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DOE OSTI2022

Linear relationships for modeling CO 2 absorption in aqueous alkanolamine solutions in a thermodynamically consistent way

A thermodynamically consistent model for the carbon dioxide (CO 2 ) absorption in aqueous alkanolamine system is of great importance in the research and development of a CO 2 capture process. To facilitate the development of thermodynamic models, linear Gibbs free energy, enthalpy, and heat capacity relationships using well-known amines as reference are used to correlate the standard reference state properties of ionic species with those of molecular species in the electrolyte system, which has been approved to provide a reliable and consistent way to estimate required parameters when there is minimal or no appropriate experimental data available. Here, the proposed relationships have been applied to the development of an electrolyte nonrandom two liquid (NRTL) activity coefficient model for CO 2 absorption in aqueous 1-amino-2-propanol (A2P) solution, as an example to demonstration the methodology. With limited vapor–liquid equilibrium data and other thermodynamic properties, the parameters in the electrolyte NRTL model are identified with good accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2011

GRAVITATIONAL FRAGMENTATION OF EXPANDING SHELLS. I. LINEAR ANALYSIS

We perform a linear perturbation analysis of expanding shells driven by expansions of H II regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the density profile across the thickness. It is found that the time evolution of the density profile can be divided into three evolutionary phases: deceleration-dominated, intermediate, and self-gravity-dominated phases. The density peak moves relatively from the shock front to the contact discontinuity as the shell expands. We perform a linear analysis taking into account the asymmetric density profile obtained by the semi-analytic method, and imposing the boundary conditions for the shock front and the contact discontinuity while the evolutionary effect of the shell is neglected. It is found that the growth rate is enhanced compared with previous studies based on the thin-shell approximation. This is due to the boundary effect of the contact discontinuity and asymmetric density profile that were not taken into account in previous works.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2008

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Cantrell, John H., Jr.↗

DOE OSTI2019

Composition-Based Density Model for High Level Waste Glasses

In this report, the Savannah River National Laboratory (SRNL) provides a first-principles model capable of predicting the density of high-level waste (HLW) glass based on the glass composition. The model relies on the additivity of the specific volume of bound glass oxides to obtain a quantitative evaluation of the approximate glass density. A database of glass densities and compositions was compiled from various sources including previous Defense Waste Processing Facility (DWPF) variability study glasses, HLW studies from other institutions, and literature references. There are a total of 1104 glass compositions in the database with densities ranging from 2.224 g/cm 3 to 3.997 g/cm 3 . The breadth of the compositional coverage space is reported as well. A predictive method was investigated in which the glass density was calculated as a function of the weighted partial molar volumes of the individual glass oxides and the molar mass of the glass. This method yielded a high correlation between the predicted density and the measured density. In addition, a linear regression of these predictions indicated that the predicted value was equal to the measured within the bounds of analytical uncertainty. The following conclusions were drawn from the results of these analyses: 1. Measured glass density is highly correlated with glass composition (R 2 ≈ 0.95). 2. The correlation between glass density and glass composition can be expressed as either: a. A weighted sum of the individual oxide glass-component densities, or b. A weighted sum of the individual oxide glass-component partial molar volumes. 3. A linear regression of the predicted density via partial molar volume method to the measured density yields a slope of 0.9975 and an intercept of -0.0007 – the uncertainty interval associated with these coefficients contain one and zero, respectively. 4. The fitted coefficients and associated uncertainty intervals of the linear regression of the predicted density via the partial molar volume method to the measured density suggest that the predicted theoretical density is, within analysis uncertainty, equal to the measured density of the glass. It is recommended that glass density measurements included with the variability study for each sludge batch be discontinued. In their place, SRNL will calculate a bounding glass density value for the frit/sludge system using the model. It is also recommended that DWPF implement the density model as part of the fissile loading determination portion of the SME acceptability process. Details for implementation are provided in this report.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

Diffusion Synthetic Acceleration for High Order S{sub N} Transport on Meshes with Curved Surfaces

