Groups > comp.soft-sys.math.mathematica > #1295

Bloch Equation, NDSolve, and strange behaviors

From	michael partensky <partensky@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Bloch Equation, NDSolve, and strange behaviors
Date	2011-03-30 09:18 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<imusgl$ibo$1@smc.vnet.net> (permalink)

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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

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Bloch Equation, NDSolve, and strange behaviors michael partensky <partensky@gmail.com> - 2011-03-30 09:18 +0000

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