6,111 research outputs found
Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system
We present a heuristic derivation of Gaussian approximations for stochastic
chemical reaction systems with distributed delay. In particular we derive the
corresponding chemical Langevin equation. Due to the non-Markovian character of
the underlying dynamics these equations are integro-differential equations, and
the noise in the Gaussian approximation is coloured. Following on from the
chemical Langevin equation a further reduction leads to the linear-noise
approximation. We apply the formalism to a delay variant of the celebrated
Brusselator model, and show how it can be used to characterise noise-driven
quasi-cycles, as well as noise-triggered spiking. We find surprisingly
intricate dependence of the typical frequency of quasi-cycles on the delay
period.Comment: 14 pages, 9 figure
Dynamic behavior of porous electrode systems final report
Mathematical model of flooded porous electrodes under dynamic and static conditions - Methods for measuring porous electrode reaction distributio
The formation of ultra-compact dwarf galaxies and nucleated dwarf galaxies
Ultra compact dwarf galaxies (UCDs) have similar properties as massive
globular clusters or the nuclei of nucleated galaxies. Recent observations
suggesting a high dark matter content and a steep spatial distribution within
groups and clusters provide new clues as to their origins. We perform
high-resolution N-body / smoothed particle hydrodynamics simulations designed
to elucidate two possible formation mechanisms for these systems: the merging
of globular clusters in the centre of a dark matter halo, or the massively
stripped remnant of a nucleated galaxy. Both models produce density profiles as
well as the half light radii that can fit the observational constraints.
However, we show that the first scenario results to UCDs that are underluminous
and contain no dark matter. This is because the sinking process ejects most of
the dark matter particles from the halo centre. Stripped nuclei give a more
promising explanation, especially if the nuclei form via the sinking of gas,
funneled down inner galactic bars, since this process enhances the central dark
matter content. Even when the entire disk is tidally stripped away, the nucleus
stays intact and can remain dark matter dominated even after severe stripping.
Total galaxy disruption beyond the nuclei only occurs on certain orbits and
depends on the amount of dissipation during nuclei formation. By comparing the
total disruption of CDM subhaloes in a cluster potential we demonstrate that
this model also leads to the observed spatial distribution of UCDs which can be
tested in more detail with larger data sets.Comment: 8 pages, 8 figures, final version accepted for publication in MNRA
A heuristic quantum theory of the integer quantum Hall effect
Contrary to common belief, the current emitted by a contact embedded in a
two-dimensional electron gas (2DEG) is quantized in the presence of electric
and magnetic fields. This observation suggests a simple, clearly defined model
for the quantum current through a Hall device that does not invoke disorder or
interactions as the cause of the integer quantum Hall effect (QHE), but is
based on a proper quantization of the classical electron drift motion. The
theory yields a quantitative description of the breakdown of the QHE at high
current densities that is in agreement with experimental data. Furthermore,
several of its key points are in line with recent findings of experiments that
address the dependency of the QHE on the 2DEG bias voltage, results that are
not easily explained within the framework of conventional QHE models.Comment: 20 pages, 6 figure
Laser frequency stabilization to a single ion
A fundamental limit to the stability of a single-ion optical frequency
standard is set by quantum noise in the measurement of the internal state of
the ion. We discuss how the interrogation sequence and the processing of the
atomic resonance signal can be optimized in order to obtain the highest
possible stability under realistic experimental conditions. A servo algorithm
is presented that stabilizes a laser frequency to the single-ion signal and
that eliminates errors due to laser frequency drift. Numerical simulations of
the servo characteristics are compared to experimental data from a frequency
comparison of two single-ion standards based on a transition at 688 THz in
171Yb+. Experimentally, an instability sigma_y(100 s)=9*10^{-16} is obtained in
the frequency difference between both standards.Comment: 15 pages, 5 figures, submitted to J. Phys.
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