Bistable systems with propagating fronts leading to pattern formation

FWN – Publicaties zonder aanstelling Universiteit Leide

Propagation and Structure of Planar Streamer Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations. In the present long paper, you find the physics of the model and the interfacial approach further explained. As a first ingredient of this approach, we here analyze planar fronts, their profile and velocity. We encounter a selection problem, recall some knowledge about such problems and apply it to planar streamer fronts. We make analytical predictions on the selected front profile and velocity and confirm them numerically. (abbreviated abstract)Comment: 23 pages, revtex, 14 ps file

Bistable Systems with Propagating Fronts Leading to Pattern Formation

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

A universal modified van der Waals equation of state. Part I: Polymer and mineral glass formers

PVT data of glass formers (minerals and polymers) published in the literature are re-analyzed. All the polymer glass formers (PS, PVAc, PVME, PMMA, POMS, PBMA, PVC, PE, PP, PMPS, PMTS, PPG) present two main properties which have never been noted: a) the isobars P(V) have a fan structure characterized by the two parameters T* and V*; b) the isotherms verify the principle of temperature-pressure superposition for P < P *. From these properties we show that the Equation Of State (EOS) can be put on a modified van der Waals form (VW-EOS), (V − V *) = (V0 − V *)P */(P + P *) . The characteristic pressure P* and the covolume V* are T and P independent. In polymer glass formers P* and V* have same values in the α (melt) and β (glass) domains. The characteristic temperatures T * deduced from the Fan Structure of the Isobar (FSIb) above and below T g are different. The characteristic temperature T *(α) of the melt state is found near the Vogel temperature T 0 for linear polymers and more than 100 K below T 0 for atactic polymers (with pendent groups). This difference in atactic polymers (and in some low molecular weight compounds) is explained by the importance of the β motions due to the pendent groups. The independence of T 0 on P is discussed. A modified VFT equation (analogous to the compensation law and Meyer-Neldel rule) giving the relaxation time τ of the α motions as a function of P and T is proposed. The fan structure of the isotherm logτ versus P is explained. It is shown that organic non-polymeric liquids (C6H12, C6H14, DHIQ, OTP, Glycerol, Salol, PDE, DGEBA), mineral glass (SiO2, Se, GeSe4, GeSe2, GeO2, As2O3 and two metallic glasses (LaCe and CaAl alloys) verify this VW-EOS with similar accuracy. The relation P * = B 0/γ B among the characteristic pressure P *, the zero-pressure modulus B 0 and the Slatter-Grüneisen anharmonicity parameter γ B deduced from the VW-EOS, is observed in all the glass formers