Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “AMD”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Characterizing GPU Energy Usage in Exascale-Ready Portable Science Applications

We characterize the GPU energy usage of two widely adopted exascale-ready applications representing two classes of particle and mesh solvers: (i) QMCPACK, a quantum Monte Carlo package, and (ii) AMReX-Castro, an adaptive mesh astrophysical code. We analyze power, temperature, utilization, and energy traces from double-/single (mixed)-precision benchmarks on NVIDIA’s A100 and H100 and AMD’s MI250X GPUs using queries in NVML and rocm_smi_lib, respectively. We explore application-specific metrics to provide insights on energy vs. performance trade-offs. Our results suggest that mixed-precision energy savings range between 6–25% on QMCPACK and 45% on AMReX-Castro. Also, we found gaps in the AMD tooling used on Frontier GPUs that need to be understood, while query resolutions on NVML have little variability between 1 ms-1 s. Overall, application level knowledge is crucial to define energy-cost/science-benefit opportunities for the codesign of future supercomputer architectures in the post-Moore era.

Godoy, William [ORNL] (ORCID:0000000225905178)↗

GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading

Fourier pseudo-spectral methods for nonlinear partial differential equations are of wide interest in many areas of advanced computational science, including direct numerical simulation of three-dimensional (3-D) turbulence governed by the Navier-Stokes equations in fluid dynamics. This paper presents a new capability for simulating turbulence at a new record resolution up to 35 trillion grid points, on the world's first exascale computer, Frontier, comprising AMD MI250x GPUs with HPE's Slingshot interconnect and operated by the US Department of Energy's Oak Ridge Leadership Computing Facility (OLCF). Key programming strategies designed to take maximum advantage of the machine architecture involve performing almost all computations on the GPU which has the same memory capacity as the CPU, performing all-to-all communication among sets of parallel processes directly on the GPU, and targeting GPUs efficiently using OpenMP offloading for intensive number-crunching including 1-D Fast Fourier Transforms (FFT) performed using AMD ROCm library calls. With 99% of computing power on Frontier being on the GPU, leaving the CPU idle leads to a net performance gain via avoiding the overhead of data movement between host and device except when needed for some I/O purposes. Memory footprint including the size of communication buffers for MPI_ALLTOALL is managed carefully to maximize the largest problem size possible for a given node count. Detailed performance data including separate contributions from different categories of operations to the elapsed wall time per step are reported for five grid resolutions, from 2048 3 on a single node to 32768 3 on 4096 or 8192 nodes out of 9408 on the system. Both 1D and 2D domain decompositions which divide a 3D periodic domain into slabs and pencils respectively are implemented. The present code suite (labeled by the acronym GESTS, GPUs for Extreme Scale Turbulence Simulations) achieves a figure of merit (in grid points per second) exceeding goals set in the Center for Accelerated Application Readiness (CAAR) program for Frontier. The performance attained is highly favorable in both weak scaling and strong scaling, with notable departures only for 2048 3 where communication is entirely intra-node, and for 32768 3 , where a challenge due to small message sizes does arise. Communication performance is addressed further using a lightweight test code that performs all-to-all communication in a manner matching the full turbulence simulation code. Performance at large problem sizes is affected by both small message size due to high node counts as well as dragonfly network topology features on the machine, but is consistent with official expectations of sustained performance on Frontier. Overall, although not perfect, the scalability achieved at the extreme problem size of 32768 3 (and up to 8192 nodes — which corresponds to hardware rated at just under 1 exaflop/sec of theoretical peak computational performance) is arguably better than the scalability observed using prior state-of-the-art algorithms on Frontier's predecessor machine (Summit) at OLCF. New science results for the study of intermittency in turbulence enabled by this code and its extensions are to be reported separately in the near future.

