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Register a new userCellular Automata Simulation of Grain Growth of Powder Metallurgy Nickel-Based Superalloy
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Yiling Jiang
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Primary {gamma} phase instead of carbides and borides plays an important role in suppressing grain growth during solution at 1433K of FGH98 nickel-based polycrystalline alloys. Results illustrate that as-fabricated FGH98 has equiaxed grain structure and after heat treatment, grains remain equiaxed but grow larger. In order to clarify the effects of the size and volume fraction of the primary {gamma} phase on the grain growth during heat treatment, this paper establish a 2D Cellular Automata (CA) model based on the thermal activation and the lowest energy principle. The CA results are compared with the experimental results and show a good fit with an error less than 10%. Grain growth kinetics are depicted and simulations in real time for various sizes and volume fractions of primary {gamma} particles work out well with the Zener relation. The coefficient n value in Zener relation is theoretically calculated and its minimum value is 0.23 when the radius of primary {gamma} is 2.8{mu}m.
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This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the figures at some particular iteration might be helpful for some specific application. The hardware circuit implementation can be done using opto-electronic components [1-7].
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via dimensional reduction, finding a classification by the first homology group of the manifold modulo torsion. Second, in two dimensions, we show that an extension of this index theory (including torsion) fully classifies quantum cellular automata, at least in the absence of fermionic degrees of freedom. This complete classification in one and two dimensions by index theory is not expected to extend to higher dimensions due to recent evidence of a nontrivial automaton in three dimensions. Finally, we discuss some group theoretical aspects of the classification of quantum cellular automata and consider these automata on higher dimensional real projective spaces.
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Demosthenes Ellinas
, Elena P. Papadopoulou
, Yiannis G. Saridakisn (Department of Sciences
2000
A method of quantization of classical soliton cellular automata (QSCA) is put forward that provides a description of their time evolution operator by means of quantum circuits that involve quantum gates from which the associated Hamiltonian describing a quantum chain model is constructed. The intrinsic parallelism of QSCA, a phenomenon first known from quantum computers, is also emphasized.
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