SEARCH · Search NASA

Results for “matrix product state”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Thermalization from quantum entanglement: Jet simulations in the massive Schwinger model

We investigate the emergence of thermalization in a quantum-field-theoretic model mimicking the production of jets in QCD: the massive lattice Schwinger model coupled to external sources. Specifically, we compute the expectation values of local operators as functions of time and compare them to their thermal counterparts, quantify the overlap between the evolving density matrix and the thermal one, and compare the dynamics of the energy-momentum tensor to predictions from relativistic hydrodynamics. Through these studies, we find that the system approaches thermalization at late times and elucidate the mechanisms by which quantum entanglement drives thermalization in closed field-theoretic systems. Our results show how thermodynamic behavior emerges in real time from unitary quantum dynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Photoaging of phenolic secondary organic aerosol in the aqueous phase: evolution of chemical and optical properties and effects of oxidants

Abstract. While gas-phase reactions are well established to have significant impacts on the mass concentration, chemical composition, and optical properties of secondary organic aerosol (SOA), the aqueous-phase aging of SOA remains poorly understood. In this study, we performed a series of long-duration photochemical aging experiments to investigate the evolution of the composition and light absorption of the aqueous SOA (aqSOA) from guaiacyl acetone (GA), a semivolatile phenolic carbonyl that is common in biomass burning smoke. The aqSOA was produced from reactions of GA with hydroxyl radical (•OH-aqSOA) or a triplet excited state of organic carbon (3C∗-aqSOA) and was then photoaged in water under conditions that simulate sunlight exposure in northern California for up to 48 h. The effects of increasing aqueous-phase •OH or 3C∗ concentration on the photoaging of the aqSOA were also studied. High-resolution aerosol mass spectrometry (HR-AMS) and UV–Vis spectroscopy were utilized to characterize the composition and the light absorptivity of the aqSOA and to track their changes during aging. Compared to •OH-aqSOA, the 3C∗-aqSOA is produced more rapidly and shows less oxidation, a greater abundance of oligomers, and higher light absorption. Prolonged photoaging promotes fragmentation and the formation of more volatile and less light-absorbing products. More than half of the initial aqSOA mass is lost, and substantial photobleaching occurs after 10.5 h of prolonged aging under simulated sunlight illumination for 3C∗-aqSOA and 48 h for •OH-aqSOA. By performing positive matrix factorization (PMF) analysis of the combined HR-AMS and UV–Vis spectral data, we resolved three generations of aqSOA with distinctly different chemical and optical properties. The first-generation aqSOA shows significant oligomer formation and enhanced light absorption at 340–400 nm. The second-generation aqSOA is enriched in functionalized GA species and has the highest mass absorption coefficients in 300–500 nm, while the third-generation aqSOA contains more fragmented products and is the least light absorbing. These results suggest that intermediately aged phenolic aqSOA is more light absorbing than other generations, and that the light absorptivity of phenolic aqSOA results from a competition between brown carbon (BrC) formation and photobleaching, which is dependent on aging time. Although photoaging generally increases the oxidation of aqSOA, a slightly decreased O/C of the •OH-aqSOA is observed after 48 h of prolonged photoaging with additional •OH exposure. This is likely due to greater fragmentation and evaporation of highly oxidized compounds. Increased oxidant concentration accelerates the transformation of aqSOA and promotes the decay of BrC chromophores, leading to faster mass reduction and photobleaching. In addition, compared with •OH, photoaging by 3C∗ produces more low-volatility functionalized products, which counterbalances part of the aqSOA mass loss due to fragmentation and evaporation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Natural orbitals for the ab initio no-core configuration interaction approach

Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of such calculations is limited by the finite dimensions which are computationally feasible for the truncated many-body space. We therefore seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupation of low-lying orbitals, thus accelerating convergence in a configuration-interaction basis, while also possibly providing physical insight into the single-particle structure of the many-body wave function. We describe the implementation of natural orbitals in the NCCI framework and examine the nature of the natural orbitals thus obtained, the properties of the resulting many-body wave functions, and the convergence of observables. After taking 3 He as an illustrative testbed, we explore aspects of NCCI calculations with natural orbitals for the ground state of the p-shell neutron halo nucleus 6 He .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Impact of DMP-30 catalyst concentration on the degradation and kinetics of bisphenol A epoxy thermosets cured with linear amine hardener

Epoxy thermosets are a crucial component in carbon-fiber composites, serving as the organic binding matrix. Catalysts are commonly used in prepolymer formulations to accelerate curing of the thermosets. However, the impact of catalysts on the thermal stability, degradation pathways, and kinetics of the final thermoset is poorly understood. Here, in this work, Product-Specific Kinetics (PSK) analysis was utilized with isoconversional kinetics to provide a first look into the degradation kinetics of major pyrolysis pathways in bisphenol A (BPA) epoxy resins and determine the impact of altering catalysis concentrations on these kinetic pathways. Results revealed new insights into previously identified degradation pathways, provided evidence of multiple degradation pathways for some products, and showed that use of excess catalyst results in polymer network alterations and reduced thermal stability of the thermosets.

