A Kondo impurity in a disordered metal: Anderson's theorem revisited

We consider a local moment which is coupled by a non-random Kondo $J$ to a band of conduction electrons in a random potential. We prove an analog of Anderson's theorem in a large-N limit of this model. The theorem states that when the disorder is weak, the disorder-averaged low-temperature thermodynamics is independent of the strength of the disorder; remarkably, it further states that fluctuation effects in the long-time limit are {\it independent even of the realization of the disorder}. We discuss the relationship of this theorem to theoretical and experimental studies of similar problems.Comment: 4 pages, RevTe

Quasi-geostrophic free mode models of long-lived Jovian eddies: Forcing mechanisms and crucial observational tests

Observations of Jupiter and Saturn long-lived eddies, such as Jupiter's Great Red Spot and White Ovals, are presently compared with laboratory experiments and corresponding numerical simulations for free thermal convection in a rotating fluid that is subject to horizontal differential heating and cooling. Difficulties in determining the essential processes maintaining and dissipating stable eddies, on the basis of global energy budget studies, are discussed; such difficulties do not arise in considerations of the flow's potential vorticity budget. On Jupiter, diabatically forced and transient eddy-driven flows primarily differ in the implied role of transient eddies in transporting potential vorticity across closed geostrophic streamlines in the time mean

Transport of absolute angular momentum in quasi-axisymmetric equatorial jet streams

It is well known that prograde equatorial jet stresses cannot occur in an axisymmetric inviscid fluid, owing to the constraints of local angular momentum conservation. For a viscous fluid, the constraints of mass conservation prevent the formation of any local maximum of absolute angular momentum (m) without a means of transferring m against its gradient (delta m) in the meridional plane. The circumstances under which m can be diffused up-gradient by normal molecular viscosity are derived, and illustrated with reference to numerical simulations of axisymmetric flows in a cylindrical annulus. Viscosity is shown to act so as to tend to expel m from the interior outwards from the rotation axis. Such an effect can produce local super-rotation even in a mechanically isolated fluid. The tendency of viscosity to result in the expulsion of m is shown to be analogous in certain respects to a vorticity-mixing hypothesis for the effects of non-axisymmetric eddies of the zonally-averaged flow. It is shown how the advective and diffusive transport of m by non-axisymmetric eddies can be represented by the Transformed Eulerian Mean meridional circulation and the Eliassen-Palm (EP) flux of Andrews and McIntyre respectively, in the zonal mean. Constraints on the form and direction of the EP flux in an advective/diffusive flow for such eddies are derived, by analogy with similar constraints on the diffusive flux of m due to viscosity

How to break the density-anisotropy degeneracy in spherical stellar systems

We present a new non-parametric Jeans code, GravSphere, that recovers the density $\rho(r)$ and velocity anisotropy $\beta(r)$ of spherical stellar systems, assuming only that they are in a steady-state. Using a large suite of mock data, we confirm that with only line-of-sight velocity data, GravSphere provides a good estimate of the density at the projected stellar half mass radius, $\rho(R_{1/2})$, but is not able to measure $\rho(r)$ or $\beta(r)$, even with 10,000 tracer stars. We then test three popular methods for breaking this $\rho-\beta$ degeneracy: using multiple populations with different $R_{1/2}$; using higher order `Virial Shape Parameters' (VSPs); and including proper motion data. We find that two populations provide an excellent recovery of $\rho(r)$ in-between their respective $R_{1/2}$. However, even with a total of $\sim 7,000$ tracers, we are not able to well-constrain $\beta(r)$ for either population. By contrast, using 1000 tracers with higher order VSPs we are able to measure $\rho(r)$ over the range $0.5 < r/R_{1/2} < 2$ and broadly constrain $\beta(r)$. Including proper motion data for all stars gives an even better performance, with $\rho$ and $\beta$ well-measured over the range $0.25 < r/R_{1/2} < 4$. Finally, we test GravSphere on a triaxial mock galaxy that has axis ratios typical of a merger remnant, $[1:0.8:0.6]$. In this case, GravSphere can become slightly biased. However, we find that when this occurs the data are poorly fit, allowing us to detect when such departures from spherical symmetry become problematic.Comment: 19 pages; 1 table; 11 Figures. Version accepted for publication in MNRAS. (Minor changes from previously. Appendix B added showing decreasing bias of VSP estimators with increasing sampling.

