Luke F. Roberts

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than 100× and speedups exceeding 2×. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as 7. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S _N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable S _N calculations and supplying a promising avenue to mitigate ray effects.

Recent studies of the neutrino-driven wind from proto-neutron stars have indicated that the wind is likely proton rich for much of its lifetime, and the high flux of neutrinos can induce νp-process nucleosynthesis allowing for the formation of heavy elements. It has also been shown that gravito-acoustic waves, generated by convection within the proto-neutron star, can significantly alter the dynamics and nucleosynthesis in the wind. Therefore, we present a study of the effects of convection-driven waves on the nucleosynthesis in proton-rich neutrino-driven winds, focusing on the νp-process. We find that wave effects can strongly impact νp-process nucleosynthesis even at wave luminosities a factor of 10−5 smaller than the total neutrino luminosity. The momentum flux of the waves accelerates the wind, reducing the net neutrino heating and the persistent neutron abundance created by p($\bar{\nu }_\mathrm{ e},e^+$), which impedes νp-process nucleosynthesis. However, this effect is generally counteracted by the effects of waves on seed nucleus formation, as the acceleration of the wind and the heating that occurs as these waves shock both favour a more α-rich environment with very little heavy seed nucleus formation. Overall, higher wave luminosities correlate (albeit non-monotonically) with heavier element νp-processing, up to A ≈ 200 in some cases. At very high wave luminosities (≳10−3Lν), early shock heating by the waves disrupts α recombination, and drives a suppressed, fast-outflow r-process proceeding up to A ≈ 200. This occurs despite an assumed neutrino spectrum that predicts a proton-rich wind with equilibrium Ye = 0.6.

The neutrino-driven wind from proto-neutron stars is a proposed site for r-process nucleosynthesis, although most previous work has found that a wind heated only by neutrinos cannot produce the third r-process peak. However, several groups have noted that introducing a secondary heating source within the wind can change the hydrodynamic conditions sufficiently for a strong r-process to proceed. One possible secondary heating source is gravito-acoustic waves, generated by convection inside the proto-neutron star. As these waves propagate into the wind, they can both accelerate the wind and shock and deposit energy into the wind. Additionally, the acceleration of the wind by these waves can reduce the total number of neutrino captures and thereby reduce the final electron fraction of the wind. In neutron rich conditions, all of these effects can make conditions more favorable for r-process nucleosynthesis. Here, we present a systematic investigation of the impact of these convection-generated gravito-acousticwaves within the wind on potential nucleosynthesis.We find thatwave effects in the wind can generate conditions favorable for a strong r-process, even when the energy flux in the waves is a factor of 10⁻⁴ smaller than the total neutrino energy flux and the wind is marginally neutron-rich. Nevertheless, this depends strongly on the radius at which the waves become non-linear and form shocks. We also find that both entropy production after shock formation and the acceleration of the wind due to stresses produced by the waves prior to shock formation impact the structure and nucleosynthesis of these winds.

Both the core collapse of rotating massive stars, and the coalescence of neutron star (NS) binaries result in the formation of a hot, differentially rotating NS remnant. The timescales over which differential rotation is removed by internal angular-momentum transport processes (viscosity) have key implications for the remnant’s long-term stability and the NS equation of state (EOS). Guided by a nonrotating model of a cooling proto-NS, we estimate the dominant sources of viscosity using an externally imposed angular-velocity profile Ω(r). Although the magneto-rotational instability provides the dominant source of effective viscosity at large radii, convection and/or the Tayler–Spruit dynamo dominate in the core of merger remnants where dΩ/dr ≥ 0. Furthermore, the viscous timescale in the remnant core is sufficiently short that solid-body rotation will be enforced faster than matter is accreted from rotationally supported outer layers. Guided by these results, we develop a toy model for how the merger remnant core grows in mass and angular momentum due to accretion. We find that merger remnants with sufficiently massive and slowly rotating initial cores may collapse to black holes via envelope accretion, even when the total remnant mass is less than the usually considered threshold ≈1.2 M _TOV for forming a stable solid-body rotating NS remnant (where M _TOV is the maximum nonrotating NS mass supported by the EOS). This qualitatively new picture of the post-merger remnant evolution and stability criterion has important implications for the expected electromagnetic counterparts from binary NS mergers and for multimessenger constraints on the NS EOS.

In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the gradient of the high order moment using neural networks. This new approach is consistent with the exact closure we derive for the free streaming limit and also provides a natural output normalization. A variety of benchmark tests, including the variable scattering problem, the Gaussian source problem with both periodic and reflecting boundaries, and the two-material problem, show both good accuracy and generalizability of our machine learning closure model.