37,225 research outputs found
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
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
, 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
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