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DOE OSTI2025

Union through UNITY: Cosmology with 2000 SNe Using a Unified Bayesian Framework

Type Ia supernovae (SNe Ia) were instrumental in establishing the acceleration of the Universe’s expansion. By virtue of their combination of distance reach, precision, and prevalence, they continue to provide key cosmological constraints, complementing other cosmological probes. Individual SN surveys cover only over about a factor of 2 in redshift, so compilations of multiple SN data sets are strongly beneficial. We assemble an up-to-date “Union” compilation of 2087 cosmologically useful SNe Ia from 24 data sets (“Union3”). We take care to put all SNe on the same distance scale and update the light-curve fitting with SALT3 to use the full rest-frame optical. Over the next few years, the number of cosmologically useful SNe Ia will increase by more than a factor of 10, and keeping systematic uncertainties subdominant will be more challenging than ever. We discuss the importance of treating outliers, selection effects, light-curve shape/color populations/standardization relations, unexplained dispersion, and heterogeneous observations simultaneously. We present an updated Bayesian framework, called UNITY1.5 (Unified Nonlinear Inference for Type-Ia cosmologY), that incorporates significant improvements in our ability to model selection effects, standardization, and systematic uncertainties compared to earlier analyses. As an analysis byproduct, we also recover the posterior of the SN-only peculiar-velocity field, although we do not interpret it in this work. We compute updated cosmological constraints with Union3 and UNITY1.5, finding weak 1.7σ–2.6σ tension with flat cold dark matter and possible evidence for thawing dark energy (w0 > − 1, wa < 0). We release our SN distances, light-curve fits, and UNITY1.5 framework to the community.

Rubin, David↗

DOE OSTI2026

Revisiting the Supernova Engines in the 3C 397 and W49B Supernova Remnants

The nature of the supernova remnants (SNRs) 3C 397 and W49B has long been a subject of debate, with prior studies offering conflicting interpretations between thermonuclear and core-collapse scenarios. To help settle this debate, we present a systematic, spatially resolved, spectroscopic analysis of both remnants using XMM-Newton. By applying multicomponent thermal models, we derive key physical properties including elemental abundances, ejecta temperatures, ambient densities, and explosion energetics. We compare the inferred metal abundance ratios to a wide range of core-collapse and thermonuclear nucleosynthesis models, including new models whose explosion energies differ from the canonical value of 10 51 erg. We find that the observed Fe/Si and Ca/Si ratios in both SNRs are best matched by certain thermonuclear models. However, no model fully reproduces the complete set of observed abundance patterns. In 3C 397, high Fe enrichment and spatial abundance variations suggest interaction with a dense progenitor environment, and W49B’s composition is overall consistent with a thermonuclear origin; however, both require a low-energy (∼10 50 erg) supernova explosion. We additionally map the Fe Kα line centroid energies and find a spread, with W49B falling within the core-collapse region—highlighting both environmental complexity and the limitations of this diagnostic for supernova classification. Our results highlight the need for caution in relying on any single diagnostic or nucleosynthesis model for supernova typing, underscore the need for improved nucleosynthesis models, and motivate future high-resolution, high-throughput observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Out-of-Pile Testing and Instrumentation Transient Water Irradiation System

Current initiatives to increase the burnup of conventional nuclear fuels past the approximate 62 GWd/t limit have been spurred on by direct savings to refueling and waste storage. The technical justification for a new license limit requires extensive qualification through experimental testing. Unlike beginning-of-life fuels, high-burnup fuels are more susceptible to fuel fragmentation, relocation, and dispersal (FFRD), therefore more data is needed to characterize fuels under key accident scenarios. The Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory has developed a testing apparatus architecture to test fuels and claddings at prototypic conditions. The Transient Water Irradiation System (TWIST) is the latest iteration of a testing device capable of conducting loss of coolant accidents (LOCAs) in TREAT. The Out-of-Pile Testing and Instrumentation TWIST (OPTI-TWIST) is an electrically heated device that is analogous to TWIST. OPTI-TWIST allows for detailed instrumentation and thermal-hydraulic characterization. TWIST ultimately aims to conduct the most advanced in-situ diagnostics to evaluate FFRD in a prototypic LOCA. Moreover, it will explore the phenomenological bifurcation of a decay-energy heat up driven LOCA and a stored-energy heat up driven LOCA. The instrumentation suite includes conventional thermocouples and pressure transducers in addition to an electro impedance sensor, an acoustic emission sensor, an optical pressure sensor, and an optical pyrometer. Characterizing these instruments in OPTI-TWIST eliminates complications of irradiation effects while preserving extreme thermal-hydraulic conditions. Finally, benchmarking both devices to a thermal-hydraulic code like the Reactor Excursion and Leak Analysis Program (RELAP)5-3D provides a unique opportunity for iteration. Pre-test predictions and post-test interpretations inform the physical designs, operational procedures, test conditions, and instrumentation types and positions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Radiological Safety Analysis Computer (RSAC 7.2) Presentation