Bisphenol A↗

DOE OSTI2020

Characterization of Urbix Resources Natural Flake Graphite Material for Nuclear Applications (CRADA NFE-18-07340 Final Report)

Urbix Resources is a company specializing in graphite powder processing and purification. Urbix is looking to become the first domestic supplier of nuclear-grade graphite in the United States. This has led to a Cooperative Research and Development Agreement (CRADA) being established between the Oak Ridge National Laboratory (ORNL) and Urbix Resources, with the goal of characterizing a purified graphite feedstock supplied by Urbix Resources. The resulting data will then be used to determine the viability of a large-scale nuclear graphite production and qualification campaign. These characterization methods have been performed on the as-received graphite feedstock, a heat-treated batch of the feedstock, a milled batch of the feedstock, and a nuclear-grade graphite powder historically used in fuel production. The data from the heat-treated and milled feedstock will determine how different processing methods affect the powder’s physical properties, whereas the data from the nuclear grade graphite will provide information about the characteristics of a graphite previously accepted for nuclear applications. All of these powders have been characterized individually and as part of a resin-graphite blend (herein referred to as matrix) that has been used in past fuel experiments. The results of these experiments show that the Urbix powder and nuclear-grade graphite powder display notably different properties from one another in many cases, but this discrepancy may have been the result of the typical particle size of each powder. This hypothesis is supported by tests conducted on the milled powder, which showed a closer resemblance in properties to the nuclear-grade graphite than the as-received powder. The method for pressing the graphite matrix also had a noticeable effect on the measured properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Fast solvers for tokamak fluid models with PETSc

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful consideration of the physical model and discretization. In this work we develop the first step in applying MG methods to science and engineering relevant magnetohydrodynamics (MHD) tokamak models in the M3D-C1 (https://m3dc1.pppl.gov) fusion energy science code. The semi-implicit time integrator in M3D-C1 is composed of many linear solves. The implicit advance of the momentum equation is the most challenging and is the focus of this work. The current production solver in M3D-C1 is a block Jacobi (BJ) preconditioner within a Krylov solver, where blocks group degrees of freedom on planes of constant toroidal coordinate. BJ convergence degrades as the number of planes increases due to the spectral properties of the matrix preconditioned with BJ. The partially magnetic field-aligned, regular toroidal grid structure in M3D-C1 is amenable to semi-coarsening geometric MG in the toroidal direction. This paper develops such a solver and demonstrates competitive performance on a runaway electron model of a SPARC (https://cfs.energy/technology/sparc) disruption, and superior robustness on a stellarator model on which the BJ solver fails to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

U-Pu and Ba-Cs isotopic measurements on Trinitite by laser ablation sampling on the Neoma MC-ICP-MS

In this study we present the results of combined U-Pu and Ba-Cs isotope measurements obtained by laser ablation (LA) sampling of two glassy debris fragments (‘Trinitite’) from the world's first atomic bomb detonation conducted in New Mexico on July 16, 1945. Our primary goal in conducting these measurements was to understand whether examination of the U-Pu and Ba-Cs systematics by direct sampling (e.g. without any chemical separation or purification prior to isotope ratio measurement) could yield meaningful information that would differentiate the Trinitite fragments from glassy material lacking a nuclear fission signature. These measurements were conducted on a ThermoFisher Scientific Neoma multi collector – inductively coupled plasma – mass spectrometer (MC-ICP-MS), which is a relatively new MC-ICP-MS platform, so we also examine the behavior of these isotope systems in standards sampled in solution and via LA. Unsurprisingly, the measurements made on purified solutions of the U, Pu, and Ba isotopic standards produce high precision isotope ratios. Furthermore, this extends to the U-Pu measurements made by LA sampling, with the expected degradation in precision and accuracy related to matrix effects and signal intensity fluctuation. However, the Ba-Cs data acquired by LA is of low precision across all of the matrices examined and bears evidence of complex mass fractionation that will require further investigation to resolve. In total, our results indicate that the observed U-Pu isotope data are of sufficient quality to accurately constrain the U and Pu isotopic composition of glass containing sub-ppm levels of these elements which in turn could be used to differentiate glass containing anthropogenic fission products from natural glass whereas the Ba-Cs LA data cannot be used for this purpose until further methodological refinement is performed.

