Mantle plumes on Venus revisited

The Equatorial Highlands of Venus consist of a series of quasicircular regions of high topography, rising up to about 5 km above the mean planetary radius. These highlands are strongly correlated with positive geoid anomalies, with a peak amplitude of 120 m at Atla Regio. Shield volcanism is observed at Beta, Eistla, Bell, and Atla Regiones and in the Hathor Mons-Innini Mons-Ushas Mons region of the southern hemisphere. Volcanos have also been mapped in Phoebe Regio and flood volcanism is observed in Ovda and Thetis Regiones. Extensional tectonism is also observed in Ovda and Thetis Regiones. Extensional tectonism is also observed in many of these regions. It is now widely accepted that at least Beta, Atla, Eistla, and Bell Regiones are the surface expressions of hot, rising mantel plumes. Upwelling plumes are consistent with both the volcanism and the extensional tectonism observed in these regions. The geoid anomalies and topography of these four regions show considerable variation. Peak geoid anomalies exceed 90 m at Beta and Atla, but are only 40 m at Eistla and 24 m at Bell. Similarly, the peak topography is greater at Beta and Atla than at Eistla and Bell. Such a range of values is not surprising because terrestrial hotspot swells also have a side range of geoid anomalies and topographic uplifts. Kiefer and Hager used cylindrical axisymmetric, steady-state convection calculations to show that mantle plumes can quantitatively account for both the amplitude and the shape of the long-wavelength geoid and topography at Beta and Atla. In these models, most of the topography of these highlands is due to uplift by the vertical normal stress associated with the rising plume. Additional topography may also be present due to crustal thickening by volcanism and crustal thinning by rifting. Smrekar and Phillips have also considered the geoid and topography of plumes on Venus, but they restricted themselves to considering only the geoid-topography ratio and did not examine either the geoid and topography amplitudes separately or the shapes of anomalies

Age-dependent decay in the landscape

The picture of the "multiverse" arising in diverse cosmological scenarios involves transitions between metastable vacuum states. It was pointed out by Krauss and Dent that the transition rates decrease at very late times, leading to a dependence of the transition probability between vacua on the age of each vacuum region. I investigate the implications of this non-Markovian, age-dependent decay on the global structure of the spacetime in landscape scenarios. I show that the fractal dimension of the eternally inflating domain is precisely equal to 3, instead of being slightly below 3 in scenarios with purely Markovian, age-independent decay. I develop a complete description of a non-Markovian landscape in terms of a nonlocal master equation. Using this description I demonstrate by an explicit calculation that, under some technical assumptions about the landscape, the probabilistic predictions of our position in the landscape are essentially unchanged, regardless of the measure used to extract these predictions. I briefly discuss the physical plausibility of realizing non-Markovian vacuum decay in cosmology in view of the possible decoherence of the metastable quantum state.Comment: 10 pages, RevTeX4, 1 figure included. Clarification of approximation used, conclusions weakene

Comments on Critical Electric and Magnetic Fields from Holography

We discuss some aspects of critical electric and magnetic fields in a field theory with holographic dual description. We extend the analysis of arxiv:1109.2920, which finds a critical electric field at which the Schwinger pair production barrier drops to zero, to the case of magnetic fields. We first find that, unlike ordinary weakly coupled theories, the magnetic field is not subject to any perturbative instability originating from the presence of a tachyonic ground state in the W-boson spectrum. This follows from the large value of the 't Hooft coupling \lambda, which prevents the Zeeman interaction term to overcome the particle mass at high B. Consequently, we study the next possible B-field instability, i.e. monopole pair production, which is the S-dual version of the Schwinger effect. Also in this case a critical magnetic field is expected when the tunneling barrier drops to zero. These Schwinger-type criticalities are the holographic duals, in the bulk, to the fields E or B reaching the tension of F1 or D1 strings respectively. We then discuss how this effect is modified when electric and magnetic fields are present simultaneously and dyonic states in the spectrum can be pair produced by a generic E - B background. Finally, we analyze finite temperature effects on Schwinger criticalities, i.e. in the AdS-Schwarzshild black hole background.Comment: 33 pages, 4 figures; v2: refs added; v3: typos corrected, to appear on JHE

