Hyper-Scaling Relations in the Conformal Window from Dynamic AdS/QCD

Dynamic AdS/QCD is a holographic model of strongly coupled gauge theories with the dynamics included through the running anomalous dimension of the quark bilinear, gamma. We apply it to describe the physics of massive quarks in the conformal window of SU(N_c) gauge theories with N_f fundamental flavours, assuming the perturbative two loop running for gamma. We show that to find regular, holographic, renormalization group flows in the infra-red the decoupling of the quark flavours at the scale of the mass is important and enact it through suitable boundary conditions when the flavours become on shell. We can then compute the quark condensate and the mesonic spectrum (M_rho, M_pi, M_sigma) and decay constants. We compute their scaling dependence on the quark mass for a number of examples. The model matches perturbative expectations for large quark mass and naive dimensional analysis (including the anomalous dimensions) for small quark mass. The model allows study of the intermediate regime where there is an additional scale from the running of the coupling and we present results for the deviation of scalings from assuming only the single scale of the mass.Comment: 12 pages, 26 figures, new references adde

Inverse Magnetic Catalysis in Bottom-Up Holographic QCD

We explore the effect of magnetic field on chiral condensation in QCD via a simple bottom up holographic model which inputs QCD dynamics through the running of the anomalous dimension of the quark bilinear. Bottom up holography is a form of effective field theory and we use it to explore the dependence on the coefficients of the two lowest order terms linking the magnetic field and the quark condensate. In the massless theory, we identify a region of parameter space where magnetic catalysis occurs at zero temperature but inverse magnetic catalysis at temperatures of order the thermal phase transition. The model shows similar non-monotonic behaviour in the condensate with B at intermediate T as the lattice data. This behaviour is due to the separation of the meson melting and chiral transitions in the holographic framework. The introduction of quark mass raises the scale of B where inverse catalysis takes over from catalysis until the inverse catalysis lies outside the regime of validity of the effective description leaving just catalysis.Comment: 9 pages, 8 figure

The Law, Culture, and Economics of Fashion

Fashion is one of the world's most important creative industries. As the most immediate visible marker of self-presentation, fashion creates vocabularies for self-expression that relate individuals to society. Despite being the core of fashion and legally protected in Europe, fashion design lacks protection against copying under U.S. intellectual property law. This Article frames the debate over whether to provide protection to fashion design within a reflection on the cultural dynamics of innovation as a social practice. The desire to be in fashion - most visibly manifested in the practice of dress - captures a significant aspect of social life, characterized by both the pull of continuity with others and the push of innovation toward the new. We explain what is at stake economically and culturally in providing legal protection for original designs, and why a protection against close copies only is the proper way to proceed. We offer a model of fashion consumption and production that emphasizes the complementary roles of individual differentiation and shared participation in trends. Our analysis reveals that the current legal regime, which protects trademarks but not fashion designs from copying, distorts innovation in fashion away from this expressive aspect and toward status and luxury aspects. The dynamics of fashion lend insight into dynamics of innovation more broadly, in areas where consumption is also expressive. We emphasize that the line between close copying and remixing represents an often underappreciated but promising direction for intellectual property today. Published in Stanford Law Review, Vol. 61, March 2009.

Translational Symmetry Breaking in Higgs & Gauge Theory, and the Cosmological Constant

We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff, include terms that favour the breaking of translation (Lorentz) invariance, potentially resulting in striped, chequered board or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as $\bar{q} q$ and $\bar{q} F^{(2n)} q$. Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes RG running. A key phenomenological motive to look at such states is recent work that shows that the non-linear response in $R^2$ gravity to such short range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.Comment: 9 pages, 1 figure; minor changes. Version to be published in PR

Linear multistep methods for integrating reversible differential equations

This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for first-order differential equations are generally unstable. Here, we report on a subset of these methods -- the zero-growth methods -- that evade these instabilities. We provide an algorithm for identifying these rare methods. We find and study all zero-growth, reversible multisteps with six or fewer steps. This select group includes two well-known second-order multisteps (the trapezoidal and explicit midpoint methods), as well as three new fourth-order multisteps -- one of which is explicit. Variable timesteps can be readily implemented without spoiling the reversibility. Tests on Keplerian orbits show that these new reversible multisteps work well on orbits with low or moderate eccentricity, although at least 100 steps/radian are required for stability.Comment: 31 pages, 9 figures, in press at The Astronomical Journa

Database Analysis to Support Nutrient Criteria Development (Phase I)

The intent of this publication of the Arkansas Water Resources Center is to provide a location whereby a final report on water research to a funding agency can be archived. The Texas Commission on Environmental Quality (TCEQ) contracted with University of Arkansas researchers for a multiple year project titled “Database Analysis to Support Nutrient Criteria Development”. This publication covers the first of three phases of that project and has maintained the original format of the report as submitted to TCEQ. This report can be cited either as an AWRC publication (see below) or directly as the final report to TCEQ

Temperature transfer due to induction sealing

This thesis investigates the temperature recorded during the induction sealing process within the headspace of a container. The topic for this thesis stemmed from a question of whether or not the product inside an induction sealed bottle has the potential of being adversely affected by heat generated during the induction sealing process on a packaging line during production. The thesis demonstrated the heat generated and temperature recorded utilizing irreversible chemical temperature indicating labels during the induction sealing process on a standard bottle packaging line with an aluminum foil liner/innerseal. Based on the results of this study, the following trends were observed: as the induction seal head height increased above the container/closure system, the temperature at the foil innerseal decreased and the distance from the top of the bottle finish down into the bottle headspace that a temperature could be measured decreased. As the packaging line speed increased, the temperature at the foil innerseal decreased and the distance measured from the top of the bottle finish down into the bottle headspace that a temperature could be measured decreased. As the diameter of the foil innerseal increased with the increase in closure diameter, the temperature at the foil innerseal increased and the distance measured from the top of the bottle finish down into the headspace that a temperature could be measured increased. In no case did the temperature at the product fill level of any of the tested container/closure systems exceed 100F. Therefore it can be concluded that the induction sealing process does not introduce temperatures high enough that would adversely affect the contents of a container/closure system