3D fast Fourier transform↗

Revealing the electronic structure of van der Waals antiferromagnetic NiPS 3 through synchrotron-based 𝜇-ARPES and alkali metal dosing

Antiferromagnetic NiPS 3 has recently emerged as a quantum material of considerable interest, thanks to the discovery of multiple new couplings involving electrons, spins, orbitals, phonons, and magnons. However, controversies and open questions persist concerning the fundamental origins of these couplings. A critical piece of information required to advance the understanding is the precise electronic band structure of NiPS 3 . Angle-resolved photoemission spectroscopy (ARPES), combined with alkali metal dosing (AMD), can enable us to directly observe the subtle electronic states that appear around the Fermi surface, offering valuable insights into the intriguing quantum properties and interplays of the examined material. Here, in this study, we present a comprehensive characterization and analysis of the band structure of van der Waals layered antiferromagnet NiPS 3 , leveraging state-of-the-art μ-ARPES measurements supported by density functional theory (DFT) calculations. Theoretical DFT results identify the orbital contributions to the observed bands, providing a precise understanding of the experimental ARPES data. Crucially, AMD enables the observation of conduction band and defect-related states above the valence band maximum in NiPS 3 . Furthermore, temperature dependent ARPES results across the Néel transition temperature of NiPS 3 reveal that the paramagnetic and antiferromagnetic phases have nearly identical band structures, underlining the highly localized character of Ni d states. These findings substantially deepen our understanding of the electronic properties of NiPS 3 and lay a vital foundation for exploring the intriguing quantum phenomena it exhibits.

Cao, Yifeng [Boston Univ., MA (United States); Law↗

Enabling Scientific Applications with Performance-Portability and High-Productivity for Multi-GPU Programming with JACC.Multi

This work bridges the gap between multi-GPU computing and high-productivity, performance-portable programming solutions. Our goal is to enhance scientific applications with a productive and portable solution—program once, deploy everywhere—for multi-GPU programming with no cost to programmability. To accomplish this, we implemented JACC.Multi, which is part of the Julia for ACCelerators (JACC) performance-portable framework. JACC. Multi is the only high-level, portable metaprogramming solution that targets multi-GPU environments and is integrated in a readily accessible programming language (e.g., Julia language). With transparent GPU-to-GPU communication, JACC. Multi is optimized for scientific application workloads and is portable for NVIDIA and AMD accelerators. For the evaluation, we use two modern multi-GPU systems: Hudson, which features two NVIDIA H100 Hopper GPUs per node, and Frontier, which features four AMD MI250X GPUs per node, each with two Graphics Compute Dies (GCDs) for a total of eight GCDs per node. Additionally, as part of the evaluation, we use JACC (one GPU), MPI+JACC, and JACC. Multi codes that implement well-known and widely used scientific algorithms/kernels such as the conjugate gradient algorithm and an explicit forward Euler solver that requires GPU-to-GPU communication. Overall, JACC. Multi codes achieve better performance than MPI+JACC codes and significant speedups over JACC (one GPU), with up to 1.9× on Hudson and 6× on Frontier.

Valero Lara, Pedro [ORNL] (ORCID:0000000214794310)↗

JACC.shared: Leveraging HPC Metaprogramming and Performance Portability for Computations That Use Shared Memory GPUs

In this work, we present JACC.shared, a new feature of Julia for ACCelerators (JACC), which is the performanceportable and metaprogramming model of the just-in-time and LLVM-based Julia language. This new feature allows JACC applications to leverage the high-performance computing (HPC) capabilities of high-bandwidth, on-chip GPU memory. Historically, exploiting high-bandwidth, shared-memory GPUs has not been a priority for high-level programming solutions. JACC.shared covers that gap for the first time, thereby providing a highlevel, portable, and easy-to-use solution for programmers to exploit this memory and supporting all current major accelerator architectures. Well-known HPC and AI workloads, such as multi/hyperspectral imaging and AI convolutions, have been used to evaluate JACC.shared on two exascale GPU architectures hosted by some of the most powerful US Department of Energy supercomputers: Perlmutter (NVIDIA A100) and Frontier (AMD MI250X). The performance evaluation reports speedup of up to 3.5× by adding only one line of code to the base codes, thus providing important accelerators in a simple, portable, and transparent way and elevating the programming productivity and performance-portability capabilities for Julia/JACC HPC, AI, and scientific applications.

