Square Of Fourier Research Articles

An efficient Laplace transform-wave packet method hybrid with substructure technique

By virtue of substructure technique, the wave packet method can be applied to efficiently evaluate the thermal conduction of each phonon mode in the large periodic harmonic lattice. The substructures are connected by the inter-belts due to the long-range interatomic interaction. A parallel dynamic substructure method is presented in the Laplace transform domain, without any approximation in the condensation process. The validity and efficiency of the proposed method is demonstrated by the one- and three-dimensional cases. By launching a wide band wave packet, the whole given phonon branch can be studied by a one-time calculation. Defined as the ratio between square of Fourier transform of the transmitted and incident wave packets, the resulted transmission coefficient agrees with that obtained by the atomistic Green’s function method. Moreover the time evolution of the wave field can be given by the method, and the multilevel substructure technique can also be used.

Shifting selectivity of collinear volume holographic storage

A paraxial equation for calculating pixel-based 2-D shifting selectivity of collinear holographic storage system is proposed. The equation shows that the broader reference pattern makes high shifting selectivity. In addition, both amplitude and phase modulation make no obvious change in shifting selectivity so shifting selectivity is not affected through advanced design of reference pattern. Besides, a simplified formula based on a point signal is proposed, which shows a clear physical insight that the shifting selectivity is the square of Fourier transform of the intensity distribution of reference pattern and does not depend on thickness of the disc when a point signal is applied.

Experimental investigation of the valence orbital momentum distributions and ionization energies of the noble gases by binary (e, 2e) spectroscopy

A binary (e. 2e) spectrometer has been modified to obtain significantly improved momentum resolution ▪. Using this apparatus a systematic study of the ionization of all the valence orbitals of the noble gases: He, Ne, Ar, Kr and Xe has been carried out at an impact energy of 1200 eV plus the binding energy. Binding-energy spectra have been obtained at a series of azimuthal angles (corresponding to different electron momenta) for each target gas. In Ar, Kr and Xe the pole strength for ns ionization is severely split among several final ion states and the intensities are compared with earlier results from (e, 2e) spectroscopy. X-ray photoelectron spectroscopy and theoretical calculations. The ns and np atomic orbital (AO) electron-momentum distributions have been measured for the noble gases and the results, which give directly the squares of the AO momentum-spade wavefunctions, are compared with the square of Fourier transformed position-space wavefunctions of Hartree-Fock (HF), double-zeta (DZ) and single-zeta (SZ) quality. Excellent agreement is obtained between the experiment and Hartree-Fock calculations. Atomic orbital momentum density and position density contour maps have also been generated using Hartree-Fock wavefunctions. The maps have been used to provide a complementary discussion of position-and momentum-space properties of the noble-gas group of elements in the periodic table. Trends are discussed in the momentum distributions, density maps in position and momentum space and also the binding-energy spectra with reference to the electronic structure of the noble gases.