Ana Carpio

Fronts and pulses propagating in lattices seem to describe physical reality in many different fields: atoms adsorbed on a periodic substrate, motion of dislocations in crystals, propagation of cracks in brittle materials, domain dynamics in semiconductor superlattices, nerve impulse propagation along myelinated nerves, calcium release waves... We have analyzed travelling waves propagating in nonlinear lattices, characterizing pinning and propagation failure in different physical and biological systems by means of bifurcations and active point approximations, which yield predictions of wave profiles and wave speeds by asymptotic methods, even in the presence of stochastic noise. Aplications in biological sciences and materials science are discussed in the corresponding sections.
Additional work in this field include the introduction of nonreflecting boundary conditions for discrete waves, blow up studies and the analysis of aggregation models for bubbles in radioactive waste.

Analysis of helium bubble growth in radioactive waste (with B. Tapiador), Nonlinear Analysis-Real World Applications 11(5), 4174-4184, 2010 [pdf] [archivo]

Nonreflecting boundary conditions for discrete waves (with B. Tapiador), Journal of Computational Physics 229(5), 1879-1896, 2010 [pdf] [archivo]

Explosive behaviour in spatially discrete reaction-diffusion systems (with G. Duro), Discrete and Continuous Dynamical Systems - Series B 12(4), 693-711, 2009 [pdf] [archivo]
Instability and collapse in discrete wave equations (with G. Duro), Computational Methods in Applied Mathematics 5(3), 223-241, 2005 [pdf]
Wave trains, self-oscillations and synchronization in discrete media, Physica D-Nonlinear Phenomena 207(1-2), 117-136, 2005 [pdf] [arxiv]
Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators, Physical Review E 69(4), 046601, 2004 [pdf] [arxiv]
Oscillatory wave fronts in chains of coupled nonlinear oscillators (with L.L. Bonilla) Physical Review E 67(5), 056621, 2003 [pdf] [arxiv]
Depinning transitions in spatially discrete reaction diffusion equations (with Bonilla, L.L.), SIAM J Appl. Math., 63 (3), 1056-1082, 2003 [pdf] [arxiv]
Wavefronts for discrete two-dimensional nonlinear diffusion equations, Applied Mathematics Letters 15(4), 415-421, 2002 [pdf] [archivo]
Effects of disorder on the wave front depinning transition in spatially discrete systems (with Bonilla LL, Luzon A), Physical Review E (RC) 65(3), 035207, 2002 [pdf] [arxiv]
Wave front depinning transition in discrete one-dimensional reaction-diffusion systems (with LL Bonilla), Physical Review Letters 86(26), 6034-6037, 2001 [pdf] [arxiv]
Wave solutions for a discrete reaction-diffusion equation, (with SJ Chapman, S Hastings, JB Mcleod), European Journal of Applied Mathematics 11(4), 399-412, 2000 [pdf] [archivo]