Scholars@Duke
Aric A Wheeler

Aric A Wheeler

Phillip Griffiths Assistant Research Professor of Mathematics
Mathematics

Scholarly Works

Diffusive stability of convective Turing patterns

Journal article Mathematical Models and Methods in Applied Sciences · June 30, 2026 Following the approach of Eckhaus, Mielke, and Schneider for reaction–diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg–Landau approximation. Notabl ... Full text Cite

Convective Turing bifurcation

Journal article Mathematical Models and Methods in Applied Sciences · March 1, 2026 Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction–diffusion systems, we justify rigorously by Lyapunov–Schmidt reduction the formal amplitude (complex Ginzburg–Landau) equations describing Turing-type bifurcations of g ... Full text Cite

Majda and ZND Models for Detonation: Nonlinear Stability vs. Formation of Singularities

Journal article SIAM Journal on Mathematical Analysis · October 31, 2024 Abstract.In this paper we explore the boundaries of damping estimates by comparing and contrasting two closely related models of combustion, the Majda and ZND models. We are especially concerned with studying the ... Full text Cite

Isolas Versus Snaking of Localized Rolls

Journal article Journal of Dynamics and Differential Equations · September 2019 Full text Cite

Geometric Optics for Rayleigh Wavetrains in d-Dimensional

Journal article SIAM Journal on Mathematical Analysis · January 2018 A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been done on the problem of constructing a leading term in an approximate so ... Full text Cite