Gravitational Collapse in One Dimension

We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit \simeq 0.47, slightly but significantly shallower than the value {\gamma} = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent {\gamma}_i > {\gamma}_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique.Comment: 14 Pages, 13 Figures. Submitted to MNRA

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

AMOC Recovery in a Multicentennial Scenario Using a Coupled Atmosphere‐Ocean‐Ice Sheet Model

We simulate the two Coupled Model Intercomparison Project scenarios RCP4.5 and RCP8.5, to assess the effects of melt‐induced fresh water on the Atlantic meridional overturning circulation (AMOC). We use a newly developed climate model with high resolution at the coasts, resolving the complex ocean dynamics. Our results show an AMOC recovery in simulations run with and without an included ice sheet model. We find that the ice sheet adds a strong decadal variability on the freshwater release, resulting in intervals in which it reduces the surface runoff by high accumulation rates. This compensating effect is missing in climate models without dynamic ice sheets. Therefore, we argue to assess those freshwater hosing experiments critically, which aim to parameterize Greenland's freshwater release. We assume the increasing net evaporation over the Atlantic and the resulting increase in ocean salinity, to be the main driver of the AMOC recovery

Multifrequency Studies of the Peculiar Quasar 4C +21.35 during the 2010 Flaring Activity

The discovery of rapidly variable Very High Energy (VHE; E > 100 GeV) γ-ray emission from 4C +21.35 (PKS 1222+216) by MAGIC on 2010 June 17, triggered by the high activity detected by the Fermi Large Area Telescope (LAT) in high energy (HE; E > 100 MeV) γ-rays, poses intriguing questions on the location of the γ-ray emitting region in this flat spectrum radio quasar. We present multifrequency data of 4C +21.35 collected from centimeter to VHE during 2010 to investigate the properties of this source and discuss a possible emission model. The first hint of detection at VHE was observed by MAGIC on 2010 May 3, soon after a γ-ray flare detected by Fermi-LAT that peaked on April 29. The same emission mechanism may therefore be responsible for both the HE and VHE emission during the 2010 flaring episodes. Two optical peaks were detected on 2010 April 20 and June 30, close in time but not simultaneous with the two γ-ray peaks, while no clear connection was observed between the X-ray and γ-ray emission. An increasing flux density was observed in radio and mm bands from the beginning of 2009, in accordance with the increasing γ-ray activity observed by Fermi-LAT, and peaking on 2011 January 27 in the mm regime (230 GHz). We model the spectral energy distributions (SEDs) of 4C +21.35 for the two periods of the VHE detection and a quiescent state, using a one-zone model with the emission coming from a very compact region outside the broad line region. The three SEDs can be fit with a combination of synchrotron self-Compton and external Compton emission of seed photons from a dust torus, changing only the electron distribution parameters between the epochs. The fit of the optical/UV part of the spectrum for 2010 April 29 seems to favor an inner disk radius of <six gravitational radii, as one would expect from a prograde-rotating Kerr black hole

Commensal observing with the Allen Telescope array: software command and control

The Allen Telescope Array (ATA) is a Large-Number-Small-Diameter radio telescope array currently with 42 individual antennas and 5 independent back-end science systems (2 imaging FX correlators and 3 time domain beam formers) located at the Hat Creek Radio Observatory (HCRO). The goal of the ATA is to run multiple back-ends simultaneously, supporting multiple science projects commensally. The primary software control systems are based on a combination of Java, JRuby and Ruby on Rails. The primary control API is simplified to provide easy integration with new back-end systems while the lower layers of the software stack are handled by a master observing system. Scheduling observations for the ATA is based on finding a union between the science needs of multiple projects and automatically determining an efficient path to operating the various sub-components to meet those needs. When completed, the ATA is expected to be a world-class radio telescope, combining dedicated SETI projects with numerous radio astronomy science projects.Comment: SPIE Conference Proceedings, Software and Cyberinfrastructure for Astronomy, Nicole M. Radziwill; Alan Bridger, Editors, 77400Z, Vol 774