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

Tracing planet-induced structures in circumstellar disks using molecular lines

Circumstellar disks are considered to be the birthplace of planets. Specific structures like spiral arms, gaps, and cavities are characteristic indicators of planet-disk interaction. Investigating these structures can provide insights into the growth of protoplanets and the physical properties of the disk. We investigate the feasibility of using molecular lines to trace planet-induced structures in circumstellar disks. Based on 3D hydrodynamic simulations of planet-disk interactions, we perform self-consistent temperature calculations and produce N-LTE molecular line velocity-channel maps and spectra of these disks using our new N-LTE line radiative transfer code Mol3D. Subsequently, we simulate ALMA observations using the CASA simulator. We consider two nearly face-on inclinations, 5 disk masses, 7 disk radii, and 2 different typical pre-main-sequence host stars (T Tauri, Herbig Ae). We calculate up to 141 individual velocity-channel maps for five molecules/isotopoloques in a total of 32 rotational transitions to investigate the frequency dependence of the structures indicated above. We find that the majority of protoplanetary disks in our parameter space could be detected in the molecular lines considered. However, unlike the continuum case, gap detection is not straightforward in lines. For example, gaps are not seen in symmetric rings but are masked by the pattern caused by the global (Keplerian) velocity field. We identify specific regions in the velocity-channel maps that are characteristic of planet-induced structures. Simulations of high angular resolution molecular line observations demonstrate the potential of ALMA to provide complementary information about the planet-disk interaction as compared to continuum observations. In particular, the detection of planet-induced gaps is possible under certain conditions.(abridged)Comment: 19 pages, 19 figures, accepted for publication in A&

Minkowski Functionals of Abell/ACO Clusters

We determine the Minkowski functionals for a sample of Abell/ACO clusters, 401 with measured and 16 with estimated redshifts. The four Minkowski functionals (including the void probability function and the mean genus) deliver a global description of the spatial distribution of clusters on scales from $10$ to 60\hMpc with a clear geometric interpretation. Comparisons with mock catalogues of N--body simulations using different variants of the CDM model demonstrate the discriminative power of the description. The standard CDM model and the model with tilted perturbation spectrum cannot generate the Minkowski functionals of the cluster data, while a model with a cosmological constant and a model with breaking of the scale invariance of perturbations (BSI) yield compatible results.Comment: 10 pages, 13 Postscript figures, uses epsf.sty and mn.sty (included), submitted to MNRA

Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids

In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. In this letter, we describe how the criterion for purely elastic Taylor-Couette instability should be adapted to shear-banding flows. We derive three categories of shear-banding flows with curved streamlines, depending on their stability.Comment: 6 pages, 3 figure

Potential "ways of thinking" about the shear-banding phenomenon

Shear-banding is a curious but ubiquitous phenomenon occurring in soft matter. The phenomenological similarities between the shear-banding transition and phase transitions has pushed some researchers to adopt a 'thermodynamical' approach, in opposition to the more classical 'mechanical' approach to fluid flows. In this heuristic review, we describe why the apparent dichotomy between those approaches has slowly faded away over the years. To support our discussion, we give an overview of different interpretations of a single equation, the diffusive Johnson-Segalman (dJS) equation, in the context of shear-banding. We restrict ourselves to dJS, but we show that the equation can be written in various equivalent forms usually associated with opposite approaches. We first review briefly the origin of the dJS model and its initial rheological interpretation in the context of shear-banding. Then we describe the analogy between dJS and reaction-diffusion equations. In the case of anisotropic diffusion, we show how the dJS governing equations for steady shear flow are analogous to the equations of the dynamics of a particle in a quartic potential. Going beyond the existing literature, we then draw on the Lagrangian formalism to describe how the boundary conditions can have a key impact on the banding state. Finally, we reinterpret the dJS equation again and we show that a rigorous effective free energy can be constructed, in the spirit of early thermodynamic interpretations or in terms of more recent approaches exploiting the language of irreversible thermodynamics.Comment: 14 pages, 6 figures, tutorial revie

Higher Order Variational Integrators: a polynomial approach

We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the structural properties of these systems, like the symplectic form, the evolution of the momentum maps or the energy behaviour. Also they are easily applicable to optimal control problems based on mechanical systems as proposed in Ober-Bl\"obaum et al. [2011]. Following the same approach, we develop a family of variational integrators to which we refer as symplectic Galerkin schemes in contrast to symplectic partitioned Runge-Kutta. These two families of integrators are, in principle and by construction, different one from the other. Furthermore, the symplectic Galerkin family can as easily be applied in optimal control problems, for which Campos et al. [2012b] is a particular case.Comment: 12 pages, 1 table, 23rd Congress on Differential Equations and Applications, CEDYA 201

All Pain, Whose Gain? A Fifty-State Analysis of the Independent State Legislature Doctrine for Redistricting

The “Independent State Legislature” (ISL) doctrine has recently been offered as a reinterpretation of legislative control over federal elections and may upend decades of election law precedent. Based on Article I of the U.S. Constitution, the ISL doctrine holds that such authority of state legislatures potentially overrides state constitutions, as well as state courts, citizen initiatives, and even the governor. The original political goals of the ISL doctrine were the 2000 and 2016 Presidential elections. The doctrine has recently come before the Supreme Court in Moore v. Harper, a case concerning redistricting, and could open the door to increased gerrymandering of U.S. congressional districts. Here we analyze the practical consequences in all fifty states. We find that such a change in redistricting law would be highly asymmetric to the major political parties, giving considerable advantage to Democrats because it would undo an existing propensity for reform or judicial intervention in Democratic-leaning and swing states. This asymmetry raises questions of the desirability of introducing the ISL to questions of redistricting

The Dynamic Use of the Kawa Model: A Scoping Review

Background: The Kawa model, a framework to guide culturally relevant occupational therapy, has gained recognition and become more widely used in practice. Research on the model thus far, while still relatively sparse, provides guidance for the model’s use, including its strengths and facets that require further exploration to support its use and effectiveness in dynamic ways. Method: A scoping review was completed to gather, organize, appraise, and synthesize the current research evidence on use of the model. Results: Findings support the Kawa model’s culturally flexible application and its capacity to garner client-centered qualitative information, as well as to build therapeutic relationships in a variety of settings. Challenges to the model’s use include therapists’ inexperience limiting effectiveness and the need for additional quantitative assessment measures to supplement the qualitative findings gathered during use of the Kawa. Limitations to this review include author preconceptions, homogeneity among the authors, and inclusion of non-peer-reviewed theses. Conclusion: The Kawa model is an adaptable tool to examine and enhance well-being. It may be most effective when used by experienced therapists and in conjunction with other relevant tools. Further research is recommended to continue to evaluate its dynamic use