434 research outputs found
Minimum-Cost Coverage of Point Sets by Disks
We consider a class of geometric facility location problems in which the goal
is to determine a set X of disks given by their centers (t_j) and radii (r_j)
that cover a given set of demand points Y in the plane at the smallest possible
cost. We consider cost functions of the form sum_j f(r_j), where f(r)=r^alpha
is the cost of transmission to radius r. Special cases arise for alpha=1 (sum
of radii) and alpha=2 (total area); power consumption models in wireless
network design often use an exponent alpha>2. Different scenarios arise
according to possible restrictions on the transmission centers t_j, which may
be constrained to belong to a given discrete set or to lie on a line, etc. We
obtain several new results, including (a) exact and approximation algorithms
for selecting transmission points t_j on a given line in order to cover demand
points Y in the plane; (b) approximation algorithms (and an algebraic
intractability result) for selecting an optimal line on which to place
transmission points to cover Y; (c) a proof of NP-hardness for a discrete set
of transmission points in the plane and any fixed alpha>1; and (d) a
polynomial-time approximation scheme for the problem of computing a minimum
cost covering tour (MCCT), in which the total cost is a linear combination of
the transmission cost for the set of disks and the length of a tour/path that
connects the centers of the disks.Comment: 10 pages, 4 figures, Latex, to appear in ACM Symposium on
Computational Geometry 200
The Analyticity of a Generalized Ruelle's Operator
In this work we propose a generalization of the concept of Ruelle operator
for one dimensional lattices used in thermodynamic formalism and ergodic
optimization, which we call generalized Ruelle operator, that generalizes both
the Ruelle operator proposed in [BCLMS] and the Perron Frobenius operator
defined in [Bowen]. We suppose the alphabet is given by a compact metric space,
and consider a general a-priori measure to define the operator. We also
consider the case where the set of symbols that can follow a given symbol of
the alphabet depends on such symbol, which is an extension of the original
concept of transition matrices from the theory of subshifts of finite type. We
prove the analyticity of the Ruelle operator and present some examples
Observations of the 2019 April 4 Solar Energetic Particle Event at the Parker Solar Probe
A solar energetic particle event was detected by the Integrated Science Investigation of the Sun (ISâIS) instrument suite on Parker Solar Probe (PSP) on 2019 April 4 when the spacecraft was inside of 0.17 au and less than 1 day before its second perihelion, providing an opportunity to study solar particle acceleration and transport unprecedentedly close to the source. The event was very small, with peak 1 MeV proton intensities of ~0.3 particles (cmÂČ sr s MeV)â»Âč, and was undetectable above background levels at energies above 10 MeV or in particle detectors at 1 au. It was strongly anisotropic, with intensities flowing outward from the Sun up to 30 times greater than those flowing inward persisting throughout the event. Temporal association between particle increases and small brightness surges in the extreme-ultraviolet observed by the Solar TErrestrial RElations Observatory, which were also accompanied by type III radio emission seen by the Electromagnetic Fields Investigation on PSP, indicates that the source of this event was an active region nearly 80° east of the nominal PSP magnetic footpoint. This suggests that the field lines expanded over a wide longitudinal range between the active region in the photosphere and the corona
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Solar Energetic Particles Produced by a Slow Coronal Mass Ejection at âŒ0.25 au
We present an analysis of Parker Solar Probe (PSP) ISâIS observations of ~30â300 keV nâ»Âč ions on 2018 November 11 when PSP was about 0.25 au from the Sun. Five hours before the onset of a solar energetic particle (SEP) event, a coronal mass ejection (CME) was observed by STEREO-A/COR2, which crossed PSP about a day later. No shock was observed locally at PSP, but the CME may have driven a weak shock earlier. The SEP event was dispersive, with higher energy ions arriving before the lower energy ones. Timing suggests the particles originated at the CME when it was at ~7.4R_â. SEP intensities increased gradually from their onset over a few hours, reaching a peak, and then decreased gradually before the CME arrived at PSP. The event was weak, having a very soft energy spectrum (â4 to â5 spectral index). The earliest arriving particles were anisotropic, moving outward from the Sun, but later, the distribution was observed to be more isotropic. We present numerical solutions of the Parker transport equation for the transport of 30â300 keV nâ»Âč ions assuming a source comoving with the CME. Our model agrees well with the observations. The SEP event is consistent with ion acceleration at a weak shock driven briefly by the CME close to the Sun, which later dissipated before arriving at PSP, followed by the transport of ions in the interplanetary magnetic field
