Shaken and stirred: the effects of turbulence and rotation on disc and outflow formation during the collapse of magnetized molecular cloud cores (article)

This is the final version of the article. Available from Oxford University Press (OUP) via the DOI in this record.The dataset associated with this article is located in ORE at: http://hdl.handle.net/10871/32288We present the results of 18 magnetohydrodynamical calculations of the collapse of a molecular cloud core to form a protostar. Some calculations include radiative transfer in the flux-limited diffusion approximation, while others employ a barotropic equation of state. We cover a wide parameter space, with mass-to-flux ratios ranging from μ = 5 to 20; initial turbulent amplitudes ranging from a laminar calculation (i.e. where the Mach number, M = 0) to transonic M = 1; and initial rotation rates from βrot = 0.005 to 0.02. We first show that using a radiative transfer scheme produces warmer pseudo-discs than the barotropic equation of state, making them more stable. We then ‘shake’ the core by increasing the initial turbulent velocity field, and find that at all three mass-to-flux ratios transonic cores are weakly bound and do not produce pseudo-discs; M = 0.3 cores produce very disrupted discs; and M = 0.1 cores produce discs broadly comparable to a laminar core. In our previous paper, we showed that a pseudo-disc coupled with sufficient magnetic field is necessary to form a bipolar outflow. Here, we show that only weakly turbulent cores exhibit collimated jets. We finally take the M = 1.0, μ = 5 core and ‘stir’ it by increasing the initial angular momentum, finding that once the degree of rotational energy exceeds the turbulent energy in the core the disc returns, with a corresponding (though slower), outflow. These conclusions place constraints on the initial mixtures of rotation and turbulence in molecular cloud cores which are conducive to the formation of bipolar outflows early in the star formation process.BTL acknowledges support from an Science and Technology Facilities Counsil (STFC) Studentship. MRB was supported by the European Research Council under the European Commission’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement No.339248)

Van der Corput lemmas for Mittag-Leffler functions. II. αα-directions

The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study oscillatory integrals appearing in the analysis of time-fractional partial differential equations. More specifically, we study integral of the form $I_{\alpha,\beta}(\lambda)=\int_\mathbb{R}E_{\alpha,\beta}\left(i^\alpha\lambda \phi(x)\right)\psi(x)dx,$ for the range $00$. This extends the variety of estimates obtained in the first part, where integrals with functions $E_{\alpha,\beta}\left(i \lambda \phi(x)\right)$ have been studied. Several generalisations of the van der Corput lemmas are proved. As an application of the above results, the generalised Riemann-Lebesgue lemma, the Cauchy problem for the time-fractional Klein-Gordon and time-fractional Schr\"{o}dinger equations are considered

Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs

Let $G$ be a graph where each vertex is associated with a label. A Vertex-Labeled Approximate Distance Oracle is a data structure that, given a vertex $v$ and a label $\lambda$, returns a $(1+\varepsilon)$-approximation of the distance from $v$ to the closest vertex with label $\lambda$ in $G$. Such an oracle is dynamic if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements

Spectroscopic Confirmation of a Protocluster at z=3.786

We present new observations of the field containing the z=3.786 protocluster, PC217.96+32.3. We confirm that it is one of the largest and most overdense high-redshift structures known. Such structures are rare even in the largest cosmological simulations. We used the Mayall/MOSAIC1.1 imaging camera to image a 1.2x0.6 deg area (~150x75 comoving Mpc) surrounding the protocluster's core and discovered 165 candidate Lyman Alpha emitting galaxies (LAEs) and 788 candidate Lyman Break galaxies (LBGs). There are at least 2 overdense regions traced by the LAEs, the largest of which shows an areal overdensity in its core (i.e., within a radius of 2.5 comoving Mpc) of 14+/-7 relative to the average LAE spatial density in the imaged field. Further, the average LAE spatial density in the imaged field is twice that derived by other field LAE surveys. Spectroscopy with Keck/DEIMOS yielded redshifts for 164 galaxies (79 LAEs and 85 LBGs); 65 lie at a redshift of 3.785+/-0.010. The velocity dispersion of galaxies near the core is 350+/-40 km/s, a value robust to selection effects. The overdensities are likely to collapse into systems with present-day masses of >10^{15} solar masses and >6x10^{14} solar masses. The low velocity dispersion may suggest a dynamically young protocluster. We find a weak trend between narrow-band (Lyman Alpha) luminosity and environmental density: the Lyman Alpha luminosity is enhanced on average by 1.35X within the protocluster core. There is no evidence that the Lyman Alpha equivalent width depends on environment. These suggest that star-formation and/or AGN activity is enhanced in the higher density regions of the structure. PC217.96+32.3 is a Coma cluster analog, witnessed in the process of formation.Comment: Accepted for publication in the Astrophysical Journal (March 27, 2016

Inverse source problems for positive operators. I: Hypoelliptic diffusion and subdiffusion equations

