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Relaxation Engine

A collection of Mathematica programs, tutorials and supporting information on the subject of automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations.

Introduction to pattern matching

pattern_matching_intro.pdf - a brief outline of pattern matching in Mathematica
tutorial_1.nb - a tutorial worksheet, demonstrating the power of pattern matching in Mathematica
brw_engine_lecture.pdf - a conference lecture on the subject of automation of BRW theory processing

Pattern matching practicals

practice_1.nb - practice worksheet 1 (dipolar, hyperfine and other traceless bilinear mechanisms)
practice_2.nb - practice worksheet 2 (CSA, g-anisotropy and other traceless linear mechanicsms; includes cross-correlations)
practice_3.nb - practice worksheet 3 (ZFS relaxation in a spin-3/2 electron shell coupled to a spin-1 nucleus)
practice_4.nb - practice worksheet 4 (radical pair, including g-anisotropy, hyperfine coupling to a nucleus and all cross-correlations thereof)

Examples of relaxation theory processors 

CSA-CSA cross-correlation in a two-spin system (the general case of arbitrarily oriented CSAs with three different eigenvalues)
Point DD relaxation in a two-spin system (the classical case of point dipole relaxation in a two-spin system)
CSA-DD-CSA cross-correlation in a two-spin system (two CSA tensors and a DD tensor, all orientations arbitrary, all eigenvalues different, all cross-correlations included)
Relaxation due to the modulation of a scalar interaction in a two-spin system (the classical case of hyperfine coupling modulation by electron relaxation or conformational mobility)


R.K. Wangsness, and F. Bloch, The Dynamical Theory of Nuclear Induction, Physical Review 89 (1953) 728-739.
A.G. Redfield, On the Theory of Relaxation Processes, Ibm Journal of Research and Development 1 (1957) 19-31.
M. Goldman, Formal theory of spin-lattice relaxation, Journal of Magnetic Resonance 149 (2001) 160-187.
I. Kuprov et al, Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software, Journal of Magnetic Resonance 184 (2007) 196-206.

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