论文标题
布朗尼硬针的宏观模型的推导
Derivation of a macroscopic model for Brownian hard needles
论文作者
论文摘要
我们研究各向异性空间相互作用在坚硬的棕色针体系中的作用。尽管没有音量，但不重叠的针头排除了影响系统宏观演化的配置空间中的音量。从随机粒子系统开始，我们使用匹配的渐近扩展和形成映射的方法，以系统地得出非线性非局部偏微分方程，以在位置和方向上的种群密度进化。我们考虑了高旋转扩散的状态，从而导致空间密度的方程式，该方程使我们能够将有效排除的硬针系统的有效体积与硬球系统的有效体积进行比较。我们进一步考虑在空间均匀的溶液上，并在密度增加时找到了对列过渡的各向同性，与Onsager的理论一致。
We study the role of anisotropic steric interactions in a system of hard Brownian needles. Despite having no volume, non-overlapping needles exclude a volume in configuration space that influences the macroscopic evolution of the system. Starting from the stochastic particle system, we use the method of matched asymptotic expansions and conformal mapping to systematically derive a nonlinear nonlocal partial differential equation for the evolution of the population density in position and orientation. We consider the regime of high rotational diffusion, resulting in an equation for the spatial density that allows us to compare the effective excluded volume of a hard-needles system with that of a hard-spheres system. We further consider spatially homogeneous solutions and find an isotropic to nematic transition as density increases, consistent with Onsager's theory.
