6,041 research outputs found
Spatial damping of propagating sausage waves in coronal cylinders
Sausage modes are important in coronal seismology. Spatially damped
propagating sausage waves were recently observed in the solar atmosphere. We
examine how wave leakage influences the spatial damping of sausage waves
propagating along coronal structures modeled by a cylindrical density
enhancement embedded in a uniform magnetic field. Working in the framework of
cold magnetohydrodynamics, we solve the dispersion relation (DR) governing
sausage waves for complex-valued longitudinal wavenumber at given real
angular frequencies . For validation purposes, we also provide
analytical approximations to the DR in the low-frequency limit and in the
vicinity of , the critical angular frequency separating trapped
from leaky waves. In contrast to the standing case, propagating sausage waves
are allowed for much lower than . However, while able
to direct their energy upwards, these low-frequency waves are subject to
substantial spatial attenuation. The spatial damping length shows little
dependence on the density contrast between the cylinder and its surroundings,
and depends only weakly on frequency. This spatial damping length is of the
order of the cylinder radius for , where
and are the cylinder radius and the Alfv\'en speed in the
cylinder, respectively. We conclude that if a coronal cylinder is perturbed by
symmetric boundary drivers (e.g., granular motions) with a broadband spectrum,
wave leakage efficiently filters out the low-frequency components.Comment: 6 pages, 2 figures, to appear in Astronomy & Astrophysic
Weiqi games as a tree: Zipf's law of openings and beyond
Weiqi is one of the most complex board games played by two persons. The
placement strategies adopted by Weiqi players are often used to analog the
philosophy of human wars. Contrary to the western chess, Weiqi games are less
studied by academics partially because Weiqi is popular only in East Asia,
especially in China, Japan and Korea. Here, we propose to construct a directed
tree using a database of extensive Weiqi games and perform a quantitative
analysis of the Weiqi tree. We find that the popularity distribution of Weiqi
openings with a same number of moves is distributed according to a power law
and the tail exponent increases with the number of moves. Intriguingly, the
superposition of the popularity distributions of Weiqi openings with the number
of moves no more than a given number also has a power-law tail in which the
tail exponent increases with the number of moves, and the superposed
distribution approaches to the Zipf law. These findings are the same as for
chess and support the conjecture that the popularity distribution of board game
openings follows the Zipf law with a universal exponent. We also find that the
distribution of out-degrees has a power-law form, the distribution of branching
ratios has a very complicated pattern, and the distribution of uniqueness
scores defined by the path lengths from the root vertex to the leaf vertices
exhibits a unimodal shape. Our work provides a promising direction for the
study of the decision making process of Weiqi playing from the angle of
directed branching tree.Comment: 6 Latex pages including 6 figure
Network analysis of the worldwide footballer transfer market
The transfer of football players is an important part in football games. Most
studies on the transfer of football players focus on the transfer system and
transfer fees but not on the transfer behavior itself. Based on the 470,792
transfer records from 1990 to 2016 among 23,605 football clubs in 206 countries
and regions, we construct a directed footballer transfer network (FTN), where
the nodes are the football clubs and the links correspond to the footballer
transfers. A systemic analysis is conduced on the topological properties of the
FTN. We find that the in-degrees, out-degrees, in-strengths and out-strengths
of nodes follow bimodal distributions (a power law with exponential decay),
while the distribution of link weights has a power-law tail. We further figure
out the correlations between node degrees, node strengths and link weights. We
also investigate the general characteristics of different measures of network
centrality. Our network analysis of the global footballer transfer market sheds
new lights into the investigation of the characteristics of transfer
activities.Comment: 7 pages, 6 figure
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