262 research outputs found
Fractal Cosmology in an Open Universe
The clustering of galaxies is well characterized by fractal properties, with
the presence of an eventual cross-over to homogeneity still a matter of
considerable debate. In this letter we discuss the cosmological implications of
a fractal distribution of matter, with a possible cross-over to homogeneity at
an undetermined scale R_{homo}. Contrary to what is generally assumed, we show
that, even when R_{homo} -> \infty, this possibility can be treated
consistently within the framework of the expanding universe solutions of
Friedmann. The fractal is a perturbation to an open cosmology in which the
leading homogeneous component is the cosmic background radiation (CBR). This
cosmology, inspired by the observed galaxy distributions, provides a simple
explanation for the recent data which indicate the absence of deceleration in
the expansion (q_o \approx 0). Correspondingly the `age problem' is also
resolved. Further we show that the model can be extended back from the
curvature dominated arbitrarily deep into the radiation dominated era, and we
discuss qualitatively the modifications to the physics of the anisotropy of the
CBR, nucleosynthesis and structure formation.Comment: 7 pages, no figures, to appear in Europhysics Letter
Universality of power law correlations in gravitational clustering
We present an analysis of different sets of gravitational N-body simulations,
all describing the dynamics of discrete particles with a small initial velocity
dispersion. They encompass very different initial particle configurations,
different numerical algorithms for the computation of the force, with or
without the space expansion of cosmological models. Despite these differences
we find in all cases that the non-linear clustering which results is
essentially the same, with a well-defined simple power-law behaviour in the
two-point correlations in the range from a few times the lower cut-off in the
gravitational force to the scale at which fluctuations are of order one. We
argue, presenting quantitative evidence, that this apparently universal
behaviour can be understood by the domination of the small scale contribution
to the gravitational force, coming initially from nearest neighbor particles.Comment: 7 pages, latex, 3 postscript figures. Revised version to be published
in Europhysics Letters. Contains additional analysis showing more directly
the central role of nearest neighbour interactions in the development of
power-law correlation
Very large scale correlations in the galaxy distribution
We characterize galaxy correlations in the Sloan Digital Sky Survey by
measuring several moments of galaxy counts in spheres. We firstly find that the
average counts grows as a power-law function of the distance with an exponent
D= 2.1+- 0.05 for r in [0.5,20] Mpc/h and D = 2.8+-0.05 for r in [30,150]
Mpc/h. In order to estimate the systematic errors in these measurements we
consider the counts variance finding that it shows systematic finite size
effects which depend on the samples sizes. We clarify, by making specific
tests, that these are due to galaxy long-range correlations extending up to the
largest scales of the sample. The analysis of mock galaxy catalogs, generated
from cosmological N-body simulations of the standard LCDM model, shows that for
r<20 Mpc/h the counts exponent is D~2.0, weakly dependent on galaxy luminosity,
while D=3 at larger scales. In addition, contrary to the case of the observed
galaxy samples, no systematic finite size effects in the counts variance are
found at large scales, a result that agrees with the absence of large scale,
r~100 Mpc/h, correlations in the mock catalogs. We thus conclude that the
observed galaxy distribution is characterized by correlations, fluctuations and
hence structures, which are larger, both in amplitude and in spatial extension,
than those predicted by the standard model LCDM of galaxy formation.Comment: 6 pages, 7 figures to be published in Europhysics Letter
Gravitational force distribution in fractal structures
We study the (newtonian) gravitational force distribution arising from a
fractal set of sources. We show that, in the case of real structures in finite
samples, an important role is played by morphological properties and finite
size effects. For dimensions smaller than d-1 (being the space dimension)
the convergence of the net gravitational force is assured by the fast decaying
of the density, while for fractal dimension D>d-1 the morphological properties
of the structure determine the eventual convergence of the force as a function
of distance. We clarify the role played by the cut-offs of the distribution.
Some cosmological implications are discussed.Comment: 9 pages, latex, 2 postscript figures, also available at
http://www.phys.uniroma1.it/DOCS/PIL/pil.html Accepted for Publication in
Europhysics Letters. Minor modifications adde
The fractal structure of the universe : a new field theory approach
While the universe becomes more and more homogeneous at large scales,
statistical analysis of galaxy catalogs have revealed a fractal structure at
small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2
(Sylos Labini et al 1996). We study the thermodynamics of a self-gravitating
system with the theory of critical phenomena and finite-size scaling and show
that gravity provides a dynamical mechanism to produce this fractal structure.
We develop a field theoretical approach to compute the galaxy distribution,
assuming them to be in quasi-isothermal equilibrium. Only a limited, (although
large), range of scales is involved, between a short-distance cut-off below
which other physics intervene, and a large-distance cut-off, where the thermo-
dynamic equilibrium is not satisfied. The galaxy ensemble can be considered at
critical conditions, with large density fluctuations developping at any scale.
