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DOE OSTI2020

Guided search for desired functional responses via Bayesian optimization of generative model: Hysteresis loop shape engineering in ferroelectrics

Advances in theoretical modeling across multiple disciplines have yielded generative models capable of high veracity in predicting macroscopic functional responses of materials emerging as a result of complex non-local interactions. Correspondingly, of interest is the inverse problem of finding the model parameter that will yield desired macroscopic responses, such as stress–strain curves, ferroelectric hysteresis loops, etc. Here, we suggest and implement Gaussian process based methods that allow to effectively sample the degenerate parameter space of a complex non-local model to output regions of parameter space which yield desired functionalities. In this work, we discuss the specific adaptation of the acquisition function and sampling function to make the process efficient and balance the efficient exploration of parameter space for multiple possible minima and exploitation to densely sample the regions of interest where target behaviors are optimized. Additionally, this approach is illustrated via the hysteresis loop engineering in ferroelectric materials but can be adapted to other functionalities and generative models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Minkowski Functionals of SDSS-III BOSS: Hints of Possible Anisotropy in the Density Field?

We present measurements of the Minkowski functionals extracted from the SDSS-III BOSS catalogs. After defining the Minkowski functionals, we describe how an unbiased reconstruction of these statistics can be obtained from a field with masked regions and survey boundaries, validating our methodology with Gaussian random fields and mock galaxy snapshot data. From the BOSS galaxy data, we generate a set of four density fields in three dimensions corresponding to the northern and southern skies of LOWZ and CMASS catalogs, smoothing over large scales (Gaussian smoothing scale of 35 Mpc) such that the field is perturbatively non-Gaussian. We extract the Minkowski functionals from each data set separately, and measure their shapes and amplitudes by fitting a Hermite polynomial expansion. For the shape parameter of the Minkowski functional curves a0, that is related to the bispectrum of the field, we find that the LOWZ-South data presents a systematically lower value of a 0 = –0.080 ± 0.040 than its northern sky counterpart a 0 = 0.032 ± 0.024. Although the significance of this discrepancy is not very high, it potentially indicates some systematics in the data or that the matter density field exhibits anisotropy at low redshift. By assuming a standard isotropic flat ΛCDM cosmology, the amplitudes of the Minkowski functionals from the combination of northern and southern sky data give the constraints Ω c h 2 n s = 0.110 ± 0.006 and 0.111 ± 0.008 for CMASS and LOWZ, respectively, which is in agreement with the Planck ΛCDM best-fit Ω c h 2 n s = 0.116 ± 0.001.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Temperature and CO 2 interactively drive shifts in the compositional and functional structure of peatland protist communities

Microbes affect the global carbon cycle that influences climate change and are in turn influenced by environmental change. Here, we use data from a long-term whole-ecosystem warming experiment at a boreal peatland to answer how temperature and CO 2 jointly influence communities of abundant, diverse, yet poorly understood, non-fungi microbial Eukaryotes (protists). These microbes influence ecosystem function directly through photosynthesis and respiration, and indirectly, through predation on decomposers (bacteria and fungi). Using a combination of high-throughput fluid imaging and 18S amplicon sequencing, we report large climate-induced, community-wide shifts in the community functional composition of these microbes (size, shape, and metabolism) that could alter overall function in peatlands. Importantly, we demonstrate a taxonomic convergence but a functional divergence in response to warming and elevated CO 2 with most environmental responses being contingent on organismal size: warming effects on functional composition are reversed by elevated CO 2 and amplified in larger microbes but not smaller ones. Furthermore, these findings show how the interactive effects of warming and rising CO 2 levels could alter the structure and function of peatland microbial food webs—a fragile ecosystem that stores upwards of 25% of all terrestrial carbon and is increasingly threatened by human exploitation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Fast HARDI Uncertainty Quantification and Visualization with Spherical Sampling

In this paper, we study uncertainty quantification and visualization of orientation distribution functions (ODF), which corresponds to the diffusion profile of high angular resolution diffusion imaging (HARDI) data. The shape inclusion probability (SIP) function is the state‐of‐the‐art method for capturing the uncertainty of ODF ensembles. The current method of computing the SIP function with a volumetric basis exhibits high computational and memory costs, which can be a bottleneck to integrating uncertainty into HARDI visualization techniques and tools. We propose a novel spherical sampling framework for faster computation of the SIP function with lower memory usage and increased accuracy. In particular, we propose direct extraction of SIP isosurfaces, which represent confidence intervals indicating spatial uncertainty of HARDI glyphs, by performing spherical sampling of ODFs. Our spherical sampling approach requires much less sampling than the state‐of‐the‐art volume sampling method, thus providing significantly enhanced performance, scalability, and the ability to perform implicit ray tracing. Our experiments demonstrate that the SIP isosurfaces extracted with our spherical sampling approach can achieve up to 8164× speedup, 37282× memory reduction, and 50.2% less SIP isosurface error compared to the classical volume sampling approach. We demonstrate the efficacy of our methods through experiments on synthetic and human‐brain HARDI datasets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Development of an ultraprecise glue-free bimorph deformable mirror with a length of 460 mm

