4,012 research outputs found
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.Comment: 11 pages, 2 figure
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 modelled 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. The solutions illustrate that branching is generic for the intricate
head dynamics of streamers in the Lozansky-Firsov-limit.Comment: 4 pages, 2 figure
Segment Motion in the Reptation Model of Polymer Dynamics. II. Simulations
We present simulation data for the motion of a polymer chain through a
regular lattice of impenetrable obstacles (Evans-Edwards model). Chain lengths
range from N=20 to N=640, and time up to Monte Carlo steps. For we for the central segment find clear -behavior as an
intermediate asymptote. The also expected -range is not yet developed.
For the end segment also the -behavior is not reached. All these data
compare well to our recent analytical evaluation of the reptation model, which
shows that for shorter times (t \alt 10^{4}) the discreteness of the
elementary motion cannot be neglected, whereas for longer times and short
chains (N \alt 100) tube renewal plays an essential role also for the central
segment. Due to the very broad crossover behavior both the diffusion
coefficient and the reptation time within the range of our simulation do not
reach the asymptotic power laws predicted by reptation theory. We present
results for the center-of-mass motion, showing the expected intermediate
-behavior, but again only for very long chains. In addition we show
results for the motion of the central segment relative to the center of mass,
where in some intermediate range we see the expected increase of the effective
power beyond the -law, before saturation sets in. Analysis and
simulations agree on defining a new set of criteria as characteristic for
reptation of finite chains.Comment: 19 pages in latex plus 13 ps figures, submitted to J. Stat. Phys. on
September 18, 199
Segment Motion in the Reptation Model of Polymer Dynamics. I. Analytical Investigation
We analyze the motion of individual beads of a polymer chain using a discrete
version of De Gennes' reptation model that describes the motion of a polymer
through an ordered lattice of obstacles. The motion within the tube can be
evaluated rigorously, tube renewal is taken into account in an approximation
motivated by random walk theory. We find microstructure effects to be present
for remarkably large times and long chains, affecting essentially all present
day computer experiments. The various asymptotic power laws, commonly
considered as typical for reptation, hold only for extremely long chains.
Furthermore, for an arbitrary segment even in a very long chain, we find a rich
variety of fairly broad crossovers, which for practicably accessible chain
lengths overlap and smear out the asymptotic power laws. Our analysis suggests
observables specifically adapted to distinguish reptation from motions
dominated by disorder of the environment.Comment: 38 pages in latex plus 8 ps figures, submitted to J. Stat. Phys. on
September 18, 1997, please note part II on cond-mat/971006
High order fluid model for streamer discharges. II. Numerical solution and investigation of planar fronts
The high order fluid model developed in the preceding paper is employed here
to study the propagation of negative planar streamer fronts in pure nitrogen.
The model consists of the balance equations for electron density, average
electron velocity, average electron energy and average electron energy flux.
These balance equations have been obtained as velocity moments of Boltzmann's
equation and are here coupled to the Poisson equation for the space charge
electric field. Here the results of simulations with the high order model, with
a PIC/MC (Particle in cell/Monte Carlo) model and with the first order fluid
model based on the hydrodynamic drift-diffusion approximation are presented and
compared. The comparison with the MC model clearly validates our high order
fluid model, thus supporting its correct theoretical derivation and numerical
implementation. The results of the first order fluid model with local field
approximation, as usually used for streamer discharges, show considerable
deviations. Furthermore, we study the inaccuracies of simulation results caused
by an inconsistent implementation of transport data into our high order fluid
model. We also demonstrate the importance of the energy flux term in the high
order model by comparing with results where this term is neglected. Finally,
results with an approximation for the high order tensor in the energy flux
equation is found to agree well with the PIC/MC results for reduced electric
fields up to 1000 Townsend, as considered in this work.Comment: 26 pages, 11 figure
Why isolated streamer discharges hardly exist above the breakdown field in atmospheric air
We investigate streamer formation in the troposphere, in electric fields
above the breakdown threshold. With fully three-dimensional particle
simulations, we study the combined effect of natural background ionization and
of photoionization on the discharge morphology. In previous investigations
based on deterministic fluid models without background ionization, so-called
double-headed streamers emerged. But in our improved model, many electron
avalanches start to grow at different locations. Eventually the avalanches
collectively screen the electric field in the interior of the discharge. This
happens after what we call the `ionization screening time', for which we give
an analytical estimate. As this time is comparable to the streamer formation
time, we conclude that isolated streamers are unlikely to exist in fields well
above breakdown in atmospheric air.Comment: Changed citation information. 6 pages, 4 figures, Geophysical
Research Letters, Vol. 40, 2417-2422, 201
Spontaneous Branching of Anode-Directed Streamers between Planar Electrodes
Non-ionized 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 Firsov's limit of `ideal conductivity'. Qualitatively the tip
splitting is due to a Laplacian instability quite like in viscous fingering.
For future quantitative analytical progress, our stability analysis of planar
fronts identifies the screening length as a regularization mechanism.Comment: 4 pages, 6 figures, submitted to PRL on Nov. 16, 2001, revised
version of March 10, 200
The 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.Comment: 4 page
Bosonization in Particle Physics
Path integral techniques in collective fields are shown to be a useful
analytical tool to reformulate a field theory defined in terms of microscopic
quark (gluon) degrees of freedom as an effective theory of collective boson
(meson) fields. For illustrations, the path integral bosonization approach is
applied to derive a (non)linear sigma model from a Nambu-Jona-Lasinio (NJL)
quark model. The method can be extended to include higher order derivative
terms in meson fields or heavy-quark symmetries. It is also approximately
applicable to QCD.Comment: 12 pages, LaTeX, uses lamuphys.sty, 5 LaTeX figures, talk given at
the Workshop "Field Theoretical Tools in Polymer and Particle Physics",
University Wuppertal, June 17-19, 199
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