Volterra型积分方程晶核成长模型及其数值算法

Crystal nucleus growth model of Volterra integral equation and its numerical algorithm

在高性能催化剂颗粒的制备过程中,介尺度晶核成核与生长可描述为一类非线性耦合的三维Volterra型积分方程模型。针对该模型,首先根据均相成核理论,进行先验信息假设,获得了同时反演成核率和生长率的唯一性结论;然后针对该反问题的不稳定性和数值格式的病态性,提出了该反问题的正则化方法,构造了数值算法,数值算例结果验证了数值算法的有效性。理论结果及数值模拟结果显示了介尺度成核与生长规律,可为催化剂制备提供一定的科学依据。

During the preparation of high performance catalyst particles,mesoscale nucleation and crystal growth can be described as a nonlinear coupled 3-dimensional model of Volterra integral equation.For this model,an apriori information hypothesis was firstly proposed based on homogeneous nucleation theory and the uniqueness result was obtained by inverting nucleation rate and growth rate simultaneously.Then,due to the instability of the inverse problem and the ill-posedness of numerical format,a regularization method was put forward to solve it.A numerical algorithm was constructed and numerical results verified the effectiveness of the numerical algorithm.The theoretical results and numerical simulation results show the law of mesoscale nucleation and growth,which can provide a scientific basis for the preparation of catalysts.