Facet Connectedness of Arithmetic Discrete Hyperplanes with Non-Zero Shift

Author(s):  
Eric Domenjoud ◽  
Bastien Laboureix ◽  
Laurent Vuillon
Keyword(s):  
1994 ◽  
Vol 116 (4) ◽  
pp. 550-555 ◽  
Author(s):  
M. Gremaud ◽  
W. Cheng ◽  
I. Finnie ◽  
M. B. Prime

Introducing a thin cut from the surface of a part containing residual stresses produces a change in strain on the surface. When the strains are measured as a function of the depth of the cut, residual stresses near the surface can be estimated using the compliance method. In previous work, the unknown residual stress field was represented by a series of continuous polynomials. The present paper shows that for stress states with steep gradients, superior predictions are obtained by using “overlapping piecewise functions” to represent the stresses. The stability of the method under the influence of random errors and a zero shift is demonstrated by numerical simulation.


2009 ◽  
Vol 52 (3) ◽  
pp. 286-291
Author(s):  
A. A. Gromov ◽  
N. A. Ivashin ◽  
M. D. Sobolev

2010 ◽  
Vol 37 (3) ◽  
pp. 1161-1163 ◽  
Author(s):  
Frédéric Tessier ◽  
Brian D. Hooten ◽  
Malcolm R. McEwen

2015 ◽  
Vol 177 ◽  
pp. 33-50 ◽  
Author(s):  
Jyothish Joy ◽  
Eluvathingal D. Jemmis ◽  
Kaipanchery Vidya

A generalized explanation is provided for the existence of the red- and blue-shifting nature of X–Z bonds (Z = H, halogens, chalcogens, pnicogens, etc.) in X–Z⋯Y complexes based on computational studies on a selected set of weakly bonded complexes and analysis of existing literature data. The additional electrons and orbitals available on Z in comparison to H make for dramatic differences between the H-bond and the rest of the Z-bonds. The nature of the X-group and its influence on the X–Z bond length in the parent X–Z molecule largely controls the change in the X–Z bond length on X–Z⋯Y bond formation; the Y-group usually influences only the magnitude of the effects controlled by X. The major factors which control the X–Z bond length change are: (a) negative hyperconjugative donation of electron density from X-group to X–Z σ* antibonding molecular orbital (ABMO) in the parent X–Z, (b) induced negative hyperconjugation from the lone pair of electrons on Z to the antibonding orbitals of the X-group, and (c) charge transfer (CT) from the Y-group to the X–Z σ* orbital. The exchange repulsion from the Y-group that shifts partial electron density at the X–Z σ* ABMO back to X leads to blue-shifting and the CT from the Y-group to the σ* ABMO of X–Z leads to red-shifting. The balance between these two opposing forces decides red-, zero- or blue-shifting. A continuum of behaviour of X–Z bond length variation is inevitable in X–Z⋯Y complexes.


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