Model for current patterns in physical systems with two charge carriers

Abstract

The temporal and spatial evolution of patterns in physical systems due to electrical current flow can be described for a certain class of systems, which includes certain semiconductor and gas discharge systems, by a two-layer model in terms of the electrical current density and the electrical potential. An equation for the nonlinear layer is derived, the characteristic parameters of which can be obtained from experiments at the respective systems without inhomogeneous patterns lateral to the main current direction. The resulting equation takes into account diffusion and drift effects in the nonlinear layer. It turns out that the drift effects occur only if there is a "net space charge. " Two special cases are derived depending on which of the two layers gives the main contribution to the displacement current density, and the typical static and dynamic behavior is studied by numerical calculations. Furthermore, the application of the model to rea1 devices is discussed, and a comparison is made with experimental results obtained with a dc glow-discharge system.

Period doubling cascade in glow discharges: Local versus global differential conductivity

“…There is no systematic way to reduce this model to a simpler one [4,[15][16][17][18][19][20][21][22] with two scalar parameters such as voltage U and current J. We draw this conclusion both from direct analysis and from the occurence of period doubling in the numerical solutions.…”

“…(ii) A glow discharge in a simple electric circuit shows more complex behavior than can be expected from the proposed reaction-diffusion models [4,[15][16][17][18][19][20][21][22] for voltage U and current J with (global) negative differential conductivity dU / dJ Ͻ 0.…”

“…In Refs. [4,[16][17][18], an effective reaction-diffusion model in the two dimensions transversal to the current is proposed. Roughly, it consists of two nonlinear partial differential equations for the current J and the voltage U of the form ‫ץ‬ t U͑x,y,t͒ = F͑U,J͒, ‫ץ‬ t J͑x,y,t͒ = G͑U,J͒ ͑1͒…”

“…Negative differential conductivity of the glow discharge should then be the driving force of pattern formation. A number of authors [4,[15][16][17][18][19][20][21][22] actually have aimed at deriving such models from gas discharge physics, but not in a systematic manner.…”

Dynamical structures in binary media of potassium-driven neurons

“…For a given non vanishing value of z it results in an additional shift of the y-nullcline decreasing effectively the excitability value a. Mathematically we can call it a second activator which was previously introduced in models for nonlinear semiconductors [31] .…”