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At least 145 records · Page 8

Symmetry structure of a Riccati equation appearing in penetration mechanics

In the design of projectile penetration experiments a matter of considerable interest is scaling: that is, the potential relevance of small-scale experiments to their full-scale counterparts, in a manner analogous to that most often encountered in the context of fluid mechanics. From the theoretical standpoint, phenomena associated with scaling and scalability can be assessed using the well-established tools of dimensional analysis and the Buckingham-Pi Theorem. However, the familiar precepts of dimensional analysis are themselves a specific manifestation of the broader group invariance properties or symmetries of a mathematical model. Here, this work explores these notions – that is, dimensional analysis, the conditions for realizing complete similarity, and any additional symmetry structures – in the context of a Riccati differential equation appearing in the context of penetration mechanics. The aim of the investigation is twofold: 1) to complement existing empirical considerations with a concrete theoretical basis, and 2) to provide a deeper theoretical understanding of the projectile penetration model and its many implications.

97 MATHEMATICS AND COMPUTING↗

Grid ancillary services using electrolyzer-Based power-to-Gas systems with increasing renewable penetration

Increasing penetrations of renewable-based generation have led to a decrease in the bulk power system inertia and an increase in intermittency and uncertainty in generation. Energy storage is considered to be an important factor to help manage renewable energy generation at greater penetrations. Hydrogen is a viable long-term storage alternative. This paper analyzes and presents use cases for leveraging electrolyzer-based power-to-gas systems for electric grid support. The paper also discusses some grid services that may favor the use of hydrogen-based storage over other forms such as battery energy storage. Real-time controls are developed, implemented and demonstrated using a power-hardware-in-the-loop(PHIL) setup with a 225-kW proton-exchange-membrane electrolyzer stack. These controls demonstrate frequency and voltage support for the grid for different levels of renewable penetration (0%, 25%, and 50%). A comparison of the results shows the changes in respective frequencies and voltages as seen as different buses as a result of support from the electrolyzers and notes the impact on hydrogen production as a result of grid support. Finally, the paper discusses the practical nuances of implementing the tests with physical hardware, such as inverter/electrolyzer efficiency, as well as the related constraints and opportunities.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Impact of Penetrating Kelvin Waves on MJO Rainfall Propagation Through Deep Convection Modulation

The Madden‐Julian Oscillation (MJO) is a dominant intraseasonal oscillation in the tropics. As MJOs propagate over the Indian Ocean, some of them can be penetrated by fast‐moving equatorial Kelvin waves originating to the west of the MJOs. Through a series of sensitivity experiments, we demonstrate that these penetrating Kelvin waves can modulate the eastward propagation speed of MJO rainfall. Deep convection in the western MJO rainfall envelope initiates more frequently and produces greater lifetime rainfall when a convectively active Kelvin phase is present, while the opposite occurs during a convectively suppressed Kelvin phase. This alteration in deep convection activity can lead to notable changes in the propagation of the large‐scale MJO rainfall envelope. The modulation of deep convection lifetime rainfall by penetrating Kelvin waves primarily occurs through their impact on deep convection rainfall area, which is closely related to the variations in lower‐tropospheric moisture induced by the Kelvin waves.

Chen, Xingchao [Pennsylvania State Univ., Universi↗

Multiseriate cortical sclerenchyma enhance root penetration in compacted soils

Mechanical impedance limits soil exploration and resource capture by plant roots. We examine the role of root anatomy in regulating plant adaptation to mechanical impedance and identify a root anatomical phene in maize (Zea mays) and wheat (Triticum aestivum) associated with penetration of hard soil: Multiseriate cortical sclerenchyma (MCS). We characterize this trait and evaluate the utility of MCS for root penetration in compacted soils. Roots with MCS had a greater cell wall-to-lumen ratio and a distinct UV emission spectrum in outer cortical cells. Genome-wide association mapping revealed that MCS is heritable and genetically controlled. We identified a candidate gene associated with MCS. Across all root classes and nodal positions, maize genotypes with MCS had 13% greater root lignin concentration compared to genotypes without MCS. Genotypes without MCS formed MCS upon exogenous ethylene exposure. Genotypes with MCS had greater lignin concentration and bending strength at the root tip. In controlled environments, MCS in maize and wheat was associated improved root tensile strength and increased penetration ability in compacted soils. Maize genotypes with MCS had root systems with 22% greater depth and 49% greater shoot biomass in compacted soils in the field compared to lines without MCS. Of the lines we assessed, MCS was present in 30 to 50% of modern maize, wheat, and barley cultivars but was absent in teosinte and wild and landrace accessions of wheat and barley. MCS merits investigation as a trait for improving plant performance in maize, wheat, and other grasses under edaphic stress.

