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Phase Transformation and Singularity Theory
Author(s) -
Simon Werner
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510135
Subject(s) - singularity , gravitational singularity , singularity theory , phase diagram , transformation (genetics) , diagram , point (geometry) , phase (matter) , mathematics , construct (python library) , theoretical physics , computer science , physics , geometry , mathematical analysis , quantum mechanics , biochemistry , chemistry , statistics , gene , programming language
Phase transformation plays an important role in thermodynamics and materials science. Based on the theory of singularities, a new method to construct phase diagrams is presented. Analysing singularities on base of root sequences, see Tamaschke [16], will help to develop singularity graphs, where workings by H. Whitney, R. Thom, and V. I. Arnold provide fundamentals. The generated singularity graphs build the starting point for singularity phase diagrams. A powerful characteristic of such singularity graphs is that higher‐dimensional surfaces can be transformed to a two‐dimensional diagram. The attained singularity diagram can be used in materials science for analytical models of temperature‐concentrated diagrams. As tools from algebra and analysis build a sound basis for singularity diagrams, it is possible to evolve computer software generating these phase diagrams. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)