论文标题
异质系统中化学反应网络的空间测量值模型
A spatial measure-valued model for chemical reaction networks in heterogeneous systems
论文作者
论文摘要
我们提出了一个新颖的测量值过程，该过程模拟了化学反应网络在空间异质系统中的行为。它模拟了不同分子物种之间的反应动力学和太空中分子的连续运动。空间位置的反应速率与当地存在的不同物种的质量成正比，并且与位置的特定化学速率可能是局部或全球物种质量的函数。我们获得该过程的渐近极限，根据不同分子类型的丰富度进行适当的重新缩放。特别是，当某些物种在缩放极限中的质量是离散的，而其他物种的质量是连续的，我们会获得一种新型的空间随机演化过程。在某些情况下，可以显示此过程，以对应于测量值的分段确定性马尔可夫过程，其中该过程的离散质量随机地演变出来，并且连续质量以确定性的方式在离散部分的连续跳跃时间之间发展。
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in space. Reactions rates at a spatial location are proportional to the mass of different species present locally and to a location specific chemical rate, which may be a function of the local or global species mass as well. We obtain asymptotic limits for the process, with appropriate rescaling depending on the abundance of different molecular types. In particular, when the mass of some species in the scaling limit is discrete while the mass of the others is continuous, we obtain a new type of spatial random evolution process. This process can be shown, in some situations, to correspond to a measure-valued piecewise deterministic Markov process in which the discrete mass of the process evolves stochastically, and the continuous mass evolves in a deterministic way between consecutive jump times of the discrete part.
