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At least 271 records · Page 15

Application of chaos analyses methods on East Anatolian Fault Zone fractures

Nonlinear time series analysis techniques have large application areas on the geoscience and geophysics fields. Modern nonlinear methods are provided considerable evidence for explain seismicity phenomena. In this study nonlinear time series analysis, fractal analysis and spectral analysis have been carried out for researching the chaotic behaviors of release radon gas ({sup 222}Rn) concentration occurring during seismic events. Nonlinear time series analysis methods (Lyapunov exponent, Hurst phenomenon, correlation dimension and false nearest neighbor) were applied for East Anatolian Fault Zone (EAFZ) Turkey and its surroundings where there are about 35,136 the radon measurements for each region. In this paper were investigated of {sup 222}Rn behavior which it’s used in earthquake prediction studies.

58 GEOSCIENCES↗

Dark matter directional detection in non-relativistic effective theories

We extend the formalism of dark matter directional detection to arbitrary one-body dark matter-nucleon interactions. The new theoretical framework generalizes the one currently used, which is based on 2 types of dark matter-nucleon interaction only. It includes 14 dark matter-nucleon interaction operators, 8 isotope-dependent nuclear response functions, and the Radon transform of the first 2 moments of the dark matter velocity distribution. We calculate the recoil energy spectra at dark matter directional detectors made of CF{sub 4}, CS{sub 2} and {sup 3}He for the 14 dark matter-nucleon interactions, using nuclear response functions recently obtained through numerical nuclear structure calculations. We highlight the new features of the proposed theoretical framework, and present our results for a spherical dark matter halo and for a stream of dark matter particles. This study lays the foundations for model independent analyses of dark matter directional detection experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Regulatory framework for NORM residues in Belgium

The Belgian radiation protection authority (Federal Agency for Nuclear Control - FANC) has published in March 2013 a decree regulating the acceptance of NORM residues by nonradioactive waste treatment facilities. This regulation is based on the concept of 'work activities involving natural radiation sources' in the sense of article 40 of the 96/29/EURATOM directive. The disposal or processing facilities which accept NORM residues with an activity concentration above a generic exemption level will be considered as 'work activities' and submitted to declaration according to the Belgian radiation protection regulations. On basis of this declaration, specific acceptance criteria for the different types of processing/ disposal of the residues (disposal on landfill, recycling into building materials, etc.) are imposed. FANC has drafted guidelines for these acceptance criteria. A methodological guide for the operators of the concerned facilities was also published. Moreover, sites where significant quantities of NORM residues are or have been disposed, are subjected to an environmental monitoring in the framework of the national program of radiological surveillance of FANC. FANC also introduced in its regulations the concept of anthropogenic radon-prone areas: e.g. former phosphogypsum stacks have been defined as anthropogenic radon-prone areas, which allows some form of regulatory control of these sites. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

SU-D-206-07: CBCT Scatter Correction Based On Rotating Collimator

Purpose: Scatter correction in cone-beam computed tomography (CBCT) has obvious effect on the removal of image noise, the cup artifact and the increase of image contrast. Several methods using a beam blocker for the estimation and subtraction of scatter have been proposed. However, the inconvenience of mechanics and propensity to residual artifacts limited the further evolution of basic and clinical research. Here, we propose a rotating collimator-based approach, in conjunction with reconstruction based on a discrete Radon transform and Tchebichef moments algorithm, to correct scatter-induced artifacts. Methods: A rotating-collimator, comprising round tungsten alloy strips, was mounted on a linear actuator. The rotating-collimator is divided into 6 portions equally. The round strips space is evenly spaced on each portion but staggered between different portions. A step motor connected to the rotating collimator drove the blocker to around x-ray source during the CBCT acquisition. The CBCT reconstruction based on a discrete Radon transform and Tchebichef moments algorithm is performed. Experimental studies using water phantom and Catphan504 were carried out to evaluate the performance of the proposed scheme. Results: The proposed algorithm was tested on both the Monte Carlo simulation and actual experiments with the Catphan504 phantom. From the simulation result, the mean square error of the reconstruction error decreases from 16% to 1.18%, the cupping (τcup) from 14.005% to 0.66%, and the peak signal-to-noise ratio increase from 16.9594 to 31.45. From the actual experiments, the induced visual artifacts are significantly reduced. Conclusion: We conducted an experiment on CBCT imaging system with a rotating collimator to develop and optimize x-ray scatter control and reduction technique. The proposed method is attractive in applications where a high CBCT image quality is critical, for example, dose calculation in adaptive radiation therapy. We want to thank Dr. Lei Xing and Dr. Yong Yang in the Stanford University School of Medicine for this work. This work was jointly supported by NSFC (61471226), Natural Science Foundation for Distinguished Young Scholars of Shandong Province (JQ201516), and China Postdoctoral Science Foundation (2015T80739, 2014M551949).

