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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Economic and Environmental Assessment of Biological Conversions of Agile BioFoundry (ABF) Bio-Derived Chemicals

Bio-derived chemicals are an essential part of the growing bioeconomy. They possess the potential to boost a new domestic bioproduct industry, improve the sustainability of integrated biomanufacturing, and reduce U.S. dependence on fossil energy. The Agile BioFoundry (ABF) consortium, a Department of Energy (DOE)-sponsored collaboration, is investigating biobased pathways to produce advantaged products including advanced biofuels, fuel intermediates, and bioproducts. ABF is integrating advanced computational tools for biological engineering, process design and data analysis, and economic/sustainability modeling tools into a comprehensive and dynamic platform for biomanufacturing of microbes and using them to produce key metabolic intermediates or beachhead molecules which may be derivatized into several distinct bioproducts of industrial interest. In this presentation, we first discuss a methodology to select a single exemplar product molecule to represent each beachhead pathway based on similarities with other end-molecule options (yields/titers/rates, fermentation operation mode, oxygen requirements, general separations challenges, etc.), in order to maintain a reasonable number of cases for rigorous process simulation. We then use techno-economic analysis (TEA) and life-cycle analysis (LCA) to highlight sensitivities and trends around economic performance and environmental footprint, reflecting examples for two selected ABF technology pathways to bio-derived chemicals: 1) adipic acid production via muconic acid fermentation from mixed sugars with Pseudomonas putida and 2) cineole via geranyl diphosphate with Rhodosporidium toruloides. We present multi-variable scan plots highlighting key drivers on costs and greenhouse gas emissions in order to identify the parameter space in which each pathway could ultimately achieve economic and environmental sustainability meeting or exceeding commodity product benchmarks, thus prioritizing future R&D focus areas.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

Modes and Mechanisms of Pacific Decadal-Scale Variability

The modes of Pacific decadal-scale variability (PDV), traditionally defined as statistical patterns of variance, reflect to first order the ocean's integration (i.e., reddening) of atmospheric forcing that arises from both a shift and a change in strength of the climatological (time-mean) atmospheric circulation. While these patterns concisely describe PDV, they do not distinguish among the key dynamical processes driving the evolution of PDV anomalies, including atmospheric and ocean teleconnections and coupled feedbacks with similar spatial structures that operate on different timescales. In this review, we synthesize past analysis using an empirical dynamical model constructed from monthly ocean surface anomalies drawn from several reanalysis products, showing that the PDV modes of variance result from two fundamental low-frequency dynamical eigenmodes: the North Pacific–central Pacific (NP-CP) and Kuroshio–Oyashio Extension (KOE) modes. Both eigenmodes highlight how two-way tropical–extratropical teleconnection dynamics are the primary mechanisms energizing and synchronizing the basin-scale footprint of PDV. While the NP-CP mode captures interannual- to decadal-scale variability, the KOE mode is linked to the basin-scale expression of PDV on decadal to multidecadal timescales, including contributions from the South Pacific.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Spatial and temporal variability of tritium in precipitation within South Africa and it's bearing on hydrological studies

