On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity

We analyze the effects induced by the bulk viscosity on the dynamics associated to the extreme gravitational collapse. Aim of the work is to investigate whether the presence of viscous corrections to the evolution of a collapsing gas cloud influence the fragmentation process. To this end we study the dynamics of a uniform and spherically symmetric cloud with corrections due to the negative pressure contribution associated to the bulk viscosity phenomenology. Within the framework of a Newtonian approach (whose range of validity is outlined), we extend to the viscous case either the Lagrangian, either the Eulerian motion of the system and we treat the asymptotic evolution in correspondence to a viscosity coefficient of the form $\zeta=\zeta_0 \rho^{nu}$ ($\rho$ being the cloud density and $\zeta_0=const.$). We show how, in the adiabatic-like behavior of the gas (i.e. when the politropic index takes values $4/3<\gamma\leq5/3$), density contrasts acquire, asymptotically, a vanishing behavior which prevents the formation of sub-structures. We can conclude that in the adiabatic-like collapse the top down mechanism of structures formation is suppressed as soon as enough strong viscous effects are taken into account. Such a feature is not present in the isothermal-like (i.e. $1\leq\gamma<4/3$) collapse because the sub-structures formation is yet present and outlines the same behavior as in the non-viscous case. We emphasize that in the adiabatic-like collapse the bulk viscosity is also responsible for the appearance of a threshold scale beyond which perturbations begin to increase.Comment: 13 pages, no figur

A Near-Infrared Spectroscopic Study of the Accreting Magnetic White Dwarf SDSS J121209.31+013627.7 and its Substellar Companion

The nature of the excess near-infrared emission associated with the magnetic white dwarf commonly known as SDSS 1212 is investigated primarily through spectroscopy, and also via photometry. The inferred low mass secondary in this system has been previously detected by the emission and variation of H$\alpha$, and the $1-2.5$ $\mu$m spectral data presented here are consistent with the presence of a late L or early T dwarf. The excess flux seen beyond 1.5 $\mu$m in the phase-averaged spectrum is adequately modeled with an L8 dwarf substellar companion and cyclotron emission in a 7 MG magnetic field. This interesting system manifests several observational properties typical of polars, and is most likely an old interacting binary with a magnetic white dwarf and a substellar donor in an extended low state.Comment: 28 pages, 5 figures, Accepted to Ap

Implicit Solutions of PDE's

Further investigations of implicit solutions to non-linear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which differential equations of second order for a single unknown $\phi$ are solved by the imposition of an inhomogeneous quadratic relationship among the independent variables, whose coefficients are functions of $\phi$ is discussed, and it is shown that if the discriminant of the quadratic vanishes, then an implicit solution of the so-called Universal Field Equation is obtained. The relation to the general solution is discussed.Comment: 11 pages LaTeX2

The generation of nonlinear internal waves

Author Posting. © The Oceanography Society, 2012. This article is posted here by permission of The Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 25, No. 2 (2012): 108–123, doi:10.5670/oceanog.2012.46.Nonlinear internal waves are found in many parts of the world ocean. Their widespread distribution is a result of their origin in the barotropic tide and in the variety of ways they can be generated, including by lee waves, tidal beams, resonance, plumes, and the transformation of the internal tide. The differing generation mechanisms and diversity of generation locations and conditions all combine to produce waves that range in scale from a few tens of meters to kilometers, but with all properly described by solitary wave theory. The ability of oceanic nonlinear internal waves to persist for days after generation and the key role internal waves play in connecting large-scale tides to smaller-scale turbulence make them important for understanding the ocean environment.Christopher Jackson gratefully acknowledges the support of the Office of Naval Research through contract N0001409C0224

Electronic doping of graphene by deposited transition metal atoms

We perform a phenomenological analysis of the problem of the electronic doping of a graphene sheet by deposited transition metal atoms, which aggregate in clusters. The sample is placed in a capacitor device such that the electronic doping of graphene can be varied by the application of a gate voltage and such that transport measurements can be performed via the application of a (much smaller) voltage along the graphene sample, as reported in the work of Pi et al. [Phys. Rev. B 80, 075406 (2009)]. The analysis allows us to explain the thermodynamic properties of the device, such as the level of doping of graphene and the ionisation potential of the metal clusters in terms of the chemical interaction between graphene and the clusters. We are also able, by modelling the metallic clusters as perfect conducting spheres, to determine the scattering potential due to these clusters on the electronic carriers of graphene and hence the contribution of these clusters to the resistivity of the sample. The model presented is able to explain the measurements performed by Pi et al. on Pt-covered graphene samples at the lowest metallic coverages measured and we also present a theoretical argument based on the above model that explains why significant deviations from such a theory are observed at higher levels of coverage.Comment: 16 pages, 10 figure