Order theory and interpolation in operator algebras

We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator algebra and the C*-algebra it generates. In much of this it is not necessary that the algebra have an approximate identity. Many of our results apply immediately to function algebras, but we will not take the time to point these out, although most of these applications seem new.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1308.272

Assessing atmospheric predictability on Mars using numerical weather prediction and data assimilation

Introduction: Studies of the time series of surface measurements of wind, pressure and temperature at the two Viking landers by Barnes [1], [2] revealed that baroclinic transient travelling waves on Mars occur mostly during northern hemisphere autumn, winter and early spring, and typically take the form of highly coherent patterns with planetary wavenumbers 1-3 that can persist for intervals of up to 30-60 sols before changing erratically. Such behaviour is almost unknown on Earth, where individual baroclinic weather systems typically persist for no longer than 5-10 days and seldom remain coherent around entire latitude circles. This occurrence of planetary-scale coherent baroclinic wave-like weather systems on Mars led to suggestions [3] that Mars' atmospheric circulation operates in a quite different dynamical regime to that of the Earth, one that tends to favour regular, symmetrical baroclinic wave activity in a manner reminiscent of the regular wave regimes found in laboratory fluid dynamics experiments on sloping convection in a rotating, thermally-driven fluid annulus (e.g. [4], [5]). In its extreme form, this hypothetical comparison would suggest the possibility of a fully non-chaotic atmospheric circulation on Mars, though subsequent modelling work [6] indicated that perturbations due to the thermal tide would lead to chaotic transitions back and forth between different intransitive wave states. This form of (relatively low-dimensional) chaotic modeflipping appeared to be consistent with the Viking observations of Mars, suggesting nevertheless that the intrinsic predictability of Mars' mid-latitude meteorology was qualitatively and quantitatively quite different from that of the Earth

Monte Carlo Planning method estimates planning horizons during interactive social exchange

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities related to each agent's preference for equity with their partner, beliefs about the partner's appetite for equity, beliefs about the partner's model of their partner, and so on. Agents may also plan different numbers of steps into the future. Providing a computationally precise account of the behaviour is an essential step towards understanding what underlies choices. A natural framework for this is that of an interactive partially observable Markov decision process (IPOMDP). However, the various complexities make IPOMDPs inordinately computationally challenging. Here, we show how to approximate the solution for the multi-round trust task using a variant of the Monte-Carlo tree search algorithm. We demonstrate that the algorithm is efficient and effective, and therefore can be used to invert observations of behavioural choices. We use generated behaviour to elucidate the richness and sophistication of interactive inference

Potential vorticity, angular momentum and inertial instabilities in the Martian atmospheric circulation from assimilated analyses of MGS/TES

Data based on re-analyses of the MGS/TES observations have been used to map distributions of potential vorticity and axial absolute angular momentum per unit mass. The data, discussed in more details in [1] and [2] stretches over nearly three Martian years and cover a wide range of atmospheric conditions. The spatial distribution and variation in time of angular momentum and potential vorticity are closely related to the zonal-mean circulation. Maps of potential vorticity distributions have been used to establish regions and times favourable for inertial instabilities. A narrow region near the equator which extends throughout the atmosphere is shown to be able to sustain inertial instabilities at different times of the year. The presence of inertial instabilities is predicted from the necessary (but not sufficient) condition for the occurrence of regions of atmosphere with PV of opposite sign to that of the planetary vorticity (PVanomalies). These regions are characterized as being favorable to mixing on small scales, while at larger scales there may be potential links to Rossby wave breaking (Knox et. al. 2005][3]. Analyses of the data indicates a hemispheric asymmetry where the northern hemisphere is more favorable to inertial instabilities particularly during NH winter. Barnes et. al. (1996)[4] used a global Martian circulation model to find that, during dusty solstice conditions, the Martian tropical and mid-latitude atmospheric circulation approximates to an angular-momentum conserving Hadley circulation, and is responsible for creating regions near the equator of low potential vorticity. Using the assimilated data we re-examine these results for a wider range of atmospheric states, including the period of the 2001 planet-encircling dust storm