MCMC paper finished

Abstract:

Many nuclei probed by NMR are relatively insensitive to detection, requiring methods such as the Carr-Purcell Meiboom-Gill (CPMG) pulse sequence. Experiments which follow this general approach are composed of pulse trains, giving rise to characteristic spikelet patterns in the frequency domain. In the presence of multiple underlying chemical sites, each spikelet intensity is a sum of some unknown proportion of contributions from each site. This work outlines a modeling approach based around Markov Chain Monte Carlo (MCMC), which negates the need for intensive simulations using density matrix formalism. In support of this technique, a spikelet pattern is produced using the density matrix formalism for an ensemble of spin 1/2 nuclei, and the underlying chemical shifts and intensities reproduced using the method outlined. Finally, MCMC is used to model the CPMG spectrum of a (3,3,3-trifluoropropyl)dimethylchlorosilane (TFS) treated aluminosilicate, providing evidence in support of a particular model of silanol group surface attachment to the bulk.

MQMAS sim paper in press

Abstract: The majority of nuclei available for study in solid state Nuclear Magnetic Resonance have half-integer spin I > 1/2, with corresponding electric quadrupole moment. As such, they may couple with a surrounding electric field gradient. This effect introduces anisotropic line broadening to spectra, arising from distinct chemical species within polycrystalline solids. In Multiple Quantum Magic Angle Spinning (MQMAS) experiments, a second frequency dimension is created, devoid of quadrupolar anisotropy. As a result, the center of gravity of peaks in the high resolution dimension are functions of isotropic quadrupole and chemical shifts alone. However, for complex materials, these parameters take on a stochastic nature due in turn to structural and chemical disorder. Lineshapes may still overlap in the isotropic dimension, complicating the task of assignment and interpretation. A distributed computational approach is presented here which permits simulation of the MQMAS spectrum, generated by random variates from model distributions of isotropic chemical and quadrupole shifts. Owing to the non-convex nature of the least squared cost function between experimental and simulated spectra, simulated annealing is used to optimize the simulation parameters. In this manner, local chemical environments for disordered materials may be characterized, and via a re-sampling approach, error estimates for parameters produced.

Key words: Nuclear Magnetic Resonance, Multiple Quantum Magic Angle Spinning, OpenMP, Sobol sequence, quasi-random numbers, simulated annealing, distribution functions, quadrupole interaction.

SDE scripts

Mostly a  reworking of  fortran code from Kloeden & Platen into Matlab/Octave. Includes important things like Karhunen-Loéve expansions, Stratonovich integrals for higher order methods, Ito summation etc and also a Markov Chain Monte Carlo example

SDE scripts

SIR filter; resample step in octave

a little implementation for your viewing pleasure (assumes you are keeping a full particle & weight history):