Lead zirconate titanate (PZT) bimorph mirrors are essential for performing multiple functions, such as beam shaping, wavefront correction, and dynamic focusing with adjustable beam sizes. They typically consist of a mirror substrate with PZT electrodes bonded to the substrate using a thin epoxy film. However, glue-bonded PZT mirrors exhibit low reproducibility in measurement results. One source of this variability is water absorption by the substrate’s epoxy adhesive during wet fabrication processes, such as elastic emission machining (EEM), which leads to swelling and deformation. Additionally, longer deformable bimorph mirrors require larger PZT electrodes, further complicating their design and fabrication, particularly during bonding and ultraprecise metrology. To address these challenges, silver nanoparticles were employed to bond PZT elements to the silicon (Si) mirror, eliminating the need for epoxy glue. Here, in this study, we developed an inorganic-glue-free PZT bimorph mirror with a length of 460 mm and 28 channels. The glue-free bonding method successfully ensured the high reproducibility of measurements after water immersion. This approach resulted in a shape error of only 0.41 nm root mean square after the figure correction process using an ultraprecise EEM process. Scanning acoustic tomography and basic response function tests confirmed the success of the bonding process, showing no critical voids. Furthermore, the shape changes induced by applying voltages to the PZT electrodes closely matched predictions obtained from simulations. These results demonstrate the reliability and precision of the proposed glue-free bonding technique, paving the way for improved performance of new PZT bimorph mirrors.

Ichii, Yoshio [SLAC National Accelerator Laborator↗

DOE OSTI2023

Linear Viscoelastic Properties of Putative Cyclic Polymers Synthesized by Reversible Radical Recombination Polymerization (R3P)

Linear viscoelastic properties in both melt and solution states are reported for a series of poly(3,6-dioxa-1,8-octanedithiol) (polyDODT) made by reversible radical recombination polymerization (R 3 P) under conditions designed to produce linear (LDODT), cyclic (RDODT) and linear-cyclic mixtures (LRDODT). PolyDODT is amorphous (T g < -50 °C) and highly flexible (entanglement molecular weight M e,lin ≈ 1850 g/mol for LDODT). PolyDODT’s low T g and low M e,lin enable characterization over a wide dynamic range and a wide range of dimensionless weight-average molecular weight Z w = M w /M e,lin . Measurements at temperatures from -57 °C to 100 °C provide up to 18 deades of reduced frequency, which is necessary to characterize RDODT melts with Z w from 23 to 300. The two highest molecular weight polymers in the present RDODT series have such high M w (406k and 556k g/mol) that mass spectrometry, NMR spectroscopy, and even chemical assays for chain ends are unable to rule out up to 2 mol% linear contaminant. By studying the samples in solution (using dilution to reduce Z w ) we could compare their dynamics with those of previously established high-purity polystyrene (PS) rings (limited to Z w ≤ 13.6). RDODT solutions with Z w < 15 (concentrations <5wt% for RDODT-406k and 556k) have dynamic moduli G^* that accord with LCCC-purified PS rings in terms of the frequency dependence (including the absence of a plateau), the progression of shapes of G* as a function of Z w , and the linear scaling of their zero-shear viscosity η0 with M w . The shape of G* as a function of Z w for solutions of RDODT-406k and -556k also accord with lower M w RDODT melts (which have ≤ 1.3mol% linear contaminant). Thus, measurement of the linear viscoelastic properties of appropriate concentrations of high M w (>200k g/mol) putative cyclic polymers, in which linear chains evade spectroscopic detection, may provide an alternative means (though not fully proven) of validation of sample purity. When Z w > 15 (including all seven RDODT melts and eight of their solutions), G* has a rubbery plateau. This suggests that the onset of entanglement-like behavior in rings requires 4-5-fold greater Z w than is required for linear chains. Further, the plateau moduli of RDODT samples are indistinguishable from G N o of the corresponding LDODT (melt or matched-concentration solutions). In entangled linear polymers, the observation that G N o is independent of Z w follows from limitations on lateral fluctuations due to neighboring chains becoming independent of position along a given chain. The present results for RDODT suggest that this holds for sufficiently long endless chains, too. While the RDODT have the same G N o as entangled LDODT, when Z w > 60 the terminal relaxation, if reached at all, of RDODT extends to orders of magnitude lower frequency than an entangled linear polymer of the same Z w . Consequently, the viscosity of RDODT with Z w > 60 increases with Z w much more strongly than the 3.4-power observed for entangled linear polymers. Lastly, these novel polymers, with disulfide-linked backbone and broad relaxation time distribution may prove important in relation to biodegradable elastomers and materials with exceptional low-frequency dissipation, extending at least 12 decades below the onset of the rubbery plateau.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Functional succession of actively growing soil microorganisms during rewetting is shaped by precipitation history