Ba-Cs↗

DOE OSTI2025

The Carbon Storage Technical Viability Approach (CS TVA)

The Carbon Storage Technical Viability Approach (CS TVA) StoryMap provides an in-depth overview of the products created during the CS TVA research effort. In detail, the StoryMap addresses the CS TVA Matrix, Database Version 2.0, Database Catalog, Workflow, and Data Availability Result Database, discussing how each was developed and implemented. Information on how the matrix, database, and database catalog are interconnected, and their usage is also explained. The workflow section provides information on the CS TVA product development from the data-gathering stage to the final data availability results. A section on an expansion of the CS TVA workflow that utilizes Natural Language processing (NLP) section was included. Finally, the Data Availability Results Database is discussed. These results provide data science-informed insights into potential data gaps when assessing the viability of carbon storage in a given area or region.

Carbon Storage↗

DOE OSTI2021

First measurement of the cross section for top quark pair production with additional charm jets using dileptonic final states in pp collisions at $\sqrt{s}$= 13 TeV

The first measurement of the inclusive cross section for top quark pairs ($t\bar{t}$) produced in association with two additional charm jets is presented. The analysis uses the dileptonic final states of $t\bar{t}$ events produced in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 41.5 fb -1 recorded by the CMS experiment at the LHC. A new charm jet identification algorithm provides input to a neural network that is trained to distinguish among $t\bar{t}$ events with two additional charm ($t\bar{t}c\bar{c}$), bottom ($t\bar{t}b\bar{b}$), and light-flavour or gluon ($t\bar{t}LL$) jets. By means of a template fitting procedure, the inclusive $t\bar{t}c\bar{c}$, $t\bar{t}b\bar{b}$, and $t\bar{t}LL$ cross sections are simultaneously measured, together with their ratios to the inclusive $t\bar{t}$ + two jets cross section. This provides measurements of the $t\bar{t}c\bar{c}$ and $t\bar{t}b\bar{b}$ cross sections of 10.1 ± 1.2 (stat) ± 1.4 (syst) pb and 4.54 ± 0.35 (stat) ± 0.56 (syst) pb, respectively, in the full phase space. The results are compared and found to be consistent with predictions from two different matrix element generators with next-to-leading order accuracy in quantum chromodynamics, interfaced with a parton shower simulation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

A 28 nm multiply-accumulate ASIC architecture for on-chip data compression in MHz frame rate X-ray and electron pixel detectors

Modern X-ray detector systems urgently require compact, efficient, and fast data compression schemes to handle the transmission of big data from pixel arrays, enabling frame rates in the MHz regime. Here, in this work, a data compression ASIC that implements a streaming fixed-length lossy compression scheme is introduced and analyzed, proving the feasibility and benefits of on-chip compression. The compression scheme utilizes a vector matrix product logic, which performs a number of floating-point multiplications, additions, and accumulations. The logic is verified, synthesized, and shown to fit in the area resource available for the X-ray detector under study, which comprises 192 × 168 pixels each of 12-bit width, and having a total area of 20 mm× 20 mm, about 2 mm× 20 mm of which are available for the digital logic. Several system architectures, precisions, and compression ratios ranging from 100 to 250 were analyzed to pave the way for on-chip fixed-length compression (e.g., principal component analysis, singular value decomposition) and data reduction (e.g., azimuthal integration) for X-ray and electron detectors.

Data compression↗

DOE OSTI2026

Plutonium migration and phase evolution in irradiated U-Pu-Zr metallic fuels: An integrated EPMA-SEM-TEM study

