Local unitary transformation method toward practical electron correlation           calculations with scalar relativistic effect in large-scale molecules

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

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Implementation of Analytical Energy Gradient of Spin-Dependent General Hartree–Fock Method Based on the Infinite-Order Douglas–Kroll–Hess Relativistic Hamiltonian with Local Unitary Transformation

Journal of Chemical Theory and Computation ◽

10.1021/acs.jctc.5b00928 ◽

2016 ◽

Vol 12 (5) ◽

pp. 2181-2190 ◽

Cited By ~ 5

Author(s):

Yuya Nakajima ◽

Junji Seino ◽

Hiromi Nakai

Keyword(s):

Unitary Transformation ◽

Infinite Order ◽

Hartree Fock ◽

Energy Gradient ◽

Local Unitary Transformation

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Electron Transport Phenomena in NiS2−xSex Single Crystals

MRS Proceedings ◽

10.1557/proc-453-291 ◽

1996 ◽

Vol 453 ◽

Cited By ~ 3

Author(s):

X. Yao ◽

S. Ehrlich ◽

G. Liedlb ◽

T. Hogan ◽

C. Kannewurf ◽

...

Keyword(s):

Electrical Resistivity ◽

Seebeck Coefficient ◽

Single Crystals ◽

Electron Correlation ◽

Large Scale ◽

Structural Changes ◽

Dominant Role ◽

Magnetic Ordering ◽

Structural Studies ◽

Complex Temperature

AbstractStructural studies, electrical resistivity, and Seebeck coefficient measurements are reported in the range 4.2 − 300 K for single crystals of NiS2−xSex (0 ≤ x ≤ 0.71) grown from a Te melt. Over the entire temperature and composition ranges there are no large scale structural changes concomitant to a variety of magnetic ordering phenomena, and to a changeover from insulating to metallic characteristics as x increases. Thus, the evolution in transport characteristics with x can be studied without interference from the lattice; moreover, the electron count is unaffected by substitution of Se for S. The existence of anomalous peaks in resistivity as a function of temperature is attributed to significant electron correlation phenomena which allow the entropy of charge carrier to play a dominant role. The complex temperature dependence of the Seebeck coefficient is attributed to the participation of both electrons and holes in charge transport.

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Smart Well Pattern Optimization Using Gradient Algorithm

Journal of Energy Resources Technology ◽

10.1115/1.4031208 ◽

2015 ◽

Vol 138 (1) ◽

Cited By ~ 10

Author(s):

Liming Zhang ◽

Kai Zhang ◽

Yuxue Chen ◽

Meng Li ◽

Jun Yao ◽

...

Keyword(s):

Large Scale ◽

Production Control ◽

Optimization Procedure ◽

Transformation Method ◽

Economic Benefits ◽

Gradient Algorithm ◽

Generation Process ◽

Field Development ◽

Well Pattern ◽

Well Pattern Optimization

For a long time, well pattern optimization mainly relies on human experience, numerical simulations are used to test different development plans and then a preferred program is chosen for field implementation. However, this kind of method cannot provide suitable optimal well pattern layout for different geological reservoirs. In recent years, more attentions have been paid to propose well placement theories combining optimization algorithm with reservoir simulation. But these theories are mostly applied in a situation with a small amount of wells. For numerous wells in a large-scale reservoir, it is of great importance to pursue the optimal well pattern in order to obtain maximum economic benefits. The idea in this paper is originated from the idea presented by Onwunalu and Durlofsky (2011, “A New Well-Pattern-Optimization Procedure for Large-Scale Field Development,” SPE J., 16(3), pp. 594-607), which focuses on well pattern optimization, and the innovations are as follows: (1) Combine well pattern variation with production control to get the optimal overall development plan. (2) Rechoose and simplify the optimization variables, deduce the new generation process of well pattern, and use perturbation gradient to solve mathematical model in order to ensure efficiency and accuracy of final results. (3) Constrain optimization variables by log-transformation method. (4) Boundary wells are reserved by shifting into boundary artificially to avoid abrupt change of objective function which leads to a nonoptimal result due to gradient discontinuity at reservoir edge. The method is illustrated by examples of homogeneous and heterogeneous reservoirs. For homogeneous reservoir, perturbation gradient algorithm yields a quite satisfied result. Meanwhile, heterogeneous reservoir tests realize optimization of various well patterns and indicate that gradient algorithm converges faster than particle swarm optimization (PSO).

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