Title page for ETD etd-11152005-173234

Type of Document Dissertation
Author Yadav, Aniruddha
URN etd-11152005-173234
Title Boundary Effects on Non-Equilibrium Localized Structures in Spatially Extended Systems
Degree Doctor of Philosophy (Ph.D.)
Department Physics & Astronomy
Advisory Committee
Advisor Name Title
Dana Browne Committee Chair
Juhan Frank Committee Member
Luis Lehner Committee Member
Phillip Sprunger Committee Member
Murad Abu-Farsakh Dean's Representative
  • solvability conditions
  • singular perturbation
  • fronts
  • pattern formation
  • non linear dynamics
  • boundary conditions
Date of Defense 2005-10-26
Availability unrestricted
A study of the effects of system boundaries on bistable front

propagation in nonequilibrium reaction-diffusion systems is presented. Two

model partial differential equations displaying bistable fronts, with

distinct experimental motivations and mathematical structure, are examined in

detail utilizing simulations and perturbation techniques. We see that

propagating fronts in both models bounce, trap, pin, or oscillate at the

boundary, contingent on the imposed boundary condition, initial front speed and

distance from the boundary. The similarities in front boundary interactions

in these two models is traced to the fact that they display the same front

instability (Ising-Bloch bifurcation) that controls the speed of propagation.

A simplified dynamical picture based on ordinary differential equations that

captures the essential features of front motion described by the original

partial differential equations, is derived and analyzed for both models.

In addition to addressing experimentally important boundary effects, we

establish the universality of the Ising-Bloch bifurcation. Useful analytical

insights into perturbative analysis of reaction diffusion systems are also


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