154,652 research outputs found
Modeling temporal fluctuations in avalanching systems
We demonstrate how to model the toppling activity in avalanching systems by
stochastic differential equations (SDEs). The theory is developed as a
generalization of the classical mean field approach to sandpile dynamics by
formulating it as a generalization of Itoh's SDE. This equation contains a
fractional Gaussian noise term representing the branching of an avalanche into
small active clusters, and a drift term reflecting the tendency for small
avalanches to grow and large avalanches to be constricted by the finite system
size. If one defines avalanching to take place when the toppling activity
exceeds a certain threshold the stochastic model allows us to compute the
avalanche exponents in the continum limit as functions of the Hurst exponent of
the noise. The results are found to agree well with numerical simulations in
the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also
provides a method for computing the probability density functions of the
fluctuations in the toppling activity itself. We show that the sandpiles do not
belong to the class of phenomena giving rise to universal non-Gaussian
probability density functions for the global activity. Moreover, we demonstrate
essential differences between the fluctuations of total kinetic energy in a
two-dimensional turbulence simulation and the toppling activity in sandpiles.Comment: 14 pages, 11 figure
Dark Energy and Extending the Geodesic Equations of Motion: Connecting the Galactic and Cosmological Length Scales
Recently, an extension of the geodesic equations of motion using the Dark
Energy length scale was proposed. Here, we apply this extension to the
analyzing the motion of test particles at the galactic scale and longer. A
cosmological check of the extension is made using the observed rotational
velocity curves and core sizes of 1393 spiral galaxies. We derive the density
profile of a model galaxy using this extension, and with it, we calculate
to be ; this is within experimental error of the
WMAP value of . We then calculate to be
kpc, which is in reasonable agreement with observations.Comment: 25 pages. Accepted for publication in General Relativity and
Gravitation. Paper contains the published version of the second half of
arXiv:0711.3124v2 with corrections include
Modified Dark Matter: Relating Dark Energy, Dark Matter and Baryonic Matter
Modified dark matter (MDM) is a phenomenological model of dark matter,
inspired by gravitational thermodynamics. For an accelerating Universe with
positive cosmological constant (), such phenomenological
considerations lead to the emergence of a critical acceleration parameter
related to . Such a critical acceleration is an effective
phenomenological manifestation of MDM, and it is found in correlations between
dark matter and baryonic matter in galaxy rotation curves. The resulting MDM
mass profiles, which are sensitive to , are consistent with
observational data at both the galactic and cluster scales. In particular, the
same critical acceleration appears both in the galactic and cluster data fits
based on MDM. Furthermore, using some robust qualitative arguments, MDM appears
to work well on cosmological scales, even though quantitative studies are still
lacking. Finally, we comment on certain non-local aspects of the quanta of
modified dark matter, which may lead to novel non-particle phenomenology and
which may explain why, so far, dark matter detection experiments have failed to
detect dark matter particles
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