Construction and test of a moving boundary model for negative streamer discharges.

Starting from the minimal model for the electrically interacting densities of electrons and ions in negative streamer discharges, we derive a moving boundary approximation for the ionization fronts. Solutions of the moving boundary model have already been discussed, but the derivation of the model was postponed to the present paper. The key ingredient of the model is the boundary condition on the moving front.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions.

Streamer branching rationalized by conformal mapping techniques.

Spontaneous branching of discharge channels is frequently observed, but not well understood. We recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields. We here present analytical results for such streamers in the Lozansky-Firsov limit where they can be modeled as moving equipotential ionization fronts.

Experimental evidence for an intrinsic route to polymer melt fracture phenomena: a nonlinear instability of viscoelastic Poiseuille flow.

The production rate of polymer fibers by extrusion is usually limited by the appearance of a series of instabilities ("melt fracture") that lead to unwanted undulations of the surface. We present both qualitative and quantitative experimental evidence that-in addition to previously known polymer-specific scenarios-there is an intrinsic route towards melt fracture type phenomena: a nonlinear ("subcritical") instability of viscoelastic Poiseuille flow.

Intrinsic route to melt fracture in polymer extrusion: a weakly nonlinear subcritical instability of viscoelastic poiseuille flow.

As is well known, the extrusion rate of polymers from a cylindrical tube or slit (a "die") is in practice limited by the appearance of "melt fracture" instabilities which give rise to unwanted distortions or even fracture of the extrudate. We present the results of a weakly nonlinear analysis which gives evidence for an intrinsic generic route to melt fracture via a weakly nonlinear subcritical instability of viscoelastic Poiseuille flow. This instability and the onset of associated melt fracture phenomena appear at a well-defined ratio of the elastic stresses to viscous stresses of the polymer solution.