This presentation will be for the graduate seminar class for the University of New Mexico. We will discuss the Radiological Safety Analysis Computer (RSAC) version 7.2, a critical tool in radiological consequence analysis within the nuclear safety domain. We will begin with an introduction to radiological consequence analysis and the importance of dose modeling in nuclear safety, referencing key regulatory frameworks such as DOE-STD-3009 and 10 CFR 20. The presentation will provide an overview of RSAC, including its history, primary functions, and the inputs and outputs involved in its calculations. A detailed examination of RSAC's atmospheric dispersion model, based on the Gaussian plume methodology, will be presented, highlighting how meteorological factors influence the results. We will discuss the regulatory alignment of RSAC with DOE and NRC guidelines, emphasizing the assumptions required for compliance and the balance between conservative and realistic inputs. The presentation will also address the limitations and assumptions inherent in RSAC, comparing it with other consequence analysis codes like MACCS, HotSpot, and RASCAL. An example RSAC run will be demonstrated, showcasing a hypothetical accident scenario and interpreting the resulting dose calculations. Finally, we will introduce new ideas to enhance the current RSAC framework. This future work aims to provide multi-industry adaptability and integration with new dispersion models, addressing the evolving needs of DOE and NRC. The presentation will conclude with a discussion on RSAC's ongoing role in nuclear safety and the opportunities for future innovation.

computer program↗

DOE OSTI2023

Gaussian process hydrodynamics

Abstract We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and Navier-Stokes (NS) equations. Similar to smoothed particle hydrodynamics (SPH), GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow. However, these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow. Closure is achieved by placing a divergence-free GP prior ξ on the velocity field and conditioning it on the vorticity at the particle locations. Known physics (e.g., the Richardson cascade and velocity increment power laws) is incorporated into the GP prior by using physics-informed additive kernels. This is equivalent to expressing ξ as a sum of independent GPs ξ l , which we call modes, acting at different scales (each mode ξ l self-activates to represent the formation of eddies at the corresponding scales). This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes, and enables us to analyze coarse-grain turbulence statistically rather than deterministically. Because GPH is formulated by using the vorticity equations, it does not require solving a pressure equation. By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel, GPH requires significantly fewer particles than SPH. Because GPH has a natural probabilistic interpretation, the numerical results come with uncertainty estimates, enabling their incorporation into an uncertainty quantification (UQ) pipeline and adding/removing particles (quanta of information) in an adapted manner. The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss. Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability. Because the proposed approach uses a Bayesian interpretation, it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

Mathematics↗

DOE OSTI2025

Mapping Hsp104 interactions using cross‐linking mass spectrometry

Molecular machines from the AAA+ (ATPases Associated with diverse cellular Activity) superfamily of protein disaggregases play important roles in protein folding, disaggregation and DNA processing. Recent cryo-EM structures of AAA+ molecular machines have uncovered nuanced changes in their conformation that underlie their specialized functions. Structural knowledge of these molecular machines in complex with substrates begins to explain their mechanism of activity. Here, we explore how cross-linking mass spectrometry (XL-MS) can be used to interpret changes in conformation induced by ATP in Hsp104 and how a substrate may interact with Hsp104. We applied a panel of cross-linking reagents to produce cross-linking maps of Hsp104 and interpret our data on previously determined X-ray and cryo-EM structures of Hsp104 from a thermophilic yeast, Calcarisporiella thermophila. We developed an analysis pipeline to differentiate between intra-subunit and inter-subunit contacts within the hexameric homo-oligomer. We identify cross-links that break the asymmetry that is present in Hsp104 in an ATP-hydrolysis competent conformation but is absent in an ATP-hydrolysis-defective mutant. Finally, we identify contacts between Hsp104 and a selected protein (proprotein convertase subtilisin/kexin type 9 PCSK9) to reveal contacts on the central channel of Hsp104 across the length of this protein indicating that we might have trapped interactions consistent with its translocation. Our simple and robust XL-MS-based experiments and methods help interpret how these molecular machines change conformation and bind to other proteins even in the context of homo-oligomeric assemblies enabling coupling state-of-the-art modeling approaches with XL-MS.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

DeepLearnMOR: a deep-learning framework for fluorescence image-based classification of organelle morphology