54 ENVIRONMENTAL SCIENCES↗

A scaling law of the neutral penetration length and Balmer- α wing shape in high-temperature plasmas

Hydrogen atoms penetrating deep inside high-temperature magnetically confined plasmas by repetitive charge-exchange collisions result in a particle source of the plasma, which affects the plasma transport significantly. In this paper, we present an approximate solution of the fluid equations for neutral transport and an analytical representation of the neutral penetration length, in a simplified plasma geometry. This analysis predicts a power-law decay in the Balmer-α line wings which reflects the velocity distribution of the neutral atoms, with the power-law exponent analytically represented as well. These scaling laws are compared with a simple Monte–Carlo simulation and spectroscopic observations of Large Helical Device plasmas. Since the Balmer-α line wings are experimentally accessible, our formulation opens the possibility to quickly estimate the neutral penetration length from spectroscopic observations.

neutral opacity↗

Campbell penetration depth in low carrier density superconductor YPtBi

Magnetic penetration depth, λ m , was measured as a function of temperature and magnetic field in single crystals of low carrier density superconductor YPtBi by using a tunnel-diode oscillator technique. Measurements in zero DC magnetic field yield London penetration depth, λ L ( T ) , but in the applied field the signal includes the Campbell penetration depth, λ C ( T ) , which is the characteristic length of the attenuation of small excitation field, H AC , into the Abrikosov vortex lattice due to its elasticity. Whereas the magnetic field dependent λ C exhibit λ C ~ B p with p = 1 / 2 in most of the conventional and unconventional superconductors, we found that p ≈ 0.23 << 1 / 2 in YPtBi due to rapid suppression of the pinning strength. From the measured λ C ( T , H ) , the critical current density is j c ≈ 40 A / cm 2 at 75 mK. We find that this is orders of magnitude lower than that of conventional superconductors of comparable T c .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Discrete and Integrated Solutions for Hybrid PV Plants Without Momentary Cessation in Low SCR and High Penetration PE Grids

With the increased penetration of power electronic (PE) based loads and sources, advanced solutions may be required for the enhancement of grid stability in regions with low short circuit ratio (SCR) and high penetration PE grids. The requirement of advanced solutions arises from the gradual paradigm shift of the electric grid from the traditional electric machine dominant system to a high penetration of PE-based system. One of the major challenges with such systems in recent times is the momentary cessation during alternating current (ac) grid transmission faults. During momentary cessation, PE-based resources cease to operate, thus creating probable reliability challenges for the grid. In this paper, potential feasible options to provide continuity of operation during such scenarios are presented. The options are considered through identifying upgrades in existing and upcoming discrete development of photovoltaic (PV) and energy storage systems (ESS) termed as discrete hybrid PV plants. Additionally, an advanced concept of integrated development of PV and ESS connecting to ac transmission grid links called multi-port autonomous reconfigurable solar power plant (MARS) is evaluated. The developed new solutions are evaluated for different grid use cases and scenarios in PSCAD.

