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All sourcesNASA NTRSDOE OSTI
NASA NTRS1968

On the Equilibrium Figure of the Earth

If de Sitter's hydrostatic equations are developed independent of the external potential theory, the hydrostatic geopotential coefficient J(sub h) occurs explicitly on the right-hand side of those equations. J(sub h) here has to be treated as an unknown in the solution, it becomes rather difficult to solve the equations independently, regardless of which of the dynamical parameters associated with the earth is taken as the initial datum. Solution is possible, however, with the help of a boundary condition derived from the external potential theory which neither assumes nor discounts the presence of equilibrium conditions in the earth's interior. If a general solution i s constructed on this basis, the three particular solutions, usually quoted in literature, stem from it in the wake of the appropriate assumptions. Of course, the only meaningful solution--of these-- is that corresponding to the polar moment of inertia as the initial datum. It is essential that the solution be constructed in this way in order to demonstrate clearly the correct structure of the problem of hydrostatic equilibrium. The anomalous gravity field of the earth referred to the hydrostatic figure is compared with that referred to the international reference ellipsoid.

Khan, M. A.↗
DOE OSTI2021

Phase transformations, microstructural refinement and defect evolution mechanisms in Al-Si alloys under non-hydrostatic diamond anvil cell compression

Non-hydrostatic compression of materials using a diamond anvil cell (DAC) can transform equilibrium microstructure of an alloy to novel, potentially metastable states. In this study, in situ synchrotron X-ray diffraction (XRD) during compression up to 24 GPa and subsequent ex situ, high resolution analytical electron microscopy (AEM) after decompression of an Al-Si alloy provided insight into the crystallographic changes during the compression as well as microstructural refinement, and defect structures caused by such a high pressure compression-decompression process. Pressure resolved in-situ synchrotron XRD was used to detail the phase transformation pathway of the eutectic Si phase in Al-Si alloy, from Si-I → Si-XI → Si-V during compression, and a final transformation predominantly to Si-III after decompression. Using scanning and transmission electron microscopy (S/TEM), site specific analysis of the alloy immediately underneath the anvil contact surface demonstrated a highly complex microstructure. A narrow region of thick amorphous Al oxide interspersed with nanocrystalline grains was found at the top surface. Underneath this Al oxide, while the majority the eutectic Si was transformed into highly-deformed, polycrystalline (PC) Si-III, a complex intermediate layer was discovered at the interface between Al and Si, comprised of a small fraction of Al nanocrystals and a majority of nanocrystalline Si-I. This combination of pressure resolved in-situ synchrotron XRD coupled with subsequent high resolution, electron microscopy resolved the phase transformation as well as non-equilibrium microstructures in a metallic alloy induced by a non-hydrostatic high pressure compression followed by decompression.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Fourfold Clusters of Rovibrational Energies in H2Te Studied With an Ab Initio Potential Energy Function

We report an ab initio investigation of the cluster effect (i.e., the formation of nearly degenerate, four member groups of rotation-vibration energy levels at higher J and K(sub a). values) in the H2Te molecule. The potential energy function has been calculated ab initio at a total of 334 molecular geometries by means of the CCSD(T) method where the (1s-4f) core electrons of Te were described by an effective core potential. The values of the potential energy function obtained cover the region up to around 10,000/cm above the equilibrium energy. On the basis of the ab initio potential, the rotation-vibration energy spectra of H2Te-130 and its deuterated isotopomers have been calculated with the MORBID (Morse Oscillator Rigid Bender Internal Dynamics) Hamiltonian and computer program. In particular, we have calculated the rotational energy manifolds for J less than or = 40 in the vibrational ground state, the upsilon(sub 2) state, the "first triad" (the upsilon(sub l)/upsilon(sub 3)/2upsilon(sub 2) interacting vibrational states), and the "second triad" (the upsilon(sub 1) + upsilon(sub 2/upsilon(sub 2) + upsilon(sub 3)/3upsilon(sub 2) states) of H2Te-130. We find that the cluster formation in H2Te is very similar to those of of H2Se and H2S, which we have studied previously. However, contrary to semiclassical predictions, we do not determine any significant displacement of the clusters towards lower J values relative to H2Se. Hence the experimental observation of the cluster states in H2Te will be at least as difficult as in H2Se.

