dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2017) , which solves the "two-language problem" and provides the missing tool for making prototype and production code become one and breaking up the technically imposed hard division of the software stack into domain science tasks (higher levels of the stack) and computer science tasks (lower levels of the stack). The Julia applications featured in this study rely on recent Julia package developments undertaken by the authors to empower domain scientists to write architecture-agnostic high-level code for parallel high-performance stencil computations on massively parallel hardware such as latest GPUaccelerated supercomputers. In this work, we present the results of analytical analysis of the PT equations for (non-)linear diffusion and incompressible visco-elastic Stokes flow problems. We motivate our selection of particular physical processes as a broad range of natural processes categorise mathematically either as diffusive, wave-like or mechanical processes, and thus constitute the main building blocks of multi-physics applications.
We derive iteration parameters' approximations from continuous, non-discretised formulations with emphasis on an analogy between these parameters and non-dimensional numbers arising from mathematical modelling of physical processes. Such a physics-inspired numerical optimisation approach has the advantage of providing a framework building on solid classical knowledge and for which various analytical approaches exist to derive or optimise parameters of interest. We assess the algorithmic and implementation performance and scalability of the 2D and 3D numerical Julia (multi-)GPU (non-)linear diffusion and visco-elastic Stokes flow implementations. We report scalability beyond terascale number of DoFs on up to 2197 Nvidia Tesla P100 GPUs on the Piz Daint supercomputer at the Swiss National Supercomputing Centre (CSCS).
We demonstrate the versatility and the robustness of our approach in handling nonlinear problems by applying the accelerated PT method to resolve spontaneous strain localisation in elasto-viscoplastic (E-VP) media in 2D and 3D, and comparing time to solution with direct-sparse solvers in 2D. We further demonstrate the convergence of the method to be mostly insensitive to arbitrary distributions of viscous inclusions with viscosity contrasts of up to 9 orders of magnitude in the incompressible viscous Stokes flow limit. The latest versions of the open-source Julia codes used in this study are available from GitHub within the PTsolvers organisation at https://github. com/PTsolvers/ PseudoTransientDiffusion. jl (last access: 16 May 2022) and https://github. com/PTsolvers/PseudoTransientStokes.
jl (last access: 16 May 2022). Past and future versions of the software are available from a permanent DOI repository (Zenodo) at: https://doi. org/10. 5281/zenodo. 6553699 (Räss and Utkin, 2022a)  and https://doi. org/10. 5281/zenodo. 6553714 (Räss and Utkin, 2022b). The README files provide the instructions to start reproducing majority of the presented results.
The two lines of physics, namely the PT updates, are here evaluated in an explicit fashion. Alternatively, one could solve qHx and H assuming that their values in the residual -the terms contained in the right-most parenthesis -are new instead of current, resulting in an implicit update. Advantages rely on enhanced stability (CFL on line 10 could be set to 1) and remove the need for defining a small number (ε in the iteration parameters definition) to prevent division by 0. The implicit approach is implemented as an alternative in the full code available online in the Pseu-doTransientDiffusion. jl GitHub repository.
The Julia multi-xPU implementation We use the Julia language  (Bezanson et al. , 2017)  to implement the suite of numerical experiments. Julia's high-level abstractions, multiple dispatch and meta-programming capabilities make it amenable to portability between back-ends (e. g. multi-core CPUs and Nvidia or AMD GPUs). Also, Julia solves the two-language problem, making it possible to fuse prototype and production applications into a single one that is both high-level and performance oriented -ultimately increasing productivity. We use the ParallelStencil. jl (Omlin and Räss, 2021b)  and ImplicitGlobalGrid. jl (Omlin and Räss, 2021a ) Julia packages that we developed as building blocks to implement the diffusion and Stokes numerical experiments. ParallelStencil. jl permits to write architecture-agnostic high-level code for parallel high-performance stencil computations on GPUs and CPUs -here referred to as xPUs.
Performance similar to native CUDA C/C++ (Nvidia GPUs) or HIP (AMD GPUs) can be achieved. ParallelStencil. jl seamlessly combines with ImplicitGlobalGrid. jl, which allows for distributed parallelisation of stencil-based xPU applications on a regular staggered grid. In addition, ParallelStencil. jl enables hiding communication behind computation, where the communication package used can, a priori, be any package that allows the user to control when communication is triggered. The overlap approach of communication and computation splits local domain calculations into two regions, i. e. boundary regions and inner region, the latter containing majority of the local domain's grid cells. After successful completion of the boundary region computations, halo update (using e. g. pointto-point MPI) overlaps with inner-point computations.