60 APPLIED LIFE SCIENCES↗

The LUX-ZEPLIN (LZ) radioactivity and cleanliness control programs

LUX-ZEPLIN (LZ) is a second-generation direct dark matter experiment with spin-independent WIMP-nucleon scattering sensitivity above 1.4×10 –48 cm 2 for a WIMP mass of 40GeV/c 2 and a 1000 days exposure. LZ achieves this sensitivity through a combination of a large 5.6 t fiducial volume, active inner and outer veto systems, and radio-pure construction using materials with inherently low radioactivity content. The LZ collaboration performed an extensive radioassay campaign over a period of six years to inform material selection for construction and provide an input to the experimental background model against which any possible signal excess may be evaluated. The campaign and its results are described in this paper. We present assays of dust and radon daughters depositing on the surface of components as well as cleanliness controls necessary to maintain background expectations through detector construction and assembly. Finally, examples from the campaign to highlight fixed contaminant radioassays for the LZ photomultiplier tubes, quality control and quality assurance procedures through fabrication, radon emanation measurements of major sub-systems, and bespoke detector systems to assay scintillator are presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Erratum to: The LUX-ZEPLIN (LZ) radioactivity and cleanliness control programs

LUX-ZEPLIN (LZ) is a second-generation direct dark matter experiment with spin-independent WIMP-nucleon scattering sensitivity above 1.4 × 10 -48 cm 2 for a WIMP mass of 40 GeV/c 2 and a 1000 d exposure. LZ achieves this sensitivity through a combination of a large 5.6 t fiducial volume, active inner and outer veto systems, and radio-pure construction using materials with inherently low radioactivity content. The LZ collaboration performed an extensive radioassay campaign over a period of six years to inform material selection for construction and provide an input to the experimental background model against which any possible signal excess may be evaluated. The campaign and its results are described in this paper. We present assays of dust and radon daughters depositing on the surface of components as well as cleanliness controls necessary to maintain background expectations through detector construction and assembly. Finally, examples from the campaign to highlight fixed contaminant radioassays for the LZ photomultiplier tubes, quality control and quality assurance procedures through fabrication, radon emanation measurements of major sub-systems, and be spoke detector systems to assay scintillator are presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Sky and Elemental Planetary Mapping Via Gamma Ray Emissions

Low-energy gamma ray emissions ((is) approximately 30keV to (is) approximately 30MeV) are significant to astrophysics because many interesting objects emit their primary energy in this regime. As such, there has been increasing demand for a complete map of the gamma ray sky, but many experiments to do so have encountered obstacles. Using an innovative method of applying the Radon Transform to data from BATSE (the Burst And Transient Source Experiment) on NASA's CGRO (Compton Gamma-Ray Observatory) mission, we have circumvented many of these issues and successfully localized many known sources to 0.5 - 1 deg accuracy. Our method, which is based on a simple 2-dimensional planar back-projection approximation of the inverse Radon transform (familiar from medical CAT-scan technology), can thus be used to image the entire sky and locate new gamma ray sources, specifically in energy bands between 200keV and 2MeV which have not been well surveyed to date. Samples of these results will be presented. This same technique can also be applied to elemental planetary surface mapping via gamma ray spectroscopy. Due to our method's simplicity and power, it could potentially improve a current map's resolution by a significant factor.

