Biomedical subjects

Ute Ebert

Publications and source records attributed to Ute Ebert.

12 recordsLinked to original sources

PubMed2006

Numerical convergence of the branching time of negative streamers.

Discharge streamers in experiments branch frequently. Arrayás [Phys. Rev. Lett. 88, 174502 (2002)] presented simulations of branching streamers and interpreted them as physical branching events. The numerical results were criticized by Kulikovsky [Phys. Rev. Lett. 89, 229401 (2002)]. Using an adaptive grid algorithm, we here present numerical experiments on the effect of grid resolution on streamer branching. The convergence of branching time with stepwise finer grid sizes provides a quantitative correction on the earlier, low-resolution results in overvolted gaps. Furthermore, streamers can branch even in undervolted, but sufficiently long gaps, but fewer branching modes are accessible than in higher fields.

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PubMed2005

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. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

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PubMed2005

Oscillations in dc driven barrier discharges: numerical solutions, stability analysis, and phase diagram.

A short gas-discharge layer sandwiched with a semiconductor layer between planar electrodes shows a variety of spatiotemporal patterns. We focus on the spontaneous temporal oscillations that occur while a dc voltage is applied and while the system stays spatially homogeneous; the results for these oscillations apply equally to a planar discharge in series with any resistor with capacitance. We define the minimal model, identify its independent dimensionless parameters, and then present the results of the full time-dependent numerical solutions of the model as well as of a linear stability analysis of the stationary state. Full numerical solutions and the results of the stability analysis agree very well. The stability analysis is then used for calculating bifurcation diagrams. We find semiquantitative agreement with experiment for the diagram of bifurcations from stationary to oscillating solutions as well as for amplitude and frequency of the developing limit cycle oscillations.

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PubMed2004

Period doubling cascade in glow discharges: local versus global differential conductivity.

Short planar glow discharges coupled to a resistive layer exhibit a wealth of spontaneous spatiotemporal patterns. Due to similarities with other pattern forming systems that are described by reaction-diffusion models, several authors have tried to derive such models from discharge physics. We investigate the temporal oscillations of the discharge system and find a cascade of period doubling events. This shows that the inner structure of the discharge is more complex than can be described by a two-component reaction-diffusion-model with negative differential conductivity. We also derive an alternative reduced model.

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PubMed2004

Dependence of the transition from Townsend to glow discharge on secondary emission.

, (1991)]]. Sijacić and Ebert stated that this transition strongly depends on secondary emission gamma from the cathode. We show here that the earlier results of von Engel and Raizer on the small current expansion about the Townsend limit actually are the limit of small gamma of the Sijacić and Ebert expression, and that for larger gamma the old and the Sijacić and Ebert new results vary by no more than a factor of 2. We discuss the gamma dependence of the transition, which is rather strong for short gaps.

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PubMed2004

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. This model can be analyzed by conformal mapping techniques which allow the reduction of the dynamical problem to finite sets of nonlinear ordinary differential equations. Our solutions illustrate that branching is generic for the intricate head dynamics of streamers in the Lozansky-Firsov limit.

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PubMed2004

Stability of negative ionization fronts: Regularization by electric screening?

We recently have proposed that a reduced interfacial model for streamer propagation is able to explain spontaneous branching. Such models require regularization. In the present paper we investigate how transversal Fourier modes of a planar ionization front are regularized by the electric screening length. For a fixed value of the electric field ahead of the front we calculate the dispersion relation numerically. These results guide the derivation of analytical asymptotes for arbitrary fields: for small wave-vector k, the growth rate s(k) grows linearly with k, for large k, it saturates at some positive plateau value. We give a physical interpretation of these results.

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PubMed2002

Transition from Townsend to glow discharge: subcritical, mixed, or supercritical characteristics.

The transition from Townsend to glow discharge is investigated numerically in one space dimension in full parameter space within the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons (alpha process), secondary electron emission from the cathode (gamma process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the current that fits our numerical data very well. Depending on the two determining parameters gamma and system size pd, the transition from Townsend to glow discharge can show the textbook subcritical behavior, but for smaller values of pd, we also find supercritical or some unexpected intermediate "mixed" behavior. Our work shows the same qualitative dependence of U=U(I,pd) for fixed gamma as the old experiments by Pokrovskaya-Soboleva and Klyarfeld. Furthermore, the analysis lays the basis for understanding the complex spatiotemporal patterns in short planar barrier discharge systems.

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PubMed2002

Branching of negative streamers in free flight.

We have recently shown that a negative streamer in a sufficiently high homogeneous field can branch spontaneously due to a Laplacian instability, rather than approach a stationary mode of propagation with fixed radius. In our previous simulations, the streamer started from a wide initial ionization seed on the cathode. We here demonstrate, in improved simulations, that a streamer emerging from a single electron branches in the same way. In fact, though the evolving streamer is much more narrow, it branches after an even shorter propagation distance.

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PubMed2002

Coherent scattering function in the reptation model: analysis beyond asymptotic limits.

We calculate the coherent dynamical scattering function S(c)(q,t;N) of a flexible chain of length N, diffusing through an ordered background of topological obstacles. As an instructive generalization, we also calculate the scattering function S(c)(q,t;M,N) for the central piece of length M infinity, M fixed. The results do not support the model of a "Rouse chain in a tube." We trace this back to the nonequilibrium initial conditions of the latter model. Second, in the limit of long chains (M=N--> infinity ) and times large compared to the internal relaxation time (t/N(2)--> infinity ), our theory reproduces the results of the primitive chain model. This limiting form applies only to extremely long chains, and for chain lengths accessible in practice, effects of, e.g., tube length fluctuations are not negligible.

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PubMed2002

Spontaneous branching of anode-directed streamers between planar electrodes.

Nonionized media subject to strong fields can become locally ionized by penetration of finger-shaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that, for sufficiently large fields, the streamer tip can split. This happens close to the limit of "ideal conductivity." Qualitatively, the tip splitting is due to a Laplacian instability quite like that in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism.

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PubMed2001

Diffusion coefficient of propagating fronts with multiplicative noise.

Recent studies have shown that in the presence of noise, both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper, we derive an expression for the effective diffusion coefficient of such fronts, which was motivated before on the basis of a multiple scale ansatz. Our systematic derivation is based on the decomposition of the fluctuating front into a suitably positioned average profile plus fluctuating eigenmodes of the stability operator. While the fluctuations of the front position in this particular decomposition are a Wiener process on all time scales, the fluctuations about the time-averaged front profile relax exponentially.

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