scholarly journals Random complex zeroes, II. Perturbed lattice

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

Texture Evolution and Softening Processes in an Austenitic Ni-30Fe Alloy Subjected to Hot Deformation and Subsequent Annealing

2011 ◽  
Vol 702-703 ◽  
pp. 435-438
Author(s):  
Peter D. Hodgson ◽  
Pavel Cizek ◽  
A.S. Taylor ◽  
Hossein Beladi
Keyword(s):  
Consumption Rate ◽  
Static Recrystallization ◽  
Texture Evolution ◽  
Model Alloy ◽  
Softening Mechanism ◽  
Dynamic Softening ◽  
Random Complex ◽  
And Migration ◽  
Dislocation Annihilation ◽  
Softening Stage

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.

Microstructure Evolution and Softening Processes Occurring during Annealing of Hot Deformed Ni-30Fe Austenite

2012 ◽  
Vol 706-709 ◽  
pp. 2134-2139
Author(s):  
Peter D. Hodgson ◽  
Pavel Cizek ◽  
Hossein Beladi ◽  
A.S. Taylor
Keyword(s):  
Microstructure Evolution ◽  
Model Alloy ◽  
Recrystallization Process ◽  
Softening Mechanism ◽  
Dynamic Softening ◽  
Random Complex ◽  
And Migration ◽  
Dislocation Annihilation ◽  
Softening Stage ◽  
Prolonged Holding

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.

Random, Complex, and Quantum

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

scholarly journals Dynamics of a continued fraction of Ramanujan with random coefficients

2005 ◽  
Vol 2005 (5) ◽  
pp. 449-467 ◽  
Author(s):  
Jonathan M. Borwein ◽  
D. Russell Luke
Keyword(s):  
Dynamical Systems ◽  
Difference Equations ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Random Coefficients ◽  
Convergence Properties ◽  
Stochastic Difference Equations ◽  
Random Complex ◽  
The Stability ◽  
Complex Valued

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.

Synaptic signal streams generated by ex vivo neuronal networks contain non‐random, complex patterns

2014 ◽  
Vol 38 (1) ◽  
pp. 184-194 ◽  
Author(s):  
Sangmook Lee ◽  
Jill M. Zemianek ◽  
Abraham Shultz ◽  
Anh Vo ◽  
Ben Y. Maron ◽  
...  
Keyword(s):  
Neuronal Networks ◽  
Ex Vivo ◽  
Random Complex ◽  
Complex Patterns

scholarly journals Mean field theory of directed polymers with random complex weights

1993 ◽  
Vol 156 (2) ◽  
pp. 221-244 ◽  
Author(s):  
B. Derrida ◽  
M. R. Evans ◽  
E. R. Speer
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Directed Polymers ◽  
Random Complex
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