Tritium, the radioactive isotope of hydrogen, has been used to understand groundwater recharge processes for decades. The current variation of tritium in the atmosphere is largely attributed to stratospheric production and fall out rates as well as global circulation phenomena controlling the hydrological cycle. Global controls on the variability in atmospheric tritium activity are poorly suited to explain local variation and tritium activities in precipitation are often assumed to be uniform over both local and regional catchments and watersheds. This assumption can result in both over and under estimation of modern recharge within an aquifer when using tritium as the recharge proxy. In order to minimize the inherent prediction residuals associated with tritium based recharge investigations, the variability of tritium in precipitation was modelled from 127 spatial precipitation samples taken over a two year period, combined with a 76 precipitation sample group-set taken over a one year period in a single location. Precipitation events were traced backward in time, from the point of collection, using HYSPLIT modelling to ascertain the origins of moisture content as well as the altitudes of moisture origin reached along the particle track. Tritium activities, collected over a one year period in Paarl, range from 0.45 to 4.16 TU and have a mean of 1.59 TU. Spatial storm events in the Western Cape in 2017 and 2018 had a range from 0 to 2.2 and 0.37 to 3.27 TU, respectively, with mean activities of 1.18 (n = 34) and 1.25 TU (n = 32). Both storm events had similar tritium variability (σ = 0.5 n = 35 and 0.48 n = 32). Regional precipitation events had the largest range of tritium activities (0.55–12.2 TU). Although not all tritium activities can be explained by interrogating the water mass origin, this study suggests that approximately 90% of events can be completely or partially attributed to the origin of the water mass. The variability of tritium, both spatially and temporally, was higher than expected, confirming that when uniform tritium inputs are used, the groundwater system would provide inaccurate modern recharge estimates. Higher spatial resolution of tritium variation in precipitation for a particular region will improve our ability to relate tritium activities in groundwater to local precipitation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Scheduling and Pricing for Expected Ramp Capability in Real-Time Power Markets

Higher variable renewable generation penetrations are occurring throughout the world on different power systems. These resources increase the variability and uncertainty on the system which must be accommodated by an increase in the flexibility of the system resources in order to maintain reliability. Many scheduling strategies have been discussed and introduced to ensure that this flexibility is available at multiple timescales. To meet variability, that is, the expected changes in system conditions, two recent strategies have been introduced: time-coupled multi-period market clearing models and the incorporation of ramp capability constraints. To appropriately evaluate these methods, it is important to assess both efficiency and reliability. But it is also important to assess the incentive structure to ensure that resources asked to perform in different ways have the proper incentives to follow these directions, which is a step often ignored in simulation studies. Here we find that there are advantages and disadvantages to both approaches. We also find that look-ahead horizon length in multi-period market models can impact incentives. This paper proposes scheduling and pricing methods that ensure expected ramps are met reliably, efficiently, and with associated prices based on true marginal costs that incentivize resources to do as directed by the market. Case studies show improvements of the new method.

25 ENERGY STORAGE↗
DOE OSTI2019

Understanding the Significance of Biochemistry in the Storage, Handling, Purification, and Sampling of Amphiphilic Mycolactone

Mycolactone, the amphiphilic macrolide toxin secreted by Mycobacterium ulcerans , plays a significant role in the pathology and manifestations of Buruli ulcer (BU). Consequently, it follows that the toxin is a suitable target for the development of diagnostics and therapeutics for this disease. Yet, several challenges have deterred such development. For one, the lipophilic nature of the toxin makes it difficult to handle and store and contributes to variability associated with laboratory experimentation and purification yields. In this manuscript, we have attempted to incorporate our understanding of the lipophilicity of mycolactone in order to define the optimal methods for the storage, handling, and purification of this toxin. We present a systematic correlation of variability associated with measurement techniques (thin-layer chromatography (TLC), mass spectrometry (MS), and UV-Vis spectrometry), storage conditions, choice of solvents, as well as the impact of each of these on toxin function as assessed by cellular cytotoxicity. We also compared natural mycolactone extracted from bacterial culture with synthesized toxins in laboratory (solvents, buffers) and physiologically relevant (serum) matrices. Our results point to the greater stability of mycolactone in organic, as well as detergent-containing, solvents, regardless of the container material (plastic, glass, or silanized tubes). They also highlight the presence of toxin in samples that may be undetectable by any one technique, suggesting that each detection approach captures different configurations of the molecule with varying specificity and sensitivity. Most importantly, our results demonstrate for the very first time that amphiphilic mycolactone associates with host lipoproteins in serum, and that this association will likely impact our ability to study, diagnose, and treat Buruli ulcers in patients.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Assessing Regional Scale Variability in Extreme Value Statistics Under Altered Climate Scenarios

