Magnetic fields in molecular clouds: Limitations of the analysis of Zeeman observations

Context. Observations of Zeeman split spectral lines represent an important approach to derive the structure and strength of magnetic fields in molecular clouds. In contrast to the uncertainty of the spectral line observation itself, the uncertainty of the analysis method to derive the magnetic field strength from these observations is not been well characterized so far. Aims. We investigate the impact of several physical quantities on the uncertainty of the analysis method, which is used to derive the line-of-sight (LOS) magnetic field strength from Zeeman split spectral lines. Methods. We simulate the Zeeman splitting of the 1665 MHz OH line with the 3D radiative transfer (RT) extension ZRAD. This extension is based on the line RT code Mol3D (Ober et al. 2015) and has been developed for the POLArized RadIation Simulator POLARIS (Reissl et al. 2016). Results. Observations of the OH Zeeman effect in typical molecular clouds are not significantly affected by the uncertainty of the analysis method. We derived an approximation to quantify the range of parameters in which the analysis method works sufficiently accurate and provide factors to convert our results to other spectral lines and species as well. We applied these conversion factors to CN and found that observations of the CN Zeeman effect in typical molecular clouds are neither significantly affected by the uncertainty of the analysis method. In addition, we found that the density has almost no impact on the uncertainty of the analysis method, unless it reaches values higher than those typically found in molecular clouds. Furthermore, the uncertainty of the analysis method increases, if both the gas velocity and the magnetic field show significant variations along the line-of-sight. However, this increase should be small in Zeeman observations of most molecular clouds considering typical velocities of ~1 km/s.Comment: 9 pages, 6 figure

Guaranteed emergence of genuine entanglement in 3-qubit evolving systems

Multipartite entanglement has been shown to be of particular relevance for a better understanding and exploitation of the dynamics and flow of entanglement in multiparty systems. This calls for analysis aimed at identifying the appropriate processes that guarantee the emergence of multipartite entanglement in a wide range of scenarios. Here we carry on such analysis considering a system of two initially entangled qubits, one of which is let to interact with a third qubit according to an arbitrary unitary evolution. We establish necessary and sufficient conditions on the corresponding Kraus operators, to discern whether the evolved state pertains to either one of the classes of 3-qubit pure states that exhibit some kind of entanglement, namely biseparable, W-, and GHZ- genuine entangled classes. Our results provide a classification of the Kraus operators according to their capacity of producing 3-qubit entanglement, and pave the way for extending the analysis to larger systems and determining the particular interactions that must be implemented in order to create, enhance and distribute entanglement in a specific manner.Comment: Two new subsections included. Accepted for publication in The European Physical Journal

The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models

The validity of the cosmic no-hair theorem is investigated in the context of Newtonian cosmology with a perfect fluid matter model and a positive cosmological constant. It is shown that if the initial data for an expanding cosmological model of this type is subjected to a small perturbation then the corresponding solution exists globally in the future and the perturbation decays in a way which can be described precisely. It is emphasized that no linearization of the equations or special symmetry assumptions are needed. The result can also be interpreted as a proof of the nonlinear stability of the homogeneous models. In order to prove the theorem we write the general solution as the sum of a homogeneous background and a perturbation. As a by-product of the analysis it is found that there is an invariant sense in which an inhomogeneous model can be regarded as a perturbation of a unique homogeneous model. A method is given for associating uniquely to each Newtonian cosmological model with compact spatial sections a spatially homogeneous model which incorporates its large-scale dynamics. This procedure appears very natural in the Newton-Cartan theory which we take as the starting point for Newtonian cosmology.Comment: 16 pages, MPA-AR-94-

EUV ionization of pure He nanodroplets: Mass-correlated photoelectron imaging, Penning ionization and electron energy-loss spectra

The ionization dynamics of pure He nanodroplets irradiated by EUV radiation is studied using Velocity-Map Imaging PhotoElectron-PhotoIon COincidence (VMI-PEPICO) spectroscopy. We present photoelectron energy spectra and angular distributions measured in coincidence with the most abundant ions He+, He2+, and He3+. Surprisingly, below the autoionization threshold of He droplets we find indications for multiple excitation and subsequent ionization of the droplets by a Penning-like process. At high photon energies we evidence inelastic collisions of photoelectrons with the surrounding He atoms in the droplets

Penning ionization of doped helium nanodroplets following EUV excitation

Helium nanodroplets are widely used as a cold, weakly interacting matrix for spectroscopy of embedded species. In this work we excite or ionize doped He droplets using synchrotron radiation and study the effect onto the dopant atoms depending on their location inside the droplets (rare gases) or outside at the droplet surface (alkali metals). Using photoelectron-photoion coincidence imaging spectroscopy at variable photon energies (20-25 eV), we compare the rates of charge-transfer to Penning ionization of the dopants in the two cases. The surprising finding is that alkali metals, in contrast to the rare gases, are efficiently Penning ionized upon excitation of the (n=2)-bands of the host droplets. This indicates rapid migration of the excitation to the droplet surface, followed by relaxation, and eventually energy transfer to the alkali dopants

Bounded Model Checking for Probabilistic Programs

In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric Markov decision process, no direct adaption of existing techniques is possible. Therefore, we propose an on-the-fly approach where the operational model is successively created and verified via a step-wise execution of the program. This approach enables to take key features of many probabilistic programs into account: nondeterminism and conditioning. We discuss the restrictions and demonstrate the scalability on several benchmarks

Stochastic models in population biology and their deterministic analogs

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and non-spatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean field equations (and their first order corrections in the non-spatial case), and simulation results. These mean field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by inter-patch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting.Comment: 47 pages, 9 figure

Risk factors for the evolutionary emergence of pathogens

Recent outbreaks of novel infectious diseases (e.g. SARS, influenza H1N1) have highlighted the threat of cross-species pathogen transmission. When first introduced to a population, a pathogen is often poorly adapted to its new host and must evolve in order to escape extinction. Theoretical arguments and empirical studies have suggested various factors to explain why some pathogens emerge and others do not, including host contact structure, pathogen adaptive pathways and mutation rates. Using a multi-type branching process, we model the spread of an introduced pathogen evolving through several strains. Extending previous models, we use a network-based approach to separate host contact patterns from pathogen transmissibility. We also allow for arbitrary adaptive pathways. These generalizations lead to novel predictions regarding the impact of hypothesized risk factors. Pathogen fitness depends on the host population in which it circulates, and the ‘riskiest’ contact distribution and adaptive pathway depend on initial transmissibility. Emergence probability is sensitive to mutation probabilities and number of adaptive steps required, with the possibility of large adaptive steps (e.g. simultaneous point mutations or recombination) having a dramatic effect. In most situations, increasing overall mutation probability increases the risk of emergence; however, notable exceptions arise when deleterious mutations are available

Optical scalars in spherical spacetimes

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant energy condition and that the slice be asymptotically flat and regular at the origin. This bound can be used to derive new conditions for the formation of apparent horizons. The bounds hold even when the matter has a distribution on a shell or blows up at the origin so as to give a conical singularity