Bloch Equation, NDSolve, and strange behaviors
- To: mathgroup at smc.vnet.net
- Subject: [mg117747] Bloch Equation, NDSolve, and strange behaviors
- From: michael partensky <partensky at gmail.com>
- Date: Wed, 30 Mar 2011 04:18:37 -0500 (EST)
Hi. My question is related to the demo http://demonstrations.wolfram.com/MagneticResonanceAndBlochEquations/. I could not find the authors' emails, and decided to post it here. Actually, I have encountered a similar problem first, and only then found the demo. *Consider the following set of parameter*s: frequency detuning - arbitrary (say, 0) Rabi frequency =0 *relaxation*: all parameters =0. norm of *M *= 1, zenith angle of *M =*90, azimuth angle =0 (its value has no effect). Total duration: maximum (49.6) You are supposed to see precession of the magnetization vector *M* in xy plane, around the constant magnetic field *B*0 ={0,0,1}. Hence, the trajectory should be circular. However, it strongly deviates from this trajectory at large *t*. *My question*: what is the reason? The solution uses NDSolve. I tried changing MaxSteps, WorkingPrecision - it did not help. *Note*: The demo could be run at smaller *t*, where this error would not matter. I am trying to consider effects of small perturbations on a similar system, and having reliable 0-order trajectories becomes critical. Thanks Michael Partenskii