Jupyter in Computational Science

The articles in this special section discusses the applications supported by the Jupyter Notebook. Before notebooks, a scientist working with Python code, for instance, might have used a mixture of script files and code typed into an interactive shell. The shell is good for rapid experimentation, but the code and results are typically transient, and a linear record of everything that was tried would be long and not very clear. The notebook interface combines the convenience of the shell with some of the benefits of saving and editing code in a file, while also incorporating results, including rich output, such as plots, in a document that can be shared with others. The Jupyter Notebook is used through a web browser. Although it is often run locally, on a desktop or a laptop, this design means that it can also be used remotely, so the computation occurs, and the notebook files are saved, on an institutional server, a high-performance computing facility or in the clo

Spin-Orbit and Tensor Forces in Heavy-quark Light-quark Mesons: Implications of the New Ds state at 2.32 GeV

We consider the spectroscopy of heavy-quark light-quark mesons with a simple model based on the non-relativistic reduction of vector and scalar exchange between fermions. Four forces are induced: the spin-orbit forces on the light and heavy quark spins, the tensor force, and a spin-spin force. If the vector force is Coulombic, the spin-spin force is a contact interaction, and the tensor force and spin-orbit force on the heavy quark to order $1/m_1m_2$ are directly proportional. As a result, just two independent parameters characterize these perturbations. The measurement of the masses of three p-wave states suffices to predict the mass of the fourth. This technique is applied to the $D_s$ system, where the newly discovered state at 2.32 GeV provides the third measured level, and to the $D$ system. The mixing of the two $J^P=1^+$ p-wave states is reflected in their widths and provides additional constraints. The resulting picture is at odds with previous expectations and raises new puzzles.Comment: 6 pages, 1 figur

Enforcing dust mass conservation in 3D simulations of tightly coupled grains with the Phantom SPH code

We describe a new implementation of the one-fluid method in the SPH code PHANTOM to simulate the dynamics of dust grains in gas protoplanetary discs. We revise and extend previously developed algorithms by computing the evolution of a new fluid quantity that produces a more accurate and numerically controlled evolution of the dust dynamics. Moreover, by limiting the stopping time of uncoupled grains that violate the assumptions of the terminal velocity approximation, we avoid fatal numerical errors in mass conservation. We test and validate our new algorithm by running 3D SPH simulations of a large range of disc models with tightly and marginally coupled grains

Enforcing dust mass conservation in 3D simulations of tightly coupled grains with the Phantom SPH code

We describe a new implementation of the one-fluid method in the SPH code Phantom to simulate the dynamics of dust grains in gas protoplanetary discs. We revise and extend previously developed algorithms by computing the evolution of a new fluid quantity that produces a more accurate and numerically controlled evolution of the dust dynamics. Moreover, by limiting the stopping time of uncoupled grains that violate the assumptions of the terminal velocity approximation, we avoid fatal numerical errors in mass conservation. We test and validate our new algorithm by running 3D SPH simulations of a large range of disc models with tightly and marginally coupled grains

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Dual-Wavelength ALMA Observations of Dust Rings in Protoplanetary Disks

We present new Atacama Large Millimeter/submillimeter Array (ALMA) observations for three protoplanetary disks in Taurus at 2.9\,mm and comparisons with previous 1.3\,mm data both at an angular resolution of $\sim0.''1$ (15\,au for the distance of Taurus). In the single-ring disk DS Tau, double-ring disk GO Tau, and multiple-ring disk DL Tau, the same rings are detected at both wavelengths, with radial locations spanning from 50 to 120\,au. To quantify the dust emission morphology, the observed visibilities are modeled with a parametric prescription for the radial intensity profile. The disk outer radii, taken as 95\% of the total flux encircled in the model intensity profiles, are consistent at both wavelengths for the three disks. Dust evolution models show that dust trapping in local pressure maxima in the outer disk could explain the observed patterns. Dust rings are mostly unresolved. The marginally resolved ring in DS Tau shows a tentatively narrower ring at the longer wavelength, an observational feature expected from efficient dust trapping. The spectral index ($\alpha_{\rm mm}$) increases outward and exhibits local minima that correspond to the peaks of dust rings, indicative of the changes in grain properties across the disks. The low optical depths ($\tau\sim$0.1--0.2 at 2.9\,mm and 0.2--0.4 at 1.3\,mm) in the dust rings suggest that grains in the rings may have grown to millimeter sizes. The ubiquitous dust rings in protoplanetary disks modify the overall dynamics and evolution of dust grains, likely paving the way towards the new generation of planet formation.Comment: accepted for publication in Ap

A Triple Protostar System Formed via Fragmentation of a Gravitationally Unstable Disk

Binary and multiple star systems are a frequent outcome of the star formation process, and as a result, almost half of all sun-like stars have at least one companion star. Theoretical studies indicate that there are two main pathways that can operate concurrently to form binary/multiple star systems: large scale fragmentation of turbulent gas cores and filaments or smaller scale fragmentation of a massive protostellar disk due to gravitational instability. Observational evidence for turbulent fragmentation on scales of $>$1000~AU has recently emerged. Previous evidence for disk fragmentation was limited to inferences based on the separations of more-evolved pre-main sequence and protostellar multiple systems. The triple protostar system L1448 IRS3B is an ideal candidate to search for evidence of disk fragmentation. L1448 IRS3B is in an early phase of the star formation process, likely less than 150,000 years in age, and all protostars in the system are separated by $<$200~AU. Here we report observations of dust and molecular gas emission that reveal a disk with spiral structure surrounding the three protostars. Two protostars near the center of the disk are separated by 61 AU, and a tertiary protostar is coincident with a spiral arm in the outer disk at a 183 AU separation. The inferred mass of the central pair of protostellar objects is $\sim$1 M$_{sun}$, while the disk surrounding the three protostars has a total mass of $\sim$0.30 M_{\sun}. The tertiary protostar itself has a minimum mass of $\sim$0.085 M$_{sun}$. We demonstrate that the disk around L1448 IRS3B appears susceptible to disk fragmentation at radii between 150~AU and 320~AU, overlapping with the location of the tertiary protostar. This is consistent with models for a protostellar disk that has recently undergone gravitational instability, spawning one or two companion stars.Comment: Published in Nature on Oct. 27th. 24 pages, 8 figure