75,521 research outputs found
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
On Gravity localization under Lorentz Violation in warped scenario
Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane
scenario with one extra dimension where he found a non-zero mass for the
four-dimensional graviton. This leads to the conclusion that five-dimensional
models with LIV are not phenomenologically viable. In this work we re-examine
the issue of Lorentz Invariance Violation in the context of higher dimensional
theories. We show that a six-dimensional geometry describing a string-like
defect with a bulk-dependent cosmological constant can yield a massless 4D
graviton, if we allow the cosmological constant variation along the bulk, and
thus can provides a phenomenologically viable solution for the gauge hierarchy
problem.Comment: 13 pages, 2 figures. To appear in Physics Letters
Gravitational waves in the generalized Chaplygin gas model
The consequences of taking the generalized Chaplygin gas as the dark energy
constituent of the Universe on the gravitational waves are studied and the
spectrum obtained from this model, for the flat case, is analyzed. Besides its
importance for the study of the primordial Universe, the gravitational waves
represent an additional perspective (besides the CMB temperature and
polarization anisotropies) to evaluate the consistence of the different dark
energy models and establish better constraints to their parameters. The
analysis presented here takes this fact into consideration to open one more
perspective of verification of the generalized Chapligin gas model
applicability. Nine particular cases are compared: one where no dark energy is
present; two that simulate the -CDM model; two where the gas acts like
the traditional Chaplygin gas; and four where the dark energy is the
generalized Chaplygin gas. The different spectra permit to distinguish the
-CDM and the Chaplygin gas scenarios.Comment: Latex file, 9 pages, 11 figures eps forma
Is the transition redshift a new cosmological number?
Observations from Supernovae Type Ia (SNe Ia) provided strong evidence for an
expanding accelerating Universe at intermediate redshifts. This means that the
Universe underwent a transition from deceleration to acceleration phases at a
transition redshift of the order unity whose value in principle depends
on the cosmology as well as on the assumed gravitational theory. Since
cosmological accelerating models endowed with a transition redshift are
extremely degenerated, in principle, it is interesting to know whether the
value of itself can be observationally used as a new cosmic
discriminator. After a brief discussion of the potential dynamic role played by
the transition redshift, it is argued that future observations combining SNe
Ia, the line-of-sight (or "radial") baryon acoustic oscillations, the
differential age of galaxies, as well as the redshift drift of the spectral
lines may tightly constrain , thereby helping to narrow the parameter
space for the most realistic models describing the accelerating Universe.Comment: 12 pages, 5 figures. Some discussions about how to estimate the
transition redshift have been added. New data by Planck and H(z) data have
been mentioned. New references have been adde
Coordinated balancing of muscle oxidative metabolism through PGC-1α increases metabolic flexibility and preserves insulin sensitivity
The peroxisome proliferator-activated receptor γ coactivator 1α (PGC-1α) enhances oxidative metabolism in skeletal muscle. Excessive lipid oxidation and electron transport chain activity can, however, lead to the accumulation of harmful metabolites and impair glucose homeostasis. Here, we investigated the effect of over-expression of PGC-1α on metabolic control and generation of insulin desensitizing agents in extensor digitorum longus (EDL), a muscle that exhibits low levels of PGC-1α in the untrained state and minimally relies on oxidative metabolism. We demonstrate that PGC-1α induces a strictly balanced substrate oxidation in EDL by concomitantly promoting the transcription of activators and inhibitors of lipid oxidation. Moreover, we show that PGC-1α enhances the potential to uncouple oxidative phosphorylation. Thereby, PGC-1α boosts elevated, yet tightly regulated oxidative metabolism devoid of side products that are detrimental for glucose homeostasis. Accordingly, PI3K activity, an early phase marker for insulin resistance, is preserved in EDL muscle. Our findings suggest that PGC-1α coordinately coactivates the simultaneous transcription of gene clusters implicated in the positive and negative regulation of oxidative metabolism and thereby increases metabolic flexibility. Thus, in mice fed a normal chow diet, over-expression of PGC-1α does not alter insulin sensitivity and the metabolic adaptations elicited by PGC-1α mimic the beneficial effects of endurance training on muscle metabolism in this context
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