scholarly journals Second-Order Exchange-Dispersion Energy Based on a Multireference Description of Monomers

2019 ◽  
Vol 15 (12) ◽  
pp. 6712-6723 ◽  
Author(s):  
Michał Hapka ◽  
Michał Przybytek ◽  
Katarzyna Pernal
Keyword(s):  
Second Order ◽  
Dispersion Energy

Second‐Order Dispersion‐Energy Series for Axially Symmetric Molecules

1969 ◽  
Vol 10 (3) ◽  
pp. 539-544 ◽  
Author(s):  
Johannes H. van der Merwe ◽  
Alwyn J. van der Merwe
Keyword(s):  
Second Order ◽  
Axially Symmetric ◽  
Dispersion Energy ◽  
Order Dispersion

A Generalized Structure-Dependent Semi-Explicit Method for Structural Dynamics

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Jinze Li ◽  
Kaiping Yu ◽  
Xiangyang Li
Keyword(s):  
Second Order ◽  
Numerical Dispersion ◽  
The Novel ◽  
Explicit Method ◽  
Dispersion Energy ◽  
Time Step ◽  
Linear Elastic ◽  
Special Cases ◽  
Stability And Accuracy ◽  
Stiffness Softening

In this paper, a novel generalized structure-dependent semi-explicit method is presented for solving dynamical problems. Some existing algorithms with the same displacement and velocity update formulas are included as the special cases, such as three Chang algorithms. In general, the proposed method is shown to be second-order accurate and unconditionally stable for linear elastic and stiffness softening systems. The comprehensive stability and accuracy analysis, including numerical dispersion, energy dissipation, and the overshoot behavior, are carried out in order to gain insight into the numerical characteristics of the proposed method. Some numerical examples are presented to show the suitable capability and efficiency of the proposed method by comparing with other existing algorithms, including three Chang algorithms and Newmark explicit method (NEM). The unconditional stability and second-order accuracy make the novel methods take a larger time-step, and the explicitness of displacement at each time-step succeeds in avoiding nonlinear iterations for solving nonlinear stiffness systems.

Second-Order Dispersion Energy Based on Multireference Description of Monomers

2018 ◽  
Vol 15 (2) ◽  
pp. 1016-1027 ◽  
Author(s):  
Michał Hapka ◽  
Michał Przybytek ◽  
Katarzyna Pernal
Keyword(s):  
Second Order ◽  
Dispersion Energy ◽  
Order Dispersion

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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