Evolving turbulence and magnetic fields in galaxy clusters

We discuss, using simple analytical models and MHD simulations, the origin and parameters of turbulence and magnetic fields in galaxy clusters. Three physically distinct regimes can be identified in the evolution of cluster turbulence and magnetic fields. Firstly, the fluctuation dynamo will produce microgauss-strong, random magnetic fields during cluster formation and major mergers. Turbulent velocity of about 300 km/s can be maintained at scales 100-200 kpc. The magnetic field is intermittent, has a smaller scale of 20-30 kpc and average strength of 2 microgauss. Secondly, when major mergers end, turbulent speed and magnetic field undergo a power-law decay, decreasing in strength but increasing in scale by a factor of about two. Thirdly, smaller-mass subclusters and cluster galaxies produce turbulent wakes, with turbulent speeds and magnetic field strengths similar to those quoted above. The velocity scales are about 200 kpc and 10 kpc respectively, and the magnetic field scale is about 6 times smaller. Although these wakes may fill only a small fraction of the cluster volume, their area covering factor can be close to unity. So one can potentially reconcile observations that indicate the coexistence of turbulence with ordered filamentary gas structures, as in the Perseus cluster. Random Faraday rotation measure is estimated to be typically 100-200 rad/m^2, in agreement with observations. We predict detectable synchrotron polarization from cluster radio halos at wavelengths 3-6 cm, if observed at sufficiently high resolution (abridged).Comment: 20 pages, 9 figures, Replaced to match version accepted by MNRA

A Course on Economic Justice: The intersection of philosophy and economics

The process of teaching a topic that inhabits the upper reaches of both philosophy and economic theory, while swooping as near the earth as political policy, is both exhilarating and terrifying. To do it well is indeed rare. We present our approach, some of the characteristics and thoughts from our students, and some of the insights that we developed along the way.economics and philosophy; economic justice; interdisciplinary teaching

Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents

We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary conditions on either side of the wedge. We report on a comprehensive study of a linear chain by exact enumeration, with various attachments of the walk's ends to the surface, in wedges of angles $\pi/2$ and $\pi$, with general mixed boundary conditions.Comment: 4 pages, Latex2e, 3 figures, Eur. Phys. J. B macro

Magnetic Susceptibility of an integrable anisotropic spin ladder system

We investigate the thermodynamics of a spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solved by the Bethe Ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. A connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in the strong coupling regime is made and our results for the magnetic susceptibility fit the experimental data remarkably well.Comment: 12 pages, 12 figures included, submitted to Phys. Rev.

Motion and homogenization of vortices in anisotropic Type II superconductors

The motion of vortices in an anisotropic superconductor is considered. For a system of well-separated vortices, each vortex is found to obey a law of motion analogous to the local induction approximation, in which velocity of the vortex depends upon the local curvature and orientation. A system of closely packed vortices is then considered, and a mean field model is formulated in which the individual vortex lines are replaced by a vortex density

Solution of the dual reflection equation for An−1(1)A^{(1)}_{n-1} SOS model

We obtain a diagonal solution of the dual reflection equation for elliptic $A^{(1)}_{n-1}$ SOS model. The isomorphism between the solutions of the reflection equation and its dual is studied.Comment: Latex file 12 pages, added reference

On the stationarity of linearly forced turbulence in finite domains

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the `linear forcing', which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times, as well as the consistency of this state with a high degree of isotropy imposed by the symmetries of the domain itself. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy. Indeed, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view, emphasizing the naturalness of the Taylor microscale as a self-similarity scale in this system. In this context the stationary state emerges as a stable fixed point. Self-preservation seems to be the reason behind a noted similarity of the third order structure function between the linearly forced and freely decaying turbulence, where again the finiteness of the domain plays an significant role.Comment: 15 pages, 7 figures, changes in the discussion at the end of section VI, formula (60) correcte

Contaminant Interferences with SIMS Analyses of Microparticle Impactor Residues on LDEF Surfaces

Elemental analyses of impactor residues on high purity surface exposed to the low earth orbit (LEO) environment for 5.8 years on Long Duration Exposure Facility (LDEF) has revealed several probable sources for microparticles at this altitude, including natural micrometeorites and manmade debris ranging from paint pigments to bits of stainless steel. A myriad of contamination interferences were identified and their effects on impactor debris identification mitigated during the course of this study. These interferences included pre-, post-, and in-flight deposited particulate surface contaminants, as well as indigenous heterogeneous material contaminants. Non-flight contaminants traced to human origins, including spittle and skin oils, contributed significant levels of alkali-rich carbonaceous interferences. A ubiquitous layer of in-flight deposited silicaceous contamination varied in thickness with location on LDEF and proximity to active electrical fields. In-flight deposited (low velocity) contaminants included urine droplets and bits of metal film from eroded thermal blankets

Turbulent Pair Diffusion

Kinematic Simulations of turbulent pair diffusion in planar turbulence with a -5/3 energy spectrum reproduce the results of the laboratory measurements of Jullien Phys. Rev. Lett. 82, 2872 (1999), in particular the stretched exponential form of the PDF of pair separations and their correlation functions. The root mean square separation is found to be strongly dependent on initial conditions for very long stretches of times. This dependence is consistent with the topological picture of turbulent pair diffusion where pairs initially close enough travel together for long stretches of time and separate violently when they meet straining regions around hyperbolic points. A new argument based on the divergence of accelerations is given to support this picture

Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the non-relativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.Comment: 4 page