BATSE (the Burst and Transient Source Experiment)↗

Port Radium Canada's Original Radium/Uranium Mine, The Complete Story of Canada's Historic Radium/Uranium Mine, 1932 to 2012 - 13159

This paper provides the life story of Canada's original radium/uranium mine. In addition to the history of operations, it discusses the unique and successful approach used to identify the key issues and concerns associated with the former radium, uranium and silver mining property and the activities undertaken to define the remedial actions and subsequent remedial plan. The Port Radium Mine site, situated approximately 275 km north of Yellowknife on the east shore of Great Bear Lake, Northwest Territories, was discovered in 1930 and underground mining began in 1932. The mine operated almost continuously from 1932 to 1982, initially for recovery of radium, then uranium and finally, for recovery of silver. Tailings production totaled an estimated 900,000 tons and 800,000 tons from uranium and silver processing operations respectively. In the early days of mining, Port Radium miners were exposed to radon and associated decay product levels (in Working Level Months of exposure - WLM) hundreds of times greater than modern standards. The experience of the Port Radium miners provides important contribution to understanding the risks from radon. While the uranium mine was originally decommissioned in the early 1960's, to the standards of the day, the community of Deline (formerly Fort Franklin) had concerns about residual contamination at the mine site and the potential effects arising from use of traditional lands. The Deline people were also concerned about the possible risks to Deline Dene arising from their work as ore carriers. In the late 1990's, the community of Deline brought these concerns to national attention and consequently, the Government of Canada and the community of Deline agreed to move forward in a collaborative manner to address these concerns. The approach agreed to was to establish the Canada-Deline Uranium Table (CDUT) to provide a joint process by which the people of Deline could have their concerns expressed and addressed. A great deal of work was done through the CDUT, including efforts to assess site environment and safety issues in the context of modern reclamation standards. In addition to the environmental and remediation studies, an assessment of historic exposures of Deline ore carriers to radiation and a follow-up epidemiological feasibility study were performed. SENES Consultants Limited (SENES) carried out the dose reconstruction for the Port Radium miners in the 1990's, was the environmental consultant to the CDUT from 2000 to 2005, developed the Remedial Action Plan (RAP), engineering plans and specifications for decommissioning the Port Radium mine and vicinity sites in 2005/6, supervised the remedial works in 2007 and carried out the long term post closure monitoring from 2008 to 2012. Our firsthand experience from working cooperatively with the CDUT provides insights into effective decommissioning of historic contaminated sites. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

GPS-Based Gamma Survey for Characterizing and Decommissioning NORM Sites - 20389

Gamma survey techniques are an especially powerful decommissioning tool at naturally occurring radioactive material (NORM) sites due to both the low cost to obtain data over a large spatial scale and the abundance of gamma emitters in the uranium and thorium decay series. Gamma surveys are executed by coupling a detector - most often a sodium iodide crystal - to a global positioning system (GPS), then reporting a location and gross gamma reading coincidentally to a data logger. Systems may be carried by workers or mounted to a car, all-terrain vehicle, or unmanned aerial system (UAS). The resulting data set provides a high-resolution but low precision map of the gamma radiation field over the area surveyed. Frequently this map is also correlated to soil concentrations of NORM radionuclides (most often, Ra-226) and/or exposure rate. Gamma survey parameters such as movement speed, transect spacing, and data logging frequency define the spatial resolution of the resulting surface, and can be optimized depending on the desired survey sensitivity. This paper examines gamma survey as a tool for decommissioning NORM sites and provides an overview of current gamma survey technology designed to improve the efficiency and effectiveness of the decommissioning process. Topics to be discussed in the paper include: - An overview of gamma survey systems, and the utility of different delivery vehicles depending on desired cost, desired spatial resolution, and site topography. - The influence of physical detector characteristics on detection sensitivity and survey planning. - The tradeoff between high-resolution and large spatial extent, but inherently uncertain data, and low-resolution, low spatial extent, but highly certain data, as well as the specific utility of each of these types of data during NORM facility decommissioning. - Confounding variables that may limit the utility of gamma survey at some sites (e.g., radon gas and spatial heterogeneity / hot spots), and methods to plan for and control these conditions. Results show that the confounding variables, such as radon and data output can greatly influence the overall data quality associated with the decommissioning process. In addition, the use of real-time and aerial survey platforms provides a method for ensuring proper spatial extent of the data. When applied thoughtfully, gamma survey is a powerful tool for detecting NORM radionuclides in the environment and a cost-effective technique for identifying areas requiring remediation. However, entities performing or using gamma survey as a decommissioning tool must be aware of both its advantages and its limitations before basing remediation or regulatory action on gamma survey results. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A Rapid Sequential Separation Method for Determination of Actinides and TENORM in Fracking Wastes - 20223

