{"id":14,"date":"2019-08-07T10:33:04","date_gmt":"2019-08-07T10:33:04","guid":{"rendered":"http:\/\/spindynamics.org\/group\/?page_id=14"},"modified":"2019-08-14T19:13:42","modified_gmt":"2019-08-14T19:13:42","slug":"relaxation","status":"publish","type":"page","link":"https:\/\/spindynamics.org\/?page_id=14","title":{"rendered":"Relaxation"},"content":{"rendered":"
<\/div>
<\/p>\n

Relaxation Engine<\/h2>\n
A collection of Mathematica programs, tutorials and supporting information on the subject of automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations.<\/em><\/address>\n

Introduction to pattern matching<\/h4>\n
pattern_matching_intro.pdf<\/a>\u00a0– a brief outline of pattern matching in Mathematica<\/div>\n
tutorial_1.nb<\/a>\u00a0– a tutorial worksheet, demonstrating the power of pattern matching in Mathematica<\/div>\n
brw_engine_lecture.pdf<\/a>\u00a0– a conference lecture on the subject of automation of BRW theory processing<\/div>\n
\u00a0<\/div>\n

Pattern matching practicals<\/h4>\n
practice_1.nb<\/a>\u00a0– practice worksheet 1 (dipolar, hyperfine and other traceless bilinear mechanisms)<\/div>\n
practice_2.nb<\/a>\u00a0– practice worksheet 2 (CSA, g-anisotropy and other traceless linear mechanicsms; includes cross-correlations)<\/div>\n
practice_3.nb<\/a>\u00a0– practice worksheet 3 (ZFS relaxation\u00a0in a spin-3\/2 electron shell coupled to a spin-1 nucleus)<\/div>\n
practice_4.nb<\/a>\u00a0– practice worksheet 4 (radical pair, including g-anisotropy, hyperfine coupling to a nucleus and all cross-correlations thereof)<\/div>\n
\u00a0<\/div>\n

Examples of relaxation theory processors\u00a0<\/h4>\n
CSA-CSA cross-correlation in a two-spin system<\/a>\u00a0(the general case of arbitrarily oriented CSAs with three different eigenvalues)<\/div>\n
Point DD relaxation in a two-spin system<\/a>\u00a0(the classical case of point dipole relaxation in a two-spin system)<\/div>\n
CSA-DD-CSA\u00a0cross-correlation in a two-spin system<\/a>\u00a0(2xCSA + 1xDD, orientations arbitrary, eigenvalues different, incl. cross-correlations)<\/div>\n
Relaxation due to the modulation of a scalar interaction in a two-spin system<\/a>\u00a0(HFC modulation by electron relaxation or conformational mobility)<\/div>\n
\u00a0<\/div>\n

Literature<\/h4>\n
R.K. Wangsness, F. Bloch, The Dynamical Theory of Nuclear Induction<\/a>, Physical Review<\/em> 89 (1953) 728-739.<\/div>\n
A.G. Redfield, On the Theory of Relaxation Processes<\/a>, IBM Journal of Research and Development<\/em> 1 (1957) 19-31.<\/div>\n
M. Goldman, Formal theory of spin-lattice relaxation<\/a>, Journal of Magnetic Resonance<\/em> 149 (2001) 160-187.<\/div>\n
I. Kuprov, N. Wagner-Rundell, P.J. Hore, Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software<\/a>, Journal of Magnetic Resonance<\/em> 184 (2007) 196-206.<\/div><\/p>\n<\/div>
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