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Shocks versus kinks in a discrete model of displacive phase transitions

Trofimov, Evgueni (2010) Shocks versus kinks in a discrete model of displacive phase transitions. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

We consider dynamics of phase boundaries in a bistable one-dimensional lattice with harmonic long-range interactions. Using Fourier transform and Wiener-Hopf technique, we construct traveling wave solutions that represent both subsonic phase boundaries (kinks) and intersonic ones (shocks). We derive the kinetic relation for kinks that provides a needed closure for the continuum theory. We show that the different structure of the roots of the dispersion relation in the case of shocks introduces an additional free parameter in these solutions, which thus do not require a kinetic relation on the macroscopic level. The case of ferromagnetic second-neighbor interactions is analyzed in detail. We show that the model parameters have a significant effect on the existence, structure and stability of the traveling waves, as well as their behavior near the sonic limit.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Trofimov, Evguenievt3@pitt.eduEVT3
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairVainchtein, Annaaav4@pitt.eduAAV4
Committee MemberErmentrout, Bardbard@math.pitt.eduBARD
Committee MemberDayal, Kaushikkaushik@cmu.edu
Committee MemberTroy, Williamtroy@math.pitt.eduTROY
Date: 1 October 2010
Date Type: Completion
Defense Date: 16 July 2010
Approval Date: 1 October 2010
Submission Date: 26 July 2010
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: driving force; kinetic relation; lattice models; lattice waves; martensitic phase transitions; nonlocal interactions; shock waves
Other ID: http://etd.library.pitt.edu/ETD/available/etd-07262010-160731/, etd-07262010-160731
Date Deposited: 10 Nov 2011 19:54
Last Modified: 15 Nov 2016 13:47
URI: http://d-scholarship.pitt.edu/id/eprint/8627

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