Re: Bloch Equation, NDSolve, and strange behaviors
- To: mathgroup at smc.vnet.net
- Subject: [mg117757] Re: Bloch Equation, NDSolve, and strange behaviors
- From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
- Date: Thu, 31 Mar 2011 03:57:57 -0500 (EST)
On Wed, 30 Mar 2011, michael partensky wrote: > 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 > > Have you tried fixed precision input and then increasing AccuracyGoal and PrecisionGoal. You would like get a more useful respnse if you were to post some code that shows the issue - and * not * too * many *s Oliver