprehensive database that reflects the baseline properties of nuclear-grade graphite with regard to individual grade, billet, and position within individual billets. The physical- and mechanical-property information collected will be transferred to the Nuclear Data Management and Analysis System (NDMAS), and that database will help populate the handbook of property data available to member nations of the Generation-IV International Forum. Transfer of these data from the applicable technical lead to the dissemination databases available to other end users requires a full review of the test procedures and data-collection efforts through an analysis of the multiple summary spreadsheets and values being collected. This report represents the analysis for PCEA Billet 01D3-35 and facilitates release of associated data to the NDMAS custodians.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Baseline Characterization Database Verification Report - PCEA Billet 01S8-9

The purpose of this engineering calculations and analysis report (ECAR) is to present data collected in the Baseline Graphite Characterization Program, which is directly tasked with supporting the Idaho National Laboratory's (INL's) research and development efforts on the Advanced Reactor Technologies (ART) Program. This program populates a comprehensive database that reflects the baseline properties of nuclear-grade graphite with regard to individual grade, billet, and position within individual billets. The physical- and mechanical-property information being collected will be transferred to the Nuclear Data Management and Analysis System (NDMAS), and that database will help populate the handbook of property data available to member nations of the Generation-IV International Forum. Transfer of these data from the applicable technical lead to the dissemination databases available to other end users requires a full review of the test procedures and data-collection efforts through an analysis of the multiple summary spreadsheets and values being collected. This report represents the analysis for PCEA Billet 01S8-9 and facilitates release of associated data to the NDMAS custodians.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Transferable Water Potentials Using Equivariant Neural Networks

Machine learning interatomic potentials (MLIPs) have emerged as a technique that promises quantum theory accuracy for reduced cost. It has been proposed [J. Chem. Phys. 2023, 158, 084111] that MLIPs trained on solely liquid water data cannot accurately transfer to the vapor–liquid equilibrium while recovering the many-body decomposition (MBD) analysis of gas-phase water clusters. This suggests that MLIPs do not directly learn the physically correct interactions of water molecules, limiting transferability. In this work, we show that MLIPs using equivariant architecture and trained on 3200 liquid water structures reproduces liquid-phase water properties (e.g., density within 0.003 g/cm 3 between 230 and 365 K), vapor–liquid equilibrium properties up to 550 K, the MBD analysis of gas-phase water cluster up to six-body interactions, and the relative energy and the vibrational density of states of ice phases. We show that potentials developed using equivariant MLIPs allow transferability for arbitrary phases of water that remain stable in nanosecond long simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ECAR-1930 BASELINE CHARACTERIZATION DATABASE VERIFICATION REPORT - NBG-18 BILLET 635-14

The purpose of this Engineering Calculations and Analysis Report is to present the data being collected in the Baseline Graphite Characterization program, which is directly tasked with supporting the Idaho National Laboratory’s (INL’s) research and development efforts on the Next Generation Nuclear Plant (NGNP)/Very High Temperature Reactor (VHTR). This program is populating a comprehensive database that will reflect the baseline properties of nuclear-grade graphite with regard to individual grade, billet, and position within individual billets. The physical and mechanical property information being collected will be transferred to the NGNP Data Management and Analysis System (NDMAS), and from that database will help populate handbook of property data available to member nations of the Generation IV International Forum (GIF). The transfer of this data from the applicable technical lead to the dissemination databases available to other end users requires a full review of the test procedures and data collection efforts through an analysis of the multiple summary spreadsheets and values being collected. This report represents that analysis for a single billet of nuclear grade graphite (NBG-18 billet 635-14) and facilitates the release of the associated data to the NDMAS custodians.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Explainable machine learning for incipient anomaly detection in compact molten salt heat exchanger with overlapping feature distributions