Recent studies have suggested that low-frequency modes of climate variability can significantly influence regional climate. The climatology associated with extreme events has been shown to be particularly sensitive. This has profound implications for droughts, heat waves, and food production. We propose to examine regional climate simulations conducted over the continental United States by applying a recently developed technique which combines wavelet multi–resolution analysis with information theory metrics. This research is motivated by two fundamental questions concerning the spatial and temporal structure of extreme events. These questions are 1) what temporal scales of the extreme value distributions are most sensitive to alteration by low-frequency climate forcings and 2) what is the nature of the spatial structure of variation in these timescales? The primary objective is to assess to what extent information theory metrics can be useful in characterizing the nature of extreme weather phenomena. Specifically, we hypothesize that (1) changes in the nature of extreme events will impact the temporal probability density functions and that information theory metrics will be sensitive these changes and (2) via a wavelet multi–resolution analysis, we will be able to characterize the relative contribution of different timescales on the stochastic nature of extreme events. In order to address these hypotheses, we propose a unique combination of an established regional climate modeling approach and advanced statistical techniques to assess the effects of low-frequency modes on climate extremes over North America. The behavior of climate extremes in RCM simulations for the 20th century will be compared with statistics calculated from the United States Historical Climatology Network (USHCN) and simulations from the North American Regional Climate Change Assessment Program (NARCCAP). This effort will serve to establish the baseline behavior of climate extremes, the validity of an innovative multi–resolution information theory approach, and the ability of the RCM modeling framework to represent the low-frequency modulation of extreme climate events. Once the skill of the modeling and analysis methodology has been established, we will apply the same approach for the AR5 (IPCC Fifth Assessment Report) climate change scenarios in order to assess how climate extremes and the the influence of lowfrequency variability on climate extremes might vary under changing climate. The research specifically addresses the DOE focus area 2. Simulation of climate extremes under a changing climate. Specific results will include (1) a better understanding of the spatial and temporal structure of extreme events, (2) a thorough quantification of how extreme values are impacted by low-frequency climate teleconnections, (3) increased knowledge of current regional climate models ability to ascertain these influences, and (4) a detailed examination of the how the distribution of extreme events are likely to change under different climate change scenarios. In addition, this research will assess the ability of the innovative wavelet information theory approach to characterize extreme events. Any and all of these results will greatly enhance society’s ability to understand and mitigate the regional ramifications of future global climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Genetic algorithm based task reordering to improve the performance of batch scheduled massively parallel scientific applications

The growth in size of networked high performance computers along with novel accelerator-based node architectures has further emphasized the importance of communication efficiency in high performance computing. The world's largest high performance computers are usually operated as shared user facilities due to the costs of acquisition and operation. Applications are scheduled for execution in a shared environment and are placed on nodes that are not necessarily contiguous on the interconnect. Furthermore, the placement of tasks on the nodes allocated by the scheduler is sub-optimal, leading to performance loss and variability. Here, we investigate the impact of task placement on the performance of two massively parallel application codes on the Titan supercomputer, a turbulent combustion flow solver (S3D) and a molecular dynamics code (LAMMPS). Benchmark studies show a significant deviation from ideal weak scaling and variability in performance. The inter-task communication distance was determined to be one of the significant contributors to the performance degradation and variability. A genetic algorithm-based parallel optimization technique was used to optimize the task ordering. This technique provides an improved placement of the tasks on the nodes, taking into account the application's communication topology and the system interconnect topology. As a result, application benchmarks after task reordering through genetic algorithm show a significant improvement in performance and reduction in variability, therefore enabling the applications to achieve better time to solution and scalability on Titan during production.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A LUMINOUS BLUE VARIABLE STAR INTERACTING WITH A NEARBY INFRARED DARK CLOUD