Results We here report the performance of the accelerated PT Julia implementation of the diffusion and the Stokes flow solvers targeting Nvidia GPUs using ParallelStencil. jl's CUDA back-end. For both physical processes, we analyse the iteration count as a function of the number of grid cells (i. e. the algorithmic performance), the effective memory throughput T eff [GB s -1 ] (performing a single-GPU device problem size scaling), and the parallel efficiency E (multi-GPU weak scaling). We report the algorithmic performance as the iteration count per number of physical time steps normalised by the number of grid cells in the x direction. We do not normalise by the total number of grid cells in order to report the 1D scaling, even for 2D or 3D implementation. We motivate our choice as it permits a more accurate comparison to analytically derived results and leaves it to the reader to appreciate the actual quadratic and cubic dependence of the normalised iteration count if using the total number of grid cells in 2D and 3D configurations, respectively.
Effective memory throughput T eff [GB s -1 ] for the (a) 2D and (b) 3D nonlinear diffusion Julia GPU implementations using ParallelStencil. jl executed on various Nvidia GPUs (Tesla A100 SXM4, Tesla V100 SXM2 and P100 PCIe). The dashed lines report the measured peak memory throughput T peak (1355 GB s -1 Tesla A100, 840 GB s -1 Tesla V100, 561 GB s -1 Tesla P100) one can achieve on a specific GPU architecture, which is a theoretical upper bound of T eff. Figure  10. Effective memory throughput T eff [GB s -1 ] for the (a) 2D and (b) 3D the visco-elastic Stokes flow Julia GPU implementations using ParallelStencil. jl executed on various Nvidia GPUs (Tesla A100 SXM4, Tesla V100 SXM2 and P100 PCIe). The dashed lines report the measured peak memory throughput T peak (1355 GB s -1 Tesla A100, 840 GB s -1 Tesla V100, 561 GB s -1 Tesla P100) one can achieve on a specific GPU architecture, which is a theoretical upper bound of T eff.
Performance benefits for desktop-scale computing Besides the potential to tackle nonlinear multi-physics problems at supercomputer-scale, the ability to solve smallerscale nonlinear problems remains an important aspect. Here we investigate wall times for the simulation of the previously-described E-VP shear-band formation in 2D (Fig. 15 ). We compare a MATLAB-based direct-iterative (DI) and a Julia GPU-based PT solver, respectively. The M2Di MATLAB solver routines  (Räss et al. , 2017)  rely on a Newton linearisation of the nonlinear mechanical problem  (Duretz et al. , 2019a)  and use a performant DI solver to compute Newton steps. The solver combines outer Powell-Hestenes and inner Krylov iterations (Global Conjugate Residual) that are preconditioned with the Cholesky factorisation of the symmetrised Jacobian  (Räss et al.
, 2017). In the 2D PT solver, written in Julia using the ParallelStencil. jl packages, the evaluation of nonlinearities is embedded in the pseudo-time integration loop. The timings reported for the DI and PT schemes were produced on a 2. 9 GHz Intel Core i5 processor and on a single Nvidia Tesla A100 GPU, respectively (Fig. 15a ). Each simulation resolves 100 physical (implicit) time steps and we report the total accumulated plastic strain (Fig. 15b ) and the associated pressure fields (Fig. 15c ). Models were run on resolutions involving 62 2 to 510 2 and up to 1022 2 grid cells for the DI and PT scheme, respectively. As expected for 2D computations, reported wall times are lower using the DI scheme at very low resolutions of n x = 62. However, it is interesting to observe that the GPU-accelerated PT scheme can deliver comparable wall times at already relatively low resolutions (n x ≈ 126).
(2019a)  to tackle 3D configurations. We generate the 3D initial condition, a Gaussian random field with an exponential co-variance function, following the approach described in  Räss et al. (2019b) , available through the ParallelRandomFields. jl Julia package  (Räss and Omlin, 2021). We perform 100 implicit loading steps using the accelerated PT method and execute the parallel Julia code relying on ParallelStencil. jl and ImplicitGlob-alGrid. jl on 8 Tesla V100 on the Volta node. The scalability of the 3D E-VP implementation is comparable to the 2D ver-sion (Fig. 15a ) with similar discrepancies as reported for the visco-elastic Stokes case (Fig. 7 ). Both the 2D and 3D E-VP algorithms require only minor modifications of the visco-elastic Stokes solver discussed throughout this paper to account for brittle failure, deactivation of the serial viscous damper and viscoplastic regularisation without significantly affecting the convergence rate provided by the second-order method.
