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At least 1,081 records · Page 60

LSPRAY-IV: A Lagrangian Spray Module

LSPRAY-IV is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the code development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.

Raju, M. S.↗

Software Testing and Verification in Climate Model Development

Over the past 30 years most climate models have grown from relatively simple representations of a few atmospheric processes to a complex multi-disciplinary system. Computer infrastructure over that period has gone from punch card mainframes to modem parallel clusters. Model implementations have become complex, brittle, and increasingly difficult to extend and maintain. Existing verification processes for model implementations rely almost exclusively upon some combination of detailed analysis of output from full climate simulations and system-level regression tests. In additional to being quite costly in terms of developer time and computing resources, these testing methodologies are limited in terms of the types of defects that can be detected, isolated and diagnosed. Mitigating these weaknesses of coarse-grained testing with finer-grained "unit" tests has been perceived as cumbersome and counter-productive. In the commercial software sector, recent advances in tools and methodology have led to a renaissance for systematic fine-grained testing. We discuss the availability of analogous tools for scientific software and examine benefits that similar testing methodologies could bring to climate modeling software. We describe the unique challenges faced when testing complex numerical algorithms and suggest techniques to minimize and/or eliminate the difficulties.

Clune, Thomas L.↗

Optimizing High-Throughput Inference on Graph Neural Networks at Shared Computing Facilities with the NVIDIA Triton Inference Server

Abstract With machine learning applications now spanning a variety of computational tasks, multi-user shared computing facilities are devoting a rapidly increasing proportion of their resources to such algorithms. Graph neural networks (GNNs), for example, have provided astounding improvements in extracting complex signatures from data and are now widely used in a variety of applications, such as particle jet classification in high energy physics (HEP). However, GNNs also come with an enormous computational penalty that requires the use of GPUs to maintain reasonable throughput. At shared computing facilities, such as those used by physicists at Fermi National Accelerator Laboratory (Fermilab), methodical resource allocation and high throughput at the many-user scale are key to ensuring that resources are being used as efficiently as possible. These facilities, however, primarily provide CPU-only nodes, which proves detrimental to time-to-insight and computational throughput for workflows that include machine learning inference. In this work, we describe how a shared computing facility can use the NVIDIA Triton Inference Server to optimize its resource allocation and computing structure, recovering high throughput while scaling out to multiple users by massively parallelizing their machine learning inference. To demonstrate the effectiveness of this system in a realistic multi-user environment, we use the Fermilab Elastic Analysis Facility augmented with the Triton Inference Server to provide scalable and high-throughput access to a HEP-specific GNN and report on the outcome.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

CFD Extraction Tool for TecPlot From DPLR Solutions

This invention is a TecPlot macro of a computer program in the TecPlot programming language that processes data from DPLR solutions in TecPlot format. DPLR (Data-Parallel Line Relaxation) is a NASA computational fluid dynamics (CFD) code, and TecPlot is a commercial CFD post-processing tool. The Tec- Plot data is in SI units (same as DPLR output). The invention converts the SI units into British units. The macro modifies the TecPlot data with unit conversions, and adds some extra calculations. After unit conversions, the macro cuts a slice, and adds vectors on the current plot for output format. The macro can also process surface solutions. Existing solutions use manual conversion and superposition. The conversion is complicated because it must be applied to a range of inter-related scalars and vectors to describe a 2D or 3D flow field. It processes the CFD solution to create superposition/comparison of scalars and vectors. The existing manual solution is cumbersome, open to errors, slow, and cannot be inserted into an automated process. This invention is quick and easy to use, and can be inserted into an automated data-processing algorithm.