G79.29+0.46 is a nebula created by a luminous blue variable (LBV) star candidate characterized by two almost circular concentric shells. In order to investigate whether the shells are interacting with the infrared dark cloud (IRDC) G79.3+0.3 located at the southwestern border of the inner shell, we conducted Jansky Very Large Array observations of NH{sub 3}(1, 1), (2, 2) and c-C{sub 3}H{sub 2}, and combined them with previous Effelsberg data. The overall NH{sub 3} emission consists of one main clump, named G79A, elongated following the shape of the IRDC, plus two fainter and smaller cores to the north, which spatially match the inner infrared shell. We analyzed the NH{sub 3} spectra at each position with detected emission and inferred linewidth, rotational temperature, column density, and abundance maps, and find that: (1) the linewidth of NH{sub 3}(1, 1) in the northern cores is 0.5 km s{sup –1}, slightly larger than in their surroundings; (2) the NH{sub 3} abundance is enhanced by almost one order of magnitude toward the northwestern side of G79A; (3) there is one ''hot slab'' at the interface between the inner infrared shell and the NH{sub 3} peak of G79A; and (4) the western and southern edges of G79A present chemical differentiation, with c-C{sub 3}H{sub 2} tracing more external layers than NH{sub 3}, similar to what is found in photon-dominated regions. Overall, the kinematics and physical conditions of G79A are consistent with both shock-induced and UV radiation-induced chemistry driven by the LBV star. Therefore, the IRDC is not likely associated with the star-forming region DR15, but located farther away, near G79.29+0.46 at 1.4 kpc.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Disentangling Rotational Dynamics and Ordering Transitions in a System of Self-Organizing Protein Nanorods via Rotationally Invariant Latent Representations

The dynamics of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally invariant variational autoencoder-based analysis of orientation and shape evolution. The latter allows for disentanglement of the particle orientation from other degrees of freedom and compensates for lateral shifts. The disentangled representations in the latent space encode the rich spectrum of local transitions that can now be visualized and explored via continuous variables. The time dependence of ensemble averages allows insight into the time dynamics of the system and, in particular, illustrates the presence of the potential ordering transition. Finally, analysis of the latent variables along the single-particle trajectory allows tracing these parameters on a single-particle level. The proposed approach is expected to be universally applicable for the description of the imaging data in optical, scanning probe, and electron microscopy seeking to understand the dynamics of complex systems where rotations are a significant part of the process.

representation learning↗
DOE OSTI2025

Selection of Sampling and Surrogate Modeling Methods for State-Point Evaluations of an AGN-201M Reactor

Nuclear reactor digital twins (DTs) have been proposed for use as a safeguards technology to efficiently monitor new and novel reactors as they come online. A safeguards DT needs to be capable of detecting misuse and diversion as they occur, requiring physics models to be accurate and efficient. Mathematical surrogate models are capable of achieving the necessary efficiency and can largely maintain the accuracy of higher-order models given a quality training sample. The Multiphysics Object-Oriented Simulation Environment (MOOSE) code framework is specifically equipped to generate training samples and create surrogate models using full-order reactor physics models. Utilizing an operational AGN-201M reactor’s specifications, two surrogate types were trained on samples of variable size, and using Cartesian products, Latin hypercube sampling, and quadrature sampling, each was compared and evaluated on accuracy when compared to a full-order Monte Carlo model. Both surrogate types were able to capture reactivity changes within 0.05 $ of the Monte Carlo model while reducing the computation costs by eight orders of magnitude.

