论文标题
具有内部状态的动力传输方程的数值方案 *
Numerical scheme for kinetic transport equation with internal state *
论文作者
论文摘要
我们研究了具有内部状态的两流动力学系统的数值离散化，该系统已被引入以通过趋化性模拟细胞的运动。该内部状态模拟了细胞内甲基化水平。它在数学模型中添加了一个变量，这使得数值模拟更具挑战性。此外，已经表明，从该系统计算出的宏观或介观量在扩散缩放量表或在超质量缩放下的趋化度动力学系统中收敛到Keller-Segel系统。然后，我们注意提出相对于缩放参数统一准确的数字方案。我们表明，这些方案会融合到一些与宏观或动力学系统一致的限制方案。通过一些数值模拟和与蒙特卡洛模拟的比较来说明这项研究。
We investigate the numerical discretization of a two-stream kinetic system with an internal state, such system has been introduced to model the motion of cells by chemotaxis. This internal state models the intracellular methylation level. It adds a variable in the mathematical model, which makes it more challenging to simulate numerically. Moreover, it has been shown that the macroscopic or mesoscopic quantities computed from this system converge to the Keller-Segel system at diffusive scaling or to the velocity-jump kinetic system for chemotaxis at hyperbolic scaling. Then we pay attention to propose numerical schemes uniformly accurate with respect to the scaling parameter. We show that these schemes converge to some limiting schemes which are consistent with the limiting macroscopic or kinetic system. This study is illustrated with some numerical simulations and comparisons with Monte Carlo simulations.
