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Transcript
MAGNETIZATION DYNAMICS Roger Ellicock This is a simple model of an object becoming magnetized as it cools in the presence of an external field. In the movie, the field is constant in the z direction (up). The object is represented as a cubic array of magnetic moments that feel a torque from the external field. The magnetization is the vector sum of the moments. They evolve according to the Landau-Lifshitz (LL) equation: d m dt = −γm × Heff + λm × (m × Heff) where γ is the gyromagnetic ratio and λ is a damping factor. Heff is an effective field that combines the external field with other magnetic and quantum mechanical effects, although in this model it is taken to be a constant for simplicity. The first term causes the moment to precess around the direction of the external field. The second term dampens the motion and causes the moment vector to align with the field. A moment vector moving according to the LL equation. http://wpage.unina.it/mdaquino/PhD_thesis/main/node28.html The aligning effect is countered by random thermal fluctuations of the direction of the moment vector. This is introduced into the equation by including in the field a randomly oriented vector with magnitude proportional to temperature . The object cools as the heat leaves the object according to the heat equation. In the movie, the temperature is represented by the color of the moment vectors. RUN WITH MAGNETIZATION_DYNAMICS.M, WITH FUNCTION LL.M