Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. 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 $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, 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 $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.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

Elodie metallicity-biased search for transiting Hot Jupiters I. Two Hot Jupiters orbiting the slightly evolved stars HD118203 and HD149143

We report the discovery of a new planet candidate orbiting the subgiant star HD118203 with a period of P=6.1335 days. The best Keplerian solution yields an eccentricity e=0.31 and a minimum mass m2sin(i)=2.1MJup for the planet. This star has been observed with the ELODIE fiber-fed spectrograph as one of the targets in our planet-search programme biased toward high-metallicity stars, on-going since March 2004 at the Haute-Provence Observatory. An analysis of the spectroscopic line profiles using line bisectors revealed no correlation between the radial velocities and the line-bisector orientations, indicating that the periodic radial-velocity signal is best explained by the presence of a planet-mass companion. A linear trend is observed in the residuals around the orbital solution that could be explained by the presence of a second companion in a longer-period orbit. We also present here our orbital solution for another slightly evolved star in our metal-rich sample, HD149143, recently proposed to host a 4-d period Hot Jupiter by the N2K consortium. Our solution yields a period P=4.09 days, a marginally significant eccentricity e=0.08 and a planetary minimum mass of 1.36MJup. We checked that the shape of the spectral lines does not vary for this star as well.Comment: Accepted in A&A (6 pages, 6 figures

Detecting transit signatures of exoplanetary rings using SOAP3.0

CONTEXT. It is theoretically possible for rings to have formed around extrasolar planets in a similar way to that in which they formed around the giant planets in our solar system. However, no such rings have been detected to date. AIMS: We aim to test the possibility of detecting rings around exoplanets by investigating the photometric and spectroscopic ring signatures in high-precision transit signals. METHODS: The photometric and spectroscopic transit signals of a ringed planet is expected to show deviations from that of a spherical planet. We used these deviations to quantify the detectability of rings. We present SOAP3.0 which is a numerical tool to simulate ringed planet transits and measure ring detectability based on amplitudes of the residuals between the ringed planet signal and best fit ringless model. RESULTS: We find that it is possible to detect the photometric and spectroscopic signature of near edge-on rings especially around planets with high impact parameter. Time resolution $\leq$ 7 mins is required for the photometric detection, while 15 mins is sufficient for the spectroscopic detection. We also show that future instruments like CHEOPS and ESPRESSO, with precisions that allow ring signatures to be well above their noise-level, present good prospects for detecting rings.Comment: 13 pages, 16 figures, 2 tables , accepted for publication in A&

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