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首页> 外文期刊>IEEE Transactions on Magnetics >Computation of Magnetic Liquid-Free Surface Shape in a Quasi-Homogeneous Magnetic Field With Differential Evolution
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Computation of Magnetic Liquid-Free Surface Shape in a Quasi-Homogeneous Magnetic Field With Differential Evolution

机译：拟均质磁场中具有微分演化的无液体磁性表面形状的计算

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This paper presents a method to compute the magnetic liquid-free surface shape of a single spike in a quasi-homogeneous magnetic field produced by the Helmholtz coil. In the Rosensweig instability, the magnetic liquid-free surface deforms in a spike-like shape pattern as a magnetic field above some critical value is applied to the liquid. The free surface of the magnetic liquid is described as a polynomial function in cylindrical coordinates with the applied cylindrical symmetry. To obtain the shape deformation, the system of nonlinear magnetically augmented Young-Laplace equations is solved iteratively. The approach to the solution is executed in two steps. In the first step, magnetic field distribution along the surface is computed by the finite-element method. When magnetic field distribution is known, the second step occurs in which the system of Young-Laplace equations, defined as an optimization problem, is solved by differential evolution.
机译：本文提出了一种计算亥姆霍兹线圈产生的准均匀磁场中单个尖峰的无磁液体表面形状的方法。在Rosensweig不稳定性中，当高于某个临界值的磁场施加到液体时，无磁性液体的磁性表面会变形为尖峰状。磁性液体的自由表面被描述为具有圆柱对称性的圆柱坐标系中的多项式函数。为了获得形状变形，迭代地求解了非线性磁增强Young-Laplace方程组。解决方案的方法分两个步骤执行。第一步，通过有限元方法计算沿表面的磁场分布。当已知磁场分布时，发生第二步，其中通过微分演化法解决被定义为优化问题的Young-Laplace方程组。

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