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DOE OSTI2024

Occurrence of Gravitational Collapse in the Accreting Neutron Stars of Binary-driven Hypernovae

The binary-driven hypernova (BdHN) model proposes long gamma-ray bursts (GRBs) originate in binaries composed of a carbon–oxygen (CO) star and a neutron star (NS) companion. The CO core collapse generates a newborn NS and a supernova that triggers the GRB by accreting onto the NSs, rapidly transferring mass and angular momentum to them. This article aims to determine the conditions under which a black hole (BH) forms from NS collapse induced by the accretion and the impact on the GRB's observational properties and taxonomy. We perform three-dimensional, smoothed particle hydrodynamics simulations of BdHNe using up-to-date NS nuclear equations of state, with and without hyperons, and calculate the structure evolution in full general relativity. We assess the binary parameters leading either NS in the binary to the critical mass for gravitational collapse into a BH and its occurrence time, t col . We include a nonzero angular momentum of the NSs and find that t col ranges from a few tens of seconds to hours for decreasing NS initial angular momentum values. BdHNe I are the most compact (about 5 minute orbital period), promptly form a BH, and release ≳10 52 erg of energy. They form NS–BH binaries with tens of kiloyears merger timescales by gravitational-wave emission. BdHNe II and III do not form BHs, and release ~10 50 –10 52 erg and ≲10 50 erg of energy, respectively. They form NS–NS binaries with a range of merger timescales larger than for NS–BH binaries. In some compact BdHNe II, either NS can become supramassive, i.e., above the critical mass of a nonrotating NS. Magnetic braking by a 10 13 G field can delay BH formation, leading to BH–BH or NS–BH with tens of kiloyears merger timescales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Hydrodynamic Predictions for the Next Outburst of T Coronae Borealis: It Will Be the Brightest Classical or Recurrent Nova Ever Observed in X-Rays*

T Coronae Borealis (TCrB) is a recurrent nova with recorded outbursts in 1866 and 1946 and possible outbursts in 1217 and 1787. It is predicted to explode again in 2025 or 2026 based on multiple observational studies. The system consists of a massive ( M wd ≳ 1.35 M ⊙ ) white dwarf (WD) and a red giant (M3–M4 III). We have performed 1D hydrodynamic simulations with NOVA to predict the behavior of the next outburst. These simulations consist of a range of mass accretion rates onto ∼1.35 M ⊙ WDs, designed to bound the conditions necessary to achieve ignition of an explosion after an ≈80 yr interoutburst period. We have used both carbon–oxygen and oxygen–neon initial compositions, in order to include the possible ejecta abundances to be measured in the observations of the next outburst. As the WD in the TCrB system is observed to be massive, theoretical predictions reported here imply that the WD is growing in mass as a consequence of the thermonuclear runaway. Therefore, the secular evolution of the WD may allow it to approach the Chandrasekhar limit and either explode as a Type Ia supernova or undergo accretion-induced collapse, depending on its underlying composition. We have followed the evolution of just the WD, after removing the ejected matter from the surface layers. Our intent is to illuminate the mystery of the unique, second maximum in the two well-observed outbursts and we have found conditions that bracket the predictions.

Cataclysmic variable stars↗
DOE OSTI2025

How Do Uncertainties in Galaxy Formation Physics Impact Field-level Galaxy Bias?

Our ability to extract cosmological information from galaxy surveys is limited by uncertainties in the galaxy–dark matter halo relationship for a given galaxy population, which are governed by the intricacies of galaxy formation. To quantify these uncertainties, we examine quenched and star-forming galaxies using two distinct approaches to modeling galaxy formation: U$\scriptsize{NIVERSE}$M$\scriptsize{ACHINE}$, an empirical semianalytic model, and the I$\scriptsize{llustris}$TNG hydrodynamical simulation. We apply a second-order hybrid N-body perturbative bias expansion to each galaxy sample, enabling direct comparison of modeling approaches and revealing how uncertainties in the galaxy–halo connection affect bias parameters and non-Poisson noise across number densities and redshifts. Notably, we find that quenched and star-forming galaxies occupy distinct parts of the bias parameter space, and that the scatter induced from these different galaxy formation models is small when conditioned on similar selections of galaxies. We also detect the signature of assembly bias in our samples; this leads to small but significant deviations from analytic bias predictions, while assembly bias-removed samples match these predictions well. This work indicates that galaxy samples from a spectrum of reasonable, physically motivated models for galaxy formation give a relatively small range of field-level galaxy bias parameters. We estimate a set of priors from these models that should be useful in extracting cosmological constraints from luminous red galaxy– and emission line galaxy–like samples. Looking forward, careful estimates of the range of impacts of galaxy formation, for a given sample and cosmological analysis, will be an essential ingredient for extracting the most precise cosmological information from current and future large galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Energy Spectrum and Mass Composition of Ultra-high-energy Cosmic Rays Originating from Relativistic Jets of Nearby Radio Galaxies