From the theory of critical phenomena, we derive the two independent critical
exponents nu and eta and predict the fractal dimension D = 1/nu to be either
1.585 or 2, depending on whether the long-range behaviour is governed by the
Ising or the mean field fixed points, respectively. Both set of values are
compatible with present observations. In addition, we predict the scaling
behaviour of the gravitational potential to be r^{-(1 + eta)/2}. That is,
r^{-0.5} for mean field or r^{- 0.519} for the Ising fixed point. The theory
allows to compute the three and higher density correlators without any
assumption or Ansatz. We find that the N-points density scales as
r_1^{(N-1)(D-3)}, when r_1 >> r_i, 2 leq i leq N . There are no free parameters
in this theory.Comment: Latex, 20 pages, no figures, to be published in the Astrophysical
Journa
The complex universe: recent observations and theoretical challenges
The large scale distribution of galaxies in the universe displays a complex
pattern of clusters, super-clusters, filaments and voids with sizes limited
only by the boundaries of the available samples. A quantitative statistical
characterization of these structures shows that galaxy distribution is
inhomogeneous in these samples, being characterized by large-amplitude
fluctuations of large spatial extension. Over a large range of scales, both the
average conditional density and its variance show a nontrivial scaling
behavior: at small scales, r<20 Mpc/h, the average (conditional) density scales
as 1/r. At larger scales, the density depends only weakly (logarithmically) on
the system size and density fluctuations follow the Gumbel distribution of
extreme value statistics. These complex behaviors are different from what is
expected in a homogeneous distribution with Gaussian fluctuations. The observed
density inhomogeneities pose a fundamental challenge to the standard picture of
cosmology but it also represent an important opportunity which points to new
directions with respect to many cosmological puzzles. Indeed, the fact that
matter distribution is not uniform, in the limited range of scales sampled by
observations, rises the question of understanding how inhomogeneities affect
the large-scale dynamics of the universe. We discuss several attempts which try
to model inhomogeneities in cosmology, considering their effects with respect
to the role and abundance of dark energy and dark matter.Comment: 30 pages, 10 figure
Spinal motoneurons of the human newborn are highly synchronized during leg movements
Motoneurons of neonatal rodents show synchronous activity that modulates the development of the neuromuscular system. However, the characteristics of the activity of human neonatal motoneurons are largely unknown. Using a noninvasive neural interface, we identified the discharge timings of individual spinal motoneurons in human newborns. We found highly synchronized activities of motoneurons of the tibialis anterior muscle, which were associated with fast leg movements. Although neonates' motor units exhibited discharge rates similar to those of adults, their synchronization was significantly greater than in adults. Moreover, neonatal motor units showed coherent oscillations in the delta band, which is directly translated into force generation. These results suggest that motoneuron synchronization in human neonates might be an important mechanism for controlling fast limb movements, such as those of primitive reflexes. In addition to help revealing mechanisms of development, the proposed neural interface might monitor children at risk of developing motor disorders
Tapping into rhythm generation circuitry in humans during simulated weightlessness conditions
An ability to produce rhythmic activity is ubiquitous for locomotor pattern generation and modulation. The role that the rhythmogenesis capacity of the spinal cord plays in injured populations has become an area of interest and systematic investigation among researchers in recent years, despite its importance being long recognized by neurophysiologists and clinicians. Given that each individual interneuron, as a rule, receives a broad convergence of various supraspinal and sensory inputs and may contribute to a vast repertoire of motor actions, the importance of assessing the functional state of the spinal locomotor circuits becomes increasingly evident. Air-stepping can be used as a unique and important model for investigating human rhythmogenesis since its manifestation is largely facilitated by a reduction of external resistance. This article aims to provide a review on current issues related to the ‘locomotor’ state and interactions between spinal and supraspinal influences on the central pattern generator circuitry in humans, which may be important for developing gait rehabilitation strategies in individuals with spinal cord and brain injuries
Gravitational evolution of a perturbed lattice and its fluid limit
We apply a simple linearization, well known in solid state physics, to
approximate the evolution at early times of cosmological N-body simulations of
gravity. In the limit that the initial perturbations, applied to an infinite
perfect lattice, are at wavelengths much greater than the lattice spacing
the evolution is exactly that of a pressureless self-gravitating fluid treated
in the analagous (Lagrangian) linearization, with the Zeldovich approximation
as a sub-class of asymptotic solutions. Our less restricted approximation
allows one to trace the evolution of the discrete distribution until the time
when particles approach one another (i.e. ``shell crossing''). We calculate
modifications of the fluid evolution, explicitly dependent on i.e.
discreteness effects in the N body simulations. We note that these effects
become increasingly important as the initial red-shift is increased at fixed
. The possible advantages of using a body centred cubic, rather than simple
cubic, lattice are pointed out.Comment: 4 pages, 2 figures, version with minor modifications, accepted for
publication in Phys. Rev. Let
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