Marthi, Phani Ratna Vanamali↗

Clustering Interval Load with Weather to Create Scenarios of Behind-the-Meter Solar Penetration

Forecasting load at the feeder level has become increasingly challenging with the penetration of behind-the-meter solar, as this self-generation is only visible to the utility as aggregated net-load. This work proposes a methodology for creation of scenarios of solar penetration at the feeder level for use by forecasters to test the robustness of their algorithm to progressively higher penetrations of solar. The algorithm draws on publicly available observations of weather condition (e.g., rainy/cloudy/fair) for use as proxies to sky clearness. These observations are used to mask and weight the interval deviations of similar native usage profiles from which average interval usage is calculated and subsequently added to interval net generation to reconstruct interval total generation. This approach improves the estimate of annual energy generation by 23%; where the net generation signal currently reflects 52% of total annual gener- ation, now 75% is captured. This methodology for creation of forecast testing scenarios is data driven and extensible to service territories which lack information on irradiance measurements and geocoordinates.

solar, load↗

Utilities Perspective on Protection Challenges with High IBR Penetration

Utilities have seen rapid increase in Solar, Wind, and Battery Energy Storage Resources that interconnect to their electric system through Inverters. Inverter-Based Resources (IBRs) have fault current characteristics that are unlike the fault current response of traditional rotating-machine-based generators, which is well known and repeatable. IBR’s non-traditional fault current behavior is due to the IBR control scheme, which is configured to provide a clean AC output but also protect the inverter’s sensitive power electronics devices from damage, one source of which is overcurrent. This results in low fault current magnitude, low or no negative sequence current injection, the variability of sequence component currents, the variability of voltage with respect to current angles, and the lack of inertia. The control scheme also results in a fault current response that can vary between manufactures and between models of the same manufacturer. High penetration of IBRs can adversely affect the protection schemes applied in areas with high penetration of IBRs. With the proliferation of IBRs, utilities are finding out that conventional protection schemes are not adequately equipped to protect the electric systems. This is mainly because the existing protection elements and practices have been designed based on the fault current response of conventional rotating machines. In several cases, the available literature does not provide any clear solution for the issues when the protection scheme does not operate properly near IBRs. This presentation identifies various protection challenges due to IBRs that industry is facing, from the utility perspective. Instead of facing on one issue, we are looking broadly on all the challenges that system protection has experienced with high penetration of IBRs. Based on the IBR response from various utilities during real fault events and gathering perspective from different utility SMEs via questionnaire, the presentation summarizes on gathered data and internal experiences.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Adaptive Protection and Validated Models to Enable Deployment of High Penetrations of Solar PV (PV-MOD)