High-temperature molten salt-cooled reactors (MSCRs) are a promising next-generation nuclear technology option, offering efficient power conversion and inherent safety features. However, the reliability of these systems depends on the robust operation of heat exchangers (HXs), which are susceptible to failure due to temperature gradients and channel plugging caused by fluid freezing. Conventional monitoring methods, relying on inlet and outlet measurements, lack the spatial resolution needed to detect early-stage faults. We propose a novel design of a compact salt-to-salt matrix-type HX design consisting of interleaved arrays of parallel tubes, with integrated synthetic fiber optic distributed temperature sensing (DTS) to enable localized detection of incipient faults. To evaluate performance of this design, we generate high-fidelity synthetic data using heat transfer computational modeling to simulate channel plugging, and introduce sensor noise for realistic modeling of measurements. The dataset comprises of 97% normal operation and 3% anomaly cases, with each anomaly class representing 1% of the data. These early anomalies result in overlapping temperature profiles between normal and faulty channels, producing a non-separable dataset that challenges traditional classification techniques. We benchmark eight supervised machine learning (ML) models and demonstrate that XGBoost achieves the highest performance. To improve transparency, we develop an explainability framework combining Shapley values and partially ordered sets (POSETs) to quantify and structurally analyze feature importance. This approach identifies both dominant predictors and ambiguous feature relationships, enhancing trust and interpretability. Our results highlight the potential of combining DTS and explainable ML with intelligent feature selection to improve predictive maintenance and ensure operational resilience in advanced nuclear systems.

Prantikos, Konstantinos [Argonne National Laborato↗

Data-driven cyber-attack detection for photovoltaic systems: A transfer learning approach

With increasing exposure to software-based sensing and control, power systems are facing higher risks of cyber/physical attacks. Here, to ensure system stability and minimize the potential economic losses, it is imperative to monitor the operating states and detect those attacks at the early stage. In this paper, a transfer learning method is proposed to detect cyber-attacks in photovoltaic (PV) systems with much less training data. First of all, two PV systems with a different number of PV inverters and power ratings are analyzed and their attack models are studied. Next, an attack detection Convolutional Neural Network (CNN) model was trained with rich amount of data from PV #1. Then, transfer learning was proposed to transfer the well-trained features from PV #1 to PV #2. Lastly, the attack detection model on PV #2 was trained based on the transferred CNN model. The experiment results show that the proposed transfer learning method achieves better accuracy and a faster convergence rate with a much less training dataset than conventional deep learning.

14 SOLAR ENERGY↗

Combustion Performance and Emissions Optimization through Integration of Miniaturized High Temperature Multi Process Monitoring System

The main objective of this research program is to design, manufacture, and demonstrate a miniaturized, multi-process, monitoring system (mMPMS) for boiler condition management and easy system deployment to obtain a higher spatial resolution. This system will facilitate a Condition-Based Maintenance (CBM) philosophy that actively monitors the health of assets to predict and prevent failures and maximize availability and generating capacity at a reduced cost. CBM systems can provide boiler data that the advanced process control (APC) system can utilize for plant performance optimization, which is increasingly relevant as coal power plants shift from predominantly base-load operation to predominantly transient operation involving large load swings. The mMPMS is based on an electrochemical sensor that provides a real-time indication of the risk of damage to key locations in the radiant or convective section of a coal-fired boiler such as metal loss rates, heat flux, metal surface temperature, and deposit thickness. These indications can be utilized to optimize boiler performance as well as improve boiler availability in conjunction with corresponding operating conditions. This monitoring system was developed and tested in the high-temperature regions of coal-fired utility boilers in this project but can be applied to many other industries and applications as well. The new sensor design, leveraging the existing electrochemical noise-based monitoring system, is small enough to be installed through the webbing of the waterwalls without the need for long shut-downs to bend tubes and to make it feasible to obtain high spatial resolution in the boiler. Data can be transferred to the plant distributed control system (DCS) and any other control system. The sensor body that houses the sensor assembly was designed to ensure good conductive contact with boiler tubes to ensure the sensor is held at an identical temperature to the tube surface temperature. The data acquisition and signal conditioning modules were redesigned into a small footprint with optimized cooling of the module. System software was developed specifically for the new signal conditioning module and is compatible with plant PLCs. After the preliminary testing at a pilot-scale facility, five mMPMS were installed at a full-scale pulverized coal-fired plant, Basin Electric Power Cooperative’s Leland Olds Unit 1. The systems were demonstrated over a 6-week period during typical operation. Sensor measurements of deposit thickness were validated during the demonstration and subsequently leveraged to determine sensor-based boiler cleaning strategies. These strategies have the benefit of reduced thermal stresses on boiler tubes from over-cleaning and improved boiler water management. At the end of the project, continued development of the sensor technology was carried out at PacifiCorp’s Hunter Station. REI leveraged the permanent installation of the mMPMS in Unit 3 made possible by DOE funding on a separate program. The work at Hunter Plant focused on application of machine learning and artificial intelligence-based models for integration of sensor signals into control and optimization of Hunter Unit 3 processes.

