Fourier transform method of calculating total cross sections using the time-dependent close-coupling theory

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
J. Colgan ◽  
M. S. Pindzola ◽  
F. Robicheaux
Keyword(s):  
Fourier Transform ◽  
Cross Sections ◽  
Time Dependent ◽  
Coupling Theory ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Close Coupling ◽  
Total Cross Sections

scholarly journals Close Coupling Theory of Positron Scattering from Alkali Atoms

1994 ◽  
Vol 47 (6) ◽  
pp. 721 ◽  
Author(s):  
Jim Mitroy ◽  
Kurunathan Ratnavelu
Keyword(s):  
Cross Sections ◽  
Alkali Atom ◽  
Coupling Theory ◽  
Positron Scattering ◽  
Close Coupling ◽  
Total Cross Sections ◽  
Hartree Fock ◽  
Atom Scattering ◽  
Alkali Atoms ◽  
Rearrangement Process

The close coupling equatious for positron-alkali atom scattering are written as a set of coupled momentum-space Lippmann-Schwinger equations. The alkali atom is represented by a frozen-core model based upon the Hartree-Fock approximation. The interaction between the positronium and the residual ion is modified by the inclusion of a core potential. Similarly, a core term is present in the interaction describing the rearrangement process. Close coupling calculations of positron scattering from sodium are performed in a model containing multiple sodium (3s, 3p, 4s, 3d, 4p) and positronium (Is, 2s, 2p) states. Cross sections are reported for an energy range from threshold to 50�eV; the total cross sections are in agreement with experimental data.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

Dynamics of Cantilever Beams due to Time-Dependent Excitations and their Suppression

2012 ◽  
Vol 232 ◽  
pp. 465-468
Author(s):  
Adnan Rebei ◽  
Khalid Al-Saif
Keyword(s):  
Fourier Transform ◽  
Cantilever Beam ◽  
Low Frequency ◽  
Frequency Component ◽  
Time Dependent ◽  
Cantilever Beams ◽  
External Excitation ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Optimal Position

A Fourier Transform method is applied to determine the displacements of a cantilever beam subjected to a multi-frequency excitations at the base. To dampen the displacements of the beam, a point mass is attached to the beam. The position of the mass on the beam is determined such that the overall deflections of the beam are minimal. It is shown that these attachments to the beam are effective in reducing the vibrations of the beam but their position is frequency dependent. It is shown that the low frequency component of the external excitation is most important in finding the optimal position of the mass.

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