The availability and validation of various PV models in commercial tools differ, with some models not yet thoroughly validated for advanced inverter functionalities and reliable performance under weak system conditions. Many existing models do not fully incorporate new inverter control functions, which can affect system stability. The increasing deployment of solar PV and other inverter-based resources (IBRs), including distributed energy resources (DERs), is influencing the reliable operation of protection schemes in distribution systems and microgrids. Emerging adaptive protection schemes (APS) offer new opportunities for protecting these systems during varying configurations and DER operating conditions, though their demonstration and validation remain limited. Adaptive protection schemes face similar challenges, as they are typically designed for specific configurations. There is a growing need for tools and methodologies to streamline the deployment of adaptive protection for safe and reliable DER integration. The project main objective was to develop and validate high-fidelity generic models of solar PV facilities for stability, protection, EMT, and QSTS analyses. This objective was achieved, and these models can now be integrated into commercial software tools, enabling utilities, vendors, and developers to study high-penetration PV systems more confidently. The project also demonstrated advanced applications of these models, including the design and deployment of adaptive protection schemes in high-penetration field applications and microgrids, supporting grid safety and reliability. Several milestones were reached by the end of the project. A sophisticated inverter test plan was developed, and inverters representative of the North American marketplace were selected. EPRI and NREL tested various inverters, conforming to IEEE standards. Improvements were made to existing generic models of IBR units, IBR plants, and aggregated feeders for various analyses. The first generic electromagnetic transient (EMT) model for a solar PV plant was developed, conforming to IEEE Std 2800™-2022 and validated against laboratory measurements of a 2.2 MVA large-scale battery energy storage system (BESS) inverter. That model was then used to produce reference responses illustrating examples of validated and verified IBR plant models that pass or fail tests for technical minimum capability and performance as specified in the IEEE standard. The developed, tested, and validated generic models can be used for transmission planning, stability assessments, expansion planning, and evaluating potential future IBR interconnection requirements. They can also support interconnection screens and conformity assessments of IBR plants, including solar PV. The project significantly contributed to the ongoing standardization and model-based representation and verification of IBR responses. The project further addressed challenges of common distribution protection schemes with increasing deployment of DER by developing, validating, and demonstrating adaptive protection schemes (APS) that can improve the reliable and safe integration of DER into distribution systems. New APS were designed using improved DER models for three common distribution systems: a radial feeder, a meshed network, and a microgrid. Modeling and hardware-in-the-loop (HIL) testing of the APS were conducted, successfully showing their effectiveness and selectivity. Proof-of-concept field demonstration was achieved for two APS, i.e., one on a radial feeder and another one in a microgrid. Field demonstration could not be achieved for the APS on a meshed network, primarily due apprehension of one utility partner and also due to limited access to the protective algorithms in the network protectors. Guidelines developed from the lessons learned in the project lay out the general process followed in the design, installation, and commissioning of APS for various distribution systems. Distribution utility partners’ apprehension about field demonstration of the new APS were addressed—with varying success—by taking a stepped risk-management approach of modeling of a wide range of sensitivities first, performing in-depth proof-of-concept testing in the laboratory including HIL next, and finally deliberately implementing and commissioning the actual protection equipment and algorithms into parts of—or in parallel operation to—the three real distribution systems. Future work should include pilot projects that further show the acceptable performance of the developed APS before these schemes be rolled out more widely. Inclusion of both utility and original equipment manufacturers (OEMs) in future projects could increase chances of successful field demonstration. Despite challenges in achieving the field demonstration goal of the project for all three APS, the research significantly contributed to the innovation of adaptive protection solutions for scalable and reliable DER integration into distribution systems. This project significantly enhances the understanding of the impact of using appropriate inverter models on distribution and transmission (T&D) systems. By addressing the limitations of existing generic models, the project introduces high-fidelity models for stability, protection, electromagnetic transient (EMT), and quasi-static time series (QSTS) analyses. These models, integrated into commercial software tools, enable utilities, vendors, and developers to confidently study high-penetration PV systems. The project also demonstrates advanced applications, including adaptive protection schemes (APS) for distribution systems and microgrids, ensuring grid safety and reliability. The technical effectiveness and economic feasibility of the methods are evident through the development and validation of sophisticated inverter test plans and the selection of representative inverters. Testing by EPRI and NREL on retail, commercial, and utility-scale inverters, conforming to IEEE standards, underscores the robustness of the models. Improvements to existing generic models for various analyses further enhance their validity and applicability. The project also identifies gaps in common distribution protection schemes and designed new APS using improved DER models, demonstrating their effectiveness through modeling and hardware-in-the-loop (HIL) testing. The project’s benefits to the public are manifold. By advancing the standardization and model-based representation of IBR response, it supports transmission planning, stability assessments, and future IBR interconnection requirements. The generic models can facilitate better communication between transmission planners and developers, supporting expected IBR plant capability and performance. Additionally, the development of APS for radial feeders, meshed networks, and microgrids supports the integration of distributed energy resources (DERs) into distribution systems, enhancing grid reliability and safety. The project’s emphasis on thorough testing and simplicity in design ensures practical and scalable solutions for DER integration.

14 SOLAR ENERGY↗

Utility Perspective on Protection Challenges with High Penetration of IBRs

Utilities have seen rapid increase in Solar, Wind, and Battery Energy Storage Resources that interconnect to their electric system through Inverters. Inverter-Based Resources (IBRs) have fault current characteristics that are unlike the fault current response of traditional rotating-machine-based generators, which is well known and repeatable. IBR’s non-traditional fault current behavior is due to the IBR control scheme, which is configured to provide a clean AC output but also protect the inverter’s sensitive power electronics devices from damage, one source of which is overcurrent. This results in low fault current magnitude, low or no negative sequence current injection, the variability of sequence component currents, the variability of voltage with respect to current angles, and the lack of inertia. The control scheme also results in a fault current response that can vary between manufactures and between models of the same manufacturer. High penetration of IBRs can adversely affect the protection schemes applied in areas with high penetration of IBRs. With the proliferation of IBRs, utilities are finding out that conventional protection schemes are not adequately equipped to protect the electric systems. This is mainly because the existing protection elements and practices have been designed based on the fault current response of conventional rotating machines. In several cases, the available literature does not provide any clear solution for the issues when the protection scheme does not operate properly near IBRs. This report / presentation identifies various protection challenges due to IBRs that industry is facing, from the utility perspective. Instead of facing on one issue, this report looks broadly on all the challenges that system protection has experienced with high penetration of IBRs. Based on the IBR response from various utilities during real fault events and gathering perspective from different utility SMEs via questionnaire, the report summarizes on gathered data and internal experiences.

