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On the equivalence of polynomial GCD and squarefree factorization problems

It is shown that a closer reexamination of Yun's 1976 paper reveals the reducibility of SQFR to GCD. The natural question that follows is whether GCD is reducible to SQFR. That is answered affirmatively and the derivation actually suggests an algorithm for computing GCD's when input polynomials are already represented by their SQFR form.

Yun, D. Y. Y.

GCD TechPort Data Sheets Thermal Protection System Materials (TPSM) Project

The Thermal Protection System Materials (TPSM) Project consists of three distinct project elements: the 3-Dimensional Multifunctional Ablative Thermal Protection System (3D MAT) project element; the Conformal Ablative Thermal Protection System (CA-TPS) project element; and the Heatshield for Extreme Entry Environment Technology (HEEET) project element. 3D MAT seeks to design, develop and deliver a game changing material solution based on 3-dimensional weaving and resin infusion approach for manufacturing a material that can function as a robust structure as well as a thermal protection system. CA-TPS seeks to develop and deliver a conformal ablative material designed to be efficient and capable of withstanding peak heat flux up to 500 W/ sq cm, peak pressure up to 0.4 atm, and shear up to 500 Pa. HEEET is developing a new ablative TPS that takes advantage of state-of-the-art 3D weaving technologies and traditional manufacturing processes to infuse woven preforms with a resin, machine them to shape, and assemble them as a tiled solution on the entry vehicle substructure or heatshield.

HEEET

Mission Radiation Environment Modeling and Analysis: Avionics Trade Study for GCD Rad-Neuro Project

The two main objectives of this trade study are characterizing the mission radiation environment for multiple Design Reference Missions (DRM) and analysis of radiation effects on avionics with the goal of producing radiation tolerant Neuromorphic Computing processor chips with innovative radiation-induced fault mitigation. The NASA process for defining radiation requirements for flight avionics is applied to this domain. The effects of trapped protons and electrons in the Van Allen radiation belts predominates in Low-Earth-Orbit (LEO) and the solar wind, solar flares and Galactic Cosmic Rays (GCRs) are the dominant radiation challenge in the open space between the planets of our solar system. The nature and energy of the particles that cause circuit upset and failure is very different in the two regimes. Two results are produced from the radiation models: determining the Total Integrated Dose (TID) experienced by avionics for a given DRM and predicting the Single Event Effects (SEE) rates for avionics during high rate exposure. These tools are applied to existing semiconductors and can be used for predicting the radiation performance of future semiconductors based on early radiation testing of new devices.

Space Radiation

STMD-GCD Reactive Additive Manufacturing for Fourth Industrial Revolution Exploration Systems (RAMFIRE)

Elementum 3D, in partnership with NASA-MSFC under an ACO, seeks to help further increase launch performance and reduce launch and mission cost by advancing novel additively manufactured (AM) aluminum materials for large-scale complex rocket components and launch vehicle structures. The proposed outcome of this ACO is to advance large-scale directed energy deposition (DED) of highstrength aluminum alloys through process development, characterization, and testing.

RAMFIRE

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The Predictive Simulation Capability (PSC) Element is focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the predictive simulation capability, the GCD Program also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper will present the status of implementing and maturing particle-particle interaction constituent physics models essential in simulating the landing surface granular material flow under PSI effects. This gas-particle multi-phase interaction modeling of plume impingement flow on the extra-terrestrial soil material is performed with the Gas-Granular Flow Solver (GGFS) addressed in a companion paper. The response of regolith particle flow induced by lander PSI requires accurate representation of the regolith granular material fluidic behavior and gas-granular interactions. The lunar regolith, as the extreme example, is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking particle shapes for the very jagged particles. The combination of particle shape and size distribution has been identified as major drivers in the complex particle flow response and resulting crater shape characteristics of extraterrestrial granular material. Constituent models for spherical particles can be formulated directly from particle kinetics theory. Complex particle shapes can be modeled by gluing together elemental spherical shapes into composite particles, requiring a Discrete Element Model (DEM) particle kinetics modeling approach to extract data and formulate constituent models. Mixture constituent models for poly-disperse mixtures (i.e, containing distribution of particle sizes) have recently been developed. The required non-spherical particle mixture granular material response closure models are then obtained through small-scale unit physics DEM simulations for the range of particle shapes, mixtures and packing densities. The granular material response closure models are then implemented in the Eulerian granular flow formulation. This DEM-based constituent model extraction process and formulation of poly-disperse particle mixtures has been successfully developed by small business and academic partners in the development of the Gas-Granular Flow Solver (GGFS) simulation program simulation framework. The currently implemented capabilities have reached the capability level of modeling bi-disperse, non-spherical particle mixtures is being continuously extended towards computational modeling of full range irregular particle mixtures. Under the GCD project, this technology is being further developed, transferred to NASA analysts, and matured towards application readiness. The predictive simulation capability team under the GCD project has acquired the modeling tools and processes of the DEM based constituent model formulation from the GGFS development team and is developing the capability to replicate the existing process. This is the first important step towards the ability of the NASA team to independently perform such model development in a production setting. Further efforts are underway to migrate the DEM based model simulation process performed with the academic based tools to more capable Open Source, highly parallelized simulation tools for efficient operation on NASA HPC assets. Evaluation of the currently implemented (such as mono-disperse and bi-disperse spherical and irregular shape particle constituent model applications) and continuously evolving full-range particle physics models in the GGFS tool is performed by the NASA team to advance application readiness of the simulations. Application testing for complex PSI erosions and cratering scenarios such as the Apollo LM is performed for axi-symmetric and full 3D simulations to aid the tool developers in achieving practical application readiness for NASA projects. Important validation and application testing will further be performed against experimental data generated under the GCD PSI project experimental component.

Peter A Liever