1,567 research outputs found
Spectra of Modular Random Graphs
We compute spectra of symmetric random matrices defined on graphs exhibiting
a modular structure. Modules are initially introduced as fully connected
sub-units of a graph. By contrast, inter-module connectivity is taken to be
incomplete. Two different types of inter-module connectivity are considered,
one where the number of intermodule connections per-node diverges, and one
where this number remains finite in the infinite module-size limit. In the
first case, results can be understood as a perturbation of a superposition of
semicircular spectral densities one would obtain for uncoupled modules. In the
second case, matters can be more involved, and depend in detail on inter-module
connectivities. For suitable parameters we even find near-triangular shaped
spectral densities, similar to those observed in certain scale-free networks,
in a system of consisting of just two coupled modules. Analytic results are
presented for the infinite module-size limit; they are well corroborated by
numerical simulations.Comment: 16 pages, 4 figures. to appear in J. Phys.
Stepwise investment plan optimization for large scale and multi-zonal transmission system expansion
This paper develops a long term transmission expansion optimization methodology taking the probabilistic nature of generation and demand, spatial aspects of transmission investments and different technologies into account. The developed methodology delivers a stepwise investment plan to achieve the optimal grid expansion for additional transmission capacity between different zones. In this paper, the optimization methodology is applied to the Spanish and French transmission systems for long term optimization of investments in interconnection capacity
Double layers in the downward current region of the aurora
International audienceDirect observations of magnetic-field-aligned (parallel) electric fields in the downward current region of the aurora provide decisive evidence of naturally occurring double layers. We report measurements of parallel electric fields, electron fluxes and ion fluxes related to double layers that are responsible for particle acceleration. The observations suggest that parallel electric fields organize into a structure of three distinct, narrowly-confined regions along the magnetic field (B). In the "ramp" region, the measured parallel electric field forms a nearly-monotonic potential ramp that is localized to ~ 10 Debye lengths along B. The ramp is moving parallel to B at the ion acoustic speed (vs) and in the same direction as the accelerated electrons. On the high-potential side of the ramp, in the "beam" region, an unstable electron beam is seen for roughly another 10 Debye lengths along B. The electron beam is rapidly stabilized by intense electrostatic waves and nonlinear structures interpreted as electron phase-space holes. The "wave" region is physically separated from the ramp by the beam region. Numerical simulations reproduce a similar ramp structure, beam region, electrostatic turbulence region and plasma characteristics as seen in the observations. These results suggest that large double layers can account for the parallel electric field in the downward current region and that intense electrostatic turbulence rapidly stabilizes the accelerated electron distributions. These results also demonstrate that parallel electric fields are directly associated with the generation of large-amplitude electron phase-space holes and plasma waves
The Effects of Turbulence on Three-Dimensional Magnetic Reconnection at the Magnetopause
Two- and three-dimensional particle-in-cell simulations of a recent encounter
of the Magnetospheric Multiscale Mission (MMS) with an electron diffusion
region at the magnetopause are presented. While the two-dimensional simulation
is laminar, turbulence develops at both the x-line and along the magnetic
separatrices in the three-dimensional simulation. The turbulence is strong
enough to make the magnetic field around the reconnection island chaotic and
produces both anomalous resistivity and anomalous viscosity. Each contribute
significantly to breaking the frozen-in condition in the electron diffusion
region. A surprise is that the crescent-shaped features in velocity space seen
both in MMS observations and in two-dimensional simulations survive, even in
the turbulent environment of the three-dimensional system. This suggests that
MMS's measurements of crescent distributions do not exclude the possibility
that turbulence plays an important role in magnetopause reconnection.Comment: Revised version accepted by GR
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Electrostatic Turbulence and Debye-scale Structures in Collisionless Shocks
We present analysis of more than 100 large-amplitude bipolar electrostatic structures in a quasi-perpendicular supercritical Earth's bow shock crossing, measured by the Magnetospheric Multiscale spacecraft. The occurrence of the bipolar structures is shown to be tightly correlated with magnetic field gradients in the shock transition region. The bipolar structures have negative electrostatic potentials and spatial scales of a few Debye lengths. The bipolar structures propagate highly oblique to the shock normal with velocities (in the plasma rest frame) of the order of the ion-acoustic velocity. We argue that the bipolar structures are ion phase space holes produced by the two-stream instability between incoming and reflected ions. This is the first identification of the ion two-stream instability in collisionless shocks
Pattern Matching in Multiple Streams
We investigate the problem of deterministic pattern matching in multiple
streams. In this model, one symbol arrives at a time and is associated with one
of s streaming texts. The task at each time step is to report if there is a new
match between a fixed pattern of length m and a newly updated stream. As is
usual in the streaming context, the goal is to use as little space as possible
while still reporting matches quickly. We give almost matching upper and lower
space bounds for three distinct pattern matching problems. For exact matching
we show that the problem can be solved in constant time per arriving symbol and
O(m+s) words of space. For the k-mismatch and k-difference problems we give
O(k) time solutions that require O(m+ks) words of space. In all three cases we
also give space lower bounds which show our methods are optimal up to a single
logarithmic factor. Finally we set out a number of open problems related to
this new model for pattern matching.Comment: 13 pages, 1 figur
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