Abstract The proper biogenesis, morphogenesis, and dynamics of subcellular organelles are essential to their metabolic functions. Conventional techniques for identifying, classifying, and quantifying abnormalities in organelle morphology are largely manual and time-consuming, and require specific expertise. Deep learning has the potential to revolutionize image-based screens by greatly improving their scope, speed, and efficiency. Here, we used transfer learning and a convolutional neural network (CNN) to analyze over 47,000 confocal microscopy images from Arabidopsis wild-type and mutant plants with abnormal division of one of three essential energy organelles: chloroplasts, mitochondria, or peroxisomes. We have built a deep-learning framework, DeepLearnMOR (Deep Learning of the Morphology of Organelles), which can rapidly classify image categories and identify abnormalities in organelle morphology with over 97% accuracy. Feature visualization analysis identified important features used by the CNN to predict morphological abnormalities, and visual clues helped to better understand the decision-making process, thereby validating the reliability and interpretability of the neural network. This framework establishes a foundation for future larger-scale research with broader scopes and greater data set diversity and heterogeneity.

Plant Sciences↗

DOE OSTI2022

Explainable Bayesian Neural Network for Probabilistic Transient Stability Analysis Considering Wind Energy

While several data-driven models have been developed for transient stability assessment, how to consider the uncertainties from load and renewable generations and provide interpretation of data-driven assessment results are still open. This paper proposes an explainable Bayesian Neural Network (BNN) for probabilistic transient stability assessment (TSA). By extracting the uncertainties from loads and wind farms, the BNN model can make a reliable prediction and quantify the prediction uncertainties. We also develop the Gradient Shap algorithm to make the global and local explanations for the probabilistic TSA model, a significant advantage over existing black-box data-driven methods. Numerical results on the modified IEEE 39-bus system show that the proposed method outperforms the existing methods in terms of prediction accuracy and uncertainty quantification capabilities. The explainability of the proposed method allows system operators to design preventive controls for enhancing system stability.

Bayesian Neural Network↗

DOE OSTI2020

One Planet or Two Planets? The Ultra-sensitive Extreme-magnification Microlensing Event KMT-2019-BLG-1953

We present the analysis of a very high-magnification (A ∼ 900) microlensing event KMT-2019-BLG-1953. A single-lens single-source (1L1S) model appears to approximately delineate the observed light curve, but the residuals from the model exhibit small but obvious deviations in the peak region. A binary-lens (2L1S) model with a mass ratio of q ∼ 2 × 10{sup −3} improves the fits by Δχ {sup 2} = 181.8, indicating that the lens possesses a planetary companion. From additional modeling by introducing an extra planetary lens component (3L1S model) and an extra source companion (2L2S model), it is found that the residuals from the 2L1S model further diminish, but claiming these interpretations is difficult due to the weak signals with Δχ {sup 2} = 16.0 and 13.5 for the 3L1S and 2L2L models, respectively. From a Bayesian analysis, we estimate that the host of the planets has a mass of M{sub host}=0.31{sub −0.17}{sup +0.37} M{sub ⊙} and that the planetary system is located at a distance of D{sub L}=7.04{sub −1.33}{sup +1.10} kpc toward the Galactic center. The mass of the securely detected planet is M{sub p}=0.64{sub −0.35}{sup +0.76} M{sub J}. The signal of the potential second planet could have been confirmed if the peak of the light curve had been more densely observed by follow-up observations, and thus the event illustrates the need for intensive follow-up observations for very high-magnification events even in the current generation of high-cadence surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Tandem pyrolysis evolved gas–gas chromatography–mass spectrometry

Analysis of byproducts from thermal degradation of polymer materials provides a wealth of information about a materials’ composition, thermal stability, degradation mechanisms, and kinetics. However, regardless of the instrumentation used, only limited information is obtainable from a single experiment. Microfurnace technology, when interfaced to a gas chromatography-mass spectrometry (GC-MS), can be used to obtain both thermal and chemical information via evolved gas analysis-MS (EGA-MS) and GC-MS analysis modes. While both EGA-MS and Py-GC-MS are valuable when characterizing polymer materials, at least two experiments on distinct samples are required, which can be a liability for clear interpretation of results from inhomogeneous samples. Here, we seek to overcome this limitation by combining EGA-MS and Py-GC-MS modes in a single experimental setup. Further, this was done by developing new gas line modifications to allow for tandem Pyrolysis Evolved Gas-Gas Chromatography-Mass Spectrometry (Py/EG-GC-MS) analysis. Verification of Py/EG-GC-MS analysis was performed using a polystyrene standard. Results demonstrate successful Py/EG-GC-MS analysis for the first-time showing the potential of these modifications for application in areas where sample is limited or direct correlation of products to the thermal profile is desirable such as in forensics or product-specific kinetics.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Analysis of the ratio of ℓ 1 and ℓ 2 norms in compressed sensing

