Magnetic fields in circumstellar disks: The potential of Zeeman observations

Context. Recent high angular resolution polarimetric continuum observations of circumstellar disks provide new insights into their magnetic field. However, direct constraints are limited to the plane of sky component of the magnetic field. Observations of Zeeman split spectral lines are a potential approach to enhance these insights by providing complementary information. Aims. We investigate which constraints for magnetic fields in circumstellar disks can be obtained from Zeeman observations of the $113~\mathrm{GHz}$ CN lines. Furthermore, we analyze the requirements to perform these observations and their dependence on selected quantities. Methods. We simulate the Zeeman splitting with the radiative transfer (RT) code POLARIS (Reissl et al. 2016) extended by our Zeeman splitting RT extension ZRAD (Brauer et al. 2017), which is based on the line RT code Mol3D (Ober et al. 2015). Results. We find that Zeeman observations of the $113~\mathrm{GHz}$ CN lines provide significant insights into the magnetic field of circumstellar disks. However, with the capabilities of recent and upcoming instrument/observatories, even spatially unresolved observations would be challenging. Nevertheless, these observations are feasible for the most massive disks with a strong magnetic field and high abundance of CN/H. The most restrictive quantity is the magnetic field strength, which should be at least in the order of $\sim1~\mathrm{mG}$. In addition, the inclination of the disk should be around $60\deg$ to preserve the ability to derive the line-of-sight (LOS) magnetic field strength and to obtain a sufficiently high circularly polarized flux.Comment: 15 pages, 14 figure

Fully-coupled analysis of jet mixing problems. Part 1. Shock-capturing model, SCIPVIS

A computational model, SCIPVIS, is described which predicts the multiple cell shock structure in imperfectly expanded, turbulent, axisymmetric jets. The model spatially integrates the parabolized Navier-Stokes jet mixing equations using a shock-capturing approach in supersonic flow regions and a pressure-split approximation in subsonic flow regions. The regions are coupled using a viscous-characteristic procedure. Turbulence processes are represented via the solution of compressibility-corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive analysis of the wake-like mixing process occurring behind Mach discs is handled in a rigorous manner. Calculations are presented exhibiting the fundamental interactive processes occurring in supersonic jets and the model is assessed via comparisons with detailed laboratory data for a variety of under- and overexpanded jets

The Complexity of Relating Quantum Channels to Master Equations

Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find it's form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P=NP: any efficiently computable criterion for Markovianity would imply P=NP; whereas a proof that P=NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.Comment: V1: 43 pages, single column, 8 figures. V2: titled changed; added proof-overview and accompanying figure; 50 pages, single column, 9 figure

The semigroup structure of Gaussian channels

We investigate the semigroup structure of bosonic Gaussian quantum channels. Particular focus lies on the sets of channels which are divisible, idempotent or Markovian (in the sense of either belonging to one-parameter semigroups or being infinitesimal divisible). We show that the non-compactness of the set of Gaussian channels allows for remarkable differences when comparing the semigroup structure with that of finite dimensional quantum channels. For instance, every irreversible Gaussian channel is shown to be divisible in spite of the existence of Gaussian channels which are not infinitesimal divisible. A simpler and known consequence of non-compactness is the lack of generators for certain reversible channels. Along the way we provide new representations for classes of Gaussian channels: as matrix semigroup, complex valued positive matrices or in terms of a simple form describing almost all one-parameter semigroups.Comment: 20 page

Self streamlining wind tunnel: Low speed testing and transonic test section design

Comprehensive aerodynamic data on an airfoil section were obtained through a wide range of angles of attack, both stalled and unstalled. Data were gathered using a self streamlining wind tunnel and were compared to results obtained on the same section in a conventional wind tunnel. The reduction of wall interference through streamline was demonstrated