Geodesic
Time delay in chemical exchange during an NMR pulse
Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 155-162

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MR Zbl
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all relevant cases. Also non-oscillating terms in the solution were found by studying the same determinant using similar parameter values.
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all relevant cases. Also non-oscillating terms in the solution were found by studying the same determinant using similar parameter values.
DOI : 10.21136/MB.2014.143846
Classification : 11C20, 34C26, 34K06, 82D40
Keywords: magnetic resonance; spin exchange; delay differential equation; characteristic equation 
Gamliel, Dan. Time delay in chemical exchange during an NMR pulse. Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 155-162. doi: 10.21136/MB.2014.143846
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