Travelling waves in electroconvection of the nematic Phase 5: A test of the weak electrolyte model

We investigated travelling waves appearing as the primary pattern-forming instability in the nematic Phase 5 (Merck) in the planar geometry in order to test the recently developed weak electrolyte model of ac-driven electroconvection [M. Treiber and L. Kramer, Mol. Cryst. Liq. Cryst 261, 311 (1995)]. Travelling waves are observed over the full conductive range of applied frequencies for three cells of different layer thickness d. We also measured the elastic constants, the electric conductivity, and the dielectric constant. The other parameters of Phase 5 are known, apart from the (relatively unimportant) viscosity $\alpha_1$ and the two parameters of the weak electrolyte model that are proportional to the geometric mean of the mobilities, and the recombination rate, respectively. Assuming a sufficiently small recombination rate, the predicted dependence of the frequency of the travelling waves at onset (Hopf frequency) on d and on the applied frequency agreed quantitatively with the experiments, essentially without fit parameters. The absolute value of the Hopf frequency implies that the geometric mean of the mobilities amounts to $1.1 \times 10^{-10} m^2/(Vs)$.Comment: ReVTeX, 24 pages, 4 figures, to appear in Journal de Physique I

Abnormal Rolls and Regular Arrays of Disclinations in Homeotropic Electroconvection

We present the first quantitative verification of an amplitude description for systems with (nearly) spontaneously broken isotropy, in particular for the recently discovered abnormal-roll states. We also obtain a conclusive picture of the 3d director configuration in a spatial period doubling phenomenon involving disclination loops (CRAZY rolls). The first observation of two Lifshitz frequencies in electroconvection is reported.Comment: 4 pages; 4 figure

Überkritische Kohlenstoffdioxid-Mikroemulsionen als Vorstufen für Nanoschäume - Darstellung, Charakterisierung und Nanostruktur

Überkritische Kohlenstoffdioxid (CO2) - Mikroemulsionen stellen die Basis zur Herstellung neuartiger, hochisolierender Nanoschäume nach dem von STREY et al. entwickelten POSME-Verfahren (Principle Of Supercritical Microemulsion Expansion) dar. Diese Arbeit legt den Schwerpunkt auf der Darstellung effizienter überkritischer CO2-Mikroemulsionen und der Charakterisierung des Phasenverhaltens sowie der Nanostruktur. Startpunkt war eine ineffiziente CO2-Mikroemulsion mit nichtfluorierten Tensiden. Durch den Einsatz von technischen, nichtionischen, fluorierten Tensiden konnte die Effizienz der Mikroemulsion um rund 70% gesteigert werden. Einblicke in die Nanostruktur dieser effizienten CO2-Mikroemulsionen gaben verschiedene Streumethoden: die Kleinwinkelneutronenstreuung (SANS) und die dynamische Lichtstreuung (DLS). Diese wurden möglich durch den Aufbau zweier neuer Hochdruckzellen HPSANS und HPDLS. Eine bikontinuierliche Nanostruktur von CO2-Mikroemulsionen konnte so zum ersten Mal mit SANS-Experimenten nachgewiesen werden, wobei sich Strukturgrößen zwischen 2 - 26 nm ergaben. Die Charakterisierung der Tröpfchenstruktur erfolgte mit beiden Hochdruckzellen HPSANS und HPDLS und ergab den gleichen Durchmesser für eine Probe gleicher Zusammensetzung. Aus Drucksprungexperimenten an einer Tröpfchen-Mikroemulsion konnte mit HPDLS gezeigt werden, dass es eine reversible Druckabhängigkeit des Tröpfchenradius gibt: Mit sinkendem Druck wird der Radius größer, mit steigendem Druck kleiner. Zusätzlich wurde ein weiterer Meilenstein in der Verwirklichung fixierbarer Mikroemulsionen gesetzt, indem erfolgreich eine hochviskose Mikroemulsion mit 75% Zucker als Modellmonomer in der hydrophilen Phase und nahekritischem Propan bei einem Druck von 250 bar formuliert wurde. Damit wurde erstmals gezeigt, dass die ersten zwei Stufen des POSME-Prinzips zur Herstellung neuartiger Nanoschäume auf der Basis von überkritischen CO2-Mikroemulsionen technisch realisierbar sind

On propagation failure in 1 and 2 dimensional excitable media

We present a non-perturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behaviour of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity and scaling behavior. The results are compared with numerical simulations and show good agreement.Comment: accepted for publication in Chao

A normal form for excitable media

We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behaviour of single pulses in a periodic domain and also the richer behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao

Many-body theory for systems with particle conversion: Extending the multiconfigurational time-dependent Hartree method

We derive a multiconfigurational time-dependent Hartree theory for systems with particle conversion. In such systems particles of one kind can convert to another kind and the total number of particles varies in time. The theory thus extends the scope of the available and successful multiconfigurational time-dependent Hartree methods -- which were solely formulated for and applied to systems with a fixed number of particles -- to new physical systems and problems. As a guiding example we treat explicitly a system where bosonic atoms can combine to form bosonic molecules and vise versa. In the theory for particle conversion, the time-dependent many-particle wavefunction is written as a sum of configurations made of a different number of particles, and assembled from sets of atomic and molecular orbitals. Both the expansion coefficients and the orbitals forming the configurations are time-dependent quantities that are fully determined according to the Dirac-Frenkel time-dependent variational principle. Particular attention is paid to the reduced density matrices of the many-particle wavefunction that appear in the theory and enter the equations of motion. There are two kinds of reduced density matrices: particle-conserving reduced density matrices which directly only couple configurations with the same number of atoms and molecules, and particle non-conserving reduced density matrices which couple configurations with a different number of atoms and molecules. Closed-form and compact equations of motion are derived for contact as well as general two-body interactions, and their properties are analyzed and discussed.Comment: 46 page