Further, hiding communication behind computations permits the achievement of parallel efficiency of more than 96 % on various distributedmemory systems and up to 2197 GPUs. The physics we selected for the numerical experiments represent key building blocks to further tackle various multi-physics coupling, usually the combination of mechanical and diffusive processes. Our systematic results on the multi-inclusion setup with huge viscosity contrasts provide some preliminary results assessing the robustness of the accelerated PT method, which we further employ to resolve shear-band formation in 3D as a result of plastic yielding in E-VP materials. Our study paves the way for resolving coupled and nonlinear multi-physics applications in natural sciences and engineering on extremely high resolutions on the next generation of exascale-capable supercomputers, revamping elegant iterative techniques and implementing them with the portable Julia language.
Räss et al. :Accelerated pseudo-transient method Swiss Geocomputing Centre, University of Lausanne, for computing resources on the Octopus supercomputer and are grateful to Philippe Logean for continuous technical support. Financial support. This research has been supported by the Swiss University Conference and the Swiss Council of Federal Institutes of Technology through the Platform for Advanced Scientific Computing (PASC) program. This research has been supported by the Swiss National Supercomputing Centre (CSCS) (project ID c23). This research has been supported by the Russian Science Foundation (grant no. 19-47-02015). Publisher's note: the article processing charges for this publication were not paid by a Russian or Belarusian institution. Review statement. This paper was edited by James Kelly and reviewed by Lawrence Hongliang Wang, Boris Kaus, and one anonymous referee.
Code availability. The various software developed and used in the scope of this study is licensed under MIT License. The latest versions of the code is available from GitHub at: https://github. com/ PTsolvers/PseudoTransientDiffusion. jl (last access: 16 May 2022) and https://github. com/PTsolvers/PseudoTransientStokes. jl (last access: 16 May 2022). Past and future versions of the software are available from a permanent DOI repository (Zenodo) at: https://doi. org/10. 5281/zenodo. 6553699 (Räss and Utkin, 2022a) and https://doi. org/10. 5281/zenodo. 6553714 (Räss and Utkin, 2022b). Both the PseudoTransientDiffusion. jl and the Pseu-doTransientStokes. jl repositories contain most Julia multi-xPU code examples implementing the accelerated PT method and can be readily used to reproduce the figures of the paper.
Primordial black holes (PBHs) are convenient candidates to explain the elusive dark matter (DM). However, years of constraints from various astronomical observations have constrained their abundance over a wide range of masses, leaving only a narrow window open at 10 17 g M 10 22 g for all DM in the form of PBHs. We reexamine this disputed window with a critical eye, interrogating the general hypotheses underlying the direct photon constraints. We review 4 levels of assumptions: (i) instrument characteristics, (ii) prediction of the (extra)galactic photon flux, (iii) statistical method of signal-to-data comparison and (iv) computation of the Hawking radiation rate. Thanks to Isatis, a new tool designed for the public Hawking radiation code BlackHawk, we first revisit the existing and prospective constraints on the PBH abundance and investigate the impact of assumptions (i)-(iv).
Most of the more recent studies now take into account the effect of having a nonzero PBH spin, which enhances the photon emission and thus results in more stringent constraints for Kerr (rotating) PBHs  [9, 13, 18, 19, 25, 28, 32, 37, 38, 41] , or an extended PBH mass distribution, that should be more realistic regarding the channels of PBH formation  [13, 15, 16, 18, 24, 25, 29, 32, 41]. Exotic studies have also derived constraints on non-standard (other than Kerr) PBHs  [42] [43] [44]  or PBH-DM mixed scenarios  [45] [46] [47] [48]. To do so, recent constraints make use of the public code BlackHawk  [49, 50]  1 to compute the precise Hawking radiation spectra, and we are using the latest version 2. 1 of this code in our analysis. Photon constraints are handy thanks to several simplifications: photons are massless particles, thus any PBH mass is compatible with the emission of photons with the corresponding mean energy; 1 BlackHawk is available at https://blackhawk.
