论文标题
将活动粒子的固定分布作为三阶微分方程的问题
Positing the problem of stationary distributions of active particles as third-order differential equation
论文作者
论文摘要
在这项工作中，我们获得了三阶线性微分方程，用于在谐波陷阱中以二维的固定分布进行固定分布。方程表示条件$ j = 0 $，其中$ j $是通量，并在限制条件下使用不同的已知结果从推理中获得。由于被动布朗颗粒的类似方程是一阶，因此第二阶和三阶项必须是主动运动的特征。除了将问题提出为三阶方程外，我们还以两个分布的卷积形式获得解决方案，由于热波动而引起的高斯分布以及在零温度下的主动运动引起的β分布。解决方案的卷积形式表明两个随机过程是独立的，总分布是这两个过程的总和。
In this work, we obtain third order linear differential equation for stationary distributions of run-and-tumble particles in two-dimensions in a harmonic trap. The equation represents the condition $j = 0$ where $j$ is a flux and is obtained from inference, using different known results in the limiting conditions. Since the analogous equation for passive Brownian particles is first order, a second and third order term must be a feature of active motion. In addition to formulating the problem as third order equation, we obtain solutions in the form of convolution of two distributions, the Gaussian distribution due to thermal fluctuations, and the beta distribution due to active motion at zero temperature. The convolution form of the solution indicates that the two random processes are independent and the total distribution is the sum of those two processes.