Gravito-magnetic instabilities in anisotropically expanding fluids

Gravitational instabilities in a magnetized Friedman - Robertson - Walker (FRW) Universe, in which the magnetic field was assumed to be too weak to destroy the isotropy of the model, are known and have been studied in the past. Accordingly, it became evident that the external magnetic field disfavors the perturbations' growth, suppressing the corresponding rate by an amount proportional to its strength. However, the spatial isotropy of the FRW Universe is not compatible with the presence of large-scale magnetic fields. Therefore, in this article we use the general-relativistic (GR) version of the (linearized) perturbed magnetohydrodynamic equations with and without resistivity, to discuss a generalized Jeans criterion and the potential formation of density condensations within a class of homogeneous and anisotropically expanding, self-gravitating, magnetized fluids in curved space-time. We find that, for a wide variety of anisotropic cosmological models, gravito-magnetic instabilities can lead to sub-horizonal, magnetized condensations. In the non-resistive case, the power spectrum of the unstable cosmological perturbations suggests that most of the power is concentrated on large scales (small k), very close to the horizon. On the other hand, in a resistive medium, the critical wave-numbers so obtained, exhibit a delicate dependence on resistivity, resulting in the reduction of the corresponding Jeans lengths to smaller scales (well bellow the horizon) than the non-resistive ones, while increasing the range of cosmological models which admit such an instability.Comment: 10 pages RevTex, 4 figures, accepted for publication in the International Journal of Modern Physics

Airway events in obese vs. non-obese elective surgical patients: a cross-sectional observational study

Obesity is an increasingly prevalent comorbidity within the UK population. The aim of this study was to determine the proportion of obese patients in an elective surgical population. The second aim was to determine the choice of airway equipment and incidence of airway events in obese vs. non-obese patients. We conducted a cross-sectional observational study over two 24-h periods in March 2018 across 39 hospitals in the greater London area. Data were collected regarding 1874 patients. The incidence of obesity was 32% in the study population compared with 26% in the general UK population (p < 0.0001). Minor airway events were defined as: desaturation to Sp O2 < 90%; failed mask ventilation; supraglottic airway device problem; aspiration; airway trauma and difficult intubation; or recognised oesophageal intubation. Major airway events were defined as: unrecognised oesophageal intubation; a 'cannot intubate cannot oxygenate' emergency; the need for unplanned front-of-neck airway; cardiac arrest; or unplanned intensive care unit admission due to an airway event. In total, 89 minor and two major airway events were recorded. Obese patients were more likely to experience a minor airway event (RR 2.39, 95%CI 1.60-3.57), the most common being desaturation (Sp O2 < 90%). The use of a supraglottic airway device in obese vs. non-obese patients was associated with increased airway events (RR 3.46 [1.88-6.40]). Tracheal intubation vs. supraglottic airway device use increased with obesity class but was not associated with a decrease in airway events (RR 0.90 [0.53-1.55]). Our data suggest that obesity is more common in the elective surgical vs. general population and minor airway events are more common in obese vs. non-obese elective patients

On the Origin of the Eccentricities of Extrasolar Planets

We develop a phenomenological theory that aims to account for the origin of the large eccentricities of extrasolar planets and that of the small eccentricities in the solar system, the preference for apsidal alignment in non-resonant multiplanet systems, and the origin of the similarities in the eccentricity distribution of extra-solar planets and that of spectroscopic binary stars. We show that if a physical process is weakly dependent on the local dynamics of the companion and imparts a small relative acceleration to the star-companion system, the eccentricity of the companion's orbit is excited to large values depending on the direction and duration of acceleration. A natural candidate for such processes are asymmetric stellar jets and star-disk winds. When the acceleration originates from a precessing jet, large eccentricities can be excited by the resonance of the jet's precession frequency with the induced acceleration's excitation frequency even for nearly perpendicular jets. Precession also reduces the eccentricity amplitude far inside the resonance radius. The acceleration's strength is best constrained in multiplanet systems because of the companions' mutual gravitational perturbations, while the acceleration's duration is bounded by the condition that the residual velocity imparted to the star is smaller than the stellar velocity dispersion in the Galaxy. In the outer parts of the star-companion system where the acceleration excitation time is comparable to or smaller than the orbital period, significant radial migration takes place which may have important consequences for the dynamics of the minor body populations in the solar system. The theory is illustrated with the $\upsilon$ Andromedae binary system.Comment: 41 pages, 14 figures, accepted for publication in the Astronomical Journa

Equation of the field lines of an axisymmetric multipole with a source surface

Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surface magnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree ℓ and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplace’s equation for the magnetostatic potential