Valero Lara, Pedro [ORNL] (ORCID:0000000214794310)↗

Integrating ORNL’s HPC and Neutron Facilities with a Performance-Portable CPU/GPU Ecosystem

We explore the development of a performance-portable CPU/GPU ecosystem to integrate two of the US Department of Energy’s (DOE’s) largest scientific instruments, the Oak Ridge Leadership Computing facility and the Spallation Neutron Source (SNS), both of which are housed at Oak Ridge National Laboratory. We select a relevant data reduction workflow use-case to obtain the differential scattering cross-section from data collected by SNS’s CORELLI and TOPAZ instruments. We compare the current CPU-only production implementation using the Garnet Python multiprocess package based on the Mantid C++ framework against our proposed CPU/GPU implementation that uses the LLVM-based, just-in-time Julia scientific language and the JACC.jl performance-portable package. Two proxy apps were developed: (i) an app for extracting relevant Mantid kernels (MDNorm) in C++ and (ii) the Julia MiniVATES.jl miniapp. We present performance results for NVIDIA A100 and AMD MI100 GPUs and AMD EPYC 7513 and 7662 CPUs. The results provide insights for future generations of data reduction software that can embrace performance portability for an integrated research infrastructure across DOE’s experimental and computational facilities.

Hahn, Steven↗

DIMPLES: Distributed Influence Maximization for Pandemic pLanning on Exascale Systems

We study exascale parallel algorithms for the selection of intervention or monitoring strategies in massive realistic socio-technical networks through scalable Influence Maximization (InfMax) algorithms. We employ novel techniques to enable efficient scaling on up to 8k nodes of OLCF Frontier, with 65k AMD GPUs and 458k AMD CPU cores. Current state-of-the-art InfMax tools are limited to networks with only a few million actors (vertices) and a few hundred million interactions (edges). By overcoming these limitations, we show that our approach is capable of processing a realistic social contact network of the United States with 285 million nodes and about 8 billion edges. This two orders-of-magnitude improvement over the previous state-of-the-art is obtained by leveraging algorithmic advancements for the InfMax problem and designing several problem-specific approaches to overlap communication with computation, improve GPU efficiency, and lower the application’s memory requirements. We evaluate strong scaling for computing 10k most influential seeds using up to 8k nodes of an exascale system, and weak scaling from 128 to 8k system nodes for seed sets ranging from 625 to 40k seeds. We achieve the fastest-known runtime of 25 minutes while performing 48 million diffusion simulations totaling 2.31 petabytes to identify 40k influential seeds using 8k nodes, and take 5.75 minutes to identify 10k seeds while using 4k nodes.

Minutoli, Marco [Pacific Northwest National Labora↗

Clacc: OpenACC for C/C++ in Clang

The Clacc project has developed OpenACC compiler, runtime, and profiling interface support for C/C++ by extending Clang and LLVM. A key Clacc design feature is that it translates OpenACC to OpenMP to leverage the OpenMP offloading support that is actively being developed for Clang and LLVM. A benefit of this design is support for two compilation modes: traditional compilation mode produces a binary, and source-to-source mode produces OpenMP source. Clacc has been deployed on Oak Ridge National Laboratory’s (ORNL’s) Frontier, on which Clacc is the only OpenACC implementation for C/C++. Clacc supports x86_64, POWER9, AMD GPUs, and NVIDIA GPUs. Clacc’s OpenACC profiling interface support has been integrated with TAU, which is also deployed on Frontier. While Clacc has always supported C as a base language, Clacc also has increasing C++ support, including support for Kokkos’s OpenACC back end. Clacc itself is hosted publicly on GitHub. In this paper, we describe Clacc’s design and mapping from OpenACC directives to OpenMP. We also present a performance evaluation on ORNL’s Frontier (AMD MI250x GPU offload) and Argonne National Laboratory’s (ANL’s) Polaris (NVIDIA A100 GPU offload) for various SPEC ACCEL and Kokkos OpenACC back end benchmarks.

97 MATHEMATICS AND COMPUTING↗

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗

Ristra Project FY23 L2 Milestone Report, Rev.1: MRT #8541: Multiphysics Scaling on EAS-3

The findings of this report were used to close out the ATDM milestone MRT# 8541, which was designed to demonstrate readiness of ATDM multiphysics codes for mission-relevant work on ATS-4, El Capitan. To this end, the closure criteria were to run a 3D shaped charge problem at scale up to 50% of the El Capitan early-access system, RZVernal (AMD Trento CPUs and AMD MI-250X GPUs), demonstrate scalability, and document challenges with the software stack and environment. LANL’s approach to this milestone was to test our modular software capability by developing an entirely new code, Moya, built upon our FleCSI framework. The physics capability and the GPU infrastructure needed for the shaped charge problem on GPUs was added to Moya, and the required calculations were performed at scale. Moya showed good scaling without any fine-tuning of GPU kernels; there is still significant room for performance enhancements, especially for the Legion backend. Tied up in this L2 milestone was a closeout of KPP-3s for the ECP ST Projects at LANL; this material will be covered in a separate document.