Rewetting of seasonally dry soils induces a burst of microbial activity and carbon mineralization that changes nutrient availability and leads to succession. Yet the microbial functions that underpin this succession are not well described. Further, it’s unclear how previous precipitation frames microbial capacities after rewetting and how long these effects persist. We used isotopically-labeled water to rewet seasonally dry annual grassland soil that experienced either mean annual or reduced precipitation during the previous two years, and sampled at five subsequent time points. We used quantitative stable isotope probing (qSIP)-informed genome- resolved metagenomics to identify growing microorganisms, predict their capabilities, and analyze how these traits differed over time and between precipitation treatments. Organisms that grew after wetup were more abundant than non-growing organisms prior to the wet-up, suggesting that traits that initiate succession are pre-defined at the end of the prior plant growing season or via survival over the summer. Fast-growing organisms had fewer carbohydrate active enzyme (CAZy) genes per genome than slower-growing organisms, suggesting that although fast-growers were capable of degrading complex C, they may not specialize in this process. Differential abundance of CAZy genes in growing organisms throughout the succession implies that substrate availability varied with time. In contrast, the abundance of peptidases in growing organisms differed between precipitation treatments, but not over time following wet-up. Before wet-up, the soil organisms’ gene inventories were different between the two precipitation treatments. Surprisingly, this legacy effect waned after just one week. Thus, pre-wetup differences in microbial functional capacity converged shortly after rewetting.

Sieradzki, E T↗

DOE OSTI2021

Contrasting Community Assembly Forces Drive Microbial Structural and Potential Functional Responses to Precipitation in an Incipient Soil System

Microbial communities in incipient soil systems serve as the only biotic force shaping landscape evolution. However, the underlying ecological forces shaping microbial community structure and function are inadequately understood. We used amplicon sequencing to determine microbial taxonomic assembly and metagenome sequencing to evaluate microbial functional assembly in incipient basaltic soil subjected to precipitation. Community composition was stratified with soil depth in the pre-precipitation samples, with surficial communities maintaining their distinct structure and diversity after precipitation, while the deeper soil samples appeared to become more uniform. The structural community assembly remained deterministic in pre- and post-precipitation periods, with homogenous selection being dominant. Metagenome analysis revealed that carbon and nitrogen functional potential was assembled stochastically. Sub-populations putatively involved in the nitrogen cycle and carbon fixation experienced counteracting assembly pressures at the deepest depths, suggesting the communities may functionally assemble to respond to short-term environmental fluctuations and impact the landscape-scale response to perturbations. We propose that contrasting assembly forces impact microbial structure and potential function in an incipient landscape; in situ landscape characteristics (here homogenous parent material) drive community structure assembly, while short-term environmental fluctuations (here precipitation) shape environmental variations that are random in the soil depth profile and drive stochastic sub-population functional dynamics.

