1,148 research outputs found
An Algorithm for the Longest Common Subsequence and Substring Problem
In this note, we first introduce a new problem called the longest common
subsequence and substring problem. Let and be two strings over an
alphabet . The longest common subsequence and substring problem for
and is to find the longest string which is a subsequence of and a
substring of . We propose an algorithm to solve the problem
An Algorithm for the Constrained Longest Common Subsequence and Substring Problem
Let be an alphabet. For two strings , , and a constrained
string over the alphabet , the constrained longest common
subsequence and substring problem for two strings and with respect to
is to find a longest string which is a subsequence of , a substring
of , and has as a subsequence. In this paper, we propose an algorithm
for the constrained longest common subsequence and substring problem for two
strings with a constrained string.Comment: arXiv admin note: text overlap with arXiv:2308.0092
Efficient numerical methods for Anisotropic Diffusion of Galactic Cosmic Rays
Anisotropic diffusion is imperative in understanding cosmic ray diffusion
across the Galaxy, the heliosphere, and the interplay of cosmic rays with the
Galactic magnetic field. This diffusion term contributes to the highly stiff
nature of the cosmic ray transport equation. To conduct numerical simulations
of time-dependent cosmic ray transport, implicit integrators (namely,
Crank-Nicolson (CN)) have been traditionally favoured over the CFL-bound
explicit integrators in order to be able to take large step sizes. We propose
exponential methods to treat the linear anisotropc diffusion equation in the
presence of advection and time-independent and time-dependent sources. These
methods allow us to take even larger step sizes that can substantially speed-up
the simulations whilst generating highly accurate solutions. In or subsequent
work, we will use these exponential solvers in the Picard code to study
anisotropic cosmic ray diffusion and we will consider additional physical
processes such as continuous momentum losses and reacceleration.Comment: The 38th International Cosmic Ray Conference (ICRC2023
LeXInt: Package for Exponential Integrators employing Leja interpolation
We present a publicly available software for exponential integrators that
computes the functions using polynomial interpolation. The
interpolation method at Leja points have recently been shown to be competitive
with the traditionally-used Krylov subspace method. The developed framework
facilitates easy adaptation into any Python software package for time
integration.Comment: Publicly available software available at
https://github.com/Pranab-JD/LeXInt, in submissio
Tracking Advanced Planetary Systems (TAPAS) with HARPS-N. V.: A Massive Jupiter orbiting the very low metallicity giant star BD+03 2562 and a possible planet around HD~103485
We present two evolved stars from the TAPAS (Tracking Advanced PlAnetary
Systems) with HARPS-N project devoted to RV precision measurements of
identified candidates within the PennState - Torun Centre for Astronomy Planet
Search. Evolved stars with planets are crucial to understand the dependency of
the planet formation mechanism on the mass and metallicity of the parent star
and to study star-planet interactions. The paper is based on precise radial
velocity (RV) measurements, for HD 103485 we collected 57 epochs over 3317 days
with the Hobby-Eberly Telescope and its High Resolution Spectrograph and 18
ultra-precise HARPS-N data over 919 days. For BD+03 2562 we collected 46 epochs
of HET data over 3380 days and 19 epochs of HARPS-N data over 919 days. We
present the analysis of the data and the search for correlations between the RV
signal and stellar activity, stellar rotation and photometric variability.
Based on the available data, we interpret the RV variations measured in both
stars as Keplerian motion. Both stars have masses close to Solar (1.11 and
1.14), very low metallicities ([Fe/H]=-0.50 and -0.71), and, both have Jupiter
planetary mass companions (m sin i=7 and 6.4 Mj), in close to terrestrial
orbits (1.4 and 1.3~au), with moderate eccentricities (e=0.34 and 0.2).
However, we cannot totally exclude that the signal in the case of HD~103485 is
due to rotational modulation of active regions. Based on the current data, we
conclude that BD+03 2562 has a bona fide planetary companion while for HD
103485 we cannot totally exclude that the best explanation for the RV signal
modulations is not the existence of a planet but stellar activity. If, the
interpretation remains that both stars have planetary companions they represent
systems orbiting very evolved stars with very low metallicities, a challenge to
the conditions required for the formation of massive giant gas planets.Comment: Acepted A&A 12 pages, 11 figure
Revisit of non-linear Landau damping for electrostatic instability driven by blazar-induced pair beams
We revisit the effect of non-linear Landau (NL) damping on the electrostatic
instability of blazar-induced pair beams, using a realistic pair-beam
distribution. We employ a simplified 2D model in -space to study the
evolution of the electric-field spectrum and to calculate the relaxation time
of the beam. We demonstrate that the 2D model is an adequate representation of
the 3D physics. We find that non-linear Landau damping, once it operates
efficiently, transports essentially the entire wave energy to small wavenumbers
where wave driving is weak or absent. The relaxation time also strongly depends
on the IGM temperature, , and for eV, and
in the absence of any other damping mechanism, the relaxation time of the pair
beam is longer than the inverse Compton (IC) scattering time. The weak
late-time beam energy losses arise from the accumulation of wave energy at
small , that non-linearly drains the wave energy at the resonant
of the pair-beam instability. Any other dissipation process
operating at small would reduce that wave-energy drain and hence lead to
stronger pair-beam energy losses. As an example, collisions reduce the
relaxation time by an order of magnitude, although their rate is very small.
Other non-linear processes, such as the modulation instability, could provide
additional damping of the non-resonant waves and dramatically reduce the
relaxation time of the pair beam. An accurate description of the spectral
evolution of the electrostatic waves is crucial for calculating the relaxation
time of the pair beam
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