Advanced Sensors, Corrosion, Ash Deposition, Optim↗

Combustion Performance and Emissions Optimization Through Integration of a Miniaturized High-Temperature Multi Process Monitoring System

The main objective of this research program is to design, manufacture, and demonstrate a miniaturized, multi-process, monitoring system (mMPMS) for boiler condition management and easy system deployment to obtain a higher spatial resolution. This system will facilitate a Condition-Based Maintenance (CBM) philosophy that actively monitors the health of assets to predict and prevent failures and maximize availability and generating capacity at a reduced cost. CBM systems can provide boiler data that the advanced process control (APC) system can utilize for plant performance optimization, which is increasingly relevant as coal power plants shift from predominantly base-load operation to predominantly transient operation involving large load swings. The mMPMS is based on an electrochemical sensor that provides a real-time indication of the risk of damage to key locations in the radiant or convective section of a coal-fired boiler such as metal loss rates, heat flux, metal surface temperature, and deposit thickness. These indications can be utilized to optimize boiler performance as well as improve boiler availability in conjunction with corresponding operating conditions. This monitoring system was developed and tested in the high-temperature regions of coal-fired utility boilers in this project but can be applied to many other industries and applications as well. The new sensor design, leveraging the existing electrochemical noise-based monitoring system, is small enough to be installed through the webbing of the waterwalls without the need for long shut-downs to bend tubes and to make it feasible to obtain high spatial resolution in the boiler. Data can be transferred to the plant distributed control system (DCS) and any other control system. The sensor body that houses the sensor assembly was designed to ensure good conductive contact with boiler tubes to ensure the sensor is held at an identical temperature to the tube surface temperature. The data acquisition and signal conditioning modules were redesigned into a small footprint with optimized cooling of the module. System software was developed specifically for the new signal conditioning module and is compatible with plant PLCs. After the preliminary testing at a pilot-scale facility, five mMPMS were installed at a full-scale pulverized coal-fired plant, Basin Electric Power Cooperative’s Leland Olds Unit 1. The systems were demonstrated over a 6-week period during typical operation. Sensor measurements of deposit thickness were validated during the demonstration and subsequently leveraged to determine sensor-based boiler cleaning strategies. These strategies have the benefit of reduced thermal stresses on boiler tubes from over-cleaning and improved boiler water management. At the end of the project, continued development of the sensor technology was carried out at PacifiCorp’s Hunter Station. REI leveraged the permanent installation of the mMPMS in Unit 3 made possible by DOE funding on a separate program. The work at Hunter Plant focused on application of machine learning and artificial intelligence-based models for integration of sensor signals into control and optimization of Hunter Unit 3 processes.

Advanced Sensors, Corrosion, Ash Deposition, Optim↗

Combustion Performance and Emissions Optimization Through Integration of a Miniaturized High-Temperature Multi Process Monitoring System

The main objective of this research program is to design, manufacture, and demonstrate a miniaturized, multi-process, monitoring system (mMPMS) for boiler condition management and easy system deployment to obtain a higher spatial resolution of wall conditions in utility boilers. This system will facilitate a Condition-Based Maintenance (CBM) philosophy that actively monitors the health of assets to predict and prevent failures and maximize availability and generating capacity at a reduced cost. CBM systems can provide boiler data that the advanced process control (APC) system can utilize for plant performance optimization, which is increasingly relevant as coal power plants shift from predominantly base-load operation to predominantly transient operation involving large load swings. The mMPMS is based on an electrochemical sensor that provides a real-time indication of the risk of damage to key locations in the radiant or convective section of a coal-fired boiler such as metal loss rates, heat flux, metal surface temperature, and deposit thickness. These indications can be utilized to optimize boiler performance as well as improve boiler availability in conjunction with corresponding operating conditions. This monitoring system was developed and tested in the high-temperature regions of a coal-fired utility boiler in this project but can be applied to many other industries and applications as well. The new sensor design, leveraging the existing electrochemical noise-based monitoring system, is small enough to be installed through the webbing of the waterwalls without the need for long shut-downs to bend tubes and to make it feasible to obtain high spatial resolution in the boiler. Data can be transferred to the plant distributed control system (DCS) and any other control system. The sensor body that houses the sensor assembly was designed to ensure good conductive contact with boiler tubes to ensure the sensor is held at an identical temperature to the tube surface temperature. The data acquisition and signal conditioning modules were redesigned into a small footprint with optimized cooling of the module. System software was developed specifically for the new signal conditioning module and is compatible with plant PLCs. After the preliminary testing at a pilot-scale facility, five mMPMS were installed at a full-scale pulverized coal-fired plant, Basin Electric Power Cooperative’s Leland Olds Unit 1. The systems were demonstrated over a 6-week period during typical operation. Sensor measurements of deposit thickness were validated during the demonstration and subsequently leveraged to determine sensor-based boiler cleaning strategies. These strategies have the benefit of reduced thermal stresses on boiler tubes from over-cleaning and improved boiler water management. At the end of the project, continued development of the sensor technology was carried out at PacifiCorp’s Hunter Station. REI leveraged the permanent installation of the mMPMS in Unit 3 made possible by DOE funding on a separate program. The work at Hunter Plant focused on application of machine learning and artificial intelligence-based models for integration of sensor signals into control and optimization of Hunter Unit 3 processes.