Thermal radiation transport is integral to multiphysics applications such as inertial confinement fusion and astrophysics. Materials in these problems can be exceptionally optically thick and diffusive. A transport solver must be capable of accurate and efficient solutions to such problems. Previously, Woods et al. established a proof-of-concept for high order (HO) discontinuous Galerkin finite element (DGFEM) transport on meshes with curved surfaces. They numerically demonstrated the spatial convergence is order p + 1. Remarkably, these convergence rates are relatively invariant to the amount of curvature of the spatial mesh. We present here an extension of this work that demonstrates a rapidly-convergent iterative solver for the FEM transport equations on meshes with curved sides. We use the modified interior penalty (MIP) diffusion synthetic acceleration (DSA) established by Wang and Ragusa. The partially consistent MIP equations stem from the symmetric interior penalty (IP) derivation of the diffusion equation. The IP method is not stable for optically thick cells so it was combined with the diffusion conforming form (DCF), a discretized diffusion equation derived from the discretized S N equations that is not stable for intermediate optical thicknesses. The MIP equations adapt a 'switch' to the IP method in optically thinner regions and the DCF method in optically thicker regions. The literature does not reveal any Fourier analyses performed for iterative transport on meshes with curved surfaces. Wang and Ragusa performed a Fourier analysis for orthogonal meshes and our results appear to be as expected. Previous literature has reported on some of the sensitivities that affect the spectral radius of DSA schemes: polynomial order, and scattering ratios. Presently, we focus on the sensitivity of the spectral radius to polynomial order, scattering ratio, the constant C, and mesh curvature for varying cell thicknesses. We also numerically study the behavior of the spectral radius to verify our DSA implementation. A sequence of problems is designed to exercise the acceleration. As the problems become more optically thick and diffusive, the accelerated solution continues to converge toward the analytic solution. We employ the Modular Finite Element Methods (MFEM) package, developed at Lawrence Livermore National Laboratory, to generate the linear algebraic system of equations for each angle in the discrete ordinates quadrature set, and use UMFPack to solve this system of equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

“Third-body” collision parameters for hydrocarbons, alcohols, and hydroperoxides and an effective internal rotor approach for estimating them

Collision rate constants and third-body collision efficiencies are calculated for more than 300 alkanes, alcohols, and hydroperoxides, for the bath gases He, Ar, H 2 , and N 2 , and from 300 to 2000 K. The data set includes highly branched species and species with as many as 16 nonhydrogen atoms N , and it is analyzed to develop strategies for estimating collision properties more generally. Simple analytic formulas describing the Lennard-Jones collision parameters $σ$ and $ε$ are obtained for each of the three classes of systems as a function of N . Trends in the collision efficiency range parameter $α$ = $\langle$Δ E d $\rangle$ are more complicated, and a method is developed and validated for estimating $α$ based on the numbers and types of internal rotors and oxygen-containing groups. Specifically, the approach maps the expected value of $α$ for a branched alkane, alcohol, or hydroperoxide onto those for the corresponding normal (linear) series via an effective number of nonhydrogen atoms N eff . The prescription for N eff is based on counting internal rotor types and is shown to be insensitive to temperature and fairly insensitive to the identity of the bath gas. Together, these strategies allow for the ready estimation of the collision parameters $σ$, $ε$, and $α$ so long as results for the associated linear series are available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow

In this work, we advance a quantitative description of the critical shear rate $\dot{\gamma}_{c}$ needed to dislodge a spherical particle resting on a surface with a model asperity in laminar and turbulent fluid flows. We have built a cone-plane experimental apparatus which enables measurement of $\dot{\gamma}_{c}$ over a wide range of particle Reynolds number Re p from 10–3 to 1.5 × 10 3 . The condition to dislodge the particle is found to be consistent with the torque balance condition after including the torque component due to drag about the particle center. The data for Re p < 0.5 is in good agreement with analytical calculations of the drag and lift coefficients in the Re p → 0 limit. For higher Rep, where analytical results are unavailable, the hydrodynamic coefficients are found to approach a constant for Re p > 1000. We show that a linear combination of the hydrodynamic coefficients found in the viscous and inertial limits can describe the observed $\dot{\gamma}_{c}$ as a function of the particle and fluid properties.