Jensen, Per↗
DOE OSTI2024

Characterization of Deformational Isomerization Potential and Interconversion Dynamics with Ultrafast X-ray Solution Scattering

Dimeric complexes composed of d 8 square planar metal centers and rigid bridging ligands provide model systems to understand the interplay between attractive dispersion forces and steric strain in order to assist the development of reliable methods to model metal dimer complexes more broadly. [Ir 2 (dimen) 4 ] 2+ (dimen = para-diisocyanomenthane) presents a unique case study for such phenomena, as distortions of the optimal structure of a ligand with limited conformational flexibility counteract the attractive dispersive forces from the metal and ligand to yield a complex with two ground state deformational isomers. Here, in this work, we use ultrafast X-ray solution scattering (XSS) and optical transient absorption spectroscopy (OTAS) to reveal the nature of the equilibrium distribution and the exchange rate between the deformational isomers. The two ground state isomers have spectrally distinct electronic excitations that enable the selective excitation of one isomer or the other using a femtosecond duration pulse of visible light. We then track the dynamics of the nonequilibrium depletion of the electronic ground state population—often termed the ground state hole—with ultrafast XSS and OTAS, revealing a restoration of the ground state equilibrium in 2.3 ps. This combined experimental and theoretical study provides a critical test of various density functional approximations in the description of bridged d 8 –d 8 metal complexes. The results show that density functional theory calculations can reproduce the primary experimental observations if dispersion interactions are added, and a hybrid functional, which includes exact exchange, is used.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Estimating coil features from an equilibrium

We present an explicit theoretical framework for constructing artificial modular coils for vacuum stellarator fields based solely on equilibrium properties, achieved through the formulation of a current potential defined on flux surfaces. Contours of constant Boozer toroidal angle can be directly interpreted as proxy coils, and so we demonstrate that key measures of coil complexity—particularly coil non-planarity—are strongly governed by local magnetic-field properties. This approach shows promise as predictor for more realistic coil configurations, providing both a pathway toward deeper understanding of equilibrium–coil relationships and a potential practical proxy for coil design.

Rodríguez, Eduardo [Max Planck Institute for Plasm↗
DOE OSTI2020

Potential Control of Oxygen Non-Stoichiometry in Cerium Oxide and Phase Transition Away from Equilibrium

Cerium oxide (ceria, CeO 2 ) is a technologically important material for energy conversion applications. Its activities strongly depend on redox states and oxygen vacancy concentration. Understanding the functionality of chemical active species and behavior of oxygen vacancy during operation, especially in high-temperature solid-state electrochemical cells, is the key to advance future material design. Herein, the structure evolution of ceria is spatially resolved using bulk-sensitive operando X-ray diffraction and spectroscopy techniques. During water electrolysis, ceria undergoes reduction, and its oxygen non-stoichiometry shows a dependence on the electrochemical current. Cerium local bonding environments vary concurrently to accommodate oxygen vacancy formation, resulting in changes in Ce-O coordination number and Ce 3+ /Ce 4+ redox couple. When reduced enough, a crystallographic phase transition occurs from α to an α' phase with more oxygen vacancies. Nevertheless, the transition behavior is intriguingly different from the one predicted in the standard phase diagram of ceria. This work demonstrates a feasible means to control oxygen non-stoichiometry in ceria via electrochemical potential. It also sheds light on the mechanism of phase transitions induced by electrochemical potential. For electrochemical systems, effects from a large-scale electrical environment should be taken into consideration, besides effective oxygen partial pressure and temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

MP-ALOE: an r2SCAN dataset for universal machine learning interatomic potentials

We present MP-ALOE, a dataset of nearly 1 million DFT calculations using the accurate r2SCAN meta-generalized gradient approximation. Covering 89 elements, MP-ALOE was created using active learning and primarily consists of off-equilibrium structures. We benchmark a machine learning interatomic potential trained on MP-ALOE, and evaluate its performance on a series of benchmarks, including predicting the thermochemical properties of equilibrium structures; predicting forces of far-from-equilibrium structures; maintaining physical soundness under static extreme deformations; and molecular dynamic stability under extreme temperatures and pressures. MP-ALOE shows strong performance on all of these benchmarks and is made public for the broader community to utilize.

