论文标题
相对论恒星中随机扰动和分析的形式主义
Formalism for stochastic perturbations and analysis in relativistic stars
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Perturbed Einstein's equations with a linear response relation and a stochastic source, applicable to a relativistic star model are worked out . These perturbations which are stochastic in nature, are of significance for building a non-equilibrium statistical theory in connections with relativistic astrophysics. A fluctuation dissipation relation for a spherically symmetric star in its simplest form is obtained. The FD relation shows how the random velocity fluctuations in the background of the unperturbed star can dissipate into Lagrangian displacement of fluid trajectories of the dense matter. Interestingly in a simple way, a constant (in time) coefficient of dissipation is obtained without a delta correlated noise. This formalism is also extended for perturbed TOV equations which have a stochastic contribution, and show up in terms of the effective or root mean square pressure perturbations. Such contributions can shed light on new ways of analysing the equation of state for dense matter. One may obtain contributions of first and second order in the equation of state using this stochastic approach.
