Exact beta function from the holographic loop equation of large-N QCD_4

We construct and study a previously defined quantum holographic effective action whose critical equation implies the holographic loop equation of large-N QCD_4 for planar self-avoiding loops in a certain regularization scheme. We extract from the effective action the exact beta function in the given scheme. For the Wilsonean coupling constant the beta function is exacly one loop and the first coefficient agrees with its value in perturbation theory. For the canonical coupling constant the exact beta function has a NSVZ form and the first two coefficients agree with their value in perturbation theory.Comment: 42 pages, latex. The exponent of the Vandermonde determinant in the quantum effective action has been changed, because it has been employed a holomorphic rather than a hermitean resolution of identity in the functional integral. Beta function unchanged. New explanations and references added, typos correcte

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

Re-examining the relationship between audiometric profile and tinnitus pitch

Objective: We explored the relationship between audiogram shape and tinnitus pitch to answer questions arising from neurophysiological models of tinnitus: ‘Is the dominant tinnitus pitch associated with the edge of hearing loss?’ and ‘Is such a relationship more robust in people with narrow tinnitus bandwidth or steep sloping hearing loss?’ Design: A broken-stick fitting objectively quantified slope, degree and edge of hearing loss up to 16 kHz. Tinnitus pitch was characterized up to 12 kHz. We used correlation and multiple regression analyses for examining relationships with many potentially predictive audiometric variables. Study Sample: 67 people with chronic bilateral tinnitus (43 men and 24 women, aged from 22 to 81 years). Results: In this ample of 67 subjects correlation failed to reveal any relationship between the tinnitus pitch and the edge frequency. The tinnitus pitch generally fell within the area of hearing loss. The pitch of the tinnitus in a subset of subjects with a narrow tinnitus bandwidth (n = 23) was associated with the audiometric edge. Conclusions: Our findings concerning subjects with narrow tinnitus bandwidth suggest that this can be used as an a priori inclusion criterion. A large group of such subjects should be tested to confirm these results

Twisted local systems solve the (holographic) loop equation of large-N QCD_4

We construct a holographic map from the loop equation of large-N QCD in d=2 and d=4, for planar self-avoiding loops, to the critical equation of an equivalent effective action. The holographic map is based on two ingredients: an already proposed holographic form of the loop equation, such that the quantum contribution is reduced to a regularized residue; a new conformal map from the region encircled by the based loop to a cuspidal fundamental domain in the upper half-plane, such that the regularized residue vanishes at the cusp. As a check, we study the first coefficient of the beta function and that part of the second coefficient which arises from the rescaling anomaly, in passing from the Wilsonian to the canonically normalised (holographic) effective action.Comment: 42 pages, latex; abstract shortened and a reference added as suggested by the referee; typos in Eq.(72,76,77,82,83,84) correcte

Strategies for Controlled Placement of Nanoscale Building Blocks

The capability of placing individual nanoscale building blocks on exact substrate locations in a controlled manner is one of the key requirements to realize future electronic, optical, and magnetic devices and sensors that are composed of such blocks. This article reviews some important advances in the strategies for controlled placement of nanoscale building blocks. In particular, we will overview template assisted placement that utilizes physical, molecular, or electrostatic templates, DNA-programmed assembly, placement using dielectrophoresis, approaches for non-close-packed assembly of spherical particles, and recent development of focused placement schemes including electrostatic funneling, focused placement via molecular gradient patterns, electrodynamic focusing of charged aerosols, and others

Transport impacts on atmosphere and climate: Aviation

Aviation alters the composition of the atmosphere globally and can thus drive climate change and ozone depletion. The last major international assessment of these impacts was made by the Intergovernmental Panel on Climate Change (IPCC) in 1999. Here, a comprehensive updated assessment of aviation is provided. Scientific advances since the 1999 assessment have reduced key uncertainties, sharpening the quantitative evaluation, yet the basic conclusions remain the same. The climate impact of aviation is driven by long-term impacts from CO2 emissions and shorter-term impacts from non-CO2 emissions and effects, which include the emissions of water vapour, particles and nitrogen oxides (NOx). The presentday radiative forcing from aviation (2005) is estimated to be 55 mW m2 (excluding cirrus cloud enhancement), which represents some 3.5% (range 1.3–10%, 90% likelihood range) of current anthropogenic forcing, or 78 mW m2 including cirrus cloud enhancement, representing 4.9% of current forcing (range 2–14%, 90% likelihood range). According to two SRES-compatible scenarios, future forcings may increase by factors of 3–4 over 2000 levels, in 2050. The effects of aviation emissions of CO2 on global mean surface temperature last for many hundreds of years (in common with other sources), whilst its non-CO2 effects on temperature last for decades. Much progress has been made in the last ten years on characterizing emissions, although major uncertainties remain over the nature of particles. Emissions of NOx result in production of ozone, a climate warming gas, and the reduction of ambient methane (a cooling effect) although the overall balance is warming, based upon current understanding. These NOx emissions from current subsonic aviation do not appear to deplete stratospheric ozone. Despite the progress made on modelling aviation’s impacts on tropospheric chemistry, there remains a significant spread in model results. The knowledge of aviation’s impacts on cloudiness has also improved: a limited number of studies have demonstrated an increase in cirrus cloud attributable to aviation although the magnitude varies: however, these trend analyses may be impacted by satellite artefacts. The effect of aviation particles on clouds (with and without contrails) may give rise to either a positive forcing or a negative forcing: the modelling and the underlying processes are highly uncertain, although the overall effect of contrails and enhanced cloudiness is considered to be a positive forcing and could be substantial, compared with other effects. The debate over quantification of aviation impacts has also progressed towards studying potential mitigation and the technological and atmospheric tradeoffs. Current studies are still relatively immature and more work is required to determine optimal technological development paths, which is an aspect that atmospheric science has much to contribute. In terms of alternative fuels, liquid hydrogen represents a possibility and may reduce some of aviation’s impacts on climate if the fuel is produced in a carbon-neutral way: such fuel is unlikely to be utilized until a ‘hydrogen economy’ develops. The introduction of biofuels as a means of reducing CO2 impacts represents a future possibility. However, even over and above land-use concerns and greenhouse gas budget issues, aviation fuels require strict adherence to safety standards and thus require extra processing compared with biofuels destined for other sectors, where the uptake of such fuel may be more beneficial in the first instance