88 research outputs found
Incompressible Stars and Fractional Derivatives
Fractional calculus is an effective tool in incorporating the effects of
non-locality and memory into physical models. In this regard, successful
applications exist rang- ing from signal processing to anomalous diffusion and
quantum mechanics. In this paper we investigate the fractional versions of the
stellar structure equations for non radiating spherical objects. Using
incompressible fluids as a comparison, we develop models for constant density
Newtonian objects with fractional mass distributions or stress conditions. To
better understand the fractional effects, we discuss effective values for the
density, gravitational field and equation of state. The fractional ob- jects
are smaller and less massive than integer models. The fractional parameters are
related to a polytropic index for the models considered
A Singularity-Free Cosmological Model with a Conformally Coupled Scalar Field
We explore the possibility of describing our universe with a
singularity--free, closed, spatially homogeneous and isotropic cosmological
model, using only general relativity and a suitable equation of state which
produces an inflationary era. A phase transition to a radiation--dominated era
occurs as a consequence of boundary conditions expressing the assumption that
the temperature cannot exceed the Planck value. We find that over a broad range
of initial conditions, the predicted value of the Hubble parameter is
approximately km~s~Mpc. Inflation is driven by a
scalar field, which must be conformally coupled to the curvature if the
Einstein equivalence principle has to be satisfied. The form of the scalar
field potential is derived, instead of being assumed a priori.Comment: 19 pages, figures and tables available from the author
Do Rotations Beyond the Cosmological Horizon Affect the Local Inertial Frame?
If perturbations beyond the horizon have the velocities prescribed everywhere
then the dragging of inertial frames near the origin is suppressed by an
exponential factor. However if perturbations are prescribed in terms of their
angular momenta there is no such suppression.
We resolve this paradox and in doing so give new explicit results on the
dragging of inertial frames in closed, flat and open universe with and without
a cosmological constant.Comment: 12 page
Quantum Tunneling Effect in Oscillating Friedmann Cosmology
It is shown that the tunneling effect in quantum cosmology is possible not
only at the very beginning or the very end of the evolution, but also at the
moment of maximum expansion of the universe. A positive curvature expanding
Friedmann universe changes its state of evolution spontaneously and completely,
{\it without} any changes in the matter content, avoiding recollapse, and
falling into oscillations between the nonzero values of the scale factor. On
the other hand, an oscillating nonsingular universe can tunnel spontaneously to
a recollapsing regime. The probability of such kind of tunneling is given
explicitly. It is inversely related to the amount of nonrelativistic matter
(dust), and grows from a certain fixed value to unity if the negative
cosmological constant approaches zero.Comment: 18 pages Latex + 2 figures available by fax upon reques
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Notch signaling regulates metabolic heterogeneity in glioblastoma stem cells.
Glioblastoma (GBM) stem cells (GSCs) reside in both hypoxic and vascular microenvironments within tumors. The molecular mechanisms that allow GSCs to occupy such contrasting niches are not understood. We used patient-derived GBM cultures to identify GSC subtypes with differential activation of Notch signaling, which co-exist in tumors but occupy distinct niches and match their metabolism accordingly. Multipotent GSCs with Notch pathway activation reside in perivascular niches, and are unable to entrain anaerobic glycolysis during hypoxia. In contrast, most CD133-expressing GSCs do not depend on canonical Notch signaling, populate tumors regardless of local vascularity and selectively utilize anaerobic glycolysis to expand in hypoxia. Ectopic activation of Notch signaling in CD133-expressing GSCs is sufficient to suppress anaerobic glycolysis and resistance to hypoxia. These findings demonstrate a novel role for Notch signaling in regulating GSC metabolism and suggest intratumoral GSC heterogeneity ensures metabolic adaptations to support tumor growth in diverse tumor microenvironments
Accelerated expansion from braneworld models with variable vacuum energy
In braneworld models a variable vacuum energy may appear if the size of the
extra dimension changes during the evolution of the universe. In this scenario
the acceleration of the universe is related not only to the variation of the
cosmological term, but also to the time evolution of and, possibly, to the
variation of other fundamental "constants" as well. This is because the
expansion rate of the extra dimension appears in different contexts, notably in
expressions concerning the variation of rest mass and electric charge. We
concentrate our attention on spatially-flat, homogeneous and isotropic,
brane-universes where the matter density decreases as an inverse power of the
scale factor, similar (but at different rate) to the power law in FRW-universes
of general relativity.
We show that these braneworld cosmologies are consistent with the observed
accelerating universe and other observational requirements. In particular,
becomes constant and asymptotically in
time. Another important feature is that the models contain no "adjustable"
parameters. All the quantities, even the five-dimensional ones, can be
evaluated by means of measurements in 4D. We provide precise constrains on the
cosmological parameters and demonstrate that the "effective" equation of state
of the universe can, in principle, be determined by measurements of the
deceleration parameter alone. We give an explicit expression relating the
density parameters , and the deceleration
parameter . These results constitute concrete predictions that may help in
observations for an experimental/observational test of the model.Comment: References added, typos correcte
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