1,026 research outputs found
The subdivision of large simplicial cones in Normaliz
Normaliz is an open-source software for the computation of lattice points in
rational polyhedra, or, in a different language, the solutions of linear
diophantine systems. The two main computational goals are (i) finding a system
of generators of the set of lattice points and (ii) counting elements
degree-wise in a generating function, the Hilbert Series. In the homogeneous
case, in which the polyhedron is a cone, the set of generators is the Hilbert
basis of the intersection of the cone and the lattice, an affine monoid.
We will present some improvements to the Normaliz algorithm by subdividing
simplicial cones with huge volumes. In the first approach the subdivision
points are found by integer programming techniques. For this purpose we
interface to the integer programming solver SCIP to our software. In the second
approach we try to find good subdivision points in an approximating overcone
that is faster to compute.Comment: To appear in the proceedings of the ICMS 2016, published by Springer
as Volume 9725 of Lecture Notes in Computer Science (LNCS
An eigenfunction method for particle acceleration at ultra-relativistic shocks
We adapt and modify the eigenfunction method of computing the power-law
spectrum of particles accelerated at a relativistic shock front via the
first-order Fermi process (Kirk, J.G., Schneider, P., Astrophysical Journal
315, 425 (1987)) to apply to shocks of arbitrarily high Lorentz factor. The
power-law index of accelerated particles undergoing isotropic small-angle
scattering at an ultrarelativistic, unmagnetized shock is found to be s=4.23
+/- 0.2 (where s=d\ln f/ d\ln p, with f the Lorentz-invariant phase-space
density and p the momentum), in agreement with the results of Monte-Carlo
simulations. We present results for shocks in plasmas with different equations
of state and for Lorentz factors ranging from 5 to infinity.Comment: 4 pages, 2 figures, contribution to the Proceedings of the 5th
Huntsville GRB Symposiu
Particle Acceleration at Ultra-Relativistic Shocks and the Spectra of Relativistic Fireballs
We examine Fermi-type acceleration at relativistic shocks, and distinguish
between the initial boost of the first shock crossing cycle, where the energy
gain per particle can be very large, and the Fermi process proper with repeated
shock crossings, in which the typical energy gain is of order unity. We
calculate by means of numerical simulations the spectrum and angular
distribution of particles accelerated by this Fermi process, in particular in
the case where particle dynamics can be approximated as small-angle scattering.
We show that synchrotron emission from electrons or positrons accelerated by
this process can account remarkably well for the observed power-law spectra of
GRB afterglows and Crab-like supernova remnants. In the context of a
decelerating relativistic fireball, we calculate the maximum particle energy
attainable by acceleration at the external blast wave, and discuss the minimum
energy for this acceleration process and its consequences for the observed
spectrum.Comment: To appear in Proceedings of the 5th Huntsville Gamma-Ray Burst
Symposium. LaTeX, 6 pages, 2 figures, uses aipproc.sty and epsfi
Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum
We use kinetic simulations of diffusive shock acceleration (DSA) to study the
time-dependent evolution of plane, quasi-parallel, cosmic-ray (CR) modified
shocks. Thermal leakage injection of low energy CRs and finite Alfv\'en wave
propagation and dissipation are included. Bohm diffusion as well as the
diffusion with the power-law momentum dependence are modeled. As long as the
acceleration time scale to relativistic energies is much shorter than the
dynamical evolution time scale of the shocks, the precursor and subshock
transition approach the time-asymptotic state, which depends on the shock sonic
and Alfv\'enic Mach numbers and the CR injection efficiency. For the diffusion
models we employ, the shock precursor structure evolves in an approximately
self-similar fashion, depending only on the similarity variable, x/(u_s t).
During this self-similar stage, the CR distribution at the subshock maintains a
characteristic form as it evolves: the sum of two power-laws with the slopes
determined by the subshock and total compression ratios with an exponential
cutoff at the highest accelerated momentum, p_{max}(t). Based on the results of
the DSA simulations spanning a range of Mach numbers, we suggest functional
forms for the shock structure parameters, from which the aforementioned form of
CR spectrum can be constructed. These analytic forms may represent approximate
solutions to the DSA problem for astrophysical shocks during the self-similar
evolutionary stage as well as during the steady-state stage if p_{max} is
fixed.Comment: 38 pages, 12 figures, ApJ accepte
Reconsidering the Impact of Informational Provision on Opinions of Suspended Sentences in the Netherlands: The Importance of Cultural Frames
A recent study scrutinized the effects of providing people with information about suspended sentences on their opinions of these sentences, and concluded that the impact is modest or even absent. Re-analyzing the original data, we demonstrate that this conclusion greatly underestimates the relevance of informational provision. Recognizing that information is framed differently by people with different cultural predispositions, we show that the effects of informational provision are much stronger among groups with specific penal attitudes than analyses of mere âdirectâ effects suggest. Even more importantly, the direction of these effects also depends on peopleâs penal attitudes; among specific groups, more information leads to less, instead of more, favorable opinions on suspended sentences
Particle acceleration at ultrarelativistic shocks: an eigenfunction method
We extend the eigenfunction method of computing the power-law spectrum of
particles accelerated at a relativistic shock fronts to apply to shocks of
arbitrarily high Lorentz factor. In agreement with the findings of Monte-Carlo
simulations, we find the index of the power-law distribution of accelerated
particles which undergo isotropic diffusion in angle at an ultrarelativistic,
unmagnetized shock is s=4.23 (where s=-d(ln f)/dp with f the Lorentz invariant
phase-space density and p the momentum). This corresponds to a synchrotron
index for uncooled electrons of a=0.62 (taking cooling into account a=1.12),
where a=-d(ln F)/dn, F is the radiation flux and n the frequency. We also
present an approximate analytic expression for the angular distribution of
accelerated particles, which displays the effect of particle trapping by the
shock: compared with the non-relativistic case the angular distribution is
weighted more towards the plane of the shock and away from its normal. We
investigate the sensitivity of our results to the transport properties of the
particles and the presence of a magnetic field. Shocks in which the ratio of
Poynting to kinetic energy flux upstream is not small are less compressive and
lead to larger values of .Comment: Minor additions on publicatio
Filaments in the southern giant lobe of Centaurus A : Constraints on nature and origin from modelling and GMRT observations
Date of acceptance: 22/05/2014We present results from imaging of the radio filaments in the southern giant lobe of CentaurusA using data from Giant Metrewave Radio Telescope observations at 325 and 235 MHz, and outcomes from filament modelling. The observations reveal a rich filamentary structure, largely matching the morphology at 1.4 GHz. We find no clear connection of the filaments to the jet. We seek to constrain the nature and origin of the vertex and vortex filaments associated with the lobe and their role in high-energy particle acceleration. We deduce that these filaments are at most mildly overpressuredwith respect to the global lobe plasma showing no evidence of largescale efficient Fermi I-type particle acceleration, and persist for ~2-3 Myr. We demonstrate that the dwarf galaxy KK 196 (AM 1318-444) cannot account for the features, and that surface plasma instabilities, the internal sausage mode and radiative instabilities are highly unlikely. An internal tearing instability and the kink mode are allowed within the observational and growth time constraints and could develop in parallel on different physical scales. We interpret the origin of the vertex and vortex filaments in terms of weak shocks from transonic magnetohydrodynamical turbulence or from a moderately recent jet activity of the parent AGN, or an interplay of both.Peer reviewe
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