Constituent redistribution is a defining feature of irradiated U-Pu-Zr metallic fuels, yet its mechanisms and effects on fuel performance are not sufficiently resolved to guide model development. Although decades of irradiation testing have established broad trends, a true mechanistic understanding of constituent redistribution has not been achieved. Here, in this study, we use electron probe microanalysis (EPMA), scanning electron microscopy (SEM), and transmission electron microscopy-based (TEM) selective area electron diffraction (SAED) on a EBR-II irradiated U-19 wt.% Pu-6 wt.% Zr fuel pin cross-section to correlate the composition, porosity, and crystallographic phases formed after irradiation. Constituent redistribution is thought to consist of three distinct zones, in which uranium and zirconium migrate while plutonium remains relatively unchanged. Our EPMA results resolve eight distinct compositional regions, and more importantly, show that plutonium redistributes alongside zirconium, contrary to historical assumptions. The distribution of fission products was highly asymmetric with a few large lanthanide precipitates observed at isolated sites on the pin periphery instead of a uniform distribution of smaller precipitates around the periphery. Using thermodynamic data from TAF-ID and the measured EPMA compositions, matrix phase fractions were predicted across the fuel radius. Phase predictions based on composition did not match TEM/SAED results, which revealed a much higher fraction of α−U phase than would be expected if phases were retained from reactor temperatures. These findings highlight the need for expanded SAED phase identification to capture post-irradiation and storage effects, as well as rigorous uncertainty quantification in fuel performance and phase diagram modeling to better constrain predictions from compositional data.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Probing quantum entanglement with generalized parton distributions at the Electron-Ion Collider

Within the collinear factorization framework based on generalized parton distributions, we calculate the spin density matrix of exclusively produced quark and antiquark pairs $𝑢\bar{𝑢}$, $𝑑⁢\bar{d}$, $𝑠⁢\bar{𝑠}$, $𝑐\bar{⁢𝑐}$, $𝑏\bar{𝑏}$ in electron-proton scattering. The presence of both real and imaginary parts in the scattering amplitudes leads to a rich pattern of entanglement between the quark and the antiquark. We map out kinematical regions where the pairs exhibit entanglement, Bell nonlocality, and nonstabilizerness. We also predict that massive quarks and antiquarks are transversely polarized, similar to the well-known transverse hyperon polarization in unpolarized collisions. In strangeness, charm, and bottom productions, the polarization can reach 50%–80% in certain kinematic regions in the low-energy runs of the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

A System-Level Cost Modeling Framework for Design for Remanufacturing: A Case Study of an Agricultural Machine Transmission

Remanufacturing offers significant environmental and economic benefits by restoring end-of-life products to as-new conditions. Although extensive research has been conducted on the topic, the adoption of remanufacturing practices remains limited across various industries. A primary barrier to broader implementation is the substantial upfront investment required, which necessitates reliable cost modeling to justify potential future savings. Most existing models treat components independently and ignore inter-component dependencies. We develop a probabilistic, system-level cost modeling framework that integrates reliability, reusability, and a dependency matrix to capture cascading effects across components over multiple life cycles. Our model identifies those critical components that maximize remanufacturing benefits across a product's many lives. A toy example and an industry case study (John Deere PowrQuad transmission subassembly) illustrate how design alternatives affect cumulative cost. Using a Monte Carlo simulation (MCS) to perform life cycle cost analysis on the system with different design changes, we show the normalized average cost savings after three remanufacturing cycles. Accounting for dependencies meaningfully alters cost projections and ignoring them underestimates accumulated cost by up to 20% in our examples. Furthermore, the results of our study confirm that accounting for component interdependencies is necessary to produce cost estimates that meet industry standards.

Life Cycle Analysis and Design↗

DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Microstructural and Rheological Transitions in Bacterial Biofilms

Biofilms are aggregated bacterial communities structured within an extracellular matrix (ECM). ECM controls biofilm architecture and confers mechanical resistance against shear forces. From a physical perspective, biofilms can be described as colloidal gels, where bacterial cells are analogous to colloidal particles distributed in the polymeric ECM. However, the influence of the ECM in altering the cellular packing fraction (Φ) and the resulting viscoelastic behavior of biofilm remains unexplored. Using biofilms of Pantoea sp. (WT) and its mutant (ΔUDP), the correlation between biofilm structure and its viscoelastic response is investigated. Experiments show that the reduction of exopolysaccharide production in ΔUDP biofilms corresponds with a seven-fold increase in Φ, resulting in a colloidal glass-like structure. Consequently, the rheological signatures become altered, with the WT behaving like a weak gel, whilst the ΔUDP displayed a glass-like rheological signature. By co-culturing the two strains, biofilm Φ is modulated which allows us to explore the structural changes and capture a change in viscoelastic response from a weak to a strong gel, and to a colloidal glass-like state. The results reveal the role of exopolysaccharide in mediating a structural transition in biofilms and demonstrate a correlation between biofilm structure and viscoelastic response.

viscoelasticity↗

DOE OSTI2025

Unravelling the origins of shale nanoporosity using small-angle neutron scattering (SANS)