The Smooth Colonel Meets the Reverend

Kernel smoothing techniques have attracted much attention and some notoriety in recent years. The attention is well deserved as kernel methods free researchers from having to impose rigid parametric structure on their data. The notoriety arises from the fact that the amount of smoothing (i.e., local averaging) that is appropriate for the problem at hand is under the control of the researcher. In this paper we provide a deeper understanding of kernel smoothing methods for discrete data by leveraging the unexplored links between hierarchical Bayesmodels and kernelmethods for discrete processes. A number of potentially useful results are thereby obtained, including bounds on when kernel smoothing can be expected to dominate non-smooth (e.g., parametric) approaches in mean squared error and suggestions for thinking about the appropriate amount of smoothing.

Thermal Evolution and Core Formation on Asteroid 4 Vesta in the Magma Ocean Regime

Geochemical observations of the eucrite and diogenite meteorites, together with observations made by NASAs Dawn spacecraft while orbiting asteroid 4 Vesta, indicate that Vesta has differentiated to form a crust, mantle, and core. Eucrite and diogenite petrology is best explained by solidification of the crust from a magma ocean constituting 60-70% of Vestas silicates [3], or a temperature of ~1550 C. The abundances of moderately siderophile elements (Ni, Co, Mo, W, and P) in eucrites require that essentially all of the metallic phase in Vesta segregated to form a core prior to eucrite formation and likely reached a temperature of 1450- 1575 C. These observations provide important constraints on Vestas thermal evolution. The high inferred temperature indicates that convective heat transport must have been important during part of Vestas thermal evolution. In this study, we model Vestas thermal evolution in the magma ocean regime

Quantum Gravity Equation In Schroedinger Form In Minisuperspace Description

We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schroedinger equation. Without any reference to the Wheeler-DeWitt equation and without invoking the expansion of exponent in WKB wavefunction in powers of Planck mass, we obtain an equation for quantum gravity in Schroedinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler-DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler-DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.Comment: 11 Pages, ReVTeX, no figur

Bisimilarity of Pushdown Systems is Nonelementary

Given two pushdown systems, the bisimilarity problem asks whether they are bisimilar. While this problem is known to be decidable our main result states that it is nonelementary, improving EXPTIME-hardness, which was the previously best known lower bound for this problem. Our lower bound result holds for normed pushdown systems as well

On the Complexity of the Equivalence Problem for Probabilistic Automata

Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test based on polynomial identity testing outperformed deterministic algorithms. In this paper we show that polynomial identity testing yields efficient algorithms for various generalisations of the equivalence problem. First, we provide a randomized NC procedure that also outputs a counterexample trace in case of inequivalence. Second, we show how to check for equivalence two probabilistic automata with (cumulative) rewards. Our algorithm runs in deterministic polynomial time, if the number of reward counters is fixed. Finally we show that the equivalence problem for probabilistic visibly pushdown automata is logspace equivalent to the Arithmetic Circuit Identity Testing problem, which is to decide whether a polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape

Hawking radiation from the quantum Lemaitre-Tolman-Bondi model

In an earlier paper, we obtained exact solutions of the Wheeler-DeWitt equation for the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse, employing a lattice regularization. In this paper, we derive Hawking radiation in non-marginally bound models from our exact solutions. We show that a non-vanishing energy function does not spoil the (approximate) Planck spectrum near the horizon. We can also reliably compute corrections to the Bogoliubov coefficient because our solutions are exact. The corrections are obtained by going beyond the near horizon region and are shown to introduce additional greybody factors, which modify the black body spectrum of radiation from the black hole.Comment: 14 page

Decoherence in the cosmic background radiation

In this paper we analyze the possibility of detecting nontrivial quantum phenomena in observations of the temperature anisotropy of the cosmic background radiation (CBR), for example, if the Universe could be found in a coherent superposition of two states corresponding to different CBR temperatures. Such observations are sensitive to scalar primordial fluctuations but insensitive to tensor fluctuations, which are therefore converted into an environment for the former. Even for a free inflaton field minimally coupled to gravity, scalar-tensor interactions induce enough decoherence among histories of the scalar fluctuations as to render them classical under any realistic probe of their amplitudes.Comment: 15 pages, accepted to be published in Classical and Quantum Gravit