论文标题
在自我复制的持续随机步行中，有多个内部状态的行进前线
Traveling fronts in self-replicating persistent random walks with multiple internal states
论文作者
论文摘要
自我激活与运输机制结合起来导致行进波，描述了聚合反应，森林火灾，肿瘤生长甚至流行病的传播。扩散是一种简单且常用的粒子传输模型。但是，许多物理和生物系统通过在多个弹道运动状态之间切换的持续随机步行来更好地描述。到目前为止，仅在特殊的简化案例中分析了持久的随机步行模型中的旅行前线。在这里，我们在此类系统中制定了反应传输过程的一般模型，并展示了如何计算任意状态数量的扩展速度。对于两态模型，我们获得了速度的闭合形式表达式，并报告其如何受到不同传输和复制参数的影响。我们还表明，非零的死亡率导致从静止向传播的不连续过渡。我们将结果与最近观察到微管紫外线中不连续的传播发作的结果进行了比较，并评论了基本机制的普遍性质。
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle transport. Many physical and biological systems are, however, better described by persistent random walks that switch between multiple states of ballistic motion. So far, traveling fronts in persistent random walk models have only been analyzed in special, simplified cases. Here, we formulate the general model of reaction-transport processes in such systems and show how to compute the expansion velocity for arbitrary number of states. For the two-state model, we obtain a closed-form expression for the velocity and report how it is affected by different transport and replication parameters. We also show that nonzero death rates result in a discontinuous transition from quiescence to propagation. We compare our results to a recent observation of a discontinuous onset of propagation in microtubule asters and comment on the universal nature of the underlying mechanism.
