Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions

We calculate the condensate and the vacuum current density induced by external static magnetic fields in (2+1)-dimensions. At the perturbative level, we consider an exponentially decaying magnetic field along one cartesian coordinate. Non-perturbatively, we obtain the fermion propagator in the presence of a uniform magnetic field by solving the Schwinger-Dyson equation in the rainbow-ladder approximation. In the large flux limit, we observe that both these quantities, either perturbative (inhomogeneous) and non-perturbative (homogeneous), are proportional to the external field, in agreement with early expectations.Comment: 8 pages, 2 figures. Accepted for publication in Phys. Rev.

The Hall instability of weakly ionized, radially stratified, rotating disks

Cool weakly ionized gaseous rotating disk, are considered by many models as the origin of the evolution of protoplanetary clouds. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Thus, a hierarchy of successive fragmentations into smaller and smaller pieces as a part of the Kant-Laplace theory of formation of the planetary system remains valid also for contemporary cosmogony. Traditionally, axisymmetric magnetohydrodynamic (MHD), and recently Hall-MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against nonaxisymmetric perturbations in compressible rotating fluids in external magnetic field is proposed as a viable mechanism for the azimuthal fragmentation of the protoplanetary disk and thus perhaps initiating the road to planet formation. The Hall instability is excited due to the combined effect of the radial stratification of the disk and the Hall electric field, and its growth rate is of the order of the rotation period.Comment: 15 pages, 2 figure

Classical Strongly Coupled QGP I: The Model and Molecular Dynamics Simulations

We propose a model for the description of strongly interacting quarks and gluon quasiparticles at $T=(1-3)T_c$, as a classical and nonrelativistic colored Coulomb gas. The sign and strength of the inter-particle interactions are fixed by the scalar product of their classical {\it color vectors} subject to Wong's equations. The model displays a number of phases as the Coulomb coupling is increased ranging from a gas, to a liquid, to a crystal with antiferromagnetic-like color ordering. We analyze the model using Molecular Dynamics (MD) simulations and discuss the density-density correlator in real time. We extract pertinent decorrelation times, diffusion and viscosity constants for all phases. The classical results when extrapolated to the sQGP suggest that the phase is liquid-like, with a diffusion constant $D\approx 0.1/T$ and a bulk viscosity to entropy density ratio $\eta/s\approx 1/3$.Comment: 11 pages, 14 figure

Destabilizing Taylor-Couette flow with suction

We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure

Making Sense of the Legendre Transform

The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform algebraically and geometrically. Then we bring in the physics to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.Comment: 11 pages, 3 figure

The Hall instability of thin weakly-ionized stratified Keplerian disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the free parameter of the model which is related to the total current through the disk. To estimate the minimal values of the equilibrium magnetic field that leads to instability, the latter is constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by a distributed electric current.Comment: 13 pages, 7 figure

Extinction and backscatter measurements of Antarctic PSC's, 1987: Implications for particle and vapor removal

The temperature dependence is examined of optical properties measured in the Antarctic during 1987 at the 70 mb level (near 18 km), a level chosen to correlate the results with in situ measurements made from the NASA-Ames ER-2 aircraft during the 1987 Airborne Antarctic Ozone Experiment (AAOE). The data set consists of extinction measurements by Sam 2 inside the Antarctic polar vortex from May to October 1987; and backscatter measurements by the UV-DIAL (Ultraviolet Differential Absorption Lidar) system aboard the Ames DC-8 aircraft during selected AAOE flights. Observed trends are compared with results from a revised version of Pole and McCormick's model to classify the PSC observations by Type (1 or 2) and infer the temporal behavior of the ambient aerosol and ambient vapor mixing ratios. The sample figures show monthly ensembles of the 70-mb Sam 2 extinction ratio (the ratio of aerosol or PSC extinction to molecule extinction) as a function of NMC temperature at the beginning (June) and (October) of the 1987 Antarctic winter. Both ensembles show two rather distinct clusters of points: one oriented in the near vertical direction which depicts the change with temperature of the ambient aerosol extinction ratio; and a second cluster oriented in the near horizontal direction whose position on the vertical scale marks a change in particle phase (i.e., PSC formation) and whose length (the extinction enhancement related to that of the ambient aerosol) is an indicator of PSC type

Novel Control Effectors for Truss Braced Wing

At cruise flight conditions very high aspect ratio/low sweep truss braced wings (TBW) may be subject to design requirements that distinguish them from more highly swept cantilevered wings. High aspect ratio, short chord length and relative thinness of the airfoil sections all contribute to relatively low wing torsional stiffness. This may lead to aeroelastic issues such as aileron reversal and low flutter margins. In order to counteract these issues, high aspect ratio/low sweep wings may need to carry additional high speed control effectors to operate when outboard ailerons are in reversal and/or must carry additional structural weight to enhance torsional stiffness. The novel control effector evaluated in this study is a variable sweep raked wing tip with an aileron control surface. Forward sweep of the tip allows the aileron to align closely with the torsional axis of the wing and operate in a conventional fashion. Aft sweep of the tip creates a large moment arm from the aileron to the wing torsional axis greatly enhancing aileron reversal. The novelty comes from using this enhanced and controllable aileron reversal effect to provide roll control authority by acting as a servo tab and providing roll control through intentional twist of the wing. In this case the reduced torsional stiffness of the wing becomes an advantage to be exploited. The study results show that the novel control effector concept does provide roll control as described, but only for a restricted class of TBW aircraft configurations. For the configuration studied (long range, dual aisle, Mach 0.85 cruise) the novel control effector provides significant benefits including up to 12% reduction in fuel burn

The Cauchy convergence of T and P-approximant templates for test-mass Kerr binary systems

In this work we examine the Cauchy convergence of both post-Newtonian (T-approximant) and re-summed post-Newtonian (P-approximant) templates for the case of a test-mass orbiting a Kerr black hole along a circular equatorial orbit. The Cauchy criterion demands that the inner product between the $n$ and $n+1$ order approximation approaches unity, as we increase the order of approximation. In previous works, it has been shown that we achieve greater fitting factors and better parameter estimation using the P-approximant templates for both Schwarzschild and Kerr black holes. In this work, we show that the P-approximant templates also display a faster Cauchy convergence making them a superior template to the standard post-Newtonian templates.Comment: 5 pages, Replaced with shortened published versio