Relativistic jets of radio galaxies (RGs) are possible sources of ultra-high-energy cosmic rays (UHECRs). Recent studies combining relativistic hydrodynamic simulations with Monte Carlo particle transport have demonstrated that UHECRs can be accelerated to energies beyond 10 20 eV through shocks, turbulence, and relativistic shear in jet-induced flows of Fanaroff–Riley type RGs. The resulting time-asymptotic UHECR spectrum is well modeled by a double power law with an “extended” exponential cutoff, primarily shaped by relativistic shear acceleration. In this study, we adopt this novel source spectrum and simulate the propagation of UHECRs from nearby RGs using the CRPropa code. We focus on Virgo A (Vir A), Centaurus A (Cen A), Fornax A (For A), and Cygnus A (Cyg A), expected to be the most prominent UHECR sources among RGs. We then analyze the energy spectrum and mass composition of UHECRs arriving at Earth. We find that, due to the extended high-energy tail in the source spectrum, UHECRs from Vir A, which has a higher Lorentz factor, exhibit a higher flux at the highest energies and a lighter mass composition at Earth compared to those from Cen A and For A with lower Lorentz factors. Despite Cyg A having an even higher Lorentz factor, the large distance limits its contribution. With a small number of nearby prominent RGs, our findings suggest that if RGs are the major sources of UHECRs, the energy spectrum and mass composition of observed UHECRs would exhibit hemispheric differences between the Northern and Southern skies at the highest energies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

ML-driven Strong Lens Discoveries: Down to θ E ~ $0^{_{''}}_{^.}03$ and M halo < 10 11 M ⊙

We present results on extending the strong lens discovery space down to much smaller Einstein radii ( θ E ≲ $0^{_{''}}_{^.}03$) and much lower halo mass (M halo < 10 11 M ⊙ ) through the combination of JWST observations and machine learning (ML) techniques. First, we forecast detectable strong lenses with JWST using CosmoDC2 as the lens catalog, and a source catalog down to 29th magnitude. By further incorporating the VELA hydrodynamical simulations of high-redshift galaxies, we simulate strong lenses. We train a ResNet on these images, achieving near-100% completeness and purity for “conventional” strong lenses ( θ E ≳ $0^{_{''}}_{^.}05$), applicable to JWST, the Hubble Space Telescope (HST), the Roman Space Telescope, and Euclid VIS. For the first time, we also search for very low halo mass strong lenses (M halo < 10 11 M ⊙ ) in simulations, with θ E << $0^{_{''}}_{^.}05$, down to the best resolution ($0^{_{''}}_{^.}03$) and depth (10,000 s) limits of JWST using ResNet. A U-Net model is employed to pinpoint these small lenses in images, which are otherwise virtually impossible for human detection. Our results indicate that JWST can find ∼17/deg 2 such low-halo-mass lenses, with the locations of ∼1.1/deg 2 of these detectable by the U-Net at ∼100% precision (and ∼7.0/deg 2 at a 99.0% precision). To validate our model for finding “conventional” strong lenses, we apply it to HST images, discovering two new strong lens candidates previously missed by human classifiers in a crowdsourcing project (E. O. Garvin et al. 2022). This study demonstrates the (potentially “superhuman”) advantages of ML combined with current and future space telescopes for detecting conventional, and especially, low-halo-mass strong lenses, which are critical for testing cold dark matter models.

