概率理论在化学动力学系统建模中的应用
The application of theory of probability to the modelling of chemical kinetics systems
AI总结：
研究基于联合概率和几何概率构建化学动力学模型，通过常微分方程组进行推广，简化数值实现与定量分析，提高并行效率，还考虑了模型在准周期反应示例中的应用及相关转换算法。
AI中文摘要：
我们考虑一种化学动力学模型，其方程推导不依赖质量作用定律，而是基于联合概率和几何概率等原理。针对该模型，构建了非均匀介质中反应扩散系统在热对流和扩散传递情况下的推广。此推广通过完全基于常微分方程组的替代方法构建，无需过渡到偏导数。该新方法描述与有限体积法有点类似，不过用统计简化位置和几何概率描述扩散过程。这极大简化了所得模型的数值实现及用动力系统理论的定量分析，还提高了数值方法并行实现的效率。此外，考虑了该模型在描述一些准周期反应示例中的应用，以及从具有维度动力学常数的标准模型到其形式体系的转换算法。
英文摘要：
We consider a model of chemical kinetics for which the derivation of equations does not rely on the law of mass action, but is rather based on such principles as the joint probability and the geometric probability. For this model a generalisation is constructed for the case of reaction-diffusion systems in heterogeneous medium with respect to the convective and diffusive transfer of heat. The construction of this generalisation is carried out by an alternative methodology which is based fully on a systems of ordinary differential equations, without a transition to the partial derivatives. The description of this new method is a bit similar to the finite volume method, except that it uses statistical simplifying positions and geometric probability to describe the diffusion processes. Such approach allows us to greatly simplify the numerical implementation of the resulting model, as well as to simplify the quantitative analysis of it with dynamical systems theory. Moreover, the efficiency of the parallel implementation of the numerical method is increased for the resulting model. In addition, we will consider an application of this model for the description of some example reaction with quasi-periodic regime, as well as consider an algorithm for the transition from standard models with dimensional kinetic constants to its formalism.