16S amplicon sequencing↗

DOE OSTI2021

Clustering of CODEX clusters

The clustering of galaxy clusters links the spatial nonuniformity of dark matter halos to the growth of the primordial spectrum of perturbations. The amplitude of the clustering signal is widely used to estimate the halo mass of astrophysical objects. The advent of cluster mass calibrations enables using clustering in cosmological studies. Aims. We analyze the autocorrelation function of a large contiguous sample of galaxy clusters, the Constrain Dark Energy with X-ray (CODEX) sample, in which we take particular care of cluster definition. These clusters were X-ray selected using the ROentgen SATellite All-Sky Survey and then identified as galaxy clusters using the code redMaPPer run on the photometry of the Sloan Digital Sky Survey. We develop methods for precisely accounting for the sample selection effects on the clustering and demonstrate their robustness using numerical simulations. Methods. Using the clean CODEX sample, which was obtained by applying a redshift-dependent richness selection, we computed the two-point autocorrelation function of galaxy clusters in the 0.1 < z < 0.3 and 0.3 < z < 0.5 redshift bins. We compared the bias in the measured correlation function with values obtained in numerical simulations using a similar cluster mass range. Results. By fitting a power law, we measured a correlation length r 0 = 18.7 ± 1.1 and slope γ = 1.98 ± 0.14 for the correlation function in the full redshift range. By fixing the other cosmological parameters to their nine-year Wilkinson Microwave Anisotropy Probe values, we reproduced the observed shape of the correlation function under the following cosmological conditions: Ω m0 = $0.22_{-0.03}^{+0.04}$ and S 8 = σ 8 (Ω m0 /0.3)0.5 = $0.85_{-0.08}^{+0.10}$ with estimated additional systematic errors of σ Ω m0 = 0.02 and σS 8 = 0.20. We illustrate the complementarity of clustering constraints by combining them with CODEX cosmological constraints based on the X-ray luminosity function, deriving Ωm = 0.25 ± 0.01 and σ 8 = $0.81_{-0.02}^{+0.01}$ with an estimated additional systematic error of σ Ω m0 = 0.07 and σ σ8 = 0.04. The mass calibration and statistical quality of the mass tracers are the dominant source of uncertainty.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The plant cell wall—dynamic, strong, and adaptable—is a natural shapeshifter

Mythology is replete with good and evil shapeshifters, who, by definition, display great adaptability and assume many different forms—with several even turning themselves into trees. Cell walls certainly fit this definition as they can undergo subtle or dramatic changes in structure, assume many shapes, and perform many functions. In this review, we cover the evolution of knowledge of the structures, biosynthesis, and functions of the 5 major cell wall polymer types that range from deceptively simple to fiendishly complex. Along the way, we recognize some of the colorful historical figures who shaped cell wall research over the past 100 years. The shapeshifter analogy emerges more clearly as we examine the evolving proposals for how cell walls are constructed to allow growth while remaining strong, the complex signaling involved in maintaining cell wall integrity and defense against disease, and the ways cell walls adapt as they progress from birth, through growth to maturation, and in the end, often function long after cell death. We predict the next century of progress will include deciphering cell type–specific wall polymers; regulation at all levels of polymer production, crosslinks, and architecture; and how walls respond to developmental and environmental signals to drive plant success in diverse environments.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Landmark-embedded Gaussian process with applications for functional data modeling

In practice, we often need to infer the value of a target variable from functional observation data. A challenge in this task is that the relationship between the functional data and the target variable is very complex: the target variable not only influences the shape but also the location of the functional data. In addition, due to the uncertainties in the environment, the relationship is probabilistic, that is, for a given fixed target variable value, we still see variations in the shape and location of the functional data. To address this challenge, we present a landmark-embedded Gaussian process model that describes the relationship between the functional data and the target variable. A unique feature of the model is that landmark information is embedded in the Gaussian process model so that both the shape and location information of the functional data are considered simultaneously in a unified manner. Gibbs-Metropolis-Hasting algorithm is used for model parameters estimation and target variable inference. The performance of the proposed framework is evaluated by extensive numerical studies and a case study of nano-sensor calibration.

42 ENGINEERING↗

DOE OSTI2022

Effect of applied potential on metal surfaces: Surface energy, Wulff shape and charge distribution

Here we use grand canonical density functional theory to predict the surface energies, Wulff shapes, charge distributions and catalytically active sites of different metal surfaces under electrochemical conditions. We propose a method for computing surface energies from grand canonical density functional theory (GC-DFT) calculations of periodic slab models and use it to compute the surface energies of the facets of Pt, Cu, and Ag crystals to predict their Wulff shapes under electrochemical conditions. GC-DFT predicts that, for the pure metals studied, solvation only slightly affects the Wulff shape while applied potentials considerably affect the surface energies and corresponding Wulff shapes. We used Bader charge analysis of GC-DFT computed electron densities to investigate the effect of applied potential on the distribution of electron density over the atoms of the surfaces of Pt, Cu, Ag, and the 75–25 Ag-Pt and Au-Ni alloys. This analysis shows that, under an applied potential, the electron density is unevenly distributed over the surface atoms and that the charges of atoms more exposed to solvent are more sensitive to bias. Our results show that the most sensitive atom to bias can be used to identify the most favorable adsorption site and thus, the active sites of electrochemical reactions, which is computationally less demanding than calculating the adsorption energies on all possible adsorption sites.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Deposit geometry and oxygen concentration spatial variations due to composition change in printed functionally graded components

