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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

The Method of Phase Field

The course is not on the list Without time-table
Code Completion Credits Range
D01MFP ZK 2P
Garant předmětu:
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Department of Mathematics
Synopsis:

The class is devoted to the description of multiphase systems by the phase-field method base on the theory of dynamic critical phenomena and on the Cahn -Hilliard theory for single-component and multi-comopnent systém in dynamics of continua. This method allows for description of material systems in very small scales where the 1-st order and 2-nd order phase changes can occur.

Requirements:
Syllabus of lectures:

1. State variables in systems out of equilibrium.2. Basics of variational calculus.3. Basics on differential geometry on hypersurfaecs.3. Thermodynamic potentials in systems with interfaces.4. Cahn -Hilliard theory.5. Phase-field equations for single -component systems.6. Phase-field equations for multi -component systems.7. Phase-field-crystal method.

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Study materials:

Key references:[1]J. W. Cahn and J. E. Hilliard, Free Energy of a Nonuniform System.I. Interfacial Free Energy, J. Chem.Phys., 1958, 28, 258-267[2]G. Caginalp, AnAnalysis of a Phase Field Model of a Free Boundary, Arch. Rational Mech. Anal., 1986, 92, 205-245 [3]S. Bulent Biner, Programing Phase-Field Modeling, Springer Switzerland 2017[4]K.-A. Wu and P. W. Voorhees, Stress-induced morphological instabilities at the nanoscale examined using the phase field crystal approach, Phys. Rev. 2009, B 80, 125408.Recommended references:[5]J.S. Rowlinson, Translation of J. D. van der Waals' 'The Thermodynamic Theory of Capillarity Underthe Hypothesis of a Continuous Variation of Density', J. Stat. Phys., 1979, 20, 197-244.[6]E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, 1984, Basel.[7]A. Visintin, Models of Phase Transitions, Birkhäuser, 1996, Boston.[8] N. Provatas and K. Elder, Phase-Field Methods in Materials Science and Engineering, Wiley VCH, Weinheim 2010.

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Data valid to 2024-05-23
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