Norman, David↗

Extended ecosystem signatures with application to Eos synergism requirements

The primary objective is to define the advantages of synergistically combining optical and microwave remote sensing measurements for the determination of biophysical properties important in ecosystem modeling. This objective was approached in a stepwise fashion starting with ground-based observations of controlled agricultural and orchard canopies and progressing to airborne observations of more natural forest ecosystems. This observational program is complemented by a parallel effort to model the visible reflectance and microwave scattering properties of composite vegetation canopies. The goals of the modeling studies are to verify our basic understanding of the sensor-scene interaction physics and to provide the basis for development of inverse models optimized for retrieval of key biophysical properties. These retrieval algorithms can then be used to simulate the expected performance of various aspects of Eos including the need for simultaneous SAR and HIRIS observations or justification for other (non-synchronous) relative timing constraints and the frequency, polarization, and angle of incidence requirements for accurate biophysical parameter extractions. This program completed a very successful series of truck-mounted experiments, made remarkable progress in development and validation of optical reflectance and microwave scattering models for vegetation, extended the scattering models to accommodate discontinuous and periodic canopies, developed inversion approaches for surface and canopy properties, and disseminated these results widely through symposia and journal publications. In addition, the third generation of the computer code for the microwave scattering models was provided to a number of other US, Canadian, Australian, and European investigators who are currently presenting and publishing results using the MIMICS research code.

Ulaby, Fawwaz T.↗

Hierarchical and Parallelizable Direct Volume Rendering for Irregular and Multiple Grids

A general volume rendering technique is described that efficiently produces images of excellent quality from data defined over irregular grids having a wide variety of formats. Rendering is done in software, eliminating the need for special graphics hardware, as well as any artifacts associated with graphics hardware. Images of volumes with about one million cells can be produced in one to several minutes on a workstation with a 150 MHz processor. A significant advantage of this method for applications such as computational fluid dynamics is that it can process multiple intersecting grids. Such grids present problems for most current volume rendering techniques. Also, the wide range of cell sizes (by a factor of 10,000 or more), which is typical of such applications, does not present difficulties, as it does for many techniques. A spatial hierarchical organization makes it possible to access data from a restricted region efficiently. The tree has greater depth in regions of greater detail, determined by the number of cells in the region. It also makes it possible to render useful 'preview' images very quickly (about one second for one-million-cell grids) by displaying each region associated with a tree node as one cell. Previews show enough detail to navigate effectively in very large data sets. The algorithmic techniques include use of a kappa-d tree, with prefix-order partitioning of triangles, to reduce the number of primitives that must be processed for one rendering, coarse-grain parallelism for a shared-memory MIMD architecture, a new perspective transformation that achieves greater numerical accuracy, and a scanline algorithm with depth sorting and a new clipping technique.

Wilhelms, Jane↗

Direct numerical simulations for hybrid rocket boundary layers: Performance modeling and scaling

This paper presents a comprehensive performance and scaling analysis of direct numerical simulations for reacting boundary layers, focusing on slab burner configurations. Using a PETSc-based finite volume CFD framework, the study evaluates the scalability and computational cost of flow, chemistry, and radiation evaluations across 2D and 3D simulations. Polymethyl methacrylate (PMMA) is the fuel with pure O 2 as the oxidizer, modeled using a detailed chemical kinetics mechanism with 113 species and 660 reactions. A ray-tracing-based radiation solver, designed for distributed memory applications, is implemented to model radiation heat transfer. Parallel scalability is analyzed for the coupled flow, chemistry, and radiation heat transfer processes. Weak and strong scaling studies are conducted on up to 15,000 computational ranks, revealing robust performance when flow cells exceed 200 per rank. Chemistry evaluations dominate the computational cost in large 3D simulations, accounting for approximately 40% of the total runtime, while flow processes contribute around 35%, and radiation solver contributions remain below 10% due to reduced evaluation frequencies. GPU accelerated chemistry evaluation, implemented with Zero-RK, demonstrates significant promise, achieving up to a 4x speedup for workloads exceeding 30,000 cells per GPU. However, diminishing returns are observed for smaller workloads due to CPU-GPU communication overhead. This study identifies key challenges, including memory bottlenecks and the effects of domain partitioning on flow scalability, while highlighting the potential of GPU-accelerated chemistry to reduce computational costs. In conclusion, these findings provide realizable run configurations for 2D, 3D, and GPU-accelerated cases, offering insights for optimizing reactive flow solvers.