Energetic Particle Increases Associated with Stream Interaction Regions
The Parker Solar Probe was launched on 2018 August 12 and completed its second orbit on 2019 June 19 with perihelion of 35.7 solar radii. During this time, the Energetic Particle Instrument-Hi (EPI-Hi, one of the two energetic particle instruments comprising the Integrated Science Investigation of the Sun, ISâIS) measured seven proton intensity increases associated with stream interaction regions (SIRs), two of which appear to be occurring in the same region corotating with the Sun. The events are relatively weak, with observed proton spectra extending to only a few MeV and lasting for a few days. The proton spectra are best characterized by power laws with indices ranging from â4.3 to â6.5, generally softer than events associated with SIRs observed at 1 au and beyond. Helium spectra were also obtained with similar indices, allowing He/H abundance ratios to be calculated for each event. We find values of 0.016â0.031, which are consistent with ratios obtained previously for corotating interaction region events with fast solar wind †600 km sâ»Âč. Using the observed solar wind data combined with solar wind simulations, we study the solar wind structures associated with these events and identify additional spacecraft near 1 au appropriately positioned to observe the same structures after some corotation. Examination of the energetic particle observations from these spacecraft yields two events that may correspond to the energetic particle increases seen by EPI-Hi earlier
Quantifying the Energy Budget in the Solar Wind from 13.3-100 Solar Radii
A variety of energy sources, ranging from dynamic processes like magnetic
reconnection and waves to quasi-steady terms like the plasma pressure, may
contribute to the acceleration of the solar wind. We utilize a combination of
charged particle and magnetic field observations from the Parker Solar Probe
(PSP) to attempt to quantify the steady-state contribution of the proton
pressure, the electric potential, and the wave energy to the solar wind proton
acceleration observed by PSP between 13.3 and ~100 solar radii (RS). The proton
pressure provides a natural kinematic driver of the outflow. The ambipolar
electric potential acts to couple the electron pressure to the protons,
providing another definite proton acceleration term. Fluctuations and waves,
while inherently dynamic, can act as an additional effective steady-state
pressure term. To analyze the contributions of these terms, we utilize radial
binning of single-point PSP measurements, as well as repeated crossings of the
same stream at different distances on individual PSP orbits (i.e. "fast radial
scans"). In agreement with previous work, we find that the electric potential
contains sufficient energy to fully explain the acceleration of the slower wind
streams. On the other hand, we find that the wave pressure plays an
increasingly important role in the faster wind streams. The combination of
these terms can explain the continuing acceleration of both slow and fast wind
streams beyond 13.3 RS
Prevalence of magnetic reconnection in the near-Sun heliospheric current sheet
During three of its first five orbits around the Sun, Parker Solar Probe (PSP) crossed the large-scale Heliospheric Current Sheet (HCS) multiple times and provided unprecedented detailed plasma and field observations of the near-Sun HCS. We report the common detections by PSP of reconnection exhaust signatures in the HCS at heliocentric distances of 29.5-107 solar radii during Encounters 1, 4 and 5. Both sunward and antisunward-directed reconnection exhausts were observed. In the sunward reconnection exhausts, PSP detected counterstreaming strahl electrons, indicating that HCS reconnection resulted in the formation of closed magnetic field lines with both ends connected to the Sun. In the antisunward exhausts, PSP observed dropouts of strahl electrons, consistent with the reconnected HCS field lines being disconnected from the Sun. The common detection of reconnection in the HCS suggests that reconnection is almost always active in the HCS near the Sun. Furthermore, the occurrence of multiple long-duration partial crossings of the HCS suggests that HCS reconnection could produce chains of large bulges with spatial dimensions of up to several solar radii. The finding of the prevalence of reconnection in the HCS is somewhat surprising since PSP has revealed that the HCS is much thicker than the kinetic scales required for reconnection onset. The observations are also in stark contrast with the apparent absence of reconnection in most of the small-scale and much more intense current sheets encountered near perihelia, many of which are associated with âswitchbacksâ. Thus, the PSP findings suggest that large-scale dynamics either locally in the solar wind or within the coronal source of the HCS (at the tip of helmet streamers) plays a critical role in triggering reconnection onset
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