Two-Loop Crossover Scaling Functions of the O(N) Model

Using Environmentally Friendly Renormalization, we present an analytic calculation of the series for the renormalization constants that describe the equation of state for the $O(N)$ model in the whole critical region. The solution of the beta-function equation, for the running coupling to order two loops, exhibits crossover between the strong coupling fixed point, associated with the Goldstone modes, and the Wilson-Fisher fixed point. The Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$, and thus the effective critical exponents associated with renormalization of the transverse vertex functions, also exhibit non-trivial crossover between these fixed points.Comment: 21 pages, 4 figures, version to appears in IJMPL

A new method for estimating the pattern speed of spiral structure in the Milky Way

In the last few decades many efforts have been made to understand the effect of spiral arms on the gas and stellar dynamics in the Milky Way disc. One of the fundamental parameters of the spiral structure is its angular velocity, or pattern speed $\Omega_p$, which determines the location of resonances in the disc and the spirals' radial extent. The most direct method for estimating the pattern speed relies on backward integration techniques, trying to locate the stellar birthplace of open clusters. Here we propose a new method based on the interaction between the spiral arms and the stars in the disc. Using a sample of around 500 open clusters from the {\it New Catalogue of Optically Visible Open Clusters and Candidates}, and a sample of 500 giant stars observed by APOGEE, we find $\Omega_p = 23.0\pm0.5$ km s$^{-1}$ kpc$^{-1}$, for a local standard of rest rotation $V_0=220$~km s$^{-1}$ and solar radius $R_0=8.0$~kpc. Exploring a range in $V_0$ and $R_0$ within the acceptable values, 200-240 km s$^{-1}$ and 7.5-8.5 kpc, respectively, results only in a small change in our estimate of $\Omega_p$, that is within the error. Our result is in close agreement with a number of studies which suggest values in the range 20-25 km s$^{-1}$ kpc$^{-1}$. An advantage of our method is that we do not need knowledge of the stellar age, unlike in the case of the birthplace method, which allows us to use data from large Galactic surveys. The precision of our method will be improved once larger samples of disk stars with spectroscopic information will become available thanks to future surveys such as 4MOST.Comment: 10 pages, 6 figures, 4 tables, accepted for publication in MNRA

Polar optical phonons in core-shell semiconductor nanowires

We obtain the the long-wavelength polar optical vibrational modes of semiconductor core-shell nanowires by means of a phenomenological continuum model. A basis for the space of solutions is derived, and by applying the appropriate boundary conditions, the transcendental equations for the coupled and uncoupled modes are attained. Our results are applied to the study of the GaAs-GaP core-shell nanowire, for which we calculate numerically the polar optical modes, analyzing the role of strain in the vibrational properties of this nanosystem

The Inter-Mammary Sticky Roll: A Novel Technique for Securing a Doppler Ultrasonic Probe to the Precordium for Venous Air Embolism Detection.

Venous air embolism is a devastating and potentially life-threatening complication that can occur during neurosurgical procedures. We report the development and use of the "inter-mammary sticky roll," a technique to reliably secure a precordial Doppler ultrasonic probe to the chest wall during neurosurgical cases that require lateral decubitus positioning. We have found that this noninvasive technique is safe, and effectively facilitates a constant Doppler signal with no additional risk to the patient

An Analytic Equation of State for Ising-like Models

Using an Environmentally Friendly Renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, $y=f(x)$, that exhibits all desired asymptotic and analyticity properties in the three limits $x\to 0$, $x\to \infty$ and $x\to -1$. The only necessary inputs are the Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$, associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N=1, we derive a one-loop equation of state for $2< d<4$ naturally parameterized by a ratio of non-linear scaling fields. For $d=3$ we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure