arXiv subjects

A. Carpio

Publications and source records attributed to A. Carpio.

42 records · Page 3Linked to original sources

arXiv2002

Depinning transitions in discrete reaction-diffusion equations

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The critical parameter values are characterized at the depinning transition and an approximation for the front speed just beyond threshold is given.

cond-mat.mtrl-sci↗

arXiv2002

Pulse propagation in discrete systems of coupled excitable cells

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simulations and discuss evolution of initial data into pulses and pulse generation at a boundary. Formulas for the speed and length of pulses are also obtained.

cond-mat.soft↗

arXiv2002

Motion of Wavefronts in Semiconductor Superlattices

An analysis of wavefront motion in weakly coupled doped semiconductor superlattices is presented. If a dimensionless doping is sufficiently large, the superlattice behaves as a discrete system presenting front propagation failure and the wavefronts can be described near the threshold currents $J_i$ ($i=1,2$) at which they depin and move. The wavefront velocity scales with current as $|J-J_i|^{1\over 2}$. If the dimensionless doping is low enough, the superlattice behaves as a continuum system and wavefronts are essentially shock waves whose velocity obeys an equal area rule.

cond-mat.mes-hall↗

arXiv2002

Effects of disorder on the wave front depinning transition in spatially discrete systems

Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and subject to random external forces. The presence of weak randomness shrinks the pinning interval and it changes the critical exponent of the wave front depinning transition from 1/2 to 3/2. This effect is derived by means of a recent asymptotic theory of the depinning transition, extended to discrete drift-diffusion models of transport in semiconductor superlattices and confirmed by numerical calculations.

cond-mat.stat-mech↗

arXiv2002

Wavefront depinning transition in discrete one-dimensional reaction-diffusion systems

cond-mat.mtrl-sci↗

arXiv2000

Wavefronts may move upstream in doped semiconductor superlattices

In weakly coupled, current biased, doped semiconductor superlattices, domain walls may move upstream against the flow of electrons. For appropriate doping values, a domain wall separating two electric field domains moves downstream below a first critical current, it remains stationary between this value and a second critical current, and it moves upstream above. These conclusions are reached by using a comparison principle to analyze a discrete drift-diffusion model, and validated by numerical simulations. Possible experimental realizations are suggested.

cond-mat.mes-hall↗