A Zeroth-Order Approximation for Bond Energies, Hybridization States, and Bond Ionicities. I. Diatomic Molecules and AI-BICrystals1a

1964 ◽  
Vol 68 (8) ◽  
pp. 2240-2248 ◽  
Author(s):  
Ricardo Ferreira
Keyword(s):  
Diatomic Molecules ◽  
Order Approximation ◽  
Bond Energies ◽  
Zeroth Order ◽  
Zeroth Order Approximation

TOWARDS (DE)CONSTRUCTING 4D YANG-MILLS THEORY

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2099-2106
Author(s):  
MASAFUMI FUKUMA ◽  
KEN-ICHI KATAYAMA
Keyword(s):  
Order Approximation ◽  
Zeroth Order ◽  
Yang Mills ◽  
Zeroth Order Approximation ◽  
Glueball Spectrum

We investigate 3D Yang-Mills theory coupled to an adjoint scalar, which can be regarded as a zeroth order approximation in (de)constructing 4D Yang-Mills theory. We develop a new algorithm to obtain the renormalized Hamiltonian with the Karabali-Nair variable, by carefully identifying finite local counterterms. We also discuss how this formalism can be applied to obtain glueball spectrum.

Exchange energy of H2calculated by the surface integral method in zeroth order approximation

1993 ◽  
Vol 99 (1) ◽  
pp. 377-388 ◽  
Author(s):  
K. T. Tang ◽  
J. Peter Toennies ◽  
C. L. Yiu
Keyword(s):  
Integral Method ◽  
Order Approximation ◽  
Exchange Energy ◽  
Zeroth Order ◽  
Surface Integral ◽  
Zeroth Order Approximation

A mathematical analysis of wind effects on a long-jumper

1991 ◽  
Vol 33 (1) ◽  
pp. 65-76 ◽  
Author(s):  
Neville de Mestre
Keyword(s):  
Mathematical Analysis ◽  
Order Approximation ◽  
Wind Effects ◽  
Zeroth Order ◽  
Perturbation Model ◽  
First Order ◽  
Zeroth Order Approximation ◽  
The Difference ◽  
Drag And Lift ◽  
Run Up

AbstractA perturbation model is used to predict the distance jumped by a long-jumper for a range of tailwinds and headwinds. The zeroth-order approximation is based on gravity being the only force present, the effects of drag and lift only being included in the first-order corrections. The difference in predicted distances produced by the zeroth and first-order approximations is less than 2% for headwinds or tailwinds upto 4 ms−1. Most increases or decreases due to wind are caused by changes in the run-up speed, and consequently the take-off angle and speed.

scholarly journals Some Aspects of Chemical Abundance Determinations in Planetary Nebulae

1978 ◽  
Vol 76 ◽  
pp. 225-233 ◽  
Author(s):  
Lawrence H. Aller
Keyword(s):  
Order Approximation ◽  
Planetary Nebulae ◽  
Chemical Compositions ◽  
Zeroth Order ◽  
Chemical Abundance ◽  
Zeroth Order Approximation ◽  
Gaseous Nebulae ◽  
First Approximation

The determination of the chemical compositions of gaseous nebulae in general and of planetary nebulae in particular is a difficult undertaking. The zeroth-order approximation is straightforward, the first approximation is challenging, and the second approximation is almost intractable.

Experimental study of stability prediction for high-speed robotic milling of aluminum

2019 ◽  
Vol 26 (7-8) ◽  
pp. 387-398 ◽  
Author(s):  
Daxian Hao ◽  
Wei Wang ◽  
Zhaoheng Liu ◽  
Chao Yun
Keyword(s):  
High Speed ◽  
Order Approximation ◽  
Low Frequency ◽  
Computer Numerical Control ◽  
Numerical Control ◽  
Zeroth Order ◽  
Regenerative Chatter ◽  
High Speed Milling ◽  
Zeroth Order Approximation ◽  
Robotic Milling

It has been fully demonstrated that the regenerative chatter theory is applicable for predicting chatter-free milling parameters for computer numerical control machine tools, but researchers are still arguing whether it is effective for robotic milling processes. The main reason is that the robot’s modes greatly shift, depending on its varying dynamic parameters and joint configurations. More experimental investigations are required to study and better understand the mechanism of vibration in robotic machining. The present paper is focusing on finding experimental support for chatter-free prediction in robot high-speed milling by the regenerative chatter theory. Modal tests are first conducted on a milling robot and used to predict stability lobes by zeroth order approximation. A number of high-speed slotting tests are then carried out to verify the prediction results. Thus, the regenerative chatter theory is proved to be also applicable to robotic high-speed milling. Furthermore, low-frequency modes of the robot structure are investigated by more modal experiments involving a laser tracker and a displacement sensor. The low-frequency modes are identified as the main part of the prediction error of the zeroth order approximation method, which could also be dominant in low-speed robotic milling processes. In addition, robots are different from computer numerical control machines in terms of stiffness, trajectory following error, forced vibration, and motion coupling. These long-period trend terms have to be carefully taken into account in the regenerative chatter theory for robotic high-speed milling.

Small Reynolds Number Electro-Hydrodynamic Flow Around Drops and the Resulting Deformation

1979 ◽  
Vol 46 (3) ◽  
pp. 510-512 ◽  
Author(s):  
M. B. Stewart ◽  
F. A. Morrison
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Order Approximation ◽  
Creeping Flow ◽  
Small Reynolds Number ◽  
Zeroth Order ◽  
Regular Perturbation ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow

Low Reynolds number flow in and about a droplet is generated by an electric field. Because the creeping flow solution is a uniformly valid zeroth-order approximation, a regular perturbation in Reynolds number is used to account for the effects of convective acceleration. The flow field and resulting deformation are predicted.

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