On Newtonian singularities in higher derivative gravity models

We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higher-derivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancellation of contributions from scalar and tensor massive modes.Comment: Added comment about the black hole solutions in Conclusions section. Fits published version, plus some misprints corrected in formulas at the end of Sect.

Macro- and microstructural descriptions of the zebrafish (Danio rerio) liver

The liver is an essential metabolically active organ, responsible for many vital life functions such as metabolism, synthesis, and storage. This study describes the macroscopic and microscopic zebrafish liver and its temporal changes during a period of 13 weeks. Forty-six adult zebrafish were used (46), of which 27 were females and were 19 males. Seven fish were euthanized initially for macroscopic evaluation and 3 fish were euthanized weekly for 13 weeks for microscopic evaluation. Routine histological technique was performed; the slides were stained with haematoxylin/eosin and periodic acid-Schiff. The volumetric (Vv(h)) and numerical (Nv(h)) densities of hepatocytes and vacuolation intensity were determined weekly. The liver was located in the coelomic cavity ventrally to the swim bladder, slightly brownish and divided into 3 hepatic lobes. Microscopically, it consisted of hepatocytes forming a muralium duplex around the sinusoids. The staining of the cytoplasm of hepatocytes was more eosinophilic and more basophilic in males and females, respectively. There was no formation of portal triads and phagocytic cells. The gallbladder had transitional epithelium, and the bile ducts had simple cuboidal epithelium. The volume and numerical density of hepatocytes during the 13 weeks was not statistically different, but these parameters displayed a positive correlation. The vacuolation was due to the presence of glycogen. The zebrafish liver has macro and micro structural particular features while, quantitatively, the volume and number of hepatocytes showed great capacity to respond to the physiological needs of the animal at the time

Optimal Control of Underactuated Mechanical Systems: A Geometric Approach

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.Comment: 20 pages, 2 figure

Star-forming dwarf galaxies in the Virgo cluster: the link between molecular gas, atomic gas, and dust

We present $^{12}$CO(1-0) and $^{12}$CO(2-1) observations of a sample of 20 star-forming dwarfs selected from the Herschel Virgo Cluster Survey, with oxygen abundances ranging from 12 + log(O/H) ~ 8.1 to 8.8. CO emission is observed in ten galaxies and marginally detected in another one. CO fluxes correlate with the FIR 250 $\mu$m emission, and the dwarfs follow the same linear relation that holds for more massive spiral galaxies extended to a wider dynamical range. We compare different methods to estimate H2 molecular masses, namely a metallicity-dependent CO-to-H2 conversion factor and one dependent on H-band luminosity. The molecular-to-stellar mass ratio remains nearly constant at stellar masses <~ 10$^9$ M$_{\odot}$, contrary to the atomic hydrogen fraction, M$_{HI}$/M$_*$, which increases inversely with M$_*$. The flattening of the M$_{H_2}$/M$_*$ ratio at low stellar masses does not seem to be related to the effects of the cluster environment because it occurs for both HI-deficient and HI-normal dwarfs. The molecular-to-atomic ratio is more tightly correlated with stellar surface density than metallicity, confirming that the interstellar gas pressure plays a key role in determining the balance between the two gaseous components of the interstellar medium. Virgo dwarfs follow the same linear trend between molecular gas mass and star formation rate as more massive spirals, but gas depletion timescales, $\tau_{dep}$, are not constant and range between 100 Myr and 6 Gyr. The interaction with the Virgo cluster environment is removing the atomic gas and dust components of the dwarfs, but the molecular gas appears to be less affected at the current stage of evolution within the cluster. However, the correlation between HI deficiency and the molecular gas depletion time suggests that the lack of gas replenishment from the outer regions of the disc is lowering the star formation activity.Comment: 19 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Universal leading quantum correction to the Newton potential

The derivation of effective quantum gravity corrections to Newton's potential is an important step in the whole effective quantum field theory approach. We hereby add new strong arguments in favor of omitting all the diagrams with internal lines of the massive sources, and we also recalculate the corrections to the Newtonian potential using functional methods in an arbitrary parametrization of the quantum fluctuations of the metric. The general proof of the gauge- and parametrization-independence within this approach is also explicitly given. On top of that, we argue that the universality of the result holds regardless of the details of the ultraviolet completion of quantum gravity theory. Indeed, it turns out that the logarithm quantum correction depends only on the low energy spectrum of the theory that is responsible for the analytic properties of loop's amplitudes

Regular multi-horizon Lee-Wick black holes

In this paper we carry out a detailed analysis of the static spherically symmetric solutions of a sixth-derivative Lee--Wick gravity model in the effective delta source approximation. Previous studies of these solutions have only considered the particular case in which the real and the imaginary part of the Lee--Wick mass $\mu=a +i b$ are equal. However, as we show here, the solutions exhibit an interesting structure when the full parameter space is considered, owing to the oscillations of the metric that depend on the ratio $b/a$. Such oscillations can generate a rich structure of horizons, a sequence of mass gaps and the existence of multiple regimes for black hole sizes (horizon position gaps). In what concerns the thermodynamics of these objects, the oscillation of the Hawking temperature determines the presence of multiple mass scales for the remnants of the evaporation process and may permit the existence of cold black holes with zero Hawking temperature~$T$ and quasi-stable intermediate configurations with $T \approx 0$ and a long evaporation lifetime. For the sake of generality, we consider two families of solutions, one with a trivial shift function and the other with a non-trivial one (dirty black hole). The latter solution has the advantage of reproducing the modified Newtonian-limit metric of Lee--Wick gravity for small and large values of~$r$.Comment: 23 pages, 10 figures, 4 table