Hydrocarbon production from tight rocks is constrained by slow diffusion within the shale matrix, limited by small pore sizes and low permeability. The nanopore proportion and size distribution significantly influence matrix permeability, a key property for optimizing hydrocarbon recovery and supporting hydrogen production while minimizing environmental impacts. Small-angle neutron scattering (SANS) has been an important tool for exploring the characteristics and structure of shale nanopores. This study used SANS to analyze nanoporosity and pore size distribution (<100 nm) in tight rocks with varying compositions to determine the influence of rock heterogeneity on SANS measurements. Results showed that nanoporosity correlates with clay content, with the highest clay-rich shale (52.48 wt% clay) exhibiting 8.8 % nanoporosity. SANS also revealed more nanopores than traditional nitrogen adsorption measurements, affirming its ability to reflect bulk mineralogy and upholding the relevance of experimental findings using this technique to optimize field operational approaches.

03 NATURAL GAS↗

DOE OSTI2024

Nuclear Fuel and Pu Redox Studies from The Glenn T. Seaborg Institute at Idaho National Laboratory

The Glenn T. Seaborg Institute at Idaho National Laboratory (INL-GTSI) focuses on advancing fundamental research in the actinide sciences by providing unique opportunities to early career scientists and engineers to gain experience studying the actinide elements and their associated systems. The INL-GTSI is built from three focus areas that are based on the expertise and supporting infrastructure at INL and include solid state chemistry and physics, solution phase chemistry and physics, and forensic and isotope science. INL is the lead Laboratory for nuclear energy research and development in the U. S. and the research on nuclear fuels performed under the INL-GTSI gives good examples of solid state studies. Uranium-Molybdenum (U-Mo) alloys are leading fuel candidates for conversion of high performance research and test reactors to low-enriched fuels. During irradiation, generated fission gas accumulates into bubbles and self-organizes into a gas bubble superlattice (GBS) that effectively stores fission gases and inhibits fuel swelling. A study on the early self- organizing behavior of the GBS shows that not only grain boundaries but the interfaces between the U-Mo matrix and uranium carbide (UC) impurities are important to GBS formation.[1] In solution, understanding the complex redox behavior of plutonium in aqueous environments is critical for establishing optimized nuclear waste reprocessing solvent systems and storage tank environments. INL-GTSI researchers have produced an experimentally validated multi-scale model of the gamma radiation induced behavior of plutonium ions in concentrated aqueous HNO3 solutions.[2] Here, gamma radiation effected only minimal steady state changes in the redox distribution of the plutonium oxidation states. The redox cycling between Pu(IV) and Pu(III) is demonstrated to be mediated by the •OH/NO3• radical oxidation of Pu(III) and the H2O2/HNO3 driven reduction of Pu(IV). The INL-GTSI offers young researchers the unique chance to work directly with actinide bearing materials in a U. S. National Laboratory environment. Further topical areas of interest to the INL-GTSI include, but are not limited to, fundamental actinide properties, structure/property (electronic, magnetic, thermal) relations, actinide quantum criticality, f- electron interactions, electron correlations, computational studies, new phases, defect effects, interface interactions, isotope production and separation, forensic analytical chemistry, structure and dynamic properties of actinides in non-aqueous media, separations chemistry and kinetics for advanced nuclear fuel cycles, radiation effects, and innovative and advanced ligand design for complexation of the actinides.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Chemical durability assessment of enhanced low-activity waste glasses through EPA method 1313

In this work, we report the progress of the Glass Leaching Assessment for Durability (GLAD) program on the implementation of the United States Environmental Protection Agency (EPA) Leaching Environmental Assessment Framework pH-dependent leach test (EPA Method 1313) to low-activity nuclear waste (LAW) glasses. The GLAD program seeks to develop new strategies to understand the chemical durability of nuclear waste glasses for the disposal in near-surface conditions. A series of 16 high-waste loading LAW glasses, currently under development, were selected using machine learning methods to study the corrosion behavior using EPA Method 1313. Reacted glass powders were examined using scanning electron microscopy and the eluate compositions were examined using inductively coupled plasma-optical emission spectroscopy. Compositional modeling was used to fit the measured elemental releases from EPA Method 1313. The compositional models demonstrated that elements such as Si reduce elemental release while B can increase elemental release (consistent with elemental modeling of the Product Consistency Test and Vapor Hydration Test) while other elements, such as Fe, exhibit pH-dependent behavior. The amount of acid added during the EPA testing was found to significantly impact the observed result, which was only apparent after preforming the present matrix study. The overall titration curves were able to be compositionally modeled for future process optimization.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