With recent advances in unconventional drilling technology in the US and around the world, the risks of environmental contamination and exposure due to technologically enhanced naturally occurring radioactive materials (TENORM) from fracking wastes have also surfaced. Although the Permian Basin (southeastern New Mexico, western Texas) has long been a modest producer of oil, the advent of fracking technology a decade ago turned it into hot property for producers. A 2018 assessment of undiscovered, technically recoverable continuous oil and gas resources by the U.S. Geological Survey estimates an average 46.3 billion barrels of oil and 281 trillion cubic feet of gas. This is likely to increase the use of unconventional drilling and TENORM generation. TENORM concentrations in oil and gas exploration and production waste can be several hundred to several thousand times higher than background TENORM concentrations. Both the thorium and uranium decay chains contribute to airborne radionuclides arising from the radon gas escaping the ground and subsequently decaying as airborne particulates. Additionally, radon decay products {sup 210}Pb and {sup 210}Po can build up in scale on the internal surfaces of oil and gas handling pipes and in sludge in refineries, becoming potential inhalation and ingestion hazards for workers. Furthermore, southeastern NM is also home to world's only licensed and operating transuranic nuclear waste repository, the DoE's Waste Isolation Pilot Plant (WIPP). Plutonium isotopes ({sup 239+240}Pu) and {sup 241}Am, are expected to account for more than 99% of the total radioactivity scheduled for disposal in the WIPP repository. Thus, an improved understanding of the environmental fate and transport of TENORM, liberated by unconventional drilling, is essential to assess how best to protect individuals and the environment. In this context, accurate measurement of TENORM and actinides in environmental and biological samples is essential. In this presentation, a new sequential method for the separation and pre-concentration of actinides (Pu, Am, Np) and TENORM (Po, U and Th) derived from oil and gas exploration is proposed. The TEVA method involves a rapid co-precipitation step to remove matrix interferences from the samples, followed by plutonium oxidation state adjustment to Pu (IV) and an incubation period of ∼ 1 hour at 50-60 deg. C to allow the resultant Po (II) to oxidize into Po(IV). The polonium, neptunium, thorium and plutonium are then separated on a TEVA column, while americium and uranium are separated on a TRU column. After separation, the alpha counting source was prepared by micro-precipitation with copper sulfide (CuS) for polonium and neodymium fluoride (NdF{sub 3}) for actinides. The efficiency and reliability of the procedures were tested by analyzing filter, drinking water and frack sand samples. The method is simple, robust and can be performed quickly with excellent removal of interferences, high chemical recovery and very good alpha peak resolution. (authors)

07 ISOTOPE AND RADIATION SOURCES↗

A Comparison of RESRAD and GoldSim Models for Assessing Radiological Dose for a RCRA Landfill - 20418