97 MATHEMATICS AND COMPUTING↗

Targeted Biomining and Machine Learning Approaches in Critical Minerals Revealed by a Biogeochemical Survey of a Coal Mine Drainage Remediation System

Abandoned coal mine drainage (AMD) remediation systems in Pennsylvania can concentrate critical minerals and materials (CMM) at levels comparable to mining-grade ores. Remediation systems have varying engineering features and are open to the environment, resulting in diverse microbial colonization and seasonal climate influences that may impact CMM speciation. The location of CMMs, the types of bacterial communities tolerant of these pollutant conditions, and the influence of localized climate on CMM rich remediation systems are not well characterized. Through a one-year spatiotemporal survey of biogeochemistry at a remediation system, we have initiated the process to address these questions. Rare Earth Elements (REE) ranged 180-1,200 ppm and greater than 1,500 bacterial ASVs were classified via 16S sequencing. Analyses indicate biogeochemical differences are heavily influenced by engineering features. Additionally, REE precipitants correlate strongly with the elements Al, Cu, Zn, Be, and U. Unearthing these trends has refined our line of inquiry to explore biological mining opportunities more closely with these metals. Furthermore, we created a Machine Learning Model for predicting AMD REE content, with 89% accuracy, using the data from this study and several others. Further training data is required to create a more reputable model. Recently, global research efforts have prioritized modeling work or the use of the few historical surveys to design experiments. Through our data, we challenge this approach, emphasizing the importance of expanding fundamental survey efforts prior to advanced product design and experimentation.

critical minerals↗

Overview of NLR Automated Mobility District Implementation Research - Phases I, II, and III. The Convergence of Automation, Electrification, and On-Demand Services: Enabling Resilient Automated Mobility Districts

A research program by the National Renewable Energy Laboratory has been investigating the implementation prospects for fully automated passenger transport systems that are deployed to operate within dense urban settings, referred to as Automated Mobility Districts (AMDs). An AMD emphasizes the deployment of automated vehicles (AV) passenger transport services within a dense urban setting and other major activity centers with intense passenger origin-destination demand patterns, such as those found in large business districts, airports, and university and medical campuses. Phase I and II surveyed 10 early deployment sites and subsequently collected and evaluated the lessons learned from these early deployment sites, with particular attention to fleet operations, impacts of service reliability, and vehicle technology evolution as the field of companies was being progressively winnowed by the challenges of full automation.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Characterizing the Impact of GPU Power Management on an Exascale System

As GPU-accelerated high-performance computing (HPC) systems approach exascale performance, controlling energy consumption without compromising throughput is essential. Architectures such as the AMD MI250X-based Frontier supercomputer provide runtime mechanisms like frequency and power capping, enabling energy tuning without modifying application code. Although both target energy reduction, they operate via distinct hardware control paths and influence workloads differently. We present a comprehensive evaluation of these strategies on a leadership-class system using diverse HPC proxy applications representative of production workloads. Our study analyzes performance–energy trade-offs across multiple capping levels, node counts (1 and 32), and application profiles. Results show that frequency capping generally achieves higher energy efficiency and scalability, with gains of up to 13.2% without performance loss, while power capping is more effective for single-node runs or bursty GPU utilization. We also provide practical guidelines to help system administrators and users balance energy efficiency and performance in large-scale scientific workloads.

Costa, Mariana [Universidade Federal do Rio Grande↗

Bringing HPE Slingshot 11 support to Open MPI

The Cray HPE Slingshot 11 network is used on the new exascale systems arriving at the U.S. Department of Energy (DoE) laboratories (e.g., Frontier, Aurora, Perlmutter). As such, the support of this network is an important capability to meet the needs of exascale applications. Here, this article highlights recent work to develop supporting infrastructure to enable Open MPI to efficiently support these new platforms. A key component of this effort involves development of a new Open Fabrics Interface (OFI) provider, LinkX. We discuss the design and development of enhancements that take advantage of the new Slingshot 11 network and AMD GPUs. We include performance data from tests on the Frontier supercomputer using synthetic communication benchmarks, and the vendor provided MPI as a baseline for comparison. The tests demonstrate full functionality of Open MPI on the system and initial results show favorable performance when compared to the highly tuned vendor implementation.

