Monotonic difference schemes for weakly coupled systems of parabolic differential equations

1969 ◽  
pp. 160-167 ◽  
Author(s):  
Rudolf Gorenflo
Keyword(s):  
Differential Equations ◽  
Difference Schemes ◽  
Coupled Systems ◽  
Parabolic Differential Equations ◽  
Weakly Coupled ◽  
Weakly Coupled Systems

Article

1999 ◽  
Vol 77 (11) ◽  
pp. 1810-1812 ◽  
Author(s):  
Alex D Bain
Keyword(s):  
Spin System ◽  
Coupled System ◽  
Coupled Systems ◽  
Physical Reason ◽  
Strongly Coupled ◽  
System Combination ◽  
First Order ◽  
Weakly Coupled ◽  
Quantum Transitions ◽  
Weakly Coupled Systems

Strongly coupled spin systems provide many curious and interesting effects in NMR spectra, one of which is the presence of unexpected (from a first-order viewpoint) lines. A physical reason is given for the presence of these combination lines. The X part of the spectrum of an ABX spin system is analysed as an example. For an ABX system, it is well known that the AB nuclei give a spectrum consisting of two AB-type spectra, corresponding to the two orientations of the X nucleus. It can also be shown that the X part of the spectrum corresponds to the X nucleus undergoing a transition in the presence of an AB-like spin system. For weakly coupled systems, the four observed lines correspond to the four different orientations of the A and B nuclei. For a strongly coupled system, two additional lines may appear, the combination lines. The resulting six lines correspond to the four spin orientations, plus the two zero-quantum transitions. It is shown that these six lines are such that there is no net excitation of the AB-like spin system associated with the X transitions. There is no AB coherence created directly by a pulse applied to X. AB coherence is created as the system evolves, and this is responsible for many of the curious effects. This is shown to be true for all spin sub-systems, which are weakly coupled to a strongly coupled sub-system.Key words: NMR, strong coupling, second-order spectra, ABX spin system, combination lines, spectral analysis.

scholarly journals Adjoint methods for obstacle problems and weakly coupled systems of PDE

2013 ◽  
Vol 19 (3) ◽  
pp. 754-779 ◽  
Author(s):  
Filippo Cagnetti ◽  
Diogo Gomes ◽  
Hung Vinh Tran
Keyword(s):  
Coupled Systems ◽  
Obstacle Problems ◽  
Adjoint Methods ◽  
Weakly Coupled ◽  
Weakly Coupled Systems
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