The Experts below are selected from a list of 21 Experts worldwide ranked by ideXlab platform
Kangxian Guo - One of the best experts on this subject based on the ideXlab platform.
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A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals
Superlattices and Microstructures, 2012Co-Authors: Guanghui Liu, Kangxian GuoAbstract:Abstract A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals is given by the plane-wave expansion method. Some mathematical formulas such as the rotation of Vector, the gradient of scalar, the divergence of the Vector, the Vector Triple Product and the conversion between scalar and Vector are employed. The eigenvalue equation in photonic crystals has become the important base for obtaining the band structure and the distribution of eigenmode.
L. R. Pratt - One of the best experts on this subject based on the ideXlab platform.
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Construction of Simulation Wavefunctions for Aqueous Species:
1998Co-Authors: M. A. Gomez, L. R. PrattAbstract:This paper investigates Monte Carlo techniques for construction of compact wavefunctions for the internal atomic motion of the D3O + ion. The polarization force field models of Stillinger, et al. and of Ojamae, et al. were used. Initial pair Product wavefunctions were obtained from the asymptotic high temperature many-body density matrix after contraction to atom pairs using Metropolis Monte Carlo. Subsequent characterization shows these pair Product wavefunctions to be well optimized for atom pair correlations despite that fact that the predicted zero point energies are too high. The pair Product wavefunctions are suitable to use within variational Monte Carlo, including excited states, and density matrix Monte Carlo calculations. Together with the pair Product wavefunctions, the traditional variational theorem permits identification of wavefunction features with significant potential for further optimization. The most important explicit correlation variable found for the D3O + ion was the Vector Triple Product rOD1·(rOD2×rOD3). Variational Monte Carlo with 9 of such explicitly correlated functions yielded a ground state wavefunction with an error of 5-6 % in the zero point energy.
A. J. B. Ward - One of the best experts on this subject based on the ideXlab platform.
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Classroom note: A teaching method for the Vector Triple Product identity
International Journal of Mathematical Education in Science and Technology, 2004Co-Authors: A. J. B. WardAbstract:In texts on Vector analysis one finds many different methods of proving the Vector Triple Product identity. Most of these rely on complicated geometrical constructions or theorems drawn from Vector space theory. The component method is generally regarded as being merely long and tedious. Yet, viewed in the correct way, the component method is actually the simplest. With correct guidance students can easily construct the proof for themselves by this method.
Guanghui Liu - One of the best experts on this subject based on the ideXlab platform.
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A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals
Superlattices and Microstructures, 2012Co-Authors: Guanghui Liu, Kangxian GuoAbstract:Abstract A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals is given by the plane-wave expansion method. Some mathematical formulas such as the rotation of Vector, the gradient of scalar, the divergence of the Vector, the Vector Triple Product and the conversion between scalar and Vector are employed. The eigenvalue equation in photonic crystals has become the important base for obtaining the band structure and the distribution of eigenmode.
Pratt L. R. - One of the best experts on this subject based on the ideXlab platform.
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Construction of Simulation Wavefunctions for Aqueous Species: D3O+
'AIP Publishing', 1998Co-Authors: Gomez M. A., Pratt L. R.Abstract:This paper investigates Monte Carlo techniques for construction of compact wavefunctions for the internal atomic motion of the D3O+ ion. The polarization force field models of Stillinger, et al and of Ojamae, et al. were used. Initial pair Product wavefunctions were obtained from the asymptotic high temperature many-body density matrix after contraction to atom pairs using Metropolis Monte Carlo. Subsequent characterization shows these pair Product wavefunctions to be well optimized for atom pair correlations despite that fact that the predicted zero point energies are too high. The pair Product wavefunctions are suitable to use within variational Monte Carlo, including excited states, and density matrix Monte Carlo calculations. Together with the pair Product wavefunctions, the traditional variational theorem permits identification of wavefunction features with significant potential for further optimization. The most important explicit correlation variable found for the D3O+ ion was the Vector Triple Product {\bf r}$_{OD1}\cdot$({\bf r}$_{OD2}\times${\bf r}$_{OD3}$). Variational Monte Carlo with 9 of such explicitly correlated functions yielded a ground state wavefunction with an error of 5-6% in the zero point energy.Comment: 17 pages including 6 figures, typos correcte