Stability Criteria for Breached Pair Superfluidity

We present simple, concrete, two-fermion models that exhibit thermodynamically stable isotropic translationally-invariant gapless superfluid states (breached pair superfluidity). The mass ratio between the components and the momentum structure of the interaction are crucial for determining the stability of such states: Idealized, momentum-independent (``contact'') interactions are insufficient.Comment: 5 pages, REVTeX4. Minor updates in response to comments. References adde

The Resonance Overlap and Hill Stability Criteria Revisited

We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit, and compare their predictions with detailed dynamical maps constructed with N-body simulations. We show that the boundary between (Hill) stable and unstable orbits is not smooth but characterized by a rich structure generated by the superposition of different mean-motion resonances which does not allow for a simple global expression for stability. We propose that, for a given perturbing mass $m_1$ and initial eccentricity $e$, there are actually two critical values of the semimajor axis. All values $a a_{\rm unstable}$ are unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is a function of the eccentricity. The second limit is virtually insensitive to the initial eccentricity, and closely resembles a new resonance overlap condition (for circular orbits) developed in terms of the intersection between first and second-order mean-motion resonances.Comment: 33 pages, 14 figures, accepte

Gravitational Fragmentation in Galaxy Mergers: A Stability Criteria

We study the gravitational stability of gaseous streams in the complex environment of a galaxy merger, because mergers are known to be places of ongoing massive cluster formation and bursts of star formation. We find an analytic stability parameter for case of gaseous streams orbiting around the merger remnant. We test our stability criteria using hydrodynamical simulations of galaxy mergers, obtaining satisfactory results. We find that our criteria successfully predicts the streams that will be gravitationally unstable to fragment into clumps.Comment: 10 pages, 2 figures. After 2nd referee repor

Necessary and Sufficient Elastic Stability Conditions in Various Crystal Systems

While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in non-cubic materials