97 MATHEMATICS AND COMPUTING↗

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Software stewardship and advancement of a high-performance computing scientific application: QMCPACK

Here, we provide an overview of the software engineering efforts and their impact in QMCPACK, a production-level ab-initio Quantum Monte Carlo open-source code targeting high-performance computing (HPC) systems. Aspects included are: (i) strategic expansion of continuous integration (CI) targeting CPUs, using GitHub Actions own runners, and NVIDIA and AMD GPUs used in pre-exascale systems, (ii) incremental reduction of memory leaks using sanitizers, (iii) incorporation of Docker containers for CI and reproducibility, and (iv) refactoring efforts to improve maintainability, testing coverage, and memory lifetime management. We quantify the value of these improvements by providing metrics to illustrate the shift towards a predictive, rather than reactive, maintenance approach. Our goal, in documenting the impact of these efforts on QMCPACK, is to contribute to the body of knowledge on the importance of research software engineering (RSE) for the stewardship and advancement of community HPC codes to enable scientific discovery at scale.

97 MATHEMATICS AND COMPUTING↗

Ammonium-coordinated exchanger (ACE) functionalized silica sorbents for recovering/removing aqueous anionic contaminants

There are limited studies of functionalized silica anion exchange sorbents used for critical/heavy metal recovery/removal relative to polymeric and other inorganic materials. This work features ammonium-coordinated exchanger (ACE) anion exchange particle sorbents prepared by either acid-washing epoxy-crosslinked polyethylenimine (PEI) hydrogen bonded within/to a silica particle sorbent (two-step method) or reacting a di-chlorinated crosslinker, α,α-dichloro-p-xylene (DPX), with PEI within silica (single-step method). Energy dispersive X-ray spectroscopy (EDS) and infrared spectroscopy confirmed the presence of -NH 2 + ···Cl - and -NH 3 + ···Cl - groups, which removed oxyanionic species –arsenate, selenate, chromate, sulfate, phosphate, and nitrate– plus bromide from ideal solutions, authentic acid mine drainage (AMD), and authentic flue gas desulfurization (FGD) wastewater. Affinity of the anions for ACE varied across single- and mixed-element solutions. However, affinity for CrO 4 2- was among the highest in both cases. Total anion uptake by the optimized ACE, PEI-E3-HCl_1.1, reached 1.2 mmol anion/g-sorb. (0.56 mmol CrO 4 2- /g), or ∼2.3 mmol negative charge/g-sorb. This was close to the 0.52 mmol CrO 4 2- /g of a commercial anion exchange resin. Near-consistent removal of 20–80 % of each anion from FGD during an eight-cycle adsorption-desorption (1 M NaCl) test predicted good ACE viability for testing under practical conditions at larger scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Delving into the depths of NGC 3783 with XRISM V. Broad-band modelling of ionized outflows

The Seyfert 1 galaxy NGC 3783 hosts a multi-phase warm absorber (WA) that has been extensively studied in the X-ray band. High-resolution spectra from 2000−2001 revealed a complex outflow with multiple ionization and velocity components. Two decades later, new XMM-Newton and XRISM observations allow us to investigate the long-term evolution of these outflows. We performed joint spectral modelling of the XMM-Newton /RGS and XRISM/Resolve time-averaged spectra using the pion photoionization code within SPEX. We derived the ionization parameter, column density, turbulent velocity, and outflow velocity for each absorption component, and investigated their thermal stability and absorption measure distribution (AMD) to characterize the physical and dynamical properties of the WA in NGC 3783 in 2024. We compared these results with the 2000−2001 epoch to assess long-term variability, stability, and possible changes in the absorber population. We identify eight WA components spanning log ξ = 1.08 − 3.38 and outflow velocities of 480−1230 km s −1 . The ranges of column densities and turbulent velocities remain broadly consistent with the WAs from 2000−2001, but the earlier data contained more low-ionization, high-velocity components. The total column density of all the outflows in 2024 is 1.5 times larger than in 2000−2001, which means that it has been replenished by fresh material. The dominant unresolved transition array (UTA) absorber (component B3) has increased its column density by a factor of three while maintaining a similar ionization parameter. The WAs in NGC 3783 have undergone significant structural and dynamical evolution over the past 24 years.

79 ASTRONOMY AND ASTROPHYSICS↗