The traveling salesman problem, conformal invariance, and dense polymers

We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag repeatedly between two regions, and in subleading corrections to the length of the tour. The universality class should be the same as for dense polymers and minimal spanning trees. The conjectures for the length of the tour on a cylinder are tested numerically.Comment: 4 pages. v2: small revisions, improved argument about dimensions d>2. v3: Final version, with a correction to the form of the tour length in a domain, and a new referenc

Dense loops, supersymmetry, and Goldstone phases in two dimensions

Loop models in two dimensions can be related to O(N) models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for N<2. We argue that this phase is generic for -2< N <2 when crossings of loops are allowed, and distinct from the model of non-crossing dense loops first studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are supported by our numerical results, and by a lattice model solved exactly by Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].Comment: RevTeX, 5 pages, 3 postscript figure

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments

Spin-Peierls states of quantum antiferromagnets on the CaV4O9Ca V_4 O_9 lattice

We discuss the quantum paramagnetic phases of Heisenberg antiferromagnets on the 1/5-depleted square lattice found in $Ca V_4 O_9$. The possible phases of the quantum dimer model on this lattice are obtained by a mapping to a quantum-mechanical height model. In addition to the ``decoupled'' phases found earlier, we find a possible intermediate spin-Peierls phase with spontaneously-broken lattice symmetry. Experimental signatures of the different quantum paramagnetic phases are discussed.Comment: 9 pages; 2 eps figure

The UARS microwave limb sounder version 5 data set: Theory, characterization, and validation

Nitric acid (HNO3) is a major player in processes controlling the springtime depletion of polar ozone. It is the main constituent of the Polar Stratospheric Clouds (PSCs) and a primary reservoir for reactive nitrogen. Potential variations in the stratospheric circulation and temperature may alter the extent and duration of PSCs activity, influencing the future ozone levels significantly. Monitoring HNO3 and its long-term variability, especially in polar region, is then crucial for better understanding issues related to ozone decline and expected recovery. In this study we present an intercomparison between ground based HNO3 measurements, carried out by means of the Ground-Based Millimeter-wave Spectrometer (GBMS), and two satellite data sets produced by the two NASA/JPL Microwave Limb Sounder (MLS) experiments. In particular, we compare UARS MLS measurements (1991-1999) with those carried out by the GBMS at South Pole, Antarctica (90°S), Fall of 1993 and 1995. A similar intercomparison is made between Aura MLS HNO3 observations (2004 - to date) and GBMS measurements obtained during the period February 2004 - March 2007, at the mid-latitudes/high altitudes station of Testa Grigia (45.9° N, 7.7° E, elev. 3500 m), and during polar winters 2008/09 and 2009/2010 at Thule Air Base (76.5°N 68.8°W), Greenland. We assess systematic differences between GBMS and both UARS and Aura HNO3 data sets at seven potential temperature levels (θ) spanning the range 465 – 960 K. The UARS data set advected to the South Pole shows a low bias, within 20% for all θ levels but the 960 K, with respect to GBMS measurements. A very good agreement, within 5%, is obtained between Aura and GBMS observations at Testa Grigia, while larger differences, possibly due to latitude dependent effects, are observed over Thule. These differences are under further investigations but a preliminary comparison over Thule among MLS v3, GBMS, and ACE-FTS measurements suggests that GBMS measurements carried out during winter 2009 might not be reliable. These comparisons have been performed in the framework of the NASA JPL GOZCARDS project, which is aimed at developing a long-term, global data record of the relevant stratospheric constituents in the context of ozone decline. GBMS has been selected in GOZCARDS since its HNO3 dataset, although sampling different latitudes in different years, is the only one spanning a sufficiently long time interval for cross-calibrating HNO3 measurements by the UARS and Aura MLS experiments

A comparative analysis of Simplified General Circulation Models of the atmosphere of Venus

Within the context of a working group supported by ISSI (Bern, Switzerland), we have made an intercomparison work between Global Circulation Models using simpli?ed parameterizations for radiative forcing and other physical processes. Even with similar schemes and parameters, the different GCMs produce different circulations, illustrating interesting differences between dynamical model cores

SU(N) Quantum Hall Skyrmions

We have investigated skyrmions in N-component quantum Hall systems. We find that SU(N) skyrmions are the lowest energy charged excitations for filling factors \nu = 1,2,...,N-1 for small enough symmetry breaking terms. N>2 skyrmions can be realized in Si QH systems based on the (110) or (111) interfaces of Si, or perhaps in Si (100) systems, where the spin and valley isospin together provide an SU(4)-symmetry, or in multilayer QH systems. We also present Hartree-Fock results for a phenomenological easy-axis SU(2)-breaking model appropriate to valley degeneracy.Comment: 5 pages, 2 figure

TEMPERATURE-DEPENDENCE OF DOMAIN-WALL COERCIVE FIELD IN MAGNETIC GARNET-FILMS

The coercive properties of magnetically uniaxial liquid-phase epitaxy garnet films were investigated between 10 K and the Neel temperature (T(N) less-than-or-equal-to 500 K). Two independent methods, the results of which are nearly identical (magnetical response of oscillating domain walls and the method of coercive loops measured in a vibrating sample magnetometer), were used. Besides the usual domain-wall coercive field, H(dw), the critical coercive pressure, p(dw), was also introduced as it describes in a direct way the interactions of the domain walls with the wall-pinning traps. Both H(dw) and p(dw) were found to increase exponentially with decreasing temperature. Three different types of wall-pinning traps were identified in the sample and their strength, their rate of change with temperature, and their temperature range of activity were determined