Stochastic dynamics describes processes in complex systems having the probabilistic nature. They can involve very different dynamical systems and occur on very different temporal and spatial scale. This paper discusses the concept of stochastic dynamics and its implementation in the popular program MBN Explorer. Stochastic dynamics in MBN Explorer relies on the Monte Carlo approach and permits simulations of physical, chemical, and biological processes. The paper presents the basic theoretical concepts underlying stochastic dynamics implementation and provides several examples highlighting its applicability to different systems, such as diffusing proteins seeking an anchor point on a cell membrane, deposition of nanoparticles on a surface leading to structures with fractal morphologies, and oscillations of compounds in an autocatalytic reaction. The chosen examples illustrate the diversity of applications that can be modeled by means of stochastic dynamics with MBN Explorer.

中文翻译：

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使用 MBN Explorer 对随机动力学过程进行多尺度建模

随机动力学描述了具有概率性质的复杂系统中的过程。它们可能涉及非常不同的动力系统，并且发生在非常不同的时间和空间尺度上。本文讨论了随机动力学的概念及其在流行程序MBN Explorer中的实现。MBN Explorer中的随机动态依赖于蒙特卡罗方法并允许模拟物理、化学和生物过程。本文介绍了随机动力学实现的基本理论概念，并提供了几个示例，突出了其在不同系统中的适用性，例如在细胞膜上寻找锚点的扩散蛋白质、纳米颗粒在表面上的沉积导致具有分形形态的结构和振荡自催化反应中的化合物。所选示例说明了可以通过MBN Explorer随机动力学建模的应用程序的多样性。