14 SOLAR ENERGY↗

SMR Containment Cable and Electrical Penetration Assembly System

GAIN Project CRADA Number NFE-21-08839, entitled “SMR Containment Cable and EPA System” was initiated by the partnership of Oak Ridge National Laboratory (ORNL) and Engineered Solutions Group (ESG) to test an ESG-designed Electrical Penetration Assembly and Containment Cabling System Qualified for not only SMR technologies, but also Advanced Reactors design. An Electrical Penetration Assembly (EPA) is a component used to allow electrical power and signal conductors as well as optical fiber through the nuclear reactor’s containment structure while maintaining a pressure barrier. The EPA ensures the containment's integrity both during the normal operation and also accident conditions by providing a sealed passage for power and signals. This project was undertaken to fill the equipment gap of EPA and Cabling Systems that require much more severe environmental requirements than legacy plant applications present due to their smaller containment volumes that result in high energy densities compared to legacy designs. This high energy density results in severe accident environments and also more severe normal operating conditions.This document describes cost effective approaches to qualify a unique EPA for Small Modular Reactor (SMR) technologies as legacy LWR EPA technologies will likely have inherent material performance insufficiencies. The DBA profiles for SMRs (and some Advanced Reactor Technologies) are more severe than the legacy qualification requirements making the design of the qualification testing system challenging as the temperatures and pressures can approach the limits permitted by ASME Pressure Vessel Code, as well as accident temperatures exceeding the capability of polymeric gaskets and dielectrics. Small Modular Reactors are designed to have, as the name suggests, modularity which implies sized for factory fabrication and subsequent assembly at the power plant site. SMR containment is much smaller than a legacy Light Water Reactor containment. The containment walls are likely to be comprised of stainless steel. Qualifying Electrical Penetration Assemblies (EPAs) through these steel vessels are of interest in this work. Methods are presented here that discuss critical safety and cost effectiveness for these SMR EPA’s test systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Engineered Solutions Group's SMR Containment Cable and Electrical Penetration Assembly System

GAIN Project CRADA Number NFE-21-08839, entitled “SMR Containment Cable and EPA System” was initiated by the partnership of Oak Ridge National Laboratory (ORNL) and Engineered Solutions Group (ESG) to test an ESG-designed Electrical Penetration Assembly and Containment Cabling System Qualified for not only legacy LWR designs, but also Small Modular Reactors designs currently being designed by several different suppliers. This project was undertaken to fill the equipment gap of EPA and Cabling Systems that require much more severe environmental requirements than legacy plant applications present due to their smaller containment volumes that result in high energy densities compared to legacy designs. This high energy density results in severe accident environments and more severe normal operating conditions as well. We developed two approaches to qualify Electrical Penetration Assembly (EPA) and Containment Cabling Systems for SMRs and Advanced Reactors. We take into consideration the more severe environmental parameters found with SMR designs. The system will need to meet a qualification test program addressing wear/cyclic aging, potential radiation exposure, thermal aging, vibration aging, thermal cycling, seismic qualification, electrical fault testing (per IEEE 317) and accident simulation. The equipment must meet the requirements of 10CFR50.49, GDC 50 in 10CFR50 Appendix A, and 10CFR50 Appendix J. NRC Regulatory Guides (RGs) identify an acceptable way of meeting regulatory requirements. RGs frequently endorse a standard for meeting these requirements. Specific to this review, equipment would be qualified in accordance with the following IEEE Standards. • IEEE 317-2013 (Electrical Penetration Assemblies), which is endorsed by RG 1.63, Rev. 3, • IEEE 323-2003 and the more current IEC/IEEE 60780-323 (Environmental Qualification of 1E Equipment) which is endorsed by RG 1.89. IEEE 323-2003 is endorsed by RG 1.209, • IEEE 344-2020 (Seismic Qualification. The 2013 version endorsed by RG 1.100, Rev. 4, with exceptions), • IEEE 383-2015 (Electrical Cables) (which is endorsed by RG 1.189 Rev. 4 and the -2003 version endorsed by RG 1.211 rev. 0), • IEEE 572-2019 (Electrical Connectors and Assemblies), which is endorsed by 1.156 Rev 1, and • [IEEE 1202 (endorsed by RG 1.189) would normally be applicable but the advanced cable designs are impervious to this cable flame test.] The primary goal of such a program is to provide an EPA design that can meet the qualification requirements for all legacy light water reactor plants currently operating as well as new plant designs including light water Small Modular Reactors. Thus, these requirements are applicable to plants licensed under 10CFR50 and 10CFR52. Other reactor designs may be evaluated, and this test system and qualification method applied to those applications if the requirements would satisfy the requirements of the intended plant. A secondary benefit of this work is to document some of the history and background in these requirements as there have been recent delays in an SMR licensing process due to NRC Requests for Additional Information in this subject matter area.

