Generating the Gaussian Basis Functions for Multi-Gaussian Beam Models

2007 ◽  
Author(s):  
Lester W. Schmerr ◽  
Ana Lopez-Sanchez ◽  
Alexander Sedov
Keyword(s):  
Gaussian Beam ◽  
Basis Functions ◽  
Gaussian Basis Functions

Approximation of Gaussian basis functions in the problem of adaptive control of nonlinear objects

2011 ◽  
Vol 47 (1) ◽  
pp. 1-10 ◽  
Author(s):  
O. G. Rudenko ◽  
A. A. Bezsonov ◽  
A. S. Liashenko ◽  
R. A. Sunna
Keyword(s):  
Adaptive Control ◽  
Basis Functions ◽  
Gaussian Basis Functions

COUPLED-CHANNELS ANALYSES OF 6He BREAKUP REACTIONS

2009 ◽  
Vol 24 (11) ◽  
pp. 2191-2197 ◽  
Author(s):  
T. MATSUMOTO ◽  
T. EGAMI ◽  
K. OGATA ◽  
Y. ISERI ◽  
M. KAMIMURA ◽  
...  
Keyword(s):  
Cross Sections ◽  
Reaction System ◽  
Basis Functions ◽  
Coulomb Breakup ◽  
Body Model ◽  
Coupled Channels ◽  
Gaussian Basis Functions ◽  
Three Body ◽  
Good Agreement ◽  
The Continuum

We present analyses of breakup effects of 6 He on the elastic scattering by the continuum-discretized coupled-channels method, in which the reaction system is described as a four-body model, n+n+4 He +target. In this analysis, three-body breakup continuum of 6 He is discretized by daiagonalizing the internal Hamiltonian of 6 He in a space spanned by the Gaussian basis functions. The calculated elastic cross sections are in good agreement with the experimental data, which shows that nuclear and Coulomb breakup effects are significant.

scholarly journals Inverse Multiquadratic Functions as the Basis for the Rectangular Collocation Method to Solve the Vibrational Schrödinger Equation

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 253 ◽  
Author(s):  
Aditya Kamath ◽  
Sergei Manzhos
Keyword(s):  
Schrödinger Equation ◽  
Vibrational Spectrum ◽  
Collocation Method ◽  
Schrodinger Equation ◽  
Basis Functions ◽  
Collocation Points ◽  
Basis Size ◽  
Six Dimensions ◽  
Gaussian Basis Functions

We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large, and for a range of IMQ exponents. The IMQ functions are; however, advantageous when a small number of functions is used or with a small number of collocation points (e.g., when using square collocation).

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