论文标题
谐波陷阱中活性布朗粒子的固定状态
Stationary states of an active Brownian particle in a harmonic trap
论文作者
论文摘要
我们通过数学计算和数值模拟研究了在谐波陷阱中在谐波陷阱中抑制过度抑制活性布朗粒子（ABP）的固定状态。除了翻译扩散外，ABP自我具有一定速度，其幅度是恒定的，但其方向可能会播放Brownian旋转。在翻译扩散可以忽略不计的极限中，粒子位置的固定分布显示在两个不同形状之间的过渡，一个具有最大的形状，另一个则在中心位于最小密度，随着陷阱刚度的增加。我们表明，这种非fokker-planck方程捕获了这种非直觉行为，在最小的假设下，这两个不同的形状之间的``相位''之间的连续``相位过渡''。随着翻译扩散系数的增加。随着平移扩散系数的增加，这两个分布都融合到了平衡的概率，并呈现了boltzmann的分析。自我推测速度在此限制中从单峰到双峰形式进行过渡。
We study the stationary states of an over-damped active Brownian particle (ABP) in a harmonic trap in two dimensions, via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with a certain velocity, whose magnitude is constant, but its direction is subject to Brownian rotation. In the limit where translational diffusion is negligible, the stationary distribution of the particle's position shows a transition between two different shapes, one with maximum and the other with minimum density at the centre, as the trap stiffness is increased. We show that this non-intuitive behaviour is captured by the relevant Fokker-Planck equation, which, under minimal assumptions, predicts a continuous ``phase transition" between the two different shapes. As the translational diffusion coefficient is increased, both these distributions converge into the equilibrium, Boltzmann form. Our simulations support the analytical predictions, and also show that the probability distribution of the orientation angle of the self-propulsion velocity undergoes a transition from unimodal to bimodal forms in this limit. We also extend our simulations to a three dimensional trap, and find similar behaviour.