Kuner, Matthew C↗
NASA NTRS1994

Computation of iodine species concentrations in water

During an evaluation of the use of iodine as a water disinfectant and the development of methods for measuring various iodine species in water onboard Space Freedom, it became necessary to compute the concentration of the various species based on equilibrium principles alone. Of particular concern was the case when various amounts of iodine, iodide, strong acid, and strong base are added to water. Such solutions can be used to evaluate the performance of various monitoring methods being considered. The authors of this paper present an overview of aqueous iodine chemistry, a set of nonlinear equations which can be used to model the above case, and a computer program for solving this system of equations using the Newton-Raphson method. The program was validated by comparing results over a range of concentrations and pH values with those previously presented by Gottardi for a given pH. Use of this program indicated that there are multiple roots to many cases and selecting an appropriate initial guess is important. Comparison of program results with laboratory results for the case when only iodine is added to water indicates the program gives high pH values for the iodine concentrations normally used for water disinfection. Extending the model to include the effects of iodate formation results in the computer pH values being closer to those observed, but the model with iodate does not agree well for the case in which base is added in addition to iodine to raise the pH. Potential explanations include failure to obtain equilibrium conditions in the lab, inaccuracies in published values for the equilibrium constants, and inadequate model of iodine chemistry and/or the lack of adequate analytical methods for measuring the various iodine species in water.

Schultz, John R.↗
DOE OSTI2021

Plasma Muon Beam Cooling for HEP

Ionization cooling has the potential to shrink the phase space of a muon beam by a factor of 10⁶ within the muons’ short lifetime (2.2 µs) because the collision frequency in a cooling medium is extremely high compared to conventional beam cooling methods. It has been realized that ionization cooling inherently produces a plasma of free electrons inside the absorber material, and this plasma can have an important effect on the muon beam. In particular, under the right circumstances, it can both improve the rate of cooling and reduce the equilibrium emittance of the beam. This has the potential to improve the performance of muon facilities based on muon cooling; in particular a future muon collider. We describe how this project will integrate Plasma muon beam cooling into both the basic Helical Cooling Channel (HCC) and extreme Parametric-resonance Ionization Cooling (PIC) techniques. This potentially whole new approach to muon cooling has exciting prospects for significantly reduced muon beam emittance.

43 PARTICLE ACCELERATORS↗
NASA NTRS2015

Survival of Organic Materials in Ancient Cryovolcanically-Produced Halite Crystals