The emission rate of a massless particle i with spin s i by a Schwarzschild BH is given by  [7] Q i (E, t) ≡ d 2 N i dtdE = 1 2π i e E/T -(-1) s i , ( 1 ) where i is the "greybody factor" (GF) that encodes the probability that the emitted particle reaches spatial infinity away from the BH horizon. The GFs deviate from the pure blackbody spectrum, with a power-law suppression at lower energies that depends on the particle's spin. Those GFs were numerically computed in the public code BlackHawk that we use in this study. 2 The BH horizon temperature is related to the BH mass through T = 1 8π M , ( 2 ) so that when the mass decreases because of evaporation, the temperature increases. The emission rate of Eq. (  1 ) is further cutoff at the particle rest mass E > μ i , which is trivial for massless photons.
3 This package considers that pions are emitted as fundamental particles instead of single quarks and gluons, and subsequently decayed into photons and leptons. Hazma, which relies on analytical decay and final state radiation formulas, undoubtedly suffers from inherent approximations. We should also implement Bremsstrahlung effects for emitted charged particles  [58]  that may dominate at very low energy, around the keV scale. Using Hazma, Ref. [10]  showed that as the emission of all the massive particles (the lightest being the electron) is exponentially suppressed for PBHs with mass M 10 17 g only primary photons, neutrinos and maybe gravitons are radiated. Secondary photons however dominate the spectrum for PBHs with lower masses, with a mean energy Ẽ well below the PBH temperature. The implementation of Hazma inside BlackHawk v2.
A numerical tool: the Isatis program For the sake of this study, we have designed Isatis, a numerical public tool that relies on the BlackHawk PBH spectra to compute the constraints with a controlled set of assumptions. The code is presented in details in the Appendix A. The idea is to use BlackHawk to obtain the direct PBH photon spectrum, and then to derive the constraint on the PBH abundance for a list of optical instruments, existing or prospective. All constraint assumption types (i)-(iv) listed in the Introduction, with different statistical methods from the nomenclature given in Fig. 1  available, can be modified. Hence, the quantitative individual impact of the assumptions on the PBH "direct" photon constraints can be investigated. This allows to compare consistently the constraints from the literature.
Conclusion In this paper, we have computed the photon emission spectrum by Hawking radiation of monochromatic Schwarzschild primordial black holes. We restricted ourselves to the direct photons resulting from the primary emission of photons and the secondary emission resulting from electroweak interactions or decay of other primary particles. We obtained the flux on Earth of photons coming from the galactic center plus the isotropic redshifted emission from past ages. We identified all the assumptions underlying the computation of this flux and ended up with a clear nomenclature of the constraining methods M j i , classifying existing and prospective constraints. Then, we used Isatis, a new public tool available inside the Hawking radiation code BlackHawk and described in the Appendix, to examine quantitatively how the constraints presented in the literature depend on those assumptions, regrouped in 4 categories: (i) instrument characteristics, (ii) (extra)galactic flux description, (iii) statistical method used and (iv) Hawking radiation uncertainties.
Technical aspects Isatis is a public C tool that relies on the BlackHawk  [49, 50]  code to compute PBH constraints. Be careful to download the last version of BlackHawk (v2. 1 as we write this article) before using it. Isatis is available as one of the "add-ons" (/scripts folder) of BlackHawk and as such can be downloaded together with the main code on the same website: https://blackhawk. hepforge. org The Isatis main folder contains:.
The BH_launcher program The folder /BH_launcher contains another BlackHawk add-on: an automatic comprehensive launcher adapted to Isatis. With this program, you can launch several Black-Hawk runs in parallel in order to obtain a set of spectra for e. g. different PBH initial masses. The script is interactive so its use should be transparent, but a README. txt file is provided anyway. First, please ensure that BH_launcher. c contains the correct path to your BlackHawk version and that the BlackHawk programs BlackHawk_inst and BlackHawk_tot are themselves compiled. We advise to compile it with #define HARDTABLES to save time at execution. To obtain the executable BH_launcher. x type the command make in the terminal from the /BH_launcher folder. BH_launcher. x dos not require any argument so just run it with the command.
/BH_launcher. x. The script launches BlackHawk the desired amount of times with the given parameters and generate several outputs: • the BlackHawk output is stored as usual inside the BlackHawk/results/ folder, To summarize, a basic use of the Isatis program consists in (supposing everything has been compiled correctly): 1. launching BH_launcher. x to generate a set of Black Hawk spectra with some varying PBH parameters, 2. launching Isatis. x to compute the corresponding PBH photon constraints, 3. using plotting. py to visualize the constraints.
Instrument implementation For existing instruments, we use the most recent data they have produced. Those data are presented in Fig. 2  together with the corresponding literature. The measured photon fluxes in the direction of the desired target (galactic center, isotropic flux) are tabulated in files constraints /photons/flux_*_**. txt. These are used to obtain the constraints labelled M 1 in the nomenclature of Fig. 1. For prospective instruments, instrument characteristics (type (i) assumptions) are directly hardcoded inside Isatis, with relevant literature listed in Table  3:  • the time of observation T obs , • the fov , • the effective area as a function of photon energy A eff (E) (tabulated in files constraints/photons We propose several (extra)galactic backgrounds inside Isatis, labeled as constraints/photons/back-ground_**.
Results. We release a catalog of 880 528 individual observations, consisting of 205 515 known and unique SSOs. The catalog completeness is estimated to be about 97% down to V = 18 mag and the purity is higher than 95% for known SSOs. The near-simultaneous photometry provides either three, two, or a single color that we use to classify 117 356 SSOs with a scheme consistent with the widely used Bus-DeMeo taxonomy. Conclusions. The present catalog contributes significantly to the sample of asteroids with known surface properties (about 40% of main-belt asteroids down to an absolute magnitude of 16). We will release more observations of SSOs with future SkyMapper data releases.
g. ,  Ivezić et al. 2001; Popescu et al. 2016; Sergeyev & Carry 2021). The catalogs are only available at the CDS via anonymous ftp to cdsarc. u-strasbg. fr (130. 79. 128. 5)  or via http://cdsarc. u-strasbg. fr/viz-bin/cat/J/A+A/658/A109 We analyze here the images from the SkyMapper Southern Survey (Minor Planet Centre (MPC) observatory code Q55), which uses a suite of filters that is well adapted to asteroid spectral characterization (Fig. 1 ), similar to those of the Sloan Digital Sky Survey (SDSS, the main source of compositional information over almost two decades;  Szabó et al. 2004; Nesvorný et al. 2005; Carvano et al. 2010; DeMeo & Carry 2013; DeMeo et al. 2014 DeMeo et al. , 2019;; Parker et al. 2008; Graves et al. 2018). While the SDSS completed its imaging survey in 2009, SkyMapper has started its operations in 2014 and is currently active.
SkyMapper survey The SkyMapper Southern Survey (SMSS) is producing a homogeneous multiband atlas of the whole southern hemisphere in u, v, g, r, i, z filters  (Wolf et al. 2018). Observations were carried out with a 1. 35 m telescope located at Siding Spring Observatory (IAU code Q55). The telescope has an f/4. 8 focal ratio and is equipped with a mosaic CCD camera with 268 million pixels. The third data release (DR3) covers an area of more than 24 000 deg 2  and contains over 200 000 images with over eight billion individual source detections (see the SkyMapper website 1  and the DR2 release article for details:  Onken et al. 2019). The data in DR3 were obtained between March 2014 and October 2019. Individual deep exposures can reach magnitudes of 20 in u, v, z, 21 in i, and 22 in g, r (10σ detections) in the AB system  (Oke & Gunn 1983).
5 0. 0 0. 5 1. 0 SkyMapper SDSS g-r boundaries SDSS g-i boundaries SDSS i-z boundaries g-r i-z g-i SDSS Fig. 9. g -r (blue), g -i (green), and iz (orange) colors from the SDSS compared with SkyMapper for a wide range of stellar classes. Red dots represent the colors of the Sun  (Holmberg et al. 2006 ). The colored horizontal lines illustrate the range of colors for the SDSS asteroid taxonomy  (Sergeyev & Carry 2021). the latest data release from the Asteroid Lightcurve Database 4 , which contains periods and amplitudes of more than 30 000 known SSOs. Then we compared SkyMapper data and selected joint asteroids. We obtained samples of more than 12 000 asteroids with g -r and iz colors and almost 8000 asteroids with g -i colors. For each asteroid in the samples, we calculated the maximum expected color change arising from asteroid rotation between the SkyMapper imaging epochs (still limited to a 20min window) as the product of the photometric amplitude and the number of half-periods represented by the SkyMapper time difference.