Super-Earths in the TW Hya disc

We test the hypothesis that the sub-millimetre thermal emission and scattered light gaps seen in recent observations of TW Hya are caused by planet-disc interactions. We perform global three-dimensional dusty smoothed particle hydrodynamics simulations, comparing synthetic observations of our models with dust thermal emission, CO emission and scattered light observations. We find that the dust gaps observed at 24 au and 41 au can be explained by two super-Earths ($\sim 4 \mathrm{M}_{\oplus}$). A planet of approximately Saturn-mass can explain the CO emission and the depth and width of the gap seen in scattered light at 94 au. Our model produces a prominent spiral arm while there are only hints of this in the data. To avoid runaway growth and migration of the planets we require a disc mass of $\lesssim 10^{-2}\,\mathrm{M}_{\odot}$ in agreement with CO observations but 10$-$100 times lower than the estimate from HD line emission.Comment: 6 pages, 5 figures, accepted for publication in MNRA

Spatial Gibbs random graphs

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with small average graph distance between vertices, but adding an edge comes at a cost measured according to the geometry of the ambient physical space. In most cases, we identify the order of magnitude of the average graph distance as a function of the parameters of the model. As the proofs reveal, hierarchical structures naturally emerge from our simple modeling assumptions. Moreover, a critical regime exhibits an infinite number of discontinuous phase transitions.Comment: 29 pages, 5 figures. Revised from previous versio

Rencontres intellectuelles et changement social: Henri La Fontaine et la Belle Époque

info:eu-repo/semantics/publishe

The contact process on finite homogeneous trees revisited

We consider the contact process with infection rate $\lambda$ on $\mathbb{T}_n^d$, the $d$-ary tree of height $n$. We study the extinction time $\tau_{\mathbb{T}_n^d}$, that is, the random time it takes for the infection to disappear when the process is started from full occupancy. We prove two conjectures of Stacey regarding $\tau_{\mathbb{T}_n^d}$. Let $\lambda_2$ denote the upper critical value for the contact process on the infinite $d$-ary tree. First, if $\lambda < \lambda_2$, then $\tau_{\mathbb{T}_n^d}$ divided by the height of the tree converges in probability, as $n \to \infty$, to a positive constant. Second, if $\lambda > \lambda_2$, then $\log \mathbb{E}[\tau_{\mathbb{T}_n^d}]$ divided by the volume of the tree converges in probability to a positive constant, and $\tau_{\mathbb{T}_n^d}/\mathbb{E}[\tau_{\mathbb{T}_n^d}]$ converges in distribution to the exponential distribution of mean 1.Comment: 22 pages, 1 figur

NGC 6302: high-ionization permitted lines. Applying X-SSN synthesis to VLT-UVES spectra

A preliminary VLT-UVES spectrum of NGC 6302 (Casassus et al. 2002, MN), which hosts one of the hottest PN nuclei known (Teff ~ 220000 K; Wright et al. 2011, MN), has been recently analysed by means of X-SSN, a spectrum synthesis code for nebulae (Morisset and P\'equignot). Permitted recombination lines from highly-ionized species are detected/identified for the first time in a PN, and some of them probably for the first time in (Astro)Physics. The need for a homogeneous, high signal-to-noise UVES spectrum for NGC 6302 is advocated.Comment: Poster contribution (2 pages, 1 figure) to IAU Symposium 283: "Planetary Nebulae: An Eye to the Future" held in Puerto de la Cruz, Tenerife, Spain in July 25th-29th 201

Contraction blockers for graphs with forbidden induced paths.

We consider the following problem: can a certain graph parameter of some given graph be reduced by at least d for some integer d via at most k edge contractions for some given integer k? We examine three graph parameters: the chromatic number, clique number and independence number. For each of these graph parameters we show that, when d is part of the input, this problem is polynomial-time solvable on P4-free graphs and NP-complete as well as W[1]-hard, with parameter d, for split graphs. As split graphs form a subclass of P5-free graphs, both results together give a complete complexity classification for Pℓ-free graphs. The W[1]-hardness result implies that it is unlikely that the problem is fixed-parameter tractable for split graphs with parameter d. But we do show, on the positive side, that the problem is polynomial-time solvable, for each parameter, on split graphs if d is fixed, i.e., not part of the input. We also initiate a study into other subclasses of perfect graphs, namely cobipartite graphs and interval graphs