02 PETROLEUM↗

DOE OSTI2019

Automated thermal extraction-desorption gas chromatography mass spectrometry: A multifunctional tool for comprehensive characterization of polymers and their degradation products

The TED-GC–MS analysis is a two-step method. A sample is first decomposed in a thermogravimetric analyzer (TGA) and the gaseous decomposition products are then trapped on a solid-phase adsorber. Subsequently, the solid-phase adsorber is analyzed with thermal desorption gas chromatography mass spectrometry (TDU-GC–MS). This method is ideally suited for the analysis of polymers and their degradation processes. A new entirely automated system is introduced which enables high sample throughput and reproducible automated fractioned collection of decomposition products. The fractionated collection together with low temperatures reduces the risk of contamination, improves instrumental stability and minimizes maintenance efforts. Through variation of the two main parameters (purge gas flow and heating rate) it is shown how the extraction process can be optimized. By measuring the decomposition products of polyethylene it is demonstrated that compounds with masses of up to 434 Da can be detected. This is achieved despite the low temperature (˜40 °C) of the solid-phase adsorber and the low thermal desorption temperature of 200 °C in the TDU unit. It is now shown that automated TED-GC–MS represents a new flexible multi-functional method for comprehensive polymer analyses. Comparable polymer characterization was previously only achievable through a combination of multiple independent analytical methods. This is demonstrated by three examples focused on practical challenges in materials analysis and identification: The first one is the analysis of wood plastic composites for which the decomposition processes of the polymer and the bio polymer (wood) could be clearly distinguished by fractionated collection using sequential adsorbers. Secondly, a fast quantitative application is shown by determining the weight concentrations of an unknown polyolefin blend through comparison with a reference material. Additionally, the determination of microplastic concentrations in environmental samples is becoming an increasingly important analytical necessity. It is demonstrated that with TED-GC–MS calibration curves showing good linearity for the most important precursors for microplastic, even complex matrix materials (suspended particulate matter) can be successfully analyzed.

36 MATERIALS SCIENCE↗

DOE OSTI2011

An efficient numerical method for computing dynamics of spin F = 2 Bose-Einstein condensates

In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross-Pitaevskii (GP) equations, which model the dynamics of spin F = 2 Bose-Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F = 2 Bose-Einstein condensates confined in a uniform/nonuniform magnetic field.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗

DOE OSTI2023

One-Parameter Analytical Derivation in Modified Budyko Framework for Unsteady-State Streamflow Elasticity in Humid Catchments

The changes in climate and catchment properties have altered the hydrological processes significantly at different spatiotemporal scales around the world. In particular for finer time scales, changes in water storage, which has been commonly neglected for long-term temporal scales, may play an important role on hydrological processes. Nevertheless, few studies addressed this question in modifying the Budyko framework, with most of them remaining a steady-state assumption on catchment characteristics. Here, in this work, we derive new analytical formulas of unsteady-state streamflow elasticity in a modified Budyko framework, incorporating both storage change and one specific parameter for catchment properties. We study 78 humid catchments in the USA with simulation data of daily hydrological processes from a probability-distribution-based hydrological model (the modified HyMOD). As indicated by results, the annual storage change ratio is linearly correlated with the annual aridity index, and this relationship can be used to estimate elasticity coefficients with our formulas. The estimated elasticity coefficients perform well in simulating the annual streamflow with the power-law model. For different catchments, variability of the unsteady-state elasticity is higher than that of the steady-state elasticity. Unsteady-state streamflow coefficients show significant linear correlation with catchment properties, such as the average slope, average elevation, and catchment area. This study provides a new analytical approach to investigate the interannual stability of catchments with varying climate and catchment properties.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

Direct structural evidence of commensurate-to-incommensurate transition of hydrocarbon adsorption in a microporous metal organic framework

Here, the efficiency of physisorption-based separation of gas-mixtures depends on the selectivity of adsorbent which is directly linked to size, shape, polarizability and other physical properties of adsorbed molecules. Commensurate adsorption is an interesting and important adsorption phenomenon, where the adsorbed amount, location, and orientation of an adsorbate are commensurate with the crystal symmetry of the adsorbent. Understanding this phenomenon is important and beneficial as it can provide vital information about adsorbate–adsorbent interaction and adsorption–desorption mechanism. So far, only sporadic examples of commensurate adsorption have been reported in porous materials such as zeolites and metal organic frameworks (MOFs). In this work we show for the first time direct structural evidence of commensurate-to-incommensurate transition of linear hydrocarbon molecules (C 2 –C7) in a microporous MOF, by employing a number of analytical techniques including single crystal X-ray diffraction (SCXRD), in situ powder X-ray diffraction coupled with differential scanning calorimetry (PXRD-DSC), gas adsorption and molecular simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