Silver, Ethan [Harvard University, Cambridge, MA (↗
DOE OSTI2025

Elemental and Isotopic Yields from T Coronae Borealis: Predictions and Uncertainties

T Coronae Borealis (T CrB) is a symbiotic recurrent nova system expected to undergo its next outburst within the next 2 yr. Recent hydrodynamic simulations have predicted the nucleosynthetic yields for both carbon–oxygen (CO) and oxygen–neon (ONe) white-dwarf models, but without accounting for thermonuclear reaction rate uncertainties. We perform detailed Monte Carlo postprocessing nucleosynthesis calculations based on updated thermonuclear reaction rates and uncertainties from the 2025 evaluation. We quantify the resulting abundance uncertainties and identify the key nuclear reactions that dominate them. Our results show that both the CO and ONe nova models robustly produce characteristic CNO isotopes. More pronounced abundance differences emerge for elements with A ≥ 20. Sulfur is the most robust observational discriminator between the CO and ONe nova models, with a model-to-model difference of a factor of ≈30 and minimal sensitivity to reaction rate uncertainties. Neon, silicon, and phosphorus exhibit even larger abundance differences (factors of ≈150–250), providing strong diagnostic potential. While their predicted yields are subject to larger uncertainties, these remain smaller than the model-to-model differences, allowing these elements to serve as useful, though less precise, tracers of white-dwarf composition. Chlorine, argon, and potassium also differ between models, but the 1σ-abundance ranges for the CO and ONe models overlap, reducing their present usefulness as composition tracers. We find that only nine nuclear reactions dominate the abundance uncertainties of the most diagnostically important isotopes, and their influence is largely independent of the underlying white-dwarf composition. These results provide guidance for future experimental efforts and for interpreting ejecta compositions in the next eruption of T CrB.

Chemical Abundances↗
DOE OSTI2025

Measurement and Modeling of Electron Temperature in Laboratory Photoionized Plasmas Relevant to Astrophysics

The electron temperature of photoionized plasmas characterizes the thermalization of photoelectrons, impacts the charge-state distribution, emissivity, and opacity through atomic recombination processes, and is needed to perform detailed comparisons with theory predictions. We discuss temperature measurements in laboratory photoionized plasmas and a comparison with model calculations done with several theory approximations and codes. These include a radiation-hydrodynamics simulation and two nonequilibrium heating and ionization models that tracked the evolution of the internal energy of the electrons. Furthermore, for the same physics model and X-ray flux time history, calculations were performed assuming steady-state or time-dependent conditions. The time history of steady-state results correlates with that of the X-ray flux, while that of the time-dependent cases does not, and it is qualitatively and quantitatively different from the steady-state case. Steady-state results significantly overestimated temperature measurements, while time-dependent results produced better approximations, which suggests the importance of transient effects in the experiment and also the need for time-resolved measurements.

Laboratory astrophysics↗
DOE OSTI2026

Dwarf Galaxy Number Counts within 25 Mpc: Predictions from Local Group Analogs in TNG50

The modern generation of wide-field galaxy surveys, such as LSST, Euclid, and Roman, will enable studies of dwarf galaxies (10 6 ≤ M * /M ⊙ ≤ 10 9 ) beyond the Local Group (LG) in unprecedented detail. Improved theoretical understanding of this population is necessary to guide these observations, since predictions in this regime are generally limited to specific environments like the LG. We present predictions for the population of dwarf galaxies from the TNG50 run of the IllustrisTNG suite of cosmological hydrodynamical simulations, focusing on the environments within 1 < D/Mpc < 25 of LG analogs at z = 0. In the simulated sample, there are ∼1000 and ∼12,000 dwarf galaxies within 10 and 25 Mpc, respectively. We compare our results with the 50 Mpc Galaxy Catalog and estimate that current observations are highly incomplete at low masses: for 10 6 ≤ M * /M ⊙ ≤ 10 7 (−13 ≲ M r ≲ −10), we find completeness fractions of ∼23% within 10 Mpc and ∼4% within 25 Mpc. The simulated galaxies below the completeness limits of the observations exist in a range of environments, with notable populations of field dwarfs at all distances and satellites around centrals with masses 10 8 ≲ M * /M ⊙ ≲ 10 11 within 10–25 Mpc. We find that there are ∼8 times more quiescent dwarf galaxies in the TNG50 sample than are currently cataloged. Our results suggest that upcoming observations should uncover a substantial population of dwarf galaxies, and that ≳15% of these will be red, currently quenched galaxies in the field.