We study the ratio of ℓ 1 and ℓ 2 norms ( ℓ 1 / ℓ 2 ) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1 / ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1 / ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1 / ℓ 2 algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Interpreting scattered neutron spectra on omega cryogenic implosions with measured backgrounds and higher-order scattering

Measurements of the areal density (⁠ρR⁠) of inertially confined implosions are critical to evaluate their performance. On OMEGA, ρR is inferred from measurements of the scattered neutron spectrum via neutron-time-of-flight (nTOF) and magnetic recoil spectrometer detectors. The nTOF measurements, in particular, have the ability to measure a wide range of neutron energies and thus scattering angles, with high precision. However, the neutrons that are backscattered into the detector must transit through the entire dense fuel assembly, and as a result are subject to rescattering effects, which have been heretofore neglected in the interpretation of OMEGA neutron spectra. At the backscatter edge, neglecting rescattering on OMEGA can lead to a ~10 to 20% reduction of the apparent areal density and therefore must be included in the analysis. The low ρR s on OMEGA also mean that backgrounds from non-target physics effects, such as scattering in the target chamber or slow scintillator decays, can significantly alter the measured signal. Here, we discuss how the Monte Carlo neutron spectrum postprocessor IRIS is used to include second-order scattering effects in the interpretation of the scattered neutron spectrum in OMEGA implosion experiments, and how dedicated implosion experiments are used to measure nTOF backgrounds in order to infer backscattered areal densities on OMEGA.

Deuterium↗

DOE OSTI2022

Applying Two-Dimensional Correlation Spectroscopy and Principal Component Analysis to Understand How Temperature Affects the Neptunium(V) Absorption Spectrum

The visible-near infrared (Vis-NIR) electronic absorption spectrum of neptunium(V) (NpO 2 + ) comprises numerous f-f electronic transitions with mostly undocumented temperature dependencies. The effect of temperature on the absorption spectrum of the pentavalent neptunyl dioxocation (NpO 2 + ) is an important factor to consider with spectrophotometric applications but has often been overlooked. Optical Vis-NIR absorption spectra (400–1700 nm) of Np(V) (0.017–0.89 M) in 1 M nitric acid were evaluated with varying temperatures (T = 10–80 °C). The intensity, position, and overall shape of the bands were sensitive to interactions with the solvent and coordination environment. Numerous temperature-induced isosbestic points were identified resulting from dynamic, overlapping peak shifts. Spectral variations were characterized using principal component analysis (PCA) and 2D correlation spectroscopy (COS). 2D-COS revealed that the absorption band near 1095 nm likely consists of two bands centered near 1087 and 1096 nm, which cannot be explained by current computational methods. 2D-COS analysis also provided an unambiguous assignment of unresolved peaks in the visible region for comparison with computational predictions. PCA was used to identify nonlinearity in the spectral response at elevated Np(V) concentrations ≥ 0.5 M. This unique experimental data and interpretation will foster a deeper understanding of the absorption spectra for complex actinyl ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

SAM Plug-in Development (Phase I Final Report)

The DOE Office of Nuclear Energy (NE) has created an extensive set of advanced modeling and simulation tools for nuclear engineering analysis. The advanced capabilities of these newer analysis codes require more in-depth training, skills, and knowledge in order to effectively utilize them for the design, analysis, and licensing of advanced nuclear systems and experiments. A high learning curve for inexperienced users may deter organizations from incorporating these tools into their internal processes. This project involved development of a plug-in to the Symbolic Nuclear Analysis Package (SNAP) for the System Analysis Module (SAM) tool. SAM is an advanced system analysis tool for reactor transient analyses being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SNAP provides a highly flexible framework for creating, modifying and documenting input for engineering analysis codes such as SAM as well as extensive functionality for submitting, monitoring, and interacting with the codes through an intuitive graphical user interface (GUI). The common user interface provided by SNAP minimizes the learning curve for engineers starting with a new analysis code and provides an intuitive framework for transitioning between different analysis codes. SNAP provides a powerful but intuitive interface to facilitate access to advanced modeling and simulation tools for inexperienced users. Unlike many “form based” GUI’s, SNAP maps each engineering code’s component input to an internal database which manages all component input parameters along with component interconnections. This level of abstraction permits SNAP to support several advanced capabilities such as renodalization, model validation and consistency checks, embedded documentation, model notebook generation, data ownership and reviewer tracking, and variable assignment for inputs to name a few. SNAP includes a built-in Python interpreter and is interfaced to several commercial and open source packages including CPython, MATLAB/OCTAVE, Microsoft Office, Open Office, and SANDIA’s DAKOTA package which provides Uncertainty Quantification analysis through the SNAP plug-ins. Phase I of this project involved development a fully functional basic SAM plug-in to SNAP. This plug-in provides the ability to import existing models, graphically construct, edit and submit models using SNAP’s extensive functionality.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

