Cauchy Relation in DenseH2O Ice VII

1995 ◽  
Vol 74 (14) ◽  
pp. 2820-2823 ◽  
Author(s):  
H. Shimizu ◽  
M. Ohnishi ◽  
S. Sasaki ◽  
Y. Ishibashi
Keyword(s):  
Cauchy Relation

Refractive Index of Molten Li NO3– KNO2 and NaNO3 - NaNO2 Systems

1985 ◽  
Vol 40 (12) ◽  
pp. 1228-1230
Author(s):  
Y. Iwadate ◽  
J. Tominaga ◽  
K. Igarashi ◽  
J. Mochinaga
Keyword(s):  
Refractive Index ◽  
Electronic Polarization ◽  
Index Data ◽  
Cauchy Relation

Goniometry was used to measure the refractive indexes of molten LiNO3-KNO2 and NaNO3-NaNO2 mixtures.The index data were smoothed as functions of temperature and wavelength using the modified Cauchy relation. Information on electronic polarization is also reported.

Failure of the cauchy relation in cubic metals

1971 ◽  
Vol 5 (9) ◽  
pp. 787-790 ◽  
Author(s):  
J.F. Thomas
Keyword(s):  
Cubic Metals ◽  
Cauchy Relation

The generalized Cauchy relation as an universal property of the amorphous state

2005 ◽  
Vol 129 ◽  
pp. 45-49 ◽  
Author(s):  
J. K. Krüger ◽  
U. Müller ◽  
R. Bactavatchalou ◽  
J. Mainka ◽  
Ch. Gilow ◽  
...  
Keyword(s):  
Amorphous State ◽  
Universal Property ◽  
Cauchy Relation

scholarly journals Different glassy states, as indicated by a violation of the generalized Cauchy relation

2003 ◽  
Vol 5 ◽  
pp. 80-80 ◽  
Author(s):  
J K Kr ger ◽  
T Britz ◽  
A le Coutre ◽  
J Baller ◽  
W Possart ◽  
...  
Keyword(s):  
Cauchy Relation

The elastic Cauchy relation and ionicity

1972 ◽  
Vol 33 (3) ◽  
pp. 749-750 ◽  
Author(s):  
R.A Bartels ◽  
P.R Son
Keyword(s):  
Cauchy Relation

Fuchs’s relations and the contribution of the free electrons to the elastic constants of metals

1962 ◽  
Vol 266 (1324) ◽  
pp. 122-129 ◽  
Keyword(s):  
Elastic Constant ◽  
Specific Heat ◽  
Elastic Constants ◽  
Electron Gas ◽  
Free Electrons ◽  
Cauchy Relation ◽  
Experimental Values ◽  
The Individual ◽  
Central Forces ◽  
Secular Determinant

The contribution of the central forces to the elastic constants of metals has been calculated by a new method from which Fuchs’s results for c 11 — c 12 , and c 44 can be obtained directly along with the individual constants c 11 and c 12 . The numerical values have been calculated for the four metals Cu, Li, Na and K . It is found that the Cauchy relation is not satisfied by the central interaction taken separately. The method of separating out the elastic constants due to central forces, which has been adopted by Fine, Leighton, Bauer and other workers on specific heat is shown to be unjustified. The contribution of free electrons to the elastic constants has been calculated by subtracting the central force elastic constants from the experimental values. As expected, the electron gas contributes only a single elastic constant which is not equal to the experimental Cauchy discrepancy. A method of setting up a secular determinant for the lattice frequencies of metals has been suggested.

scholarly journals A new gradient method via quasi-Cauchy relation which guarantees descent

2009 ◽  
Vol 230 (1) ◽  
pp. 300-305 ◽  
Author(s):  
Malik Abu Hassan ◽  
Wah June Leong ◽  
Mahboubeh Farid
Keyword(s):  
Gradient Method ◽  
Cauchy Relation

Variational formulation of boundary-value problems

2020 ◽  
pp. 215-222
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Boundary Value Problems ◽  
Variational Formulation ◽  
Solid Mechanics ◽  
Boundary Value ◽  
Small Deformation ◽  
Local Form ◽  
Virtual Power ◽  
Cauchy Relation ◽  
Principle Of Virtual Power ◽  
Balance Of Forces

This chapter discusses a variational formulation of boundary value problems in small deformation solid mechanics. It begins by introducing the important principle of virtual power, and shows that it encapsulates Cauchy’s traction law, and the local form of the basic balance of forces (equation of equilibrium), and the local from of the balance of moments (symmetry of the stress). Since the principle of virtual power encapsulates both the equation of equilibrium and the Cauchy relation for tractions, it can be used to formulate and solve boundary-value problems in solid mechanics in a variational or weak sense. Specifically, it is shown how the displacement problem of linear elastostatics may be formulated variationally using the principle of virtual power.

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