Shread, Evangela E. [California Institute of Techn↗
DOE OSTI2026

ODIN: Characterizing the Three-dimensional Structure of Two Protocluster Complexes at z = 3.1

We present a detailed study of the 3D morphology of two extended associations of multiple protoclusters at z = 3.1. These protocluster "complexes," designated COSMOS-z3.1-A and COSMOS-z3.1-C, are the most prominent overdensities of z = 3.1 Lyα emitters (LAEs) identified in the COSMOS field by the One-hundred-deg$^{2}$ DECam Imaging in Narrowbands survey. These protocluster complexes have been followed up with extensive spectroscopy from Keck, Gemini, and DESI. Using a probabilistic method that combines photometrically selected and spectroscopically confirmed LAEs, we reconstruct the 3D structure of these complexes on scales of ≈50 cMpc. We validate our reconstruction method using the IllustrisTNG300-1 cosmological hydrodynamical simulation and show that it consistently outperforms approaches relying solely on spectroscopic data. The resulting 3D maps reveal that both complexes are irregular and elongated along a single axis, emphasizing the impact of sightline on our perception of structure morphology. The complexes consist of multiple density peaks, 10 in COSMOS-z3.1-A and 4 in COSMOS-z3.1-C. The former is confirmed to be a proto-supercluster, similar to Hyperion at z = 2.4 but observed at an even earlier epoch. Multiple "tails" connected to the cores of the density peaks are seen, likely representing cosmic filaments feeding into these extremely overdense regions. The 3D reconstructions further provide strong evidence that Lyα blobs preferentially reside in the outskirts of the highest density regions. Descendant mass estimates of the density peaks suggest that COSMOS-z3.1-A and COSMOS-z3.1-C will evolve to become ultramassive structures by z = 0, with total masses log ( M / M ,⊙ ,) ≳ 15.3 , exceeding that of Coma.

Ramakrishnan, Vandana [Purdue U., West Lafayette] ↗
DOE OSTI2024

Emergence of Microphysical Bulk Viscosity in Binary Neutron Star Postmerger Dynamics

Abstract In nuclear matter in isolated neutron stars, the flavor content (e.g., proton fraction) is subject to weak interactions, establishing flavor ( β -)equilibrium. However, there can be deviations from this equilibrium during the merger of two neutron stars. We study the resulting out-of-equilibrium dynamics during the collision by incorporating direct and modified Urca processes (in the neutrino-transparent regime) into general-relativistic hydrodynamics simulations with a simplified neutrino transport scheme. We demonstrate how weak-interaction-driven bulk viscosity in postmerger simulations can emerge and assess the bulk viscous dynamics of the resulting flow. We further place limits on the impact of the postmerger gravitational-wave strain. Our results show that weak-interaction-driven bulk viscosity can potentially lead to a phase shift of the postmerger gravitational-wave spectrum, although the effect is currently on the same level as the numerical errors of our simulation.

Astronomy & Astrophysics↗
DOE OSTI2025

Measuring the Mean Free Path of H i Ionizing Photons at 3.2 ≤ z ≤ 4.6 with DESI Y1 Quasars

The mean free path of ionizing photons in the intergalactic medium (IGM; λ $^{912}_{mpf}$ ) is a crucial quantity in modeling the ionization state of the IGM and the extragalactic ultraviolet background, and it is widely used in hydrodynamical simulations of galaxies and reionization. We construct the largest quasar spectrum data set to date—12,595 signal-to-noise ratio > 3 spectra—using the Y1 observations of the Dark Energy Spectroscopic Instrument, to make the most precise model-independent measurement of the mean free path at 3.2 ≤ z ≤ 4.6. By stacking the spectra in 17 redshift bins and modeling the Lyman-continuum profile, we get a redshift evolution λ $^{912}_{mpf}$ ∝ ( 1 + z ) − 4.27 at 2 ≤ z ≤ 5, which is much shallower than the previous estimate, λ $^{912}_{mpf}$ ∝ ( 1 + z ) − 5.4 . We then explore the sources of systematic bias, including the choice of the intrinsic quasar continuum, the consideration of Lyman-series opacity and Lyman-limit opacity evolution, and the definition of λ $^{912}_{mpf}$ . Combining our results with estimates of λ $^{912}_{mpf}$ at higher redshifts, we conclude at high confidence that the evolution in λ $^{912}_{mpf}$ steepens at z ≈ 5. We interpret this inflection as the transition from the end of H i reionization to a fully ionized plasma that characterizes the IGM of the past ∼10 billion yr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Constraints on Nonthermal Pressure at Galaxy Cluster Outskirts from a Joint SPT and XMM-Newton Analysis

