A Tale of Two Fractals: The Hofstadter Butterfly and The Integral Apollonian Gaskets

This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden threefold symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions

Testing spatial noncommutativiy via the Aharonov-Bohm effect

The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives non-trivial kinematical corrections that will produce a diffraction pattern even when the magnetic flux is quantized. The scattering problem is also formulated, and the differential cross section is calculated. Our results can be extrapolated to high energy physics and the bound $\theta \sim [ 10 {TeV}]^{-2}$ is found. If this bound holds, then noncommutative effects could be explored in scattering experiments measuring differential cross sections for small angles. The bound state Aharonov- Bohm effect is also discussed.Comment: 16 pp, Revtex 4, 2 fig, new references added. To appear in PR

A 100-Year Review: A century of change in temperate grazing dairy systems

peer-reviewedFrom 1917 to 2017, dairy grazing systems have evolved from uncontrolled grazing of unimproved pastures by dual-purpose dairy-beef breeds to an intensive system with a high output per unit of land from a fit-for-purpose cow. The end of World War I signaled significant government investments in agricultural research institutes around the world, which coincided with technological breakthroughs in milk harvesting and a recognition that important traits in both plants and animals could be improved upon relatively rapidly through genetic selection. Uptake of milk recording and herd testing increased rapidly through the 1920s, as did the recognition that pastures that were rested in between grazing events yielded more in a year than those continuously grazed. This, and the invention and refinement of the electric fence, led to the development of “controlled” rotational grazing. This, in itself, facilitated greater stocking rates and a 5 to 10% increase in milk output per hectare but, perhaps more importantly, it allowed a more efficient use of nitrogen fertilizer, further increasing milk output/land area by 20%. Farmer inventions led to the development of the herringbone and rotary milking parlors, which, along with the “unshortable” electric fence and technological breakthroughs in sperm dilution rates, allowed further dairy farm expansion. Simple but effective technological breakthroughs in reproduction ensured that cows were identified in estrus early (a key factor in maintaining the seasonality of milk production) and enabled researchers to quantify the anestrus problem in grazing herds. Genetic improvement of pasture species has lagged its bovine counterpart, but recent developments in multi-trait indices as well as investment in genetic technologies should significantly increase potential milk production per hectare. Decades of research on the use of feeds other than pasture (i.e., supplementary feeds) have provided consistent milk production responses when the reduction in pasture intake associated with the provision of supplementary feed (i.e., substitution rate) is accounted for. A unique feature of grazing systems research over the last 70 yr has been the use of multi-year farm systems experimentation. These studies have allowed the evaluation of strategic changes to a component of the system on all the interacting features of the system. This technique has allowed excellent component research to be “systemized” and is an essential part of the development of the intensive grazing production system that exists today. Future challenges include the provision of skilled labor or specifically designed automation to optimize farm management and both environmental sustainability and animal welfare concerns, particularly relating to the concentration of nitrogen in each urine patch and the associated risk of nitrate leaching, as well as concerns regarding exposure of animals to harsh climatic conditions. These combined challenges could affect farmers' “social license” to farm in the future

Thermostatistics of deformed bosons and fermions

Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most important thermodynamic functions and we study the q-boson and q-fermion ideal gas in the thermodynamic limit.Comment: 14 pages, 2 figure

The Intentional Use of Service Recovery Strategies to Influence Consumer Emotion, Cognition and Behaviour

Service recovery strategies have been identified as a critical factor in the success of. service organizations. This study develops a conceptual frame work to investigate how specific service recovery strategies influence the emotional, cognitive and negative behavioural responses of . consumers., as well as how emotion and cognition influence negative behavior. Understanding the impact of specific service recovery strategies will allow service providers' to more deliberately and intentionally engage in strategies that result in positive organizational outcomes. This study was conducted using a 2 x 2 between-subjects quasi-experimental design. The results suggest that service recovery has a significant impact on emotion, cognition and negative behavior. Similarly, satisfaction, negative emotion and positive emotion all influence negative behavior but distributive justice has no effect

Accelerated forgetting of real-life events in Transient Epileptic Amnesia.

addresses: Cognitive and Behavioural Neurology, Peninsula Medical School, University of Exeter, Exeter, UK.types: Journal Article; Research Support, Non-U.S. Gov'tCopyright © 2010 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Neuropsychologia, 2010, Vol. 48, Issue 11, pp. 3235 – 3244 DOI: http://dx.doi.org/10.1016/j.neuropsychologia.2010.07.001Transient Epileptic Amnesia (TEA) is a form of temporal lobe epilepsy associated with ictal and interictal memory disturbance. Some patients with TEA exhibit Accelerated Long-term Forgetting (ALF), in which memory for verbal and non-verbal material is retained normally over short delays but fades at an unusually rapid rate over days to weeks. This study addresses three questions about ALF in TEA: (i) whether real-life events undergo ALF in a similar fashion to laboratory-based stimuli; (ii) whether ALF can be detected within 24h; (iii) whether procedural memories are susceptible to ALF. Eleven patients with TEA and eleven matched healthy controls wore a novel, automatic camera, SenseCam, while visiting a local attraction. Memory for images of events was assessed on the same day and after delays of one day, one week, and three weeks. Forgetting of real-life events was compared with forgetting of a word list and with performance on a procedural memory task. On the day of their excursion, patients and controls recalled similar numbers of primary events, associated secondary details (contiguous events, thoughts and sensory information) and items from the word list. In contrast, patients showed ALF for primary events over three weeks, with ALF for contiguous events, thoughts and words over the first day. Retention on the procedural memory task was normal over three weeks. The results indicate that accelerated forgetting in TEA: (i) affects memory for real-life events as well as laboratory stimuli; (ii) is maximal over the first day; and (iii) is specific to declarative memories

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02