D3-D7 Holographic dual of a perturbed 3D CFT

An appropriately oriented D3-D7-brane system is the holographic dual of relativistic Fermions occupying a 2+1-dimensional defect embedded in 3+1-dimensional spacetime. The Fermions interact via fields of ${\mathcal N}=4$ Yang-Mills theory in the 3+1-dimensional bulk. Recently, using internal flux to stabilize the system in the probe $N_7<<N_3$ limit, a number of solutions which are dual to conformal field theories with Fermion content have been found. We use holographic techniques to study perturbations of a particular one of the conformal field theories by relevant operators. Generally, the response of a conformal field theory to such a perturbation grows and becomes nonperturbative at low energy scales. We shall find that a perturbation which switches on a background magnetic field $B$ and Fermion mass $m$ induces a renormalization group flow that can be studied perturbatively in the limit of small $m^2/B$. We solve the leading order explicitly. We find that, for one particular value of internal flux, the system exhibits magnetic catalysis, the spontaneous breaking of chiral symmetry enhanced by the presence of the magnetic field. In the process, we derive formulae predicting the Debye screening length of the Fermion-antiFermion plasma at finite density and the diamagnetic moment of the ground state of the Fermion system in the presence of a magnetic field.Comment: 23 pages, two figures; typos corrected, some comments adde

Application of a portable FTIR for measuring on-road emissions

The objective of this work was the development of an onroad in-vehicle emissions measurement technique utilizing a relatively new, commercial, portable Fourier Transform Infra-Red (FTIR) Spectrometer capable of identifying and measuring (at approximately 3 second intervals) up to 51 different compounds. The FTIR was installed in a medium class EURO1 spark ignition passenger vehicle in order to measure on-road emissions. The vehicle was also instrumented to allow the logging of engine speed, road speed, global position, throttle position, air-fuel ratio, air flow and fuel flow in addition to engine, exhaust and catalyst temperatures. This instrumentation allowed the calculation of massbased emissions from the volume-based concentrations measured by the FTIR. To validate the FTIR data, the instrument was used to measure emissions from an engine subjected to a real-world drive cycle using an AC dynamometer. Standard analyzers were operated simultaneously for comparison with the FTIR and the standard analyzer results showed that most pollutants (NOx, CO2, CO) were within ~10% of a standard analyzer during steady state conditions and within 20% during transients. The exception to this was total HC which was generally 50% or less than actual total HC, but this was due to the limited number of hydrocarbons measured by the FTIR. In addition to the regulated emissions, five toxic hydrocarbon species were analyzed and found to be sensitive to cold starts in varying proportions. Finally, FTIR data was compared to results from a commercially available on-road measurement system (Horiba OBS- 1000), and there was good agreement

The effect of ambient temperature on cold start urban traffic emissions for a real world SI car

The influence of ambient temperature on exhaust emissions for an instrumented Euro 1 SI car was determined. A real world test cycle was used, based on an urban drive cycle that was similar to the ECE urban drive cycle. It was based on four laps of a street circuit and an emissions sample bag was taken for each lap. The bag for the first lap was for the cold start emissions. An in-vehicle direct exhaust dual bag sampling technique was used to simultaneously collect exhaust samples upstream and downstream of the three-way catalyst (TWC). The cold start tests were conducted over a year, with ambient temperatures ranging from – 2°C to 32°C. The exhaust system was instrumented with thermocouples so that the catalyst light off temperature could be determined. The results showed that CO emissions for the cold start were reduced by a factor of 8 downstream of catalyst when ambient temperature rose from -2°C to 32°C, the corresponding hydrocarbon emissions were reduced by a factor of 4. There was no clear relationship between NOx emissions and ambient temperature. For subsequent laps of the test circuit the reduction of CO and HC emissions as a function of ambient temperature was lower. The time for catalyst light off increased by 50% as the ambient temperature was reduced. The results show that the vehicle used is unlikely to meet the new – 7oC cold start CO emission regulations

Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter and Forrester, we find proof of polynomial identities for finitizations of the Virasoro characters $\chi_{b,a}^{(r-1,r)}(q)$ as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers--Ramanujan type identities for the unitary minimal Virasoro characters, conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Comment: 28 pages, Latex, 7 Postscript figure

On the number of representations providing noiseless subsystems

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function $f_d(n)$ which is the fraction of all $d$-dimensional quantum systems which preserve $n$ bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.Comment: 17 pp, 4 figs, accepted for Physical Review

A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate

Augustana Historical Society Publications Volume V

Table of Contents: C. W. Foss: an appreciation / George M. Stephenson -- Diary kept by L. P. Esbjorn, 1849 / O. L. Nordstrom -- Reports to the American Home Missionary Society, 1849-1856 / Conrad Bergendoff -- The sources of the original constitution of the Augustana Synod / Conrad Bergendoff -- Early letters to Erland Carlsson / E. W. Olson -- Sources on revolutionary Europe : A selected list from the Charles XV Collection / George Gordon Andrews -- The Augustana Historical Society, 1930-1935 / O. L. Nordstrom -- In memoriam.https://digitalcommons.augustana.edu/ahsbooks/1011/thumbnail.jp

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

The effects of dust on the optical and infrared evolution of SN 2004et

We present an analysis of multi-epoch observations of the Type II-P supernova SN 2004et. New and archival optical spectra of SN 2004et are used to study the evolution of the Halpha and [O I] 6300A line profiles between days 259 and 646. Mid-infrared imaging was carried out between 2004 to 2010. We include Spitzer `warm' mission photometry at 3.6 and 4.5um obtained on days 1779, 1931 and 2151, along with ground-based and HST optical and near-infrared observations obtained between days 79 and 1803. Multi-wavelength light curves are presented, as well as optical-infrared spectral energy distributions (SEDs) for multiple epochs. Starting from about day 300, the optical light curves provide evidence for an increasing amount of circumstellar extinction attributable to newly formed dust, with the additional extinction reaching 0.8-1.5 magnitudes in the V-band by day 690. The overall SEDs were fitted with multiple blackbody components, in order to investigate the luminosity evolution of the supernova, and then with Monte Carlo radiative transfer models using smooth or clumpy dust distributions, in order to estimate how much new dust condensed in the ejecta. The luminosity evolution was consistent with the decay of 56Co in the ejecta up until about day 690, after which an additional emission source is required, in agreement with the findings of Kotak et al. (2009). Clumped dust density distributions consisting of 20% amorphous carbons and 80% silicates by mass were able to match the observed optical and infrared SEDs, with dust masses that increased from 8x10^{-5} Msun on day 300 to 1.5x10^{-3} Msun on day 690, still significantly lower than the values needed for core collapse supernovae to make a significant contribution to the dust enrichment of galaxies.Comment: 24 pages, 12 figures, 9 tables, published in MNRA