We present joint South Pole Telescope and XMM-Newton observations of eight massive galaxy clusters (0.8–2 × 10$^{15}$ M$_{⊙}$) spanning a redshift range of 0.16–0.35. Employing a novel Sunyaev–Zel’dovich + X-ray fitting technique, we effectively constrain the thermodynamic properties of these clusters out to the virial radius. The resulting best-fit electron density, deprojected temperature, and deprojected pressure profiles are in good agreement with previous observations of massive clusters. For the majority of the cluster sample (five out of eight clusters), the entropy profiles exhibit a self-similar behavior near the virial radius. We further derive hydrostatic mass, gas mass, and gas fraction profiles for all clusters up to the virial radius. Comparing the enclosed gas fraction profiles with the universal gas fraction profile, we obtain nonthermal pressure fraction profiles for our cluster sample at >0.5R$_{500}$, demonstrating a steeper increase between R$_{500}$ and R$_{200}$ that is consistent with the hydrodynamical simulations. Our analysis yields nonthermal pressure fraction ranges of 8%–28% (median: 15% ± 11%) at R$_{500}$ and 21%–35% (median: 27% ± 12%) at R$_{200}$. Notably, weak-lensing mass measurements are available for only four clusters in our sample, and our recovered total cluster masses, after accounting for nonthermal pressure, are consistent with these measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Dark matter decay signals in cosmic filaments

Cosmic filaments form the backbone of the cosmic web, yet their properties and evolution remain uncertain. Using the EAGLE hydrodynamical simulations, we investigate the dark matter density profiles in filaments and their implications for dark matter decay signals. We show that GeV-scale dark matter particles decaying into electron-positron pairs can produce detectable radio synchrotron emission. By leveraging stacked filament radio data, we place stringent constraints on the dark matter decay lifetime, improving existing limits by up to two orders of magnitude for strong filamentary magnetic fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Constraints on cosmology and baryonic feedback with joint analysis of Dark Energy Survey Year 3 lensing data and ACT DR6 thermal Sunyaev-Zel'dovich effect observations

We present a joint analysis of weak gravitational lensing (shear) data obtained from the first three years of observations by the Dark Energy Survey and thermal Sunyaev-Zel'dovich (tSZ) effect measurements from a combination of Atacama Cosmology Telescope (ACT) and Planck data. A combined analysis of shear (which traces the projected mass) with the tSZ effect (which traces the projected gas pressure) can jointly probe both the distribution of matter and the thermodynamic state of the gas, accounting for the correlated effects of baryonic feedback on both observables. We detect the shear$~\times~$tSZ cross-correlation at a 21$\sigma$ significance, the highest to date, after minimizing the bias from cosmic infrared background leakage in the tSZ map. By jointly modeling the small-scale shear auto-correlation and the shear$~\times~$tSZ cross-correlation, we obtain $S_8 = 0.811^{+0.015}_{-0.012}$ and $\Omega_{\rm m} = 0.263^{+0.023}_{-0.030}$, results consistent with primary CMB analyses from Planck and P-ACT. We find evidence for reduced thermal gas pressure in dark matter halos with masses $M < 10^{14} \, M_{\odot}/h$, supporting predictions of enhanced feedback from active galactic nuclei on gas thermodynamics. A comparison of the inferred matter power suppression reveals a $2-4\sigma$ tension with hydrodynamical simulations that implement mild baryonic feedback, as our constraints prefer a stronger suppression. Finally, we investigate biases from cosmic infrared background leakage in the tSZ-shear cross-correlation measurements, employing mitigation techniques to ensure a robust inference. Our code is publicly available on GitHub.