Spectroscopic evidence supports the presence of Mg-Na-K salts derived from cryovolcanism on the surface of Europa. Halite (NaCl) is effective at very long-term preservation of organic phases and structures. Collection of salt crystals from Europan plumes would provide solid inclusions of organics, potentially also biomaterials, all suitable for analysis. Two thermally-metamorphosed ordinary chondrite regolith breccias (Monahans 1998 (H5) and Zag (H3-6)) contain fluid and solid inclusion-bearing halite crystals, dated to approximately 4.5 billion years, and thus the trapped aqueous fluids and solids are at least as old. Heating/freezing studies of the aqueous fluid inclusions in these halites demonstrated that they were trapped near 25 degrees Centigrade, and their continued presence in the halite grains requires that their incorporation into the H chondrite asteroid occurred after that body's metamorphism ended, since heating would have dessicated the halite. O and H isotopes of the trapped fluids are consistent with mixing of asteroidal and cometary water. Cryovolcanic Origin of the Halite: We hypothesize that these meteoritic halites derive from ancient cryovolcanism based on the following points. (1) Salts crystals are observed as products of current cryovolcanism on Enceladus. (2) In-situ spacecraft analysis of some of the icy grains associated with the Enceladus salt found minor organic or siliceous components, including methane, also found in the Monahans halite. (3) Cryovolcanic fluids are observed to be in chemical disequilibrium, reflecting incomplete reactions between interior volatiles and rocky materials. The coexistence of N2 and HCN in Enceladus' cryovolcanic fluids requires that the plume consists of a mixture of materials whose sources experienced different degrees of aqueous processing, including primordial material trapped in ice that has not been in contact with liquid water. The observed mineral assemblage within the Monahans and Zag halites is also far from equilibrium. Cryovolcanoes on Ceres are a potential source of our halite, however the processes that form halite should also be operating within Europa. Dissolution of Monahans halite grains has revealed a remarkable variety of organics, which dominate the population of solid inclusions. Thermal alteration of this macromolecular carbon (measured by Raman spectroscopy) shows remarkable diversity. We have identified highly-condensed aromatics, diamond, carbonates and chloromethane. Light organic compounds like methane tend to be water soluble and require cold formation temperatures at high hydrogen fugacity - i.e. require water ice. Another indication that these halites have not been heated is that light organics readily volatilize or aromaticize into PAHs. We are currently analyzing the organics by Raman and C-XANES, and measuring the content and exploring the potential chirality of amino acids in the halite. Implications for Europa Plumes: Organic materials and structures erupted by a Europa cryovolcano should be similarly preserved within halite, and other salts, which will be a convenient form for capture and analysis, since halite will serve to encapsulate and protect the organics from spacecraft contamination. Also, being transparent at many wavelengths halite will permit analysis by spacecraft-mounted spectroscopic techniques. In addition, halite is readily dissolved, permitting further analysis of entrained organics.

Zolensky, M.↗
DOE OSTI2020

The Technical and Economic Potential of the H2@Scale Hydrogen Concept within the United States

The U.S. energy system is evolving as society and technologies change. Renewable electricity generation - especially from wind and solar - is growing rapidly, and alternative energy sources are being developed and implemented across the residential, commercial, transportation, and industrial sectors to take advantage of their cost, security, and health benefits. Systemic changes present numerous challenges to grid resiliency and energy affordability, creating a need for synergistic solutions that satisfy multiple applications while yielding system-wide cost and emissions benefits. One such solution is an integrated hydrogen energy system. This is the focus of H2@Scale - a U.S. Department of Energy (DOE) initiative led by the Office of Energy Efficiency and Renewable Energy’s Hydrogen and Fuel Technologies Office. H2@Scale brings together stakeholders to advance affordable hydrogen production, transport, storage, and utilization in multiple energy sectors. The H2@Scale concept involves hydrogen as an energy intermediate. Hydrogen can be produced from various conventional and renewable energy sources including as a responsive load on the electric grid. Hydrogen has many current applications and many more potential applications, such as energy for transportation - used directly in fuel cell electric vehicles (FCEVs), as a feedstock for synthetic fuels, and to upgrade oil and biomass - feedstock for industry (e.g., for ammonia production, metals refining, and other end uses), heat for industry and buildings, and electricity storage. Owing to its flexibility and fungibility, a hydrogen intermediate could link energy sources that have surplus availability to markets that require energy or chemical feedstocks, benefiting both. This document builds upon a growing body of analyses of hydrogen as an energy intermediate by reporting the results from our initial analysis of the potential impacts of the H2@Scale vision by the mid-21 st century for the 48 contiguous U.S. states. Previous estimates have been based on expert elicitation and focused on hydrogen demands. We build upon them, first, by estimating hydrogen’s serviceable consumption potential for possible hydrogen applications and the technical potential for producing hydrogen from various resources. We define the serviceable consumption potential as the quantity of hydrogen that would be consumed to serve the portion of the market that could be captured without considering economics (i.e., if the price of hydrogen were $0/kg over an extended period); thus, it can be considered an upper bound for the size of the market. We define the technical potential as the resource potential constrained by real-world geography and system performance, but not by economics. We then compare the cumulative serviceable consumption potential with the technical potential of a number of possible sources. Second, we estimate economic potential: the quantity of hydrogen at an equilibrium price at which suppliers are willing to sell and consumers are willing to buy the same quantity of hydrogen. We believe this method provides a deeper understanding than was available in the previous analyses. We develop economic potentials for multiple scenarios across various market and technology-advancement assumptions.

08 HYDROGEN↗
DOE OSTI2021

Towards chemical equilibrium in thermochemical water splitting. Part 1: Thermal reduction

The efficiency of many processes strongly depends on their thermodynamic reversibility, i.e., proximity to equilibrium throughout the process. In thermochemical cycles for water and/or carbon dioxide splitting, thermochemical air separation, and thermochemical energy storage, operating near equilibrium means that the oxygen chemical potential of the solid and gas phases must not differ significantly. Herein we show that approaching this ideal is possible in thermal reduction only if the reaction step occurs at a specific, reaction coordinate- and material-dependent temperature. The resulting thermal reduction temperature profile also depends on the ratio of gas and solid flows.

08 HYDROGEN↗
DOE OSTI2021

Active motion of multiphase oil droplets: emergent dynamics of squirmers with evolving internal structure

Synthetic soft matter systems, when driven beyond equilibrium by active processes, offer the potential to achieve dynamical states and functions of a complexity found in living matter. Emulsions offer the basis of a simple yet versatile system for identification of the physicochemical principles underlying active soft matter, but how multiple internal phases within emulsion droplets (e.g., Janus morphologies) organize to impact emergent dynamics is not understood. Here, we create multiphase oil droplets with ultralow interfacial tensions but distinct viscosities, and drive them into motion in aqueous micellar solutions. Preferential solubilization of select components of the oil both drives the droplet motion and yields a progression of internal phase morphological states with distinct symmetries. In this work, we find the active droplets to exhibit five dynamical states during morphogenesis. By quantifying microscopic flow fields, we show that it is possible to map the diverse droplet behaviors to squirmer models of spherical microswimmers in Stokes flow, thus showing that multiphase droplets offer the basis of a versatile platform with which to study and engineer the hydrodynamics of microswimmers.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery

The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, and pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model on electrostatic interaction, the nonpolar interaction contribution of solvent and the conformational entropy of solute in solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of conformational entropy of solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal/mol for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.

25 ENERGY STORAGE↗
DOE OSTI2024

Visualizing the SEI formation between lithium metal and solid-state electrolyte

The solid electrolyte interphase (SEI) is regarded as the most important factor affecting the durability of lithium-metal anode in all-solid-state batteries (ASSBs). Despite its significance, the nucleation and growth mechanism of SEI is not yet well understood. Here, we elucidate the thermodynamics and kinetics governing SEI formation at the Li|β-Li 3 PS 4 interface at the atomic scale via thermodynamic phase equilibrium analysis and machine-learning-potential-assisted molecular dynamics (MD) simulations. An accurate moment tensor potential using the machine-learning method is developed for a reactive model of Li|β-Li 3 PS 4 . This potential enabled us to perform large-scale MD simulations with the model size expanded to the experimental dimensions (~40 nm) while maintaining the same level of accuracy as density functional theory calculations. The results reveal a four-stage evolution process at the Li|β-Li 3 PS 4 interface, namely (i) fast ion diffusion, (ii) nucleation, (iii) Li 2 S growth, and (iv) stabilization. Notably, we demonstrate that the SEI can be categorized into crystalline and amorphous regions. The simulated SEI thickness, structure, and composition closely match experimental findings, validating the accuracy of the MD simulations. We further disclose the significant impact of ion diffusion kinetic limitations on the phase formation and crystallization of interfacial products. Furthermore, we shed light on the detailed potential energy (PE) distribution of lithium along the direction perpendicular to the interface. Finally, this information is crucial for better understanding interfacial ion mobility.

