对流和耗散多流体系统的通量守恒形式及其对牛顿超流中子星的应用
A Flux-Conservative Formalism for Convective and Dissipative Multi-Fluid Systems, with Application to Newtonian Superfluid Neutron Stars
摘要：
我们开发了一个牛顿多流体系统的通量守恒形式，包括耗散和夹带（即允许一种流体的动量是所有流体速度的线性组合）。最大限度地利用质量、能量、线动量和角动量守恒来确定运动方程。也广泛使用的是从对流变分作用原理收集的见解，关键是每个速度和它的正则共轭动量之间的区别。通过Onsager开创的方法，耗散被纳入“热力学力”的二阶。调查的一个直接目标是更好地了解的数量和形式，独立的耗散项所需的一致的一组运动方程在多流体的背景下。一个重要的，但似乎无害的细节是，必须小心地隔离“力”，可以写为总梯度，否则在将净内力与净外力联系起来时可能会出错。我们的长期目标是提供一种形式主义，可用于模拟动态多流体系统的扰动和通过完全非线性的三维数值演化。为了阐明形式主义，我们考虑了热传导的超流中子星的标准模型，它被认为是由超流中子，超导质子和高度简并的超相对论气体的正常流体电子主导的。我们确定，在这种情况下，原则上，在最后一组方程中有19个耗散系数。
英文摘要：
We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of mass, energy, and linear and angular momentum conservation to specify the equations of motion. Also used extensively are insights gleaned from a convective variational action principle, key being the distinction between each velocity and its canonically conjugate momentum. Dissipation is incorporated to second order in the ``thermodynamic forces'' via the approach pioneered by Onsager. An immediate goal of the investigation is to understand better the number, and form, of independent dissipation terms required for a consistent set of equations of motion in the multi-fluid context. A significant, but seemingly innocuous detail, is that one must be careful to isolate ``forces'' that can be written as total gradients, otherwise errors can be made in relating the net internal force to the net externally applied force. Our long-range aim is to provide a formalism that can be used to model dynamical multi-fluid systems both perturbatively and via fully nonlinear 3D numerical evolutions. To elucidate the formalism we consider the standard model for a heat-conducting, superfluid neutron star, which is believed to be dominated by superfluid neutrons, superconducting protons, and a highly degenerate, ultra-relativistic gas of normal fluid electrons. We determine that in this case there are, in principle, 19 dissipation coefficients in the final set of equations.
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