Pandey, S. [Johns Hopkins U.; Columbia U.] (ORCID:↗
DOE OSTI2026

Dynamical Dark Energy Imprints in the Lyman-Alpha Forest

The nature of dark energy (DE) remains elusive, even though it constitutes the dominant energy-density component of the Universe and drives the late-time acceleration of cosmic expansion. By combining measurements of the expansion history from baryon acoustic oscillations, supernova surveys, and cosmic microwave background data, the Dark Energy Spectroscopic Instrument (DESI) Collaboration has inferred that the DE equation of state may evolve over time. The profound implications of a time-variable, ``dynamical" DE (DDE) that departs from a cosmological constant motivate the need for independent observational tests. In this work, we use cosmological hydrodynamical simulations of structure formation to investigate how DDE affects the properties of the Lyman-Alpha ``forest'' of absorption features produced by neutral hydrogen in the cosmic web. We find that DDE models consistent with the DESI constraints induce a spectral tilt in the forest transmitted flux power spectrum, imprinting a scale- and redshift-dependent signature relative to standard Lambda-CDM cosmologies. These models also yield higher intergalactic medium temperatures and reduced Lyman-Alpha opacity compared to Lambda-CDM. We discuss the observational implications of these trends as potential avenues for independent confirmation of DDE.

Garza, Diego [UC, Santa Cruz, Inst. Part. Phys.] (↗
DOE OSTI2026

The Challenge of Observing Patchy Reionization with CMB Optical-Depth Fluctuations

Spatial fluctuations in the Thomson optical depth encode information about the inhomogeneous nature of cosmic reionization. We compute the optical-depth angular power spectrum, $C_\ell^{ττ}$, using past lightcones constructed from five Cosmic Reionization on Computers (CROC) radiation-hydrodynamical simulations. By decomposing the electron-density field into patchy and density components, we quantify the separate contributions of ionization-fraction and baryon-density fluctuations to the optical-depth anisotropy. Because the simulations end at $z\approx5$, we supplement the reionization-era signal with an analytic estimate of the fully ionized low-redshift contribution. We find that baryon-density fluctuations dominate the high-redshift signal over most angular scales, while the accumulated low-redshift contribution exceeds the high-redshift signal across the full multipole range considered. Our results demonstrate that a significant fraction of the optical-depth power is not uniquely associated with reionization morphology, implying that future interpretations of $C_\ell^{ττ}$ must account for the density contribution in addition to patchy ionization.

Takoudes, Nick [Chicago U., Astron. Astrophys. Ctr↗
DOE OSTI2025

Simulations of Radiation Hydrodynamics in Strongly Coupled Plasmas (Final Report)

Radiation propagates throughout the Universe and is often the only information we have from distant astronomical objects. Additionally, radiation plays a key role in systems ranging from the interior of stars to the establishment of shocks at the edges of forming galaxies to neutron star mergers. Here radiative processes, absorption, emission, and scattering, are fundamental to transport of momentum and energy, as well as, the overall evolution of these and other astrophysical systems. In some cases, radiation-dominant systems are also sufficiently dense and ionized, such that, the ions are strongly coupled (ie electrostatic energy >> thermal energy or Γ >> 1), which will affect radiative processes and the transport of radiation. During this project, we developed a computational ray-tracing algorithm to study radiation transport through a simulated neutron star capsule implosion under conditions relevant to Omega-60 laser experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Spherical and sessile droplet dynamics by fluctuating hydrodynamics

We simulate the mesoscopic dynamics of droplets formed by phase-separated fluids at nanometer scales where thermal fluctuations are significant. Both spherical droplets fully immersed in a second fluid and sessile droplets which are also in contact with a solid surface are studied. Our model combines a Cahn–Hilliard formulation with incompressible fluctuating hydrodynamics; for sessile droplets, the fluid–solid contact angle is specified as a boundary condition. Deterministic simulations with an applied body force are used to measure the droplets' mobility from which a diffusion coefficient is obtained using the Einstein relation. Stochastic simulations are independently used to obtain a diffusion coefficient from a linear fit of the variance of a droplet's position with time. In some scenarios, these two measurements give the same value but not in the case of a spherical droplet initialized near a slip wall or in the case of sessile droplets with large contact angles (≥90°) on both slip and no-slip surfaces.

Bell, John B↗