Derivatization of Mirror-Image L -Nucleic Acids with 2'-OMe Modification for Thermal and Structural Stabilization

To further expand the functionality and enhance the stability of mirror-image nucleic acids as advanced agents for basic research and therapeutic design, we have synthesized 2'-deoxy-2'-methoxy- L -uridine phosphoramidite and incorporated it into L -DNA and L -RNA by solid-phase synthesis quantitatively. We found that the thermostability of L -nucleic acids is dramatically improved after introducing the modifications. Moreover, we successfully crystallized both L -DNA and L -RNA duplexes containing the 2'-OMe modifications and sharing identical sequences. Crystal structure determination and analysis revealed the overall structures of the mirror-image nucleic acids, and for the first time it was possible to interpret the structural deviations caused by 2'-OMe and 2'-OH groups in the oligonucleotides, which are very similar. In conclusion, this novel chemical nucleic acid modification has the potential to be used to design nucleic acid-based therapeutics and materials in the future.

2'-OMe-modifications↗

DOE OSTI2022

Photothermal Atomic Force Microscopy Coupled with Infrared Spectroscopy (AFM-IR) Analysis of High Extinction Coefficient Materials: A Case Study with Silica and Silicate Glasses

Photothermal atomic force microscopy coupled with infrared spectroscopy (AFM-IR) brings significant value as a spatially resolved surface analysis technique for disordered oxide materials such as glasses, but additional development and fundamental understanding of governing principles is needed to interpret AFM-IR spectra, since the existing theory described for organic materials does not work for materials with high extinction coefficients for infrared (IR) absorption. This paper describes theoretical calculation of a transient temperature profile inside the IR-absorbing material considering IR refraction at the interface as well as IR adsorption and heat transfer inside the sample. Furthermore, this calculation explains the differences in peak positions and amplitudes of AFM-IR spectra from those of specular reflectance and extinction coefficient spectra. It also addresses the information depth of the AFM-IR characterization of bulk materials. AFM-IR applied to silica and silicate glass surfaces has demonstrated novel capability of characterizing subsurface structural changes and surface heterogeneity due to mechanical stresses from physical contacts, as well as chemical alterations manifested in surface layers through aqueous corrosion.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Evaluation of Methods for Causal Discovery in Hydrometeorological Systems

Understanding causal relations is of utmost importance in hydrology and climate research for systems identification, prediction, and understanding systems behavior in a changing climate. Traditionally, researchers in hydrometeorology attempted to study causal questions by conducting controlled experiments using numerical models. This approach, however, in most cases of interest provides uncertain results because the models are approximate representation of the natural system. An alternative approach that has recently drawn significant attention in several fields is to infer causal relations from purely observational data. It possesses several traits to its utility particularly in hydrometeorology due to the rapid accumulation of in situ and remotely sensed data records. The first objective of this study is to present a brief description of four causal discovery methods (Granger causality, Transfer Entropy, graph-based algorithms, and Convergent Cross Mapping) with special emphasis on the assumptions on which they are built. Second, using synthetic data generated from a hydrological model, we assess their performance in retrieving causal information taking into account sensitivity to sample size and presence of noise. Last, we use causal analysis to examine and formulate hypotheses on causal drivers of evapotranspiration in a shrubland region during summer and winter seasons. An interpretation of the hypotheses based on canopy seasonal dynamics and evapotranspiration processes is presented. It is hoped that the results presented here can be useful in guiding researchers studying hydrometeorological systems as to which causal method is most appropriate to the characteristics of the system under study.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Generalized vs. fractional: a comparative analysis of Maxwell models applied to entangled polymer solutions

Fractional viscoelastic models provide an excellent description of rheological data for polymer systems with power-law behaviour. However, the physical interpretation of their model parameters, which carry fractional units of time, often remains elusive. We show that for poly(ethylene oxide) (PEO) solutions, the fractional Maxwell model (FMM) requires much fewer model parameters than the classical generalized Maxwell model for a good description of the data and that it can be applied consistently to solutions with varying degrees of viscoelasticity. Despite their fractional units, the parameters exhibit scaling laws similar to classical parameters as a function of polymer concentration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