32,787 research outputs found
Jeans' gravitational instability and nonextensive kinetic theory
The concept of Jeans gravitational instability is rediscussed in the
framework of nonextensive statistics and its associated kinetic theory. A
simple analytical formula generalizing the Jeans criterion is derived by
assuming that the unperturbed self- gravitating collisionless gas is
kinetically described by the -parameterized class of power law velocity
distributions. It is found that the critical values of wavelength and mass
depend explicitly on the nonextensive -parameter. The standard Jeans
wavelength derived for a Maxwellian distribution is recovered in the limiting
case =1. For power-law distributions with cutoff, the instability condition
is weakened with the system becoming unstable even for wavelengths of the
disturbance smaller than the standard Jeans length .Comment: 5 pages, including 3 figures. Accepted for publication in A&
Hamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the
one-dimensional homogeneous potential, , where and
are continuously varying parameters. In the non-relativistic case, the
exact analytical solution is determined in terms of , and the total
energy . It is also shown that the non-linear equation of motion can be
linearized by constructing a hypergeometric differential equation for the
inverse problem . A variable transformation reducing the general problem
to that one of a particle subjected to a linear force is also established. For
any value of , it leads to a simple harmonic oscillator if , an
"anti-oscillator" if , or a free particle if E=0. However, such a
reduction is not possible in the relativistic case. For a bounded relativistic
motion, the first order correction to the period is determined for any value of
. For , it is found that the correction is just twice that one
deduced for the simple harmonic oscillator (), and does not depend on the
specific value of .Comment: 12 pages, Late
Dynamical complexity of discrete time regulatory networks
Genetic regulatory networks are usually modeled by systems of coupled
differential equations and by finite state models, better known as logical
networks, are also used. In this paper we consider a class of models of
regulatory networks which present both discrete and continuous aspects. Our
models consist of a network of units, whose states are quantified by a
continuous real variable. The state of each unit in the network evolves
according to a contractive transformation chosen from a finite collection of
possible transformations, according to a rule which depends on the state of the
neighboring units. As a first approximation to the complete description of the
dynamics of this networks we focus on a global characteristic, the dynamical
complexity, related to the proliferation of distinguishable temporal behaviors.
In this work we give explicit conditions under which explicit relations between
the topological structure of the regulatory network, and the growth rate of the
dynamical complexity can be established. We illustrate our results by means of
some biologically motivated examples.Comment: 28 pages, 4 figure
Is CDM an effective CCDM cosmology?
We show that a cosmology driven by gravitationally induced particle
production of all non-relativistic species existing in the present Universe
mimics exactly the observed flat accelerating CDM cosmology with just
one dynamical free parameter. This kind of scenario includes the creation cold
dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a
particular case and also provides a natural reduction of the dark sector since
the vacuum component is not needed to accelerate the Universe. The new cosmic
scenario is equivalent to CDM both at the background and perturbative
levels and the associated creation process is also in agreement with the
universality of the gravitational interaction and equivalence principle.
Implicitly, it also suggests that the present day astronomical observations
cannot be considered the ultimate proof of cosmic vacuum effects in the evolved
Universe because CDM may be only an effective cosmology.Comment: 6 pages, 2 figures, changes in the abstract, introduction, new
references and typo correction
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