MOOSE↗
DOE OSTI2016

Order parameter re-mapping algorithm for 3D phase field model of grain growth using FEM

Phase field modeling (PFM) is a well-known technique for simulating microstructural evolution. To model grain growth using PFM, typically each grain is assigned a unique non-conserved order parameter and each order parameter field is evolved in time. Traditional approaches using a one-to-one mapping of grains to order parameters present a challenge when modeling large numbers of grains due to the computational expense of using many order parameters. This problem is exacerbated when using an implicit finite element method (FEM), as the global matrix size is proportional to the number of order parameters. While previous work has developed methods to reduce the number of required variables and thus computational complexity and run time, none of the existing approaches can be applied for an implicit FEM implementation of PFM. Here, we present a modular, dynamic, scalable reassignment algorithm suitable for use in such a system. Polycrystal modeling with grain growth and stress require careful tracking of each grain’s position and orientation which is lost when using a reduced order parameter set. In conclusion, the method presented in this paper maintains a unique ID for each grain even after reassignment, to allow the PFM to be tightly coupled to calculations of the stress throughout the polycrystal. Implementation details and comparative results of our approach are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Effects of the microstructure and porosity on properties of Ti-6Al-4V ELI alloy fabricated by electron beam melting (EBM)

Electron Beam Melting (EBM) is a metal powder bed-based Additive Manufacturing (AM) technology that makes possible the fabrication of three dimensional near-net-shaped parts directly from computer models. EBM technology has been in continuously updating, obtaining optimized properties of the processed alloys. Ti-6Al-4V titanium alloy is the most widely used and studied alloy for this technology and is the focus of this work. Several research works have been completed to study the mechanisms of microstructure formation as well as its influence on mechanical properties. However, the relationship is not completely understood, and more systematic research work is necessary in order to attain a better understanding of these features. In this work, samples fabricated at different locations, orientations, and distances from the build platform have been characterized, studying the relationship of these variables with the resulting material intrinsic characteristics and properties (surface topography, microstructure, porosity, micro-hardness and static mechanical properties). This study has revealed that porosity is the main factor controlling mechanical properties relative to the other studied variables. Therefore, in future process developments, decreasing of the porosity should be considered as the primary goal in order to improve mechanical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Explaining Snowball-in-Hell Phenomena in Heavy-Ion Collisions Using a Novel Thermodynamic Variable

A loosely bound hadronic molecule produced by a relativistic heavy-ion collision has been described as a “snowball in hell” since it emerges from a hadron resonance gas whose temperature is orders of magnitude larger than the binding energy of the molecule. This remarkable phenomenon can be explained in terms of a novel thermodynamic variable called the “contact” that is conjugate to the binding momentum of the molecule. The production rate of the molecule can be expressed in terms of the contact density at the kinetic freeze-out of the hadron resonance gas. It approaches a nonzero limit as the binding energy goes to 0.

Relativistic heavy-ion collisions↗
DOE OSTI2012

LOW-FREQUENCY (11 mHz) OSCILLATIONS IN H1743-322: A NEW CLASS OF BLACK HOLE QUASI-PERIODIC OSCILLATIONS?

We report the discovery of quasi-periodic oscillations (QPOs) at {approx}11 mHz in two RXTE and one Chandra observations of the black hole candidate H1743-322. The QPO is observed only at the beginning of the 2010 and 2011 outbursts at similar hard color and intensity, suggestive of an accretion state dependence for the QPO. Although its frequency appears to be correlated with X-ray intensity on timescales of a day, in successive outbursts eight months apart, we measure a QPO frequency that differs by less than Almost-Equal-To 2.2 mHz while the intensity had changed significantly. We show that this {approx}11 mHz QPO is different from the so-called Type C QPOs seen in black holes and that the mechanisms that produce the two flavors of variability are most probably independent. After comparing this QPO with other variability phenomena seen in accreting black holes and neutron stars, we conclude that it best resembles the so-called 1 Hz QPOs seen in dipping neutron star systems, although having a significantly lower (1-2 orders of magnitude) frequency. If confirmed, H1743-322 is the first black hole showing this type of variability. Given the unusual characteristics and the hard-state dependence of the {approx}11 mHz QPO, we also speculate whether these oscillations could instead be related to the radio jets observed in H1743-322. A systematic search for this type of low-frequency QPOs in similar systems is needed to test this speculation. In any case, it remains unexplained why these QPOs have only been seen in the last two outbursts of H1743-322.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