US Ecology Idaho (USEI) operates a Resource Conservation and Recovery Act (RCRA) Subtitle C, Hazardous Waste Treatment, Storage, and Disposal (TSD) Facility on a 640-acre property in Owyhee County, Idaho. USEI accepts a wide variety of RCRA-exempt low activity radioactive wastes, including naturally occurring radioactive material (NORM) and technologically enhanced NORM (TENORM) (USEI 2009). The performance of the landfill with regard to radiological operating permit requirements was previously assessed using a model constructed with the residual radioactivity (RESRAD) computer program, developed by Argonne National Laboratory for the U.S. Department of Energy (DOE). RESRAD supports the evaluation of several environmental transport pathways related to a radionuclide-contaminated soil source term, but it was not conceived as a model for the evaluation of landfill radiological performance. A more comprehensive and realistic model is desired in order to better support submissions to both the State of Idaho's Department of Environmental Quality as well as the U.S. Nuclear Regulatory Commission. A Performance Assessment (PA) computer model was developed using GoldSim software for the USEI RCRA Subtitle C landfill. The RESRAD computer model was specifically developed for calculating soil cleanup criteria and radiological dose and cancer risk from residual radioactive material in soil. To evaluate site-specific conditions, users may select from among a number of available environmental transport and exposure pathways and modify 'default' parameter values. In GoldSim, a user must construct the model 'from scratch.' However, this modeling is facilitated by a number of specialized elements available in GoldSim to support a radiological mass transport model. These include elements for defining radiological decay and ingrowth, container failure and radiological release, advective and diffusive transport, and other processes. Advantages afforded by the use of RESRAD for modeling radiological dose for a RCRA Subtitle C landfill include ease of use and reasonable flexibility in specifying site-specific conditions. GoldSim allows for considerably more flexibility and site-specificity than RESRAD, including evaluation of potentially relevant environmental transport processes not supported in RESRAD. The probabilistic modeling capabilities of GoldSim also far exceed those of RESRAD. The pros and cons of RESRAD and GoldSim for this modeling problem are explored with a focus on identifying approaches and critical factors in identifying the appropriate platform. The capabilities of RESRAD and GoldSim for mathematically modeling the disposal system will be contrasted and compared. For example, the existing RESRAD radiological safety assessment evaluated potentially complete exposure pathways related to infiltration to groundwater and upwards diffusion of radon. Additional transport pathways identified in the USEI Idaho facility Conceptual Site Model include deposition of radon decay products in cover material, root uptake of radionuclides in disposed wastes by native plants, and mixing of cover material by burrowing animals. Results of the two models and how the different transport and dose pathways affect results will be discussed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Low-Background Gamma Spectrometry for the International Monitoring System

PNNL has developed two very low-background gamma detectors housed in a new shallow underground laboratory. This new capability significantly improves our ability to detect trace amounts of airborne particulate that may be present in samples from the IMS field stations. The detectors were custom ordered to be fabricated using very low background materials. The combination of cosmic veto panels, dry nitrogen gas to reduce radon, low background shielding, and the shallow underground laboratory results in a reduction of the background count rate by a factor of 100 compared to an off –the-shelf commercial gamma detector operating above ground at our laboratory. Detection limits are thus reduced an order of magnitude.

gamma specgtroscopy, lo↗

Mechanical ventilation and indoor air quality in recently constructed U.S. homes in marine and cold-dry climates

Data were collected to characterize whole-house mechanical ventilation (WHMV) and indoor air quality (IAQ) in 55 homes in the Marine climate of Oregon and the Cold-Dry climate of Colorado in the U.S. Sixteen homes were monitored for two weeks, with and without WHMV operating. Ventilation airflows; airtightness; time-resolved CO 2 , PM2.5 and radon; and time-integrated NO 2 , NO X and formaldehyde were measured. Participants provided information about IAQ-impacting activities, perceptions and ventilation use. All homes had operational cooktop ventilation and bathroom exhaust. Thirty homes had equipment that could meet the ASHRAE 62.2–2010 standard with continuous or controlled runtime and 34 had some WHMV operating as found. Thirty-five of 46 participants with WHMV reported they did not know how to operate it, and only half of the systems were properly labeled. Two-week homes had lower formaldehyde, radon, CO 2 and NO (NO X -NO 2 ) when operated with WHMV, and had faster PM 2.5 decays following indoor emission events. Overall IAQ satisfaction was similar in Oregon and Colorado, but more Colorado participants (19% vs 3%) felt their IAQ could be improved and more reported dryness as a problem (58% vs. 14%). The collected data indicate that there are benefits of operating WHMV, even when continuous use may not be needed because outdoor pollutant concentrations are low and indoor sources do not present substantial challenges.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Delayed signatures of underground nuclear explosions