42 ENGINEERING↗

High-Temperature Multi-Process Sensor Development and Demonstration at a Full-scale PC Combustion System

The main objective of this research program is to design, manufacture, and demonstrate a miniaturized, multi-process, monitoring system (mMPMS) for boiler condition management and easy system deployment to obtain a higher spatial resolution of wall conditions in utility boilers. This system will facilitate a Condition-Based Maintenance (CBM) philosophy that actively monitors the health of assets to predict and prevent failures and maximize availability and generating capacity at a reduced cost. CBM systems can provide boiler data that the advanced process control (APC) system can utilize for plant performance optimization, which is increasingly relevant as coal power plants shift from predominantly base-load operation to predominantly transient operation involving large load swings. The mMPMS is based on an electrochemical sensor that provides a real-time indication of the risk of damage to key locations in the radiant or convective section of a coal-fired boiler such as metal loss rates, heat flux, metal surface temperature, and deposit thickness. These indications can be utilized to optimize boiler performance as well as improve boiler availability in conjunction with corresponding operating conditions. This monitoring system was developed and tested in the high-temperature regions of a coal-fired utility boiler in this project but can be applied to many other industries and applications as well. The new sensor design, leveraging the existing electrochemical noise-based monitoring system, is small enough to be installed through the webbing of the waterwalls without the need for long shut-downs to bend tubes and to make it feasible to obtain high spatial resolution in the boiler. Data can be transferred to the plant distributed control system (DCS) and any other control system. The sensor body that houses the sensor assembly was designed to ensure good conductive contact with boiler tubes to ensure the sensor is held at an identical temperature to the tube surface temperature. The data acquisition and signal conditioning modules were redesigned into a small footprint with optimized cooling of the module. System software was developed specifically for the new signal conditioning module and is compatible with plant PLCs. After the preliminary testing at a pilot-scale facility, five mMPMS were installed at a full-scale pulverized coal-fired plant, Basin Electric Power Cooperative’s Leland Olds Unit 1. The systems were demonstrated over a 6-week period during typical operation. Sensor measurements of deposit thickness were validated during the demonstration and subsequently leveraged to determine sensor-based boiler cleaning strategies. These strategies have the benefit of reduced thermal stresses on boiler tubes from over-cleaning and improved boiler water management. At the end of the project, continued development of the sensor technology was carried out at PacifiCorp’s Hunter Station. REI leveraged the permanent installation of the mMPMS in Unit 3 made possible by DOE funding on a separate program. The work at Hunter Plant focused on application of machine learning and artificial intelligence-based models for integration of sensor signals into control and optimization of Hunter Unit 3 processes.

Advanced Sensors, Corrosion, Ash Deposition, Optim↗

HPC Campaign Management: Remote data access with user-defined error bound using ADIOS and ZFP

Remote access to large-scale scientific datasets, like those generated by combustion simulations or other high-performance computing (HPC) applications, presents a significant challenge. Downloading entire datasets is often impractical due to their size and the bandwidth limitations of typical networks. To address this challenge, we propose a novel approach that enables efficient remote access to large datasets distributed across multiple facilities. Our method enables technologies to download only the data values of a select variable, in a select region of interest, to a user-defined accuracy. For this purpose, we extended the ADIOS IO library to provide read functions with user-defined accuracy, a remote data server that understands multidimensional selections of specific variables, steps and accuracy from an ADIOS dataset, and which uses lossy compression on the remote site to reduce the data to be transferred back to the client. In addition, our extension of the ADIOS library collects metadata from multiple datasets in small files called Campaign Archives, which can be shared among project participants on any HPC, cloud or laptop, and which can easily facilitate the discovery of content and pointers to the data location as well as remote access to the data by local tools as if data was local. This feature called Campaign Management, enables a group of scientists to manage related datasets stored in multiple files, across multiple facilities as if it was in a single file/database. We demonstrate the effectiveness of our approach using a 1.5 TB dataset from the S3D combustion simulation on Frontier at the Oak Ridge Leadership Facility. Even a single variable from this dataset, at 64 GB, is too large to be processed on a standard laptop. We show two different reading patterns for 2D plots and 3D visualization, with careful settings that a scientist studying combustion data would do and show that running the same Python scripts on Frontier directly takes comparable time than running them on the local laptop with remote access to the data on Frontier.