25 ENERGY STORAGE↗
DOE OSTI2025

Multi-scale computational screening and mechanistic insights of cyclic amines as solvents for improved lignocellulosic biomass processing

A computational screening workflow for the efficient deconstruction of cellulose, lignin and hemicellulose fractions of lignocellulosic biomass using cyclic amines as solvents. Lignocellulosic biomass is a promising feedstock for production of affordable fuels and chemicals from renewable resources. Effective solubilization and subsequent deconstruction of its cellulose, hemicellulose, and lignin fractions is essential for the viability of future biorefineries. This study used quantum chemistry-based equilibrium thermodynamics methods to evaluate the potential of 650 cyclic amines to solubilize cellulose, hemicellulose, and lignin. The activity coefficients of solvent - biopolymer interactions were predicted using the COSMO-RS (COnductor-like Screening MOdel for Real Solvents) method and used to identify cyclic amines that can efficiently dissolve and extract selective fractions of biopolymers during biomass pretreatment. Among the 650 cyclic amines, 1-piperazineethanmaine was predicted to be an effective solvent for extracting all three polymers and was experimentally shown to achieve the highest lignin removal (97.1%). Non-covalent interaction, reduced density gradient and quantum chemical calculations were performed to elucidate the dissolution mechanism of lignin, cellulose and hemicellulose and gain further molecular level insights into the interactions between the cyclic amines and biomass polymers that promote efficient solubilization and extraction. These analyses indicated that 1-piperazineethanmaine and 1-methylimidazole make noncovalent van der Waals, electrostatic interactions and hydrogen bonding with lignin, leading to enhanced lignin removal, while the strong intramolecular hydrogen bonding interactions in cellulose and hemicellulose result in weaker solvent-biopolymer interactions. Overall, the computational approach provided an efficient method for identifying cyclic amines tailored for optimal biomass pretreatment and resulted in the identification of a potential new class of solvents for effective biomass pretreatment.

Kumar, Nikhil↗
DOE OSTI2022

Transferability of data-driven, many-body models for CO 2 simulations in the vapor and liquid phases

Here, extending on the previous work by Riera et al. [J. Chem. Theory Comput. 16, 2246–2257 (2020)], we introduce a second generation family of data-driven many-body MB-nrg models for CO 2 and systematically assess how the strength and anisotropy of the CO 2 –CO 2 interactions affect the models’ ability to predict vapor, liquid, and vapor–liquid equilibrium properties. Building upon the many-body expansion formalism, we construct a series of MB-nrg models by fitting one-body and two-body reference energies calculated at the coupled cluster level of theory for large monomer and dimer training sets. Advancing from the first generation models, we employ the charge model 5 scheme to determine the atomic charges and systematically scale the two-body energies to obtain more accurate descriptions of vapor, liquid, and vapor–liquid equilibrium properties. Challenges in model construction arise due to the anisotropic nature and small magnitude of the interaction energies in CO 2 , calling for the necessity of highly accurate descriptions of the multidimensional energy landscape of liquid CO 2 . These findings emphasize the key role played by the training set quality in the development of transferable, data-driven models, which, accurately representing high-dimensional many-body effects, can enable predictive computer simulations of molecular fluids across the entire phase diagram.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics

Hydrodynamics can be formulated in terms of a perturbative series in derivatives of the temperature, chemical potential, and flow velocity around an equilibrium state. Different formulations for this series have been proposed over the years, which consequently led to the development of various hydrodynamic theories. In this work, we discuss the relativistic generalizations of the perturbative expansions put forward by Chapman and Enskog, and Hilbert, using general matching conditions in kinetic theory. This allows us to describe, in a comprehensive way, how different out-of-equilibrium definitions for the hydrodynamic fields affect the development of the hydrodynamic perturbative series. We provide a perturbative method for systematically deriving the hydrodynamic formulation recently proposed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) from relativistic kinetic theory. The various transport coefficients that appear in BDNK (at first-order) are explicitly computed using a new formulation of the relaxation time approximation for the Boltzmann equation. Assuming Bjorken flow, we also determine the hydrodynamic attractors of BDNK theory and compare the overall hydrodynamic evolution obtained using this formulation with that generated by the Israel-Stewart equations of motion and also kinetic theory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