Radionuclide signals from underground nuclear explosions (UNEs) are strongly influenced by the surrounding hydrogeologic regime. One effect of containment is delay of detonation-produced radioxenon reaching the surface as well as lengthening of its period of detectability compared to uncontained explosions. Using a field-scale tracer experiment, we evaluate important transport properties of a former UNE site. Here, we observe the character of signals at the surface due to the migration of gases from the post-detonation chimney under realistic transport conditions. Background radon signals are found to be highly responsive to cavity pressurization suggesting that large local radon anomalies may be an indicator of a clandestine UNE. Computer simulations, using transport properties obtained from the experiment, track radioxenon isotopes in the chimney and their migration to the surface. They show that the chimney surrounded by a fractured containment regime behaves as a leaky chemical reactor regarding its effect on isotopic evolution introducing a dependence on nuclear yield not previously considered. This evolutionary model for radioxenon isotopes is validated by atmospheric observations of radioxenon from a 2013 UNE in the Democratic People’s Republic of Korea (DPRK). In conclusion, our model produces results similar to isotopic observations with nuclear yields being comparable to seismic estimates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of the ion fraction and mobility of 218Po produced in 222Rn decays in liquid argon

We report measurements of the charged daughter fraction of 218Po as a result of the 222Rn alpha decay, and the mobility of 218Po+ ions, using radon-polonium coincidences from the 238U chain identified in 532 live-days of DarkSide-50 WIMP-search data. The fraction of 218Po that is charged is found to be 0.37 ± 0.03 and the mobility of 218Po+ is (8.6 ± 0.1) × 10-4 cm2/Vs.

Agnes, P↗

Operation and performance of a dual-phase crystalline/vapor xenon time projection chamber

We have built and operated a crystalline/vapor xenon TPC, with the goal of improving searches for dark matter. The motivation for this instrument is the fact that beta decays from the radon decay chain to the ground state presently limit the state-of-the-art liquid/vapor xenon experiments. In contrast, a crystalline xenon target has the potential to exclude, or tag and reject radon-chain backgrounds. As a preamble to demonstrating such capabilities, the present article makes a first demonstration of the operation of a crystalline/vapor xenon TPC with electroluminescence (gas gain) for the electron signal readout. It also shows that the scintillation yield in crystalline xenon appears to be identical to that in liquid xenon, in contrast to previous results.

47 OTHER INSTRUMENTATION↗

The Past Informs the Future: An Overview of the Million Worker Study and the Mallinckrodt Chemical Works Cohort

The purpose of this paper is to present an overview of ongoing work on the Million Worker Study (MWS), highlighting some of the key methods and progress so far as exemplified by the study of workers at the Mallinckrodt Chemical Works (MCW). The MWS began nearly 25 y ago and continues in a stepwise fashion, evaluating one study cohort at a time. It includes workers from U.S. Department of Energy (DOE) Manhattan Project facilities, U.S. Nuclear Regulatory Commission (NRC) regulated nuclear power plants, industrial radiographers, U.S. Department of Defense (DoD) nuclear weapons test participants, and physicians and technologists working with medical radiation. The purpose is to fill the major gap in radiation protection and science: What is the risk when exposure is received gradually over time rather than briefly as for the atomic bomb survivors? Studies published or planned in 2018 include leukemia (and dosimetry) among atomic veterans, leukemia among nuclear power plant workers, mortality among workers at the MCW, and a comprehensive National Council on Radiation Protection and Measurements (NCRP) Report on dosimetry for the MWS. MCW has a singular place in history: the 40 tons (T) of uranium oxide produced at MCW were used by Enrico Fermi on 2 December 1942 to produce the first manmade sustained and controlled nuclear reaction, and the atomic age was born. Seventy-six years later, the authors followed the over 2,500 MCW workers for mortality and reconstructed dose from six sources of exposure: external gamma rays from the radioactive elements in pitchblende; medical x rays from occupationally required chest examinations; intakes of pitchblende (uranium, radium, and silica) measured by urine samples; radon breath analyses and dust surveys overseen by Robley Evans and Merril Eisenbud; occupational exposures received before and after employment at MCW; and cumulative radon concentrations and lung dose from the decay of radium in the work environment. The unique exposure reconstructions allow for multiple evaluations, including estimates of silica dust. The study results are relevant today. For example, NASA is interested that radium, deposited in the brain, releases high-LET alpha particles - the only human analogue, though limited, for high energy, high-Z particles (galactic cosmic rays) traveling through space that might affect astronauts on Mars missions. In conclusion, don’t discount the past; it’s the prologue to the future!

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.

Kielstra, P Michael↗