Limits on Lorentz violation from charged-pion decay

Charged-pion decay offers many opportunities to study Lorentz violation. Using an effective field theory approach, we study Lorentz violation in the lepton, W-boson, and quark sectors and derive the differential pion-decay rate, including muon polarization. Using coordinate redefinitions we are able to relate the first-generation quark sector, in which no bounds were previously reported, to the lepton and W-boson sector. This facilitates a tractable calculation, enabling us to place bounds on the level of $10^{-4}$ on first-generation quark parameters. Our expression for the pion-decay rate can be used to constrain Lorentz violation in future experiments.Comment: 12 pages, 1 figure, Accepted for publication in Phys. Rev.

Craters as sand traps: Dynamics, history, and morphology of modern sand transport in an active Martian dune field

Aeolian transport of sand is abundant on modern-day Mars, as revealed by remote sensing measurements of the motion of dunes, and of the meter-scale ripples that mantle them. We study a large-scale natural sand trap within the Meroe Patera dune field: a 1.8-km diameter crater which features a dune-free “shadow” in its lee. We compare the volume of sand trapped within this crater to the sand volume that would be expected to cover the area of the crater and its dune-free shadow behind it if the crater were not present. We find that the crater holds less sand than this “missing” volume would predict, implying that sand escapes from the crater over time. Modern day imagery shows an apparent lack of sand escaping from the Meroe crater, however, suggesting that changes in the wind regime at the site may have allowed sand to escape in the past. The persistence of an altered dune morphology all the way to the far downwind edge of the dune field suggests consistent wind conditions over the time of the crater-dune field interaction

Effective Operator Treatment of the Lipkin Model

We analyze the Lipkin Model using effective operator techniques. We present both analytical and numerical results for effective Hamiltonians. The accuracy of the cluster approximation is investigated.Comment: To appear in Phys.Rev.

Axion-Dilaton Domain Walls and Fake Supergravity

Dynamical systems methods are used to investigate domain-wall solutions of a two-parameter family of models in which gravity is coupled to an axion, and to a dilaton with an exponential potential of either sign. A complete global analysis is presented for (i) constant axion and (ii) flat walls, including a study of bifurcations and a new exact domain-wall solution with non-constant axion. We reconsider `fake supergravity' issues in light of these results. We show, by example, how domain walls determine multi-valued superpotentials that branch at stationary points that are not stationary points of the potential, and we apply this result to potentials with anti-de Sitter vacua. We also show by example that `adapted' truncation to a single-scalar model is sometimes inconsistent, and we propose a `generalized' fake supergravity formalism that applies in some such cases.Comment: 43pp, 19 figures; minor corrections and extensions; one additional figur

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Dynamical Symmetries Reflected in Realistic Interactions

Realistic nucleon-nucleon (NN) interactions, derived within the framework of meson theory or more recently in terms of chiral effective field theory, yield new possibilities for achieving a unified microscopic description of atomic nuclei. Based on spectral distribution methods, a comparison of these interactions to a most general Sp(4) dynamically symmetric interaction, which previously we found to reproduce well that part of the interaction that is responsible for shaping pairing-governed isobaric analog 0+ states, can determine the extent to which this significantly simpler model Hamiltonian can be used to obtain an approximate, yet very good description of low-lying nuclear structure. And furthermore, one can apply this model in situations that would otherwise be prohibitive because of the size of the model space. In addition, we introduce a Sp(4) symmetry breaking term by including the quadrupole-quadrupole interaction in the analysis and examining the capacity of this extended model interaction to imitate realistic interactions. This provides a further step towards gaining a better understanding of the underlying foundation of realistic interactions and their ability to reproduce striking features of nuclei such as strong pairing correlations or collective rotational motion.Comment: 10 pages, 4 figures, Proceedings of the XXV International Workshop on Nuclear Theory, June 26-July 1, 2006, Rila Mountains, Bulgari

The mechanism of thickness selection in the Sadler-Gilmer model of polymer crystallization

Recent work on the mechanism of polymer crystallization has led to a proposal for the mechanism of thickness selection which differs from those proposed by the surface nucleation theory of Lauritzen and Hoffman and the entropic barrier model of Sadler and Gilmer. This has motivated us to reexamine the model used by Sadler and Gilmer. We again find a fixed-point attractor which describes the dynamical convergence of the crystal thickness to a value just larger than the minimum stable thickness, l_min. This convergence arises from the combined effect of two constraints on the length of stems in a layer: it is unfavourable for a stem to be shorter than l_min and for a stem to overhang the edge of the previous layer. The relationship between this new mechanism and the explanation given by Sadler and Gilmer in terms of an entropic barrier is discussed. We also examine the behaviour of the Sadler-Gilmer model when an energetic contribution from chain folds is included.Comment: 15 pages, 13 figures, revte