流体-粒子相互作用与涨落-耗散关系 I——一般线性理论与基本涨落模式
Fluid-particle interactions and fluctuation-dissipation relations I -- General linear theory and basic fluctuational patterns
AI总结：
本文提出一种统一理论，将记忆核表示为指数衰减模式的线性叠加，通过Fokker-Planck方程矩分析推导一般流体中粒子流体力学在受限几何下的涨落-耗散关系，并推广至含流体惯性效应的情形。
摘要：
本文通过涨落模式的概念，为一般流体中粒子流体力学提供了一种统一且完备的涨落-耗散关系解，在线性流体力学区域内考虑了流体动力学流体-粒子相互作用（包括描述耗散和流体惯性效应时的任意记忆核）。这一目标是通过将记忆核表示为指数衰减模式的线性叠加来实现的。给定与内部自由度相互作用的结构，并假设热力可表示为模态贡献的叠加，涨落-耗散关系便直接从相应Fokker-Planck方程的矩分析中得出，同时施加平衡时所有内部自由度与粒子速度不相关的条件。此外，所得运动方程的泛函结构对应于内部自由度之间完全解耦的原理。该理论通过推广先前包含流体惯性效应的结果，被扩展到受限几何的情形。
英文摘要：
The article provides a unitary and complete solution to the fluctuation-dissipation relations for particle hydromechanics in a generic fluid, accounting for the hydrodynamic fluid-particle interactions (including arbitrary memory kernels in the description of dissipative and fluid inertial effects) in linear hydrodynamic regimes, via the concepts of fluctuational patterns. This is achieved by expressing the memory kernels as a linear superposition of exponentially decaying modes. Given the structure of the interaction with the internal degrees of freedom, and assuming the representation of the thermal force as a superposition of modal contributions, the fluctuation-dissipation relation follows simply from the moment analysis of the corresponding Fokker-Planck equation, imposing the condition that at equilibrium all the internal degrees of freedom are uncorrelated with particle velocity. Moreover, the functional structure of the resulting equation of motion corresponds to the principle of complete decoupling amongst the internal degrees of freedom. The theory is extended to the case of confined geometries, by generalizing previous results including the effect of fluid inertia.
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