On mechanical waves and Doppler shifts from moving boundaries

We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, X s (t)=vt is the location of the source with constant velocity v. In the present work, however, we consider a source co-located with a moving boundary x=X s (t), where X s (t) can have an arbitrary functional form. For ‘slowly moving’ boundaries (i.e., ones for which the timescale set by the mechanical motion is large in comparison to the inverse of the frequency of the emitted wave), we present a multiple-scale asymptotic analysis of the moving boundary problem for the linear wave equation. Here, we obtain a closed-form leading-order (with respect to the latter small parameter) solution and show that the variable velocity of the boundary results not only in frequency modulation but also in amplitude modulation of the received signal. Consequently, our results extend the applicability of two basic tenets of the theory of a moving source on a stationary domain, specifically that (i) $.\atop{x}_s$ for non-uniform boundary motion can be inserted in place of the constant velocity v in the classical Doppler formula and (ii) that the non-uniform boundary motion introduces variability in the amplitude of the wave. The specific examples of decelerating and oscillatory boundary motion are worked out and illustrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Stellar granulation as the source of high-frequency flicker in Kepler light curves

A large fraction of cool, low-mass stars exhibit brightness fluctuations that arise from a combination of convective granulation, acoustic oscillations, magnetic activity, and stellar rotation. Much of the short-timescale variability takes the form of stochastic noise, whose presence may limit the progress of extrasolar planet detection and characterization. In order to lay the groundwork for extracting useful information from these quasi-random signals, we focus on the origin of the granulation-driven component of the variability. We apply existing theoretical scaling relations to predict the star-integrated variability amplitudes for 508 stars with photometric light curves measured by the Kepler mission. We also derive an empirical correction factor that aims to account for the suppression of convection in F-dwarf stars with magnetic activity and shallow convection zones. So that we can make predictions of specific observational quantities, we performed Monte Carlo simulations of granulation light curves using a Lorentzian power spectrum. These simulations allowed us to reproduce the so-called flicker floor (i.e., a lower bound in the relationship between the full light-curve range and power in short-timescale fluctuations) that was found in the Kepler data. The Monte Carlo model also enabled us to convert the modeled fluctuation variance into a flicker amplitude directly comparable with observations. When the magnetic suppression factor described above is applied, the model reproduces the observed correlation between stellar surface gravity and flicker amplitude. Observationally validated models like these provide new and complementary evidence for a possible impact of magnetic activity on the properties of near-surface convection.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Schwinger-Keldysh effective action for hydrodynamics with approximate symmetries

We study hydrodynamic theories with approximate symmetries in the recently developed effective action approach on the Schwinger-Keldysh contour. We employ the method of spurious symmetry transformation for small explicit symmetry-breaking parameters to systematically constrain symmetry-breaking effects in the nonequilibrium effective action for hydrodynamics. We apply our method to the hydrodynamic theory of chiral symmetry in quantum chromodynamics at finite temperature and density and its explicit breaking by quark masses. We show that the spurious symmetry and the Kubo-Martin-Schwinger relation dictate that the Ward-Takahashi identity for the axial symmetry, i.e., the partial conservation of axial vector current (PCAC) relation, contains a relaxational term proportional to the axial chemical potential, whose kinetic coefficient is at least of the second order in the quark mass. In the phase where the chiral symmetry is spontaneously broken, and the pseudo-Nambu-Goldstone pions appear as hydrodynamic variables, this relaxation effect is subleading compared to the conventional pion mass term in the PCAC relation, which is of the first order in the quark mass. On the other hand, in the chiral symmetry restored phase, we show that our relaxation term, which is of the second order in the quark mass, becomes the leading contribution to the axial charge relaxation. Therefore, the leading axial charge relaxation mechanism is parametrically different in the quark mass across a chiral phase transition.

Goldstone bosons↗