Sum-Rule Relationships among Phenomenological Coefficients: Simplifications for the Analysis of Segregation and Chemical Diffusion

2005 ◽  
Vol 26 (5) ◽  
pp. 503-509
Author(s):  
I.V. Belova ◽  
G.E. Murch
2006 ◽  
Vol 249 ◽  
pp. 17-26
Author(s):  
Irina V. Belova ◽  
Graeme E. Murch

In this overview, we discuss the sum-rule relating phenomenological coefficients in randomly mixed systems and consider several applications to collective diffusion problems. These applications include intrinsic diffusion multicomponent alloys, chemical diffusion in strongly ionic mixed cation crystals and demixing of cations in randomly mixed quaternary transition metal oxides. In each case a substantial simplification is possible as a result of the sum-rule.


2007 ◽  
Vol 263 ◽  
pp. 1-10 ◽  
Author(s):  
Irina V. Belova ◽  
Graeme E. Murch

Tracer diffusion experiments have historically furnished much of the information about fundamental diffusion processes as embodied in such quantities as tracer correlation factors and vacancy-atom exchange frequencies. As tracer diffusion experiments using radiotracers are rather less often performed nowadays, it is important to be able to process other diffusion data to provide similar fundamental information. New procedures that are primarily based around the random alloy model have been established recently for analyzing chemical diffusion data in binary and ternary alloy systems. These procedures are reviewed here. First, we review the random alloy model, the Sum-rule relating the phenomenological coefficients and three diffusion kinetics formalisms making use of the random alloy. Next, we show how atom-vacancy exchange frequency ratios and then component tracer correlation factors can be extracted from chemical diffusion data in alloy systems. Examples are taken from intrinsic diffusion and interdiffusion data in a number of binary and ternary alloys.


2003 ◽  
Vol 91 (7-8-9) ◽  
pp. 87-91
Author(s):  
P. Dawah Tankeu ◽  
A. Gruzdeva ◽  
M. Zapukhlyak ◽  
L. Doerrer ◽  
K. Goemann ◽  
...  

2020 ◽  
Vol 18 (1) ◽  
pp. 1895-1914
Author(s):  
Linlin Meng ◽  
Wen-Qing Xu ◽  
Shu Wang

Abstract We study the boundary layer problem of a Keller-Segel model in a domain of two space dimensions with vanishing chemical diffusion coefficient. By using the method of matched asymptotic expansions of singular perturbation theory, we construct an accurate approximate solution which incorporates the effects of boundary layers and then use the classical energy estimates to prove the structural stability of the approximate solution as the chemical diffusion coefficient tends to zero.


2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.


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