标题： 显式渐近解的$ν_e + e^-$中微子网络在核心坍缩超新星中的大型偏微分方程组 显示英文标题

标题： Explicit Asymptotic Solutions of $ν_e + e^-$ Neutrino Networks for Large Sets of Partial Differential Equations in Core-Collapse Supernovae

摘要： 在物理学中，准确模拟核心坍缩超新星（CCSN）和中子星合并等大尺度现象计算上具有挑战性，需要求解大量偏微分方程和常微分方程。 科学界广泛使用的传统方法主要是隐式方法，这些方法通常是近似方法，通常需要大幅简化，并且计算效率低下。 本论文介绍了名为“快速显式中微子网络”或“FENN”的新软件套件，该套件引入了一组代数稳定的显式方法，称为显式渐近方法，用于建模中微子电子散射（NES），提出了一种结合传统方法稳定性与增强计算效率的新方法。 初步结果表明，FENN可以在提高计算速度的同时为中微子网络提供精确的解决方案。 本论文进一步涵盖了超出标准能量分组限制的缩放网络的新结果，以及中微子相互作用的动力学，例如各种中微子类型——电子中微子（$\nu_e$）、电子反中微子（$\bar{\nu}_e$）以及缪子/陶中微子（$\nu_{\mu,\tau}$）及其反粒子（$\bar{\nu}_{\mu,\tau}$）——在电子上的散射。 显示英文摘要

摘要： In physics, accurately modeling large-scale phenomena such as core-collapse supernovae, (CCSN), and neutron star mergers are computationally challenging and require solving large sets of partial and ordinary differential equations. Traditional methods used widely in the scientific community are predominantly implicit, which are approximations that often require drastic simplifications and can be computationally inefficient. This thesis presents results on a new software suite titled "Fast Explicit Neutrino Networks" or "FENN", that introduces a suite of algebraically stabilized explicit methods known as explicit asymptotic for modeling Neutrino Electron Scattering, (NES), presenting a novel approach that combines the stability of traditional methods with enhanced computational efficiency. Initial results show that FENN can deliver accurate solutions for neutrino networks at improved computational speeds. This thesis further covers new results for scaled networks beyond the constraints of standard energy groupings, as well as the dynamics of neutrino interactions such as the scattering of various neutrino flavors -- electron neutrinos ($\nu_e$), electron anti-neutrinos ($\bar{\nu}_e$), and muon/tau neutrinos ($\nu_{\mu,\tau}$) as well as their anti-particles ($\bar{\nu}_{\mu,\tau}$) -- off electrons.