Predictive local field theory for interacting active Brownian spheres in two spatial dimensions
Predictive local field theory for interacting active Brownian spheres in two spatial dimensions
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DOI：
10.1088/1361-648x/ab5e0e
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发表时间：
2020-05-13
影响因子：
2.7
通讯作者：
Wittkowski, Raphael
中科院分区：
文献类型：
--
作者：
Bickmann, Jens;Wittkowski, Raphael
我们提出了一个预测的局域场理论的非平衡动力学的相互作用的活性布朗粒子的球形在两个空间维度。该理论是通过严格的粗粒化从描述单个粒子轨迹的朗之万方程开始推导的。为了理论的高精度和通用性，它包括构型序参数和导数直到无限阶。此外，我们讨论了可能的近似的理论，并提出简化模型，更容易应用。我们表明，我们的理论包含流行的模型，如主动模式B+作为特殊情况下，它提供了明确的表达式发生在这些和其他的，往往是现象学的，模型的系数。作为进一步的结果，该理论产生的密度依赖的平均游泳速度的颗粒的解析表达式。为了证明新理论的应用，我们分析了一个简单的简化模型的最低非平凡阶的衍生物，这是能够预测发病的运动诱导相分离的粒子。通过线性稳定性分析，得到了运动诱导相分离所对应的旋节线的解析表达式。这个表达式的情况下，粒子相互作用排斥的Weeks-Chandler-Andersen潜在的评估。与这些粒子相关的旋节线的分析预测被发现是在非常好的协议与布朗动力学模拟的结果是基于相同的朗之万方程作为我们的理论。此外，我们的分析结果所预测的临界点与最近的计算结果从文献中吻合得很好。
We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For high accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B+ as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Andersen potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature.