论文标题
单域粒子的Fokker-Planck方程的有限元解
Finite element solution of the Fokker-Planck equation for single domain particles
论文作者
论文摘要
由棕色得出的单个结构域粒子磁矩方向的概率密度函数得出的fokker-Planck方程是超级磁学理论的基本方程之一。通常，通过将溶液扩展到一系列球形谐波中来解决该方程，在这种情况下，这是一个复杂而笨拙的过程。本文介绍了使用有限元方法的实现过程和Fokker-Planck方程的数值解决方案的一些结果。描述了一种基于刻有二十面体的球体表面上创建一系列三角网格序列的方法。得出有限元方法的方程式，并提供了数值解的示例。在具有立方磁各向异性的粒子加热下，磁化和脱氧化的过程进行了模拟。
The Fokker-Planck equation derived by Brown for the probability density function of the orientation of the magnetic moment of single domain particles is one of the basic equations in the theory of superparamagnetism. Usually this equation is solved by expanding the solution into a series of spherical harmonics, which in this case is a complex and cumbersome procedure. This article presents the implementation procedure and some results of the numerical solution of the Fokker-Planck equation using the finite element method. A method for creating a sequence of triangular grids on the surface of a sphere based on an inscribed icosahedron is described. The equations of the finite element method are derived and examples of numerical solutions are presented. The processes of magnetization and demagnetization under heating of a particle with cubic magnetic anisotropy are simulated.
