Calculating and Modeling the Exchange Energies of Homonuclear and Heteronuclear Alkali Dimers Based on the Surface Integral Method

2014 ◽  
Vol 118 (3) ◽  
pp. 592-597 ◽  
Author(s):  
Y. M. Chen ◽  
X. Y. Kuang ◽  
X. W. Sheng ◽  
X. Z. Yan
Keyword(s):  
Integral Method ◽  
Surface Integral ◽  
Alkali Dimers

scholarly journals A Surface Integral Method for Determining Ice Loads on Offshore Structures from In Situ Measurements

1983 ◽  
Vol 4 ◽  
pp. 124-128 ◽  
Author(s):  
Jerome B. Johnson
Keyword(s):  
Mathematical Model ◽  
Integral Method ◽  
Local Stress ◽  
Offshore Structures ◽  
Surface Integral ◽  
Stress Measurements ◽  
Ice Loads ◽  
Ice Failure ◽  
Stress Variations

Two methods are presented for calculating ice loads on structures using measurements from sensors imbedded in a floating ice sheet and from instruments attached to a structure. The first method uses a mathematical model describing ice/structure interaction for a cylindrical structure to interpret stress measurements. This technique requires only a few sensors to develop an estimate of ice loads, However, analytical and experimental results indicate that using a mathematical model to interpret stress measurements can result in inaccurate load estimates due to uncertainty in the accuracy of the model and and the uncertainty of using local ice stresses to calculate total ice forces. The second method of calculating ice loads on structures utilizes Euler and Cauchy’s stress principle. In this, the surface integral method, the force acting on a structure is determined by summing the stress vectors acting on a surface which encompasses the structure. Application of this technique requires that the shear and normal components of stress be known along the surface. Sensors must be spaced close enough together so that local stress variations due to the process of ice failure around a structure can be detected. The surface integral method is a useful technique for interpreting load and stress measurements since a knowledge of the mechanism of ice/structure interactions is not needed. The accuracy of the method is determined by the density of sensors along the surface. A disadvantage of the technique is that a relatively large number of sensors are needed to determine the stress tensor along the surface of interest.The surface integral method can be used to examine the effects of grounded ice rubble on structural ice loads. Two instrumented surfaces, one enclosing a structure and the other enclosing the structure and rubble field can be used to estimate the load acting only on the structure and also on the structure/ rubble-field system.

scholarly journals Exchange Energy for Two-Active-Electron Diatomic Systems Within the Surface Integral Method

2004 ◽  
Vol 15 (2) ◽  
Author(s):  
T.C. Scott ◽  
M. Aubert-Fr�con ◽  
D. Andrae ◽  
J. Grotendorst ◽  
J.D. Morgan III ◽  
...  
Keyword(s):  
Integral Method ◽  
Exchange Energy ◽  
Surface Integral ◽  
Active Electron ◽  
Diatomic Systems
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