Podhorszki, Norbert [ORNL] (ORCID:000000019647542X↗

Combining physics-based and data-driven models for quantitatively accurate plasma profile prediction that extrapolates well; with application to DIII-D, AUG, and ITER tokamaks

For design, scenario planning, and control, ITER and all other envisioned tokamaks rely on a variety of statistical and physics-based models to extrapolate to unseen regimes; most notably from low plasma current to high. A 'meta-learning' methodology for combining the accuracy of data-driven models with the generalizability of physics-based models is described and tested, yielding a 5–10 percent improvement in performance beyond either alone for the task of extrapolating time-dependent plasma profile prediction from low- to high- plasma current DIII-D tokamak discharges. Meanwhile, it is shown that both machine learning models extrapolated far-distribution and state-of-the-art 'physics-based' profile predictors fare worse than merely assuming plasma profiles do not change from their initial values. Finally, a variety of other mechanisms for helping data-driven models generalize—transfer learning, adding contextual information from physics simulators, and adding data from the ASDEX Upgrade tokamak—are attempted for similar extrapolation tasks but, in the methodology used in this paper, yield no significant improvement beyond simple data-driven models. Results are summarized in figures 15 and 16.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Seismology in the Cloud: A New Streaming Workflow

Data-intensive research in seismology is experiencing a recent boom, driven in part by large volumes of available data and advances in the growing field of data science. However, there are significant barriers to processing large data volumes, such as long retrieval times from data repositories, complex data management, and limited computational resources. New tools and platforms have reduced the barriers to entry for scientific cluster computing, including the maturation of the commercial cloud as an accessible instrument for research. Here, we build a customized research cluster in the cloud to test a new workflow for large-scale seismic analysis, in which data are processed as a stream (retrieved on-the-fly and acted upon without storing), with data from the Incorporated Research Institutions for Seismology Data Management Center. We use this workflow to deploy a spectral peak detection algorithm over 5.6 TB of compressed continuous seismic data from 2074 stations of the USArray Transportable Array EarthScope network. Using a 50-node cluster in the cloud, we completed the noise survey in 80 hr, with an average data throughput of 1.7 GB per minute. By varying cluster sizes, we find the scaling of our analysis to be sublinear, due to a combination of algorithmic limitations and data center response times. The cloud-based streaming workflow represents an order-of-magnitude increase in acquisition and processing speed compared to a traditional download-store-process workflow, and offers the additional benefits of employing a flexible, accessible, and widely used computing architecture. It is limited, however, due to its reliance on Internet transfer speeds and data center service capacity, and may not work well for repeated analyses or those for which even higher data throughputs are needed. These research applications will require a new class of cloud-native approaches in which both data and analysis are in the cloud.

58 GEOSCIENCES↗

Progressive Tree-Based Compression of Large-Scale Particle Data

Scientific simulations and observations using particles have been creating large datasets that require effective and efficient data reduction to store, transfer, and analyze. However, current approaches either compress only small data well while being inefficient for large data, or handle large data but with insufficient compression. Toward effective and scalable compression/decompression of particle positions, we introduce new kinds of particle hierarchies and corresponding traversal orders that quickly reduce reconstruction error while being fast and low in memory footprint. Our solution to compression of large-scale particle data is a flexible block-based hierarchy that supports progressive, random-access, and error-driven decoding, where error estimation heuristics can be supplied by the user. For low-level node encoding, we introduce new schemes that effectively compress both uniform and densely structured particle distributions. Our proposed methods thus target all three phases of a tree-based particle compression pipeline, namely tree construction, tree traversal, and node encoding. In conclusion, the improved efficacy and flexibility of these methods over existing compressors are demonstrated through extensive experimentation, using a wide range of scientific particle datasets.

97 MATHEMATICS AND COMPUTING↗