Stability and bifurcations in a model of phase transitions with order parameter

Janusz Sikora, Joseph P. Cusumano, William A. Jester

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A one-dimensional model of phase transitions with convex strain energy is investigated within the limits of nonlinear bar theory. The model is a special case of a coupled field theory that has been developed by Fried and Gurtin to study the nucleation and propagation of phase boundaries. The system of governing equations studied here consists of a wave equation coupled to a nonlinear reaction-diffusion equation. Using phase plane methods, the equilibria of the system have been constructed in order to obtain the macroscopic response of the bar and the bifurcation diagram. It is demonstrated that a large number of coexisting spatially periodic, inhomogeneous solutions can occur, with the number of these solutions being inversely proportional to the diffusion coefficient in the reaction-diffusion subsystem. A stability analysis of the equilibria is presented.

Original languageEnglish (US)
Title of host publication16th Biennial Conference on Mechanical Vibration and Noise
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791880425
DOIs
StatePublished - 1997
EventASME 1997 Design Engineering Technical Conferences, DETC 1997 - Sacramento, United States
Duration: Sep 14 1997Sep 17 1997

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume1C-1997

Conference

ConferenceASME 1997 Design Engineering Technical Conferences, DETC 1997
CountryUnited States
CitySacramento
Period9/14/979/17/97

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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