Are Magnetic Wind-Driving Disks Inherently Unstable?

There have been claims in the literature that accretion disks in which a centrifugally driven wind is the dominant mode of angular momentum transport are inherently unstable. This issue is considered here by applying an equilibrium-curve analysis to the wind-driving, ambipolar diffusion-dominated, magnetic disk model of Wardle & Konigl (1993). The equilibrium solution curves for this class of models typically exhibit two distinct branches. It is argued that only one of these branches represents unstable equilibria and that a real disk/wind system likely corresponds to a stable solution.Comment: 5 pages, 2 figures, to be published in ApJ, vol. 617 (2004 Dec 20). Uses emulateapj.cl

First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory

We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of multicritical points with first- or second-order phase transitions. In particular, for second-order phase transitions, independent of the dimension d_0 of the underlying lattice, the exact predictions of the theory in the paramagnetic regions, such as the location of critical surfaces and correlation functions, are verified. Quite interestingly, we verify that the Edwards-Anderson model with d_0=2 is not thermodynamically stable under graph noise.Comment: 12 pages, 12 figures, 1 tabl

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

We consider a one dimensional transport model with nonlocal velocity given by the Hilbert transform and develop a global well-posedness theory of probability measure solutions. Both the viscous and non-viscous cases are analyzed. Both in original and in self-similar variables, we express the corresponding equations as gradient flows with respect to a free energy functional including a singular logarithmic interaction potential. Existence, uniqueness, self-similar asymptotic behavior and inviscid limit of solutions are obtained in the space $\mathcal{P}_{2}(\mathbb{R})$ of probability measures with finite second moments, without any smallness condition. Our results are based on the abstract gradient flow theory developed in \cite{Ambrosio}. An important byproduct of our results is that there is a unique, up to invariance and translations, global in time self-similar solution with initial data in $\mathcal{P}_{2}(\mathbb{R})$, which was already obtained in \textrm{\cite{Deslippe,Biler-Karch}} by different methods. Moreover, this self-similar solution attracts all the dynamics in self-similar variables. The crucial monotonicity property of the transport between measures in one dimension allows to show that the singular logarithmic potential energy is displacement convex. We also extend the results to gradient flow equations with negative power-law locally integrable interaction potentials