scholarly journals Random complex zeroes, III. Decay of the hole probability

2005 ◽  
Vol 147 (1) ◽  
pp. 371-379 ◽  
Author(s):  
Mikhail Sodin ◽  
Boris Tsirelson
2011 ◽  
Vol 702-703 ◽  
pp. 435-438
Author(s):  
Peter D. Hodgson ◽  
Pavel Cizek ◽  
A.S. Taylor ◽  
Hossein Beladi

The current work has investigated the texture development in an austenitic Ni-30Fe model alloy during deformation within the dynamic recrystallization (DRX) regime and after post-deformation annealing. Both the deformed matrix and DRX texture displayed the expected FCC shear components, the latter being dominated by the low Taylor factor grains, which was presumably caused by their lower consumption rate during DRX. The deformed matrix grains were largely characterized by organized, microband structures, while the DRX grains showed more random, complex subgrains/cell arrangements. The latter substructure type proved to be significantly less stable during post-deformation annealing. The recrystallization of the deformed matrix occurred through nucleation and growth of new grains fully replacing the deformed structure, as expected for the classical static recrystallization (SRX). Unlike the DRX grains, the SRX texture was essentially random. By contrast, a novel softening mechanism was revealed during annealing of the fully DRX microstructure. The initial post-dynamic softening stage involved rapid growth of the dynamically formed nuclei and migration of the mobile boundaries in line with the well-established metadynamic recrystallization (MDRX) mechanism, which weakened the starting DRX texture. However, in parallel, the sub-boundaries within the deformed DRX grains progressively disintegrated through dislocation climb and dislocation annihilation, which ultimately led to the formation of dislocation-free grains. Consequently, the weakened DRX texture largely remained preserved throughout the annealing process.


2012 ◽  
Vol 706-709 ◽  
pp. 2134-2139
Author(s):  
Peter D. Hodgson ◽  
Pavel Cizek ◽  
Hossein Beladi ◽  
A.S. Taylor

The current work investigates the microstructure evolution and softening processes that take place during annealing of an austenitic Ni-30Fe model alloy subjected to hot deformation in the dynamic recrystallization (DRX) regime. The substructure of the deformed matrix grains largely comprised organized microband arrays, though that of the DRX grains consisted of more random, complex subgrain/cell arrangements. This substructure disparity was also reflected by the distinct difference in the mechanism of post-deformation softening taking place during annealing of the deformed matrix and DRX grains. In the former, the recrystallization process took place through nucleation and growth of new grains fully replacing the deformed structure, as expected for the classical static recrystallization (SRX). The corresponding texture was essentially random, in contrast to that of the DRX grains dominated by low Taylor factor components. The microbands originally present within the deformed matrix grains displayed some tendency to disintegrate during annealing, nonetheless, they remained largely preserved even at prolonged holding times. During annealing of the fully DRX microstructure, a novel softening mechanism was revealed. The initial post-dynamic softening stage involved rapid growth of the dynamically formed nuclei and migration of the mobile boundaries in correspondence with the well-established metadynamic recrystallization (MDRX) mechanism. However, in contrast to the deformed matrix, SRX was not observed and the sub-boundaries within DRX grains rapidly disintegrated through dislocation climb and dislocation annihilation, which led to the formation of dislocation-free grains already at short holding times. Consequently, the DRX texture initially became slightly weakened and then remained largely preserved throughout the annealing process.


2014 ◽  
pp. 191-204
Author(s):  
Artur Ekert
Keyword(s):  

2006 ◽  
Vol 152 (1) ◽  
pp. 105-124 ◽  
Author(s):  
Mikhail Sodin ◽  
Boris Tsirelson
Keyword(s):  

2005 ◽  
Vol 2005 (5) ◽  
pp. 449-467 ◽  
Author(s):  
Jonathan M. Borwein ◽  
D. Russell Luke

We study a generalization of a continued fraction of Ramanujan with random, complex-valued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.


2014 ◽  
Vol 38 (1) ◽  
pp. 184-194 ◽  
Author(s):  
Sangmook Lee ◽  
Jill M. Zemianek ◽  
Abraham Shultz ◽  
Anh Vo ◽  
Ben Y. Maron ◽  
...  

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