Folded Plate Analysis by Minimum Energy Principle

1962 ◽  
Vol 88 (3) ◽  
pp. 1-34
Author(s):  
M. N. Fialkow
Keyword(s):  
Minimum Energy ◽  
Energy Principle ◽  
Minimum Energy Principle ◽  
Plate Analysis

scholarly journals Meteoritic amino acids as chemical tracers of parent-body chemistries

2021 ◽  
Vol 502 (3) ◽  
pp. 4064-4073
Author(s):  
Y Ellinger ◽  
M Lattelais ◽  
F Pauzat ◽  
J-C Guillemin ◽  
B Zanda
Keyword(s):  
Amino Acids ◽  
Relative Stability ◽  
Density Functional ◽  
Minimum Energy ◽  
Protonated Form ◽  
Parent Body ◽  
Chemical Formula ◽  
Energy Principle ◽  
Chemical Tracers ◽  
Minimum Energy Principle

ABSTRACT The analysis of the organic matter of meteorites made it possible to identify over 70 amino acids (AA), including 8 of those found in living organisms. However, their relative abundances vary drastically with the type of the carbonaceous chondrite, even for isomers of same chemical formula. In this report, we address the question whether this difference may have its origin in the relative stability of these isomers according to the conditions they experienced when they were formed and after. To this end, we rely on the fact that for most of the species observed so far in the interstellar medium (ISM), the most abundant isomer of a given generic chemical formula is the most stable one (minimum energy principle, MEP). Using quantum density functional theory (DFT) simulations, we investigate the relative stability of the lowest energy isomers of alanine (Ala) and amino butyric acid (ABA) in the neutral, protonated, and zwitterionic structures together with corresponding nitrile precursors. It is shown that β-alanine and γ-ABA are the most stable in a protonated form, whereas α-AA are the most stable in the zwitterionic and nitrile structures. The different composition of the carbonaceous chondrites CIs and CMs could be linked to the chemical context of the aqueous alterations of the parent bodies.

scholarly journals Prediction of Permanent Displacement of Liquefied Ground by Means of Minimum Energy Principle

1992 ◽  
Vol 32 (3) ◽  
pp. 97-116 ◽  
Author(s):  
Ikuo Towhata ◽  
Yasushi Sasaki ◽  
Ken-Ichi Tokida ◽  
Hideo Matsumoto ◽  
Yukio Tamar ◽  
...  
Keyword(s):  
Minimum Energy ◽  
Permanent Displacement ◽  
Energy Principle ◽  
Minimum Energy Principle

Elliptic inclusions in a stressed matrix

1963 ◽  
Vol 59 (4) ◽  
pp. 821-832 ◽  
Author(s):  
R. D. Bhargava ◽  
H. C. Radhakrishna
Keyword(s):  
Minimum Energy ◽  
Elastic Field ◽  
Theory Of Elasticity ◽  
Inclusion Problem ◽  
Elliptic Inclusion ◽  
Linear Elasticity Theory ◽  
Energy Principle ◽  
Uniform Tension ◽  
Minimum Energy Principle ◽  
The Matrix

AbstractThis paper treats an extension of the problem considered by the authors in a recent paper (1). The minimum energy principle of the classical theory of elasticity was used in the above paper for evaluating the elastic field when an elliptic region (the inclusion, which could be of a material different from the rest) undergoes spontaneous dimensional change in an otherwise unstrained infinite medium (the matrix). By modification of this method, it has been possible to deal with the case when the inclusion is spherical or circular and the matrix is under uniform tension at infinity (2). The present paper deals with the much more general case when the matrix is under tension, at infinity, inclined at any angle to the major axis of the elliptic inclusion. The solution has been possible by the combination of the complex variable method coupled with minimum energy principle and superposition methods of linear elasticity theory. As a consequence we immediately derive almost without further calculation many particular cases, viz. (i) the inclusion problem in a matrix under axial tension parallel to either of the axes, (ii) under all round uniform tension (or pressure) etc. It is obvious that the results for the respective cases of a circular inclusion can be deduced from these results.It also solves the problem of composite sections under external forces at infinity because of the complete freedom in choosing the elastic constant of the inclusion which can be different from that of the matrix. As a corollary, it solves the problem of a cavity under stress at infinity.

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