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544 records · Page 31

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b , where A is an m by x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as 4x(sub 1) + 6x(sub 2) + 5x (sub 3) = 10, where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or a minimum norm solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗

Benchmarking Microscale Ductility Measurements (Final Report of the Project DE-NE0008799)

Conventional macroscale experimentation is generally considered to be straightforward with few limitations. Conversely, micro/nanoscale experimentation presents numerous challenges in loading device design, sample preparation and handling, as well as accurate understanding of grain size and local texture effects on recorded measurements. Despite these challenges, nanopillar compression, MEMs based micro-tension, and nanoindentation approaches have been able to provide fundamental contributions to the understanding of material behavior at small lengthscales. However, the overarching shortcoming of these micro/nanoscale experimentation approaches, is the inability to directly translate measurements evaluated at the nm and µm length scales (e.g., hardness) to macroscale tensile material behavior (i.e., elastic modulus, yield strength, and ductility). The objectives of the proposed study are, 1) to establish best practices for obtaining tensile microscale ductility measurements, and 2) to validate methodologies to for comparing microscale ductility measurements to macroscale ductility measurements. In order to achieve these objectives, a multi-lengthscale, multi-temperature testing protocol and simulation framework are executed first on copper as a model material to validate the following approach, and second on reactor grade Zircaloy-2. Experiments are conducted on specimens extracted from the same test piece to ensure nominally identical grain size and texture from specimens to specimen. Motivated by the need to isolate the contribution of size-effects on obtained mechanical property measurements, specimens are manufactured with thicknesses at the micro- (1-10 µm), meso- (10-100's µm), and macroscales (sub-sized ASTM E8). In-situ full-field deformation techniques (scanning electron microscopy (SEM) grid methods and optical DIC) are incorporated into testing at each specimen length-scale to capture plasticity localization and evolution. Experimental testing for all specimens is conducted at both room temperature and elevated temperatures to probe the role of thermal activation on plastic deformation accommodation processes. Simulation efforts focus on examining the mechanical behavior of microscale specimens using a finite element approach with explicitly resolved grain morphologies, and an embedded crystal plasticity model. The cost-efficient implementation method allows for the modeling of a statistically significant number of both real (i.e., digital twin) and generated microstructures to obtain an understanding of the interrelationships between specimen microstructure and geometric variables (grain size, texture, specimen geometry, etc.) on microscale mechanical behavior.

36 MATERIALS SCIENCE↗

Electrodynamic Dust Shield (EDS) Preparation for MISSE-11 Launch

The dusty surfaces of the Moon, Mars, and various asteroids present a significant challenge to NASA’s manned and unmanned space exploration efforts. The fine, electrostatically charged dust is difficult to remove and has resulted in vision obscuration, false instrument readings, contamination, elevated temperatures, performance reduction, and equipment failure. To alleviate these problems, NASA KSC’s Electrostatics and Surface Physics Laboratory (ESPL) is developing active dust mitigation systems for solar system exploration and in situ resource utilization (ISRU). Part of KSC’s Swamp Works system, the lab emphasizes fast-paced, hands-on, cost-effective, and collaborative innovation. The Electrodynamic Dust Shield (EDS) is an ESPL technology being developed to prevent dust accumulation on space components. It consists of a dielectric substrate embedded with parallel electrodes which, when applied with high voltage out-of-phase waveforms, produce a traveling electric field wave that scatters dust particles from its surface via dielectrophoretic and electrostatic forces. The EDS is currently fully functional and has been tested for scalability and endurance in reduced gravity/pressure flight. Next, it will be part of the May 2019 Materials International Space Station Experiment-11 (MISSE-11) payload, which will test small shield samples for performance durability with exposure to the harsh space environment. The summer objective was to test EDS functionality before active and passive dust shield samples launch on MISSE-11, in order to screen for good flight/control samples as well as to compare pre-flight and post-flight clearing efficiencies. I imaged glass and Kapton shields of 2-phase and 3-phase electrode configurations with the Keyence VHX-5000 digital microscope to check for damage before and after all testing for a qualitative pre-flight baseline; helped with vacuum testing of high-voltage shield breakdown; assembled shields and wires using Electrobond 004 silver epoxy; and helped with vacuum and cryogenic dust clearance testing of assembled EDS systems. I learned CAD (computer-aided design) and 3D printing skills to create parts for a shaker table/motor assembly, which will allow for repeatable experiments by evening out EDS dust distribution in a consistent manner prior to dust scattering testing. I will also be improving the interfacing with Alpha Space’s prototype Data Communications Unit (DCU), a payload component to control power to the EDS and store data, by mapping the DCU structure upon power-up and writing shell scripts to improve various processes. Finally, I also CADed and 3D-printed plastic supports for three different geometries of the Electrostatic Precipitator (ESP), a project that aims to use high voltage electrodes to charge and filter out dust from the Martian atmosphere drawn for ISRU devices. This work on dust mitigation technologies will help to support future robotic and human space exploration missions, including NASA’s Journey to Mars; the EDS has especially significant applications to spacecraft solar panels, thermal radiators, viewports, and astronaut visors. This opportunity has also allowed me to become more familiar with various lab equipment and hardware testing, develop key modeling skills in SolidWorks, explore past and present components critical to America’s space program, work with inspiring peers and mentors, and ascertain my dream of working permanently for NASA.

space↗

PCB-on-DBC GaN Power Module Design with High-Density Integration and Double-Sided Cooling

Lateral gallium nitride (GaN) high-electron-mobility transistors (HEMTs) present better electrical characteristics compared to silicon or silicon carbide devices such as high switching speed and low gate charge, but also present additional challenges on the module design. Here, this paper discusses a high-density GaN power module with double-sided cooling, low inductance, on-package decoupling capacitors, and integrated gate drivers. The GaN dies as well as the gate drive are sandwiched between the printed circuit board (PCB) and direct bonded copper (DBC) substrate to achieve compact loop and double-sided cooling effect. Design considerations and thermal performance are analyzed. A module assembly procedure is presented utilizing the layer-by-layer attachment process. Finally, a 2.7 cm x 1.8 cm half-bridge GaN power module is fabricated and tested, achieving a low power-loop inductance of 1.03 nH, and the overshoot voltage of the switching waveform is less than 5% under a 400-V/25-A double-pulse test. The thermal resistance is 0.32 K/W, verified by simulation and experimental results. The design and assembly process can be generalized and applied to high power applications to achieve high power density and high performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