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Generalized Phase Field Models with Microscopic Potentials

Esenturk, Emre (2011) Generalized Phase Field Models with Microscopic Potentials. Doctoral Dissertation, University of Pittsburgh.

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    Abstract

    In this thesis we study the solidification process of systems with intrinsicanisotropy. We aim at finding a bridge between the microscopic mechanismsand macroscopic description. This is achieved by generalizing the currentphase field models in a way to incorporate microscopic physics and usingasymptotic techniques to obtain macroscopic results. Upon analysis,expressions for physically relevant quantities are obtained. Also it isfound that classical interface relations for both stationary and movinginterfaces hold. These conditions are presented in various representations.Exemplary numerical calculations are carried out to illustrate the potentialof the method as an additional tool in the study of interfaces. Furthermore,a concrete physical system with realistic parameters is considered to showhow one can use the ideas developed here in order to get results that are ofinterest to other scientific communities, e.g. materials scientists andphysicists.

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    Details

    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmail
    Committee ChairCaginalp, Gunduzcaginalp@pitt.edu
    Committee MemberRollett, Anthonyrollett@andrew.cmu.edu
    Committee MemberLennard, Chrislennard@pitt.edu
    Committee MemberChen, Xinfuxinfu@pitt.edu
    Title: Generalized Phase Field Models with Microscopic Potentials
    Status: Unpublished
    Abstract: In this thesis we study the solidification process of systems with intrinsicanisotropy. We aim at finding a bridge between the microscopic mechanismsand macroscopic description. This is achieved by generalizing the currentphase field models in a way to incorporate microscopic physics and usingasymptotic techniques to obtain macroscopic results. Upon analysis,expressions for physically relevant quantities are obtained. Also it isfound that classical interface relations for both stationary and movinginterfaces hold. These conditions are presented in various representations.Exemplary numerical calculations are carried out to illustrate the potentialof the method as an additional tool in the study of interfaces. Furthermore,a concrete physical system with realistic parameters is considered to showhow one can use the ideas developed here in order to get results that are ofinterest to other scientific communities, e.g. materials scientists andphysicists.
    Date: 25 September 2011
    Date Type: Completion
    Defense Date: 14 April 2011
    Approval Date: 25 September 2011
    Submission Date: 17 February 2011
    Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-02172011-165020
    Uncontrolled Keywords: interfaces; phase field model
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:31
    Last Modified: 20 Jan 2012 09:37
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-02172011-165020/, etd-02172011-165020

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