2,072 research outputs found
A generative model for feedback networks
We investigate a simple generative model for network formation. The model is
designed to describe the growth of networks of kinship, trading, corporate
alliances, or autocatalytic chemical reactions, where feedback is an essential
element of network growth. The underlying graphs in these situations grow via a
competition between cycle formation and node addition. After choosing a given
node, a search is made for another node at a suitable distance. If such a node
is found, a link is added connecting this to the original node, and increasing
the number of cycles in the graph; if such a node cannot be found, a new node
is added, which is linked to the original node. We simulate this algorithm and
find that we cannot reject the hypothesis that the empirical degree
distribution is a q-exponential function, which has been used to model
long-range processes in nonequilibrium statistical mechanics.Comment: 11 pages, 6 figure
Preferential attachment growth model and nonextensive statistical mechanics
We introduce a two-dimensional growth model where every new site is located,
at a distance from the barycenter of the pre-existing graph, according to
the probability law , and is attached to
(only) one pre-existing site with a probability ; is the number of links of the site of the
pre-existing graph, and its distance to the new site). Then we
numerically determine that the probability distribution for a site to have
links is asymptotically given, for all values of , by , where is the function
naturally emerging within nonextensive statistical mechanics. The entropic
index is numerically given (at least for not too large) by , and the characteristic number of links by . The particular case belongs to the same
universality class to which the Barabasi-Albert model belongs. In addition to
this, we have numerically studied the rate at which the average number of links
increases with the scaled time ; asymptotically, , the exponent being close to for , and zero otherwise.
The present results reinforce the conjecture that the microscopic dynamics of
nonextensive systems typically build (for instance, in Gibbs -space for
Hamiltonian systems) a scale-free network.Comment: 5 pages including 5 figures (the original colored figures 1 and 5a
can be asked directly to the authors
Lithium depletion in solar-like stars: effect of overshooting based on realistic multi-dimensional simulations
We study lithium depletion in low-mass and solar-like stars as a function of
time, using a new diffusion coefficient describing extra-mixing taking place at
the bottom of a convective envelope. This new form is motivated by
multi-dimensional fully compressible, time implicit hydrodynamic simulations
performed with the MUSIC code. Intermittent convective mixing at the convective
boundary in a star can be modeled using extreme value theory, a statistical
analysis frequently used for finance, meteorology, and environmental science.
In this letter, we implement this statistical diffusion coefficient in a
one-dimensional stellar evolution code, using parameters calibrated from
multi-dimensional hydrodynamic simulations of a young low-mass star. We propose
a new scenario that can explain observations of the surface abundance of
lithium in the Sun and in clusters covering a wide range of ages, from
50 Myr to 4 Gyr. Because it relies on our physical model of convective
penetration, this scenario has a limited number of assumptions. It can explain
the observed trend between rotation and depletion, based on a single additional
assumption, namely that rotation affects the mixing efficiency at the
convective boundary. We suggest the existence of a threshold in stellar
rotation rate above which rotation strongly prevents the vertical penetration
of plumes and below which rotation has small effects. In addition to providing
a possible explanation for the long standing problem of lithium depletion in
pre-main sequence and main sequence stars, the strength of our scenario is that
its basic assumptions can be tested by future hydrodynamic simulations.Comment: 7 pages, 3 figures, Accepted for publication in ApJ Letter
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