A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as well as on the fractional time diffusion (subdiffusion) equations are presented. Consequently, the obtained results are applied for the similar inverse problems for a large class of subelliptic diffusion and subdiffusion equations (with continuous spectrum). Such problems are modelled by using general homogeneous left-invariant hypoelliptic operators on general graded Lie groups. A list of examples is discussed, including Sturm-Liouville problems, differential models with involution, fractional Sturm-Liouville operators, harmonic and anharmonic oscillators, Landau Hamiltonians, fractional Laplacians, and harmonic and anharmonic operators on the Heisenberg group. The rod cooling problem for the diffusion with involution is modelled numerically, showing how to find a "cooling function", and how the involution normally slows down the cooling speed of the rod.Comment: 26 pages, 7 figures. arXiv admin note: text overlap with arXiv:1812.0133

Fossil biomass preserved as graphitic carbon in a late paleoproterozoic banded iron formation metamorphosed at more than 550°C

Metamorphism is thought to destroy microfossils, partly through devolatilization and graphitization of biogenic organic matter. However, the extent to which there is a loss of molecular, elemental and isotope signatures from biomass during high-temperature metamorphism is not clearly established. We report on graphitic structures inside and coating apatite grains from the c. 1850 Ma Michigamme silicate banded iron formation from Michigan, metamorphosed above 550°C. Traces of N, S, O, H, Ca and Fe are preserved in this graphitic carbon and X-ray spectra show traces of aliphatic groups. Graphitic carbon has an expanded lattice around 3.6 Å, forms microscopic concentrically-layered and radiating polygonal flakes and has homogeneous δ13C values around −22‰, identical to bulk analyses. Graphitic carbon inside apatite is associated with nanometre-size ammoniated phyllosilicate. Precursors of these metamorphic minerals and graphitic carbon originated from ferruginous clayrich sediments with biomass. We conclude that graphite coatings and inclusions in apatite grains indicate fluid remobilization during amphibolite-facies metamorphism of precursor biomass. This new evidence fills in observational gaps of metamorphosed biomass into graphite and supports the existence of biosignatures in the highly metamorphosed iron formation from the Eoarchean Akilia Association, which dates from the beginning of the sedimentary rock record

Characterisation of a phantom for multiwavelength quantitative photoacoustic imaging

Quantitative photoacoustic imaging (qPAI) has the potential to provide high- resolution in vivo images of chromophore concentration, which may be indicative of tissue function and pathology. Many strategies have been proposed recently for extracting quantitative information, but many have not been experimentally verified. Experimental phantom-based validation studies can be used to test the robustness and accuracy of such algorithms in order to ensure reliable in vivo application is possible. The phantoms used in such studies must have well-characterised optical and acoustic properties similar to tissue, and be versatile and stable. Polyvinyl chloride plastisol (PVCP) has been suggested as a phantom for quality control and system evaluation. By characterising its multiwavelength optical properties, broadband acoustic properties and thermoelastic behaviour, this paper examines its potential as a phantom for qPAI studies too. PVCP's acoustic properties were assessed for various formulations, as well as its intrinsic optical absorption, and scattering with added TiO2, over a range of wavelengths from 400-2000 nm. To change the absorption coefficient, pigment-based chromophores that are stable during the phantom fabrication process, were used. These yielded unique spectra analogous to tissue chromophores and linear with concentration. At the high peak powers typically used in photoacoustic imaging, nonlinear optical absorption was observed. The Grüneisen parameter was measured to be $\Gamma$   =  1.01  ±  0.05, larger than typically found in tissue, though useful for increased PA signal. Single and multiwavelength 3D PA imaging of various fabricated PVCP phantoms were demonstrated

Facebook: a blessing or a curse for grocery stores?

Abstract Purpose – Increasingly businesses are using Facebook to communicate and engage their customers. However, there is a dearth of research as to why and how customers interact with businesses on social media in the grocery sector. Therefore, this paper aims to explore the roles played by online brand communities (OBCs) and social customers in the creation as well as the destruction of value. Design/methodology/approach - Netnography was adopted as an approach to gain insight into the various ways customers engage with grocery stores on their official Facebook pages. Messages posted on Tesco’s and Wal-Mart’s Facebook pages are thematically analysed and critical discussion is linked back to the extant contemporary debate on social media. Findings – This study shows that customers respond to company posts for the following reasons: to communicate with the stores, to converse with other customers, to express their emotions, to share their experiences as employees of the stores with customers, and to share their positive or negative actions with members of the online communities. The study further highlights the role of social media in the co-creation and co-destruction of customer, consumer and supermarket value and builds contemporary theory and informs practice. Practical implications – Retailers should use social media to enrich the customer experience by encouraging customer engagement, co-creation of value and responding efficiently to customer needs in real time. Originality/value - This paper contributes to knowledge by uncovering the various ways customers react with the business. The social customer is both a curse and a blessing to Tesco and Walmart as they can create or destroy value for the business

Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives

In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for the Caputo, Riemann-Liouville and Hadamard derivatives are obtained. In addition, we show some applications of these inequalities