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Some phenomenological relaxation rate equations based on Bose–Einstein similar kinetics

 

作者: Michael J. Kuba´t,   Jan‐Fredrik Jansson,   Mats Delin,   Josef Kuba´t,   Rodney W. Rychwalski,   Sven Uggla,  

 

期刊: Journal of Applied Physics  (AIP Available online 1992)
卷期: Volume 72, issue 11  

页码: 5179-5186

 

ISSN:0021-8979

 

年代: 1992

 

DOI:10.1063/1.351998

 

出版商: AIP

 

数据来源: AIP

 

摘要:

The possibility of describing transient phenomena associated with flow and consolidation of solids, such as stress relaxation or physical aging, in terms of a kinetic mechanism comprising spontaneous and induced events is discussed. The starting point is the differential equationdn˙/dt=−an˙[1−(b/a)n˙], withndenoting the number of relaxed entities andn˙=dn/dt(a,bare constants,tis time), yielding ann˙(t) function reminiscent of a Bose–Einstein distribution. The correspondingn(t) relation describes the linear variation ofnwith log t, and the exponential dependence ofn˙ onn, as often found experimentally. Replacingn˙ in the starting equation by the relative raten˙/nyields a power‐law‐typen˙(n) dependence. A further modification, where the induction termn˙/nis not linear but raised to a power ≳1, finally produces a generalized version of the stretched exponential. When interpreted formally in terms of a spectrum of relaxation times &tgr;, all three equations produce response functions with discrete &tgr; distributions, provideda≠0.

 

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