A Superliquid in Two Dimensions and a First‐Order Change in a Condensed Monolayer I. Energy, Compressibility, and Order of Phase Transformations

1942 ◽  
Vol 10 (5) ◽  
pp. 272-286 ◽  
Author(s):  
William D. Harkins ◽  
L. E. Copeland
Keyword(s):  
Phase Transformations ◽  
Two Dimensions ◽  
First Order ◽  
Order Change

A First‐Order Change which Involves the Vaporization in Two Dimensions of N‐Heptane on the Surface of Silver

1945 ◽  
Vol 13 (11) ◽  
pp. 535-536 ◽  
Author(s):  
George Jura ◽  
E. H. Loeser ◽  
P. R. Basford ◽  
William D. Harkins
Keyword(s):  
Two Dimensions ◽  
First Order ◽  
Order Change

A Stable Mixed Element Method for the Biharmonic Equation with First-Order Function Spaces

2017 ◽  
Vol 17 (4) ◽  
pp. 601-616 ◽  
Author(s):  
Zheng Li ◽  
Shuo Zhang
Keyword(s):  
Biharmonic Equation ◽  
Two Dimensions ◽  
Zero Order ◽  
Helmholtz Decomposition ◽  
Numerical Verification ◽  
Order Function ◽  
First Order ◽  
Mixed Element ◽  
New Formulation ◽  
Element Method

AbstractThis paper studies the mixed element method for the boundary value problem of the biharmonic equation {\Delta^{2}u=f} in two dimensions. We start from a {u\sim\nabla u\sim\nabla^{2}u\sim\operatorname{div}\nabla^{2}u} formulation that is discussed in [4] and construct its stability on {H^{1}_{0}(\Omega)\times\tilde{H}^{1}_{0}(\Omega)\times\bar{L}_{\mathrm{sym}}^% {2}(\Omega)\times H^{-1}(\operatorname{div},\Omega)}. Then we utilise the Helmholtz decomposition of {H^{-1}(\operatorname{div},\Omega)} and construct a new formulation stable on first-order and zero-order Sobolev spaces. Finite element discretisations are then given with respect to the new formulation, and both theoretical analysis and numerical verification are given.

scholarly journals The challenge of transformation: Breaking the barriers

2003 ◽  
Vol 34 (3) ◽  
pp. 1-8 ◽  
Author(s):  
W. P. Esterhuyse
Keyword(s):  
South Africa ◽  
Conceptual Analysis ◽  
Second Order ◽  
First Order ◽  
Order Change ◽  
Second Order Change

One of the most commonly used concepts in post-apartheid South Africa is undoubtedly the concept ‘transformation’. In order to strip this concept of its ‘bewitchments’ (Nietzsche; Wittgenstein) a conceptual analysis is made of the meaning and usage of the term. In view of the distinction between first order change and second order change, the need for transformation (ethical and strategic), the resistance against transformation (systemic and individual) and the execution and management of transformation is discussed.

Disorder‐driven first‐order phase transformations: A model for hysteresis

1994 ◽  
Vol 75 (10) ◽  
pp. 5946-5948 ◽  
Author(s):  
Karin Dahmen ◽  
Sivan Kartha ◽  
James A. Krumhansl ◽  
Bruce W. Roberts ◽  
James P. Sethna ◽  
...  
Keyword(s):  
Phase Transformations ◽  
First Order ◽  
First Order Phase
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