Functionally graded materials (FGMs) with site specific chemical composition are commonly manufactured by directed energy deposition (DED). Although previous work fabricated an FGM with a compositional variation between a ferritic and austenitic alloy, difficulties arose due to variations in deposit shape with composition change. This problem also occurs for FGMs in literature; however, unlike other cases, the thermophysical properties of these two alloys were similar throughout the build. Here, we investigate the role of chemical composition and surface-active elements on deposit geometry during the manufacture of FGMs by laser DED. Single-track experiments for the relevant FGM compositions are analyzed with results from a well-tested, three-dimensional, transient numerical heat transfer and fluid flow model and thermodynamic calculations. Experiments showed deposit shape varied as a function of composition for constant laser power and scan speed. Thermodynamic analysis indicated that the oxygen solubility in the fusion zone varied significantly for each composition used for the FGM. Numerical modeling revealed that the change in fluid flow caused by Marangoni convection due to dissolved oxygen in the fusion zone were mainly responsible for the changes in deposit shape observed in experiments. Finally, because oxygen can be introduced into the fusion zone through the feedstock as well as the surrounding atmosphere, these findings elucidate a previously unconsidered aspect of process control during DED fabrication of FGMs.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Understanding and Strategies for Controlled Interfacial Phenomena in Lithium-Ion Batteries and Beyond

Electrolyte chemistry and properties and electrode structure and chemical properties particularly at the interfaces are crucial for the development of advanced battery components. This project focused on elucidating the roles of the electrolyte and electrode on the formation and evolution of the SEI layer and cell electrochemical performance on silicon and on Li metal anodes. For Si nano/microstructures we evaluated lithiation, volume changes, reactivity, and chemo-mechanical transformations as functions of nanoparticle size, shape, presence of coatings, electrolyte composition, electron leakage to the electrolyte, and cycling. For Li metal anodes we provided detailed analyses of the electrode and electrolyte effects on interfacial reactivity and as a function of microstructural evolution and underlying stochasticity as dendrites nucleate and grow. We thoroughly investigated and simulated how the chemistry of the various components of the electrolyte and the electrode architecture may affect the electrochemical reactions as well as cell degradation. A multiscale modeling approach was utilized, where atomistic simulations informed about the microscopic behavior of the system, and intermediate time and length scales were investigated with mesoscopic models. Results were also tested against selected experiments from our collaborators. The combined theoretical-experimental strategy saves costs by utilizing predictions from computational analyses to guide experimentation.

25 ENERGY STORAGE↗

DOE OSTI2020

Analytical integration of the tractions induced by non-singular dislocations on an arbitrary shaped triangular quadratic element

Here, an analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. Phys. Solids 54 561–587). The nodal force expressions can be used when considering both a single convolution or double convolution of the Green's function with the core distribution. A solution is also proposed for the case of a semi-infinite segment through the study of the asymptotic behavior of the analytical expressions. The proposed approach is exact and very computationally efficient. The choice of an arbitrary shaped triangular element and quadratic shape functions allow the consideration of complex geometries and comply with automatic meshing procedures. These analytical expressions could also be employed to estimate dislocation interactions with interfaces.

42 ENGINEERING↗

DOE OSTI2025

Dihadron azimuthal correlations in deep-inelastic scattering off nuclear targets

We measured the nuclear dependence of the di-pion azimuthal correlation function in deepinelastic scattering (DIS) using the CEBAF Large Acceptance Spectrometer (CLAS) and a 5 GeV electron beam. As the nuclear-target size increases, transitioning from deuterium to carbon, iron, and lead, the correlation function broadens monotonically. Its shape exhibits a significant dependence on kinematics, including the transverse momentum of the pions and the difference in their rapidity. None of the various Monte-Carlo event generators we evaluated could fully replicate the observed correlation functions and nuclear effects throughout the entire phase space. As the first study of its kind in DIS experiments, this research provides an important baseline for enhancing our understanding of the interplay between the nuclear medium and the hadronization process in these reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Elastic-instability–enabled locomotion

Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin circular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of locomotion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement––via anisotropic friction on land, and via directed inertial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of actuation are consistent with our observations. The presence of easily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments––both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing robots and other bioinspired machines at multiple scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