42 ENGINEERING↗

VRN3P: Variational Recurrent Neural Network Based Net-Load Prediction under High Solar Penetration

This is the final technical report for the SETO-funded VRN3P project (PNNL# 76914). The goal of this project, led by Pacific Northwest National Laboratory (PNNL), in collaboration with Lawrence Livermore National Laboratory (LLNL) and Portland General Electric (PGE), was to develop and validate a deep variational recurrent neural network-based net-load prediction (VRN3P) framework for probabilistic time-series forecasting of day-ahead net-load under high solar penetration scenarios. The project team reports successful design of a novel probabilistic net-load forecasting architecture, comprising of a variational autoencoder and a recurrent neural network, which demonstrates 30% improvement in forecast performance, 60% improvement in training time, and consumes 44% less memory, when compared with conventional baseline models. The team tested the VRN3P model performance on GridLAB-D test-cases representing varying BTM solar penetration levels of 20%, 30%, and 50%, with integrated time-series net-load profiles provided by the utility partner (PGE). The VRN3P model demonstrate <2% hourly MAPE (averaged over the year) for day- ahead net-load forecast on the test scenario with 20% BTM solar. Transfer learning extension of the VRN3P model has demonstrated 8.33× speed-up in training, while still achieving acceptable forecast performance of 2.24% hourly MAPE on the 30% BTM solar penetration test-scenario. A preliminary version of the VRN3P GridAPPS-D™has been developed, along with a web-based interactive user-interface (named ‘Forte’) which has made available on GitHub for public use.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Dispersion Caused by the Penetration Effect in X-ray Compressors

Chirped X-ray pulse compression is a promising approach for generating ultra-short X-ray free electron laser (XFEL) pulses. The design of X-ray pulse compressors requires the careful control of group delay dispersion (GDD), which plays a critical role in achieving optimal compression. However, the penetration dispersion of crystals and multilayers can induce an extra GDD, which may result in over-compression or under-compression. In this study, we investigate the penetration dispersion of crystals and multilayers theoretically and numerically. Our results indicate that the extra GDD induced by the penetration effect increases as the bandwidth of the rocking curve decreases. Moreover, the extra GDD is nonlinear and can be mitigated by optimizing the configuration of X-ray pulse compressors. This work provides insights into the dispersion compensation and configuration optimization of X-ray pulse compressors, which are essential for generating ultra-short XFEL pulses.

47 OTHER INSTRUMENTATION↗

Small Penetrator Instrument Concept for the Advancement of Lunar Surface Science

Fundamental scientific objectives concerning the surface and subsurface material and dynamics of the Moon are the drivers for the use and advancement of penetrators, which emplace a suite of scientific instruments by impact into a planetary surface, typically at velocities of dozens to hundreds of meters per second. Small lunar penetrators