Self-gravitating Newtonian disks revisited

Recent analytic results concerning stationary, self-gravitating fluids in Newtonian theory are discussed. We give a theorem that forbids infinitely extended fluids, depending on the assumed equation of state and the rotation law. This part extends previous results that have been obtained for static configurations. The second part discusses a Sobolev bound on the mass of the fluid and a rigorous Jeans-type inequality that is valid in the stationary case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To appear in Progress in Mathematical Relativity, Gravitation and Cosmology, Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics & Statistics, Vol. 6

Content-adaptive lenticular prints

Lenticular prints are a popular medium for producing automultiscopic glasses-free 3D images. The light field emitted by such prints has a fixed spatial and angular resolution. We increase both perceived angular and spatial resolution by modifying the lenslet array to better match the content of a given light field. Our optimization algorithm analyzes the input light field and computes an optimal lenslet size, shape, and arrangement that best matches the input light field given a set of output parameters. The resulting emitted light field shows higher detail and smoother motion parallax compared to fixed-size lens arrays. We demonstrate our technique using rendered simulations and by 3D printing lens arrays, and we validate our approach in simulation with a user study

(In)finite extent of stationary perfect fluids in Newtonian theory

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar

Near-inertial wave scattering by random flows

The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales comparable to the wavelengths, we derive a transport (or kinetic) equation governing wave-energy transfers in both physical and spectral spaces. This equation describes the scattering of the waves by the flow which results in a redistribution of energy between waves with the same frequency (or, equivalently, with the same wavenumber) and, for isotropic flows, in the isotropisation of the wave field. The time scales for the scattering and isotropisation are obtained explicitly and found to be of the order of tens of days for typical oceanic parameters. The predictions inferred from the transport equation are confirmed by a series of numerical simulations. Two situations in which near-inertial waves are strongly influenced by flow scattering are investigated through dedicated nonlinear shallow-water simulations. In the first, a wavepacket propagating equatorwards as a result from the $\beta$-effect is shown to be slowed down and dispersed both zonally and meridionally by scattering. In the second, waves generated by moving cyclones are shown to be strongly disturbed by scattering, leading again to an increased dispersion.Comment: Accepted for publication in Phys. Rev. Fluid

Spherically symmetric relativistic stellar structures

We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space, thereby avoiding the non-regularity problems associated with the Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space thus obtained is used to derive qualitative features and to prove theorems about mass-radius properties. The perfect fluids we discuss are described by barotropic equations of state that are asymptotically polytropic at low pressures and, for certain applications, asymptotically linear at high pressures. We employ dimensionless variables that are asymptotically homology invariant in the low pressure regime, and thus we generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. Our dynamical systems framework is particularly suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe

(In)finiteness of Spherically Symmetric Static Perfect Fluids

This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding perfect fluid solutions possess finite/infinite extent. In the Newtonian case, for the large class of monotonic equations of state, and in General Relativity we improve earlier results

A soliton menagerie in AdS

We explore the behaviour of charged scalar solitons in asymptotically global AdS4 spacetimes. This is motivated in part by attempting to identify under what circumstances such objects can become large relative to the AdS length scale. We demonstrate that such solitons generically do get large and in fact in the planar limit smoothly connect up with the zero temperature limit of planar scalar hair black holes. In particular, for given Lagrangian parameters we encounter multiple branches of solitons: some which are perturbatively connected to the AdS vacuum and surprisingly, some which are not. We explore the phase space of solutions by tuning the charge of the scalar field and changing scalar boundary conditions at AdS asymptopia, finding intriguing critical behaviour as a function of these parameters. We demonstrate these features not only for phenomenologically motivated gravitational Abelian-Higgs models, but also for models that can be consistently embedded into eleven dimensional supergravity.Comment: 62 pages, 21 figures. v2: added refs and comments and updated appendice

Static perfect fluids with Pant-Sah equations of state

We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the present author. Except for the Buchdahl solutions which are contained as a limiting case, the fluids have finite radius and are physically realistic for suitable parameter ranges. The equations of state can be characterized geometrically by the property that the 3-metric on the static slices, rescaled conformally with the fourth power of any linear function of the norm of the static Killing vector, has constant scalar curvature. This local property does not require spherical symmetry; in fact it simplifies the the proof of spherical symmetry of asymptotically flat solutions which we recall here for the Pant-Sah equations of state. We also consider a model in Newtonian theory with analogous geometric and physical properties, together with a proof of spherical symmetry of the asymptotically flat solutions.Comment: 32 p., Latex, minor changes and correction

Carbon density and sequestration in the temperate forests of northern Patagonia, Argentina

Introduction: Forests are a crucial part of the global carbon cycle and theirproper management is of high relevance for mitigating climate change. Thereis an urgent need to compile for each region reference data on the carbon(C) stock density and C sequestration rate of its principal forest types tosupport evidence-based conservation and management decisions in terms ofclimate change mitigation and adaptation. In the Andean Mountains of northernPatagonia, extensive areas of temperate forest have developed after massiveanthropogenic fires since the beginning of the last century.Methods: We used a plot design along belt transects to determine referencevalues of carbon storage and annual C sequestration in total live (above- andbelowground biomass) and deadwood mass, as well as in the soil organiclayer and mineral soil (to 20 cm depth) in different forest types dominated byNothofagus spp. and Austrocedrus chilensis.Results: Average total carbon stock densities and C sequestration rates rangefrom a minimum of 187 Mg.ha1 and 0.7 Mg.ha1.year1 in pure and mixed N.antarctica shrublands through pure and mixed A. chilensis forests taller than7 m and pure N. pumilio forests to a maximum in pure N. dombeyi forestswith 339 Mg.ha1 and 2.2 Mg.ha1.year1, respectively. Deadwood C representsbetween 20 and 33% of total wood mass C and is related to the amount oflive biomass, especially for the coarse woody debris component. The topsoilcontains between 33 and 57% of the total estimated ecosystem carbon in thetall forests and more than 65% in the shrublands, equaling C stocks of around100–130 Mg.ha1 in the different forest types.Conclusion: We conclude that the northern Patagonian temperate forestsactually store fairly high carbon stocks, which must be interpreted in relationto their natural post-fire development and relatively low management intensity.However, the current high stand densities of these forests may well affect their future carbon storage capacity in a warming climate, and they represent agrowing threat of high-intensity fires with the risk of a further extension ofburned areas in the future.Fil: Loguercio, Gabriel Angel. Centro de Investigación y Extensión Forestal Andino Patagónico; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Simon, Alois. Hawk University Of Applied Sciences And Arts; AlemaniaFil: Neri Winter, Ariel Fernando. Universität Göttingen; AlemaniaFil: Ivancich, Horacio Simón. Centro de Investigación y Extensión Forestal Andino Patagónico; ArgentinaFil: Reiter, Ernesto J.. Universität Göttingen; AlemaniaFil: Caselli, Marina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Centro de Investigación y Extensión Forestal Andino Patagónico; ArgentinaFil: Heinzle, Facundo Gabriel. Centro de Investigación y Extensión Forestal Andino Patagónico; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Leuschner, Christoph. Universität Göttingen; AlemaniaFil: Walentowski, Helge. No especifíca