CFD Scalability↗

Porting Gravitational Wave Signal Extraction to Parallel Virtual Machine (PVM)

Laser Interferometer Space Antenna (LISA) is a planned NASA-ESA mission to be launched around 2012. The Gravitational Wave detection is fundamentally the determination of frequency, source parameters, and waveform amplitude derived in a specific order from the interferometric time-series of the rotating LISA spacecrafts. The LISA Science Team has developed a Mock LISA Data Challenge intended to promote the testing of complicated nested search algorithms to detect the 100-1 millihertz frequency signals at amplitudes of 10E-21. However, it has become clear that, sequential search of the parameters is very time consuming and ultra-sensitive; hence, a new strategy has been developed. Parallelization of existing sequential search algorithms of Gravitational Wave signal identification consists of decomposing sequential search loops, beginning with outermost loops and working inward. In this process, the main challenge is to detect interdependencies among loops and partitioning the loops so as to preserve concurrency. Existing parallel programs are based upon either shared memory or distributed memory paradigms. In PVM, master and node programs are used to execute parallelization and process spawning. The PVM can handle process management and process addressing schemes using a virtual machine configuration. The task scheduling and the messaging and signaling can be implemented efficiently for the LISA Gravitational Wave search process using a master and 6 nodes. This approach is accomplished using a server that is available at NASA Ames Research Center, and has been dedicated to the LISA Data Challenge Competition. Historically, gravitational wave and source identification parameters have taken around 7 days in this dedicated single thread Linux based server. Using PVM approach, the parameter extraction problem can be reduced to within a day. The low frequency computation and a proxy signal-to-noise ratio are calculated in separate nodes that are controlled by the master using message and vector of data passing. The message passing among nodes follows a pattern of synchronous and asynchronous send-and-receive protocols. The communication model and the message buffers are allocated dynamically to address rapid search of gravitational wave source information in the Mock LISA data sets.

Thirumalainambi, Rajkumar↗

The Effects of Rainfall Inhomogeneity on Climate Variability of Rainfall Estimated from Passive Microwave Sensors

Passive microwave rainfall estimates that exploit the emission signal of raindrops in the atmosphere are sensitive to the inhomogeneity of rainfall within the satellite field of view (FOV). In particular, the concave nature of the brightness temperature (T(sub b)) versus rainfall relations at frequencies capable of detecting the blackbody emission of raindrops cause retrieval algorithms to systematically underestimate precipitation unless the rainfall is homogeneous within a radiometer FOV, or the inhomogeneity is accounted for explicitly. This problem has a long history in the passive microwave community and has been termed the beam-filling error. While not a true error, correcting for it requires a priori knowledge about the actual distribution of the rainfall within the satellite FOV, or at least a statistical representation of this inhomogeneity. This study first examines the magnitude of this beam-filling correction when slant-path radiative transfer calculations are used to account for the oblique incidence of current radiometers. Because of the horizontal averaging that occurs away from the nadir direction, the beam-filling error is found to be only a fraction of what has been reported previously in the literature based upon plane-parallel calculations. For a FOV representative of the 19-GHz radiometer channel (18 km X 28 km) aboard the Tropical Rainfall Measuring Mission (TRMM), the mean beam-filling correction computed in this study for tropical atmospheres is 1.26 instead of 1.52 computed from plane-parallel techniques. The slant-path solution is also less sensitive to finescale rainfall inhomogeneity and is, thus, able to make use of 4-km radar data from the TRMM Precipitation Radar (PR) in order to map regional and seasonal distributions of observed rainfall inhomogeneity in the Tropics. The data are examined to assess the expected errors introduced into climate rainfall records by unresolved changes in rainfall inhomogeneity. Results show that global mean monthly errors introduced by not explicitly accounting for rainfall inhomogeneity do not exceed 0.5% if the beam-filling error is allowed to be a function of rainfall rate and freezing level and does not exceed 2% if a universal beam-filling correction is applied that depends only upon the freezing level. Monthly regional errors can be significantly larger. Over the Indian Ocean, errors as large as 8% were found if the beam-filling correction is allowed to vary with rainfall rate and freezing level while errors of 15% were found if a universal correction is used.