The behavior of the electron plasma boundary in ultraintense laser–highly overdense plasma interaction

The structural stability of the laser/plasma interaction is discussed, for the case of a linearly polarized laser beam interacting with a solid at normal incidence. Using a semi-analytical cold fluid model, the dynamics of the electron plasma boundary (EPB), usually related to the high-order harmonic generation and laser absorption, are presented. While the well-known J × B plasma oscillations at two times the laser frequency are recovered by the model, several other periodic in time stable solutions exist for exactly the same value of the physical parameters. This novel behavior highlights the importance of the laser pulse history among other factors. Some important features, such as the synchronization between the incident laser and the EPB oscillation, depend on the solution under consideration. A description of the possible types of stable oscillations in a parametric plane involving plasma density and laser amplitude is presented. The semi-analytical model is compared with particle-in-cell and semi-Lagrangian Vlasov simulations. They show that, among all the stable solutions, the plasma preferentially evolves to a state with the EPB oscillating twice faster than the laser. The effect of the plasma temperature and the existence of a ramp in the ion density profile are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2024

Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al 2020 Phys. Plasmas 27 070701; Loizu and Bonfiglio 2023 J. Plasma Phys. 89 905890507), we make use of Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), an equilibrium solver based on the variational principle of the multi-region relaxed magnetohydrodynamics (MHDs), featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model J bs = C$\boldsymbol{\nabla}$p to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter Δ' and bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHDs code (Huang and Bhattacharjee 2016 Astrophys. J. 818 20) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical modified Rutherford equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and NTMs, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

An improved fitting formula for the dark matter bispectrum

In this paper we present an improved fitting formula for the dark matter bispectrum motivated by the previous phenomenological approach of ref. [1]. We use a set of LCDM simulations to calibrate the fitting parameters in the k-range of 0.03 h/Mpc ≤ k ≤ 0.4 h/Mpc and in the redshift range of 0 ≤ z ≤ 1.5. This new proposed fit describes well the BAO-features although it was not designed to. The deviation between the simulations output and our analytic prediction is typically less than 5% and in the worst case is never above 10%. We envision that this new analytic fitting formula will be very useful in providing reliable predictions for the non-linear dark matter bispectrum for LCDM models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Efficient calculation of cosmological neutrino clustering in the non-linear regime

We study in detail how neutrino perturbations can be followed in linear theory by using only terms up to l =2 in the Boltzmann hierarchy. We provide a new approximation to the third moment and demonstrate that the neutrino power spectrum can be calculated to a precision of better than ∼ 5% for masses up to ∼ 1 eV and k ∼< 10 h /Mpc. The matter power spectrum can be calculated far more precisely and typically at least a factor of a few better than with existing approximations. We then proceed to study how the neutrino power spectrum can be reliably calculated even in the non-linear regime by using the non-linear gravitational potential, sourced by dark matter overdensities, as it is derived from semi-analytic methods based on N -body simulations in the Boltzmann evolution hierarchy. Our results agree extremely well with results derived from N -body simulations that include cold dark matter and neutrinos as independent particles with different properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Exact quantum scars in the chiral nonlinear Luttinger liquid

While the chiral linear Luttinger liquid is integrable via bosonization, its nonlinear counterpart does not admit for an analytic solution. In this work, we find a subextensive number of exact eigenstates for a large family of density-density interaction terms. These states are embedded in a continuum of strongly correlated excited states. The real-space entanglement entropy of some exact states scales logarithmically with system size while that of others has volume-law scaling. We introduce momentum-space entanglement as an unambiguous differentiator between these exact states and the remaining excited states. With regard to momentum space, the exact states behave as bona fide quantum many-body scars: they exhibit identically zero momentum-space entanglement, while typical eigenstates behave thermally. We corroborate this finding by a level statistics analysis. Here we detail the general formalism for systematically finding all interaction terms and associated exact states, and present a number of infinite exact state sequences extending to arbitrarily high energies. Unlike many previous examples of quantum many-body scars, the exact states uncovered here do not lie at equidistant energies and do not follow from a special operator algebra. Instead, they are uniquely enabled by the interplay of Fermi statistics and chirality.

36 MATERIALS SCIENCE↗