A GENERAL METHOD FOR NUMERICAL INTEGRATION THROUGH A SADDLE-POINT SINGULARITY WITH APPLICATION TO ONE-DEMENSIONAL NONEQUILIBRIUM NOZZLE FLOW

1964 ◽  
Author(s):  
George Emanuel
Keyword(s):  
Saddle Point ◽  
Numerical Integration ◽  
Nozzle Flow ◽  
Point Singularity ◽  
General Method

Resonant Raman scattering at the saddle-point singularity inInxGa1−xAs

1985 ◽  
Vol 32 (2) ◽  
pp. 1005-1008 ◽  
Author(s):  
K. P. Jain ◽  
R. K. Soni ◽  
S. C. Abbi ◽  
M. Balkanski
Keyword(s):  
Raman Scattering ◽  
Saddle Point ◽  
Point Singularity ◽  
Resonant Raman ◽  
Resonant Raman Scattering

scholarly journals Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

2015 ◽  
Vol 92 (7) ◽  
Author(s):  
Madhab Neupane ◽  
Su-Yang Xu ◽  
R. Sankar ◽  
Q. Gibson ◽  
Y. J. Wang ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Saddle Point ◽  
Topological Phase ◽  
Point Singularity ◽  
Topological Crystalline Insulator

Electromagnetic field of a dipole on a two‐layer earth

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 309-315 ◽  
Author(s):  
W. C. Chew ◽  
J. A. Kong
Keyword(s):  
Electromagnetic Field ◽  
Saddle Point ◽  
Branch Point ◽  
Asymptotic Approximation ◽  
Spherical Wave ◽  
Geometrical Optics ◽  
Parabolic Cylinder ◽  
Point Singularity ◽  
Image Source ◽  
Free Part

The electromagnetic field due to a horizontal electric dipole placed on top of a two‐layer earth is represented in terms of fields due to a dipole over a half‐space earth and its image source fields. Integral representations of image source fields are evaluated with uniform asymptotic approximations. Leading order ordinary saddle‐point approximation, giving rise to the geometrical optics approximation (GOA), is shown to be inaccurate. This is especially true when the angle of observation is close to the critical angle, which corresponds to the presence of a branch‐point singularity near the saddle point. In the uniform asymptotic approximation, the integrand of the image source integral is split into a branch‐point free part and another part containing the branch‐point singularity. The branch‐point free part can be approximated with a spherical wave function, while the part containing the branch point can be approximated with parabolic cylinder functions. Vertical magnetic field components and the horizontal electric field component near the surface are illustrated and compared with the geometrical optics approximation, giving the direct numerical result as well as experimental measurement. It is shown that the uniform asymptotic approximation yields excellent agreement with numerical and experimental results compared to the geometrical optics approximation.

Superconductivity in the Strong Coupling Limit: Van Hove Singularity and Extended Saddle Point Singularity Scenario

1997 ◽  
Vol 11 (07) ◽  
pp. 303-309
Author(s):  
Sujit Sarkar
Keyword(s):  
Saddle Point ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Nearest Neighbor ◽  
Strong Coupling Limit ◽  
Dimensional System ◽  
Coupling Theory ◽  
Point Singularity ◽  
Van Hove Singularity ◽  
Weak Coupling Theory

The effect of orthorhombic distortion and second nearest neighbor hopping on the transition temperature (T c ) and the isotope-shift exponent (α) have been studied for a two dimensional system, within the framework of Eliashberg formalism in the van Hove singularity scenario. The behavior of T c and α have been discussed for the case of extended saddle point singularity. A comparison of the strong coupling theory results is made with the results of weak coupling theory. From our study it reveals that the effect of singularity in the density of states (DOS) in the strong coupling limit is not so significant as that in weak coupling case.

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