Kummerow, Christian↗

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Better, Cheaper, Faster Molecular Dynamics

Recent, revolutionary progress in genomics and structural, molecular and cellular biology has created new opportunities for molecular-level computer simulations of biological systems by providing vast amounts of data that require interpretation. These opportunities are further enhanced by the increasing availability of massively parallel computers. For many problems, the method of choice is classical molecular dynamics (iterative solving of Newton's equations of motion). It focuses on two main objectives. One is to calculate the relative stability of different states of the system. A typical problem that has' such an objective is computer-aided drug design. Another common objective is to describe evolution of the system towards a low energy (possibly the global minimum energy), "native" state. Perhaps the best example of such a problem is protein folding. Both types of problems share the same difficulty. Often, different states of the system are separated by high energy barriers, which implies that transitions between these states are rare events. This, in turn, can greatly impede exploration of phase space. In some instances this can lead to "quasi non-ergodicity", whereby a part of phase space is inaccessible on time scales of the simulation. To overcome this difficulty and to extend molecular dynamics to "biological" time scales (millisecond or longer) new physical formulations and new algorithmic developments are required. To be efficient they should account for natural limitations of multi-processor computer architecture. I will present work along these lines done in my group. In particular, I will focus on a new approach to calculating the free energies (stability) of different states and to overcoming "the curse of rare events". I will also discuss algorithmic improvements to multiple time step methods and to the treatment of slowly decaying, log-ranged, electrostatic effects.

Pohorille, Andrew↗

MODIS algorithm development and data visualization using ACTS

The study of the Earth as a system will require the merger of scientific and data resources on a much larger scale than has been done in the past. New methods of scientific research, particularly in the development of geographically dispersed, interdisciplinary teams, are necessary if we are to understand the complexity of the Earth system. Even the planned satellite missions themselves, such as the Earth Observing System, will require much more interaction between researchers and engineers if they are to produce scientifically useful data products. A key component in these activities is the development of flexible, high bandwidth data networks that can be used to move large amounts of data as well as allow researchers to communicate in new ways, such as through video. The capabilities of the Advanced Communications Technology Satellite (ACTS) will allow the development of such networks. The Pathfinder global AVHRR data set and the upcoming SeaWiFS Earthprobe mission would serve as a testbed in which to develop the tools to share data and information among geographically distributed researchers. Our goal is to develop a 'Distributed Research Environment' that can be used as a model for scientific collaboration in the EOS era. The challenge is to unite the advances in telecommunications with the parallel advances in computing and networking.

Abbott, Mark R.↗

Numerical thermal analyses of heat exchangers for the stirling engine application

The Regenerator, Cooler and Heater for the NASA Space Power Research Engine (SPRE) have been analyzed in detail for laminar, incompressible and oscillatory flow conditions. Each component has been analyzed independently and in detail with the regenerator being modeled as two-parallel-plates channel with a solid wall. The ends of the channel are exposed to two reservoir maintained at different temperature thus providing an axial temperature gradient along the channel. The cooler and heater components have been modeled as circular pipes with isothermal walls. Two different types of thermal boundary conditions have been investigated for the cooler and heater, namely, symmetric and asymmetric temperature inflow. In symmetric temperature inflow the flow enters the channel with the same temperature in throughout the velocity cycle whereas, in asymmetric temperature inflow the flow enters with a different temperature in each half cycle. The study was conducted over a wide range of Maximum Reynolds number (RE(max) varying from 75 to 60000, Valensi number (Va) from 2.5 to 800, and relative amplitude of fluid displacement (A(sub r) from 0.357 to 1.34. A two dimensional Finite volume method based on the SIMPLE algorithm was used to solve the governing partial differential equations. Post processing programs were developed to effectively describe the heat transfer mechanism under oscillatory flows. The computer code was validated by comparing with existing analytical solutions for oscillating flows. The thermal field have been studied with the help of temperature contour and three dimensional plots. The instantaneous friction factor, wall heat flux and heat transfer coefficient have been examined. It has been concluded that in general, the frictional factor and heat transfer coefficient are higher under oscillatory flow conditions when the Valensi number is high. Also, the thermal efficiency decreases for lower A(r) values. Further, the usual steady state definition for the heat transfer coefficient does not seem to be valid.

Kannapareddy, Mohan Raj↗

Single-shot diffusion measurement in laser-polarized Gas

A single-shot pulsed gradient stimulated echo sequence is introduced to address the challenges of diffusion measurements of laser polarized 3He and 129Xe gas. Laser polarization enhances the NMR sensitivity of these noble gases by >10(3), but creates an unstable, nonthermal polarization that is not readily renewable. A new method is presented which permits parallel acquisition of the several measurements required to determine a diffusive attenuation curve. The NMR characterization of a sample's diffusion behavior can be accomplished in a single measurement, using only a single polarization step. As a demonstration, the diffusion coefficient of a sample of laser-polarized 129Xe gas is measured via this method. Copyright 1999 Academic Press.

Non-NASA Center↗

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗

PRISMA: PARALLEL REFINEMENT AND INTEGRATION SYSTEM FOR MULTI-AZIMUTHAL ANALYSIS

The Parallel Refinement and Integration System for Multi-azimuthal Analysis (PRISMA, version 1.1.0) is a Python application for processing X-ray diffraction (XRD) image data. PRISMA wraps GSAS-II to perform azimuthally-binned peak refinement, computes per-frame strain and d-spacing from those fits, and provides three PyQt5 graphical interfaces: (1) a Recipe Builder for selecting GSAS-II control (.imctrl) files, optional mask (.immask) files or threshold-ased masking, reference and experiment image sets, peaks, zimuthal range and bin size, and an optional ceria-based auto-calibration; (2) a Batch Processor that uses Dask on local workstations and pure MPI (mpi4py.futures.MPICommExecutor) on HPC to distribute GSAS-II refinement across cores or compute nodes and write results to a 4-dimensional (peaks x frames x azimuths x measurements) Zarr dataset; and (3) a Data Analyzer that renders heatmaps of fit parameters, strain, frame-to-frame deltas, and percent-change-vs-reference, and exports user-defined subsections to CSV or Excel. The peak-refinement algorithm is deterministic. Benchmark on ALCF Crux: a 20,000-image set, single-peak fit in frame mode with 44 azimuthal bins on 128 nodes x 128 workers, 48 seconds total wall time.

Lorenzo Martin, Maria De La Cinta [Argonne Nationa↗

Physics of Rotation Powered Pulsars and Their Nebulae

This letter is my progress report for the Astrophysics Theory grant. The first goal of the research supported by this grant is to produce a time dependent theory of the unsteady relativistic collisionless shock wave terminating the relativistic wind from a pulsar, and compare the predicted surface brightness fluctuations to Hubble Space Telescope observations of the wisps in the Crab Nebula. The second goal is to model the production of electron-positron pairs over the polar caps of rotation powered pulsars, and use the results to predict the heating of the surface due to particle trapping and bombardment of the atmosphere at the base of the polar field lines. We have succeeded in creating a one dimensional hybrid code, in which the electron-positron pairs incident on the shock structure are modeled as a relativistic, adiabatic, ideal MHD fluid, while the heavy ions are treated as particles using a particle-in-cell algorithm. The electromagnetic fields are evaluated from the currents and charge densities in the pairs and the ions, while the particles and the fluid accelerate in response to the computed self-consistent electromagnetic fields. The results are promising, in that the underlying ion cyclotron instability generates finite amplitude, propagating magnetosonic waves in the pairs, whose wavelengths and frequencies, when translated into physical units, are comparable to the observed running waves of brightness observed by HST near the Crab pulsar. The code is undergoing a number of tests, to assure us that this preliminary correspondence is not an artifact. In the coming year, the observational appearance of the models will be computed and compared to the HST observations of the Crab now in hand, and used to predict the HST results which will be obtained the year after next. WE also developed a one dimensional cascade theory for pair creation over pulsars' polar caps. A linear integral equation describing the synchrotron cascade has been derived and solved by iterative techniques, in the case when a high energy electron moving parallel to a star centered dipole magnetic field initiates the cascade through curvature gamma ray emission.

Arons, Jonathan↗