Electrodiffusion of ions inside living cells

Electrodiffusion of ions, both inside and outside biologicalcells, are of utmost importance to proper cellular functions.Experiments indicate that both ion concentrations and electropotentialcan jump discontinuously across the cell membranes. We studya system of nonlinear partial differential equations modellingsuch phenomena. Jump conditions for species concentrations andelectropotential across cell membranes are imposed. Under zero-fluxboundary conditions for one-dimensional domains, the solutionsare proved to exist for all times. With further assumptions,these transient solutions will converge to the unique steady-statesolution. Numerical experiments in one- and two-dimensionaldomains are also performed in order to study some unresolvedtheoretical issues.     

On the application of magic echo cycles for quadrupolar echo spectroscopy of spin-1 nuclei

Magic echo cycles are introduced for performing quadrupolar echo spectroscopy of spin-1 nuclei. An analysis is performed via average Hamiltonian theory showing that the evolution under chemical shift or static field inhomogeneity can be refocused simultaneously with the quadrupolar interaction using these cycles. Due to the higher convergence in the Magnus expansion, with sufficient RF power, magic echo based quadrupolar echo spectroscopy outperforms the conventional two pulse quadrupolar echo in signal to noise. Experiments highlighting a signal to noise enhancement over the entire bandwidth of the quadrupolar pattern of a powdered sample of deuterated polyethelene are shown.     

Finite pulse width artifact suppression in spin-1 quadrupolar echo spectra by phase cycling

A phase cycling scheme for suppressing spectral artifacts introduced in quadrupolar echo spectroscopy of spin-1 nuclei due to finite pulse width effects is presented. The phase cycling scheme is developed using the formalism of average Hamiltonian theory and fictitious spin-1 operators. A simulation and experiment on deuterated polyethelene is performed highlighting the spectral artifact introduced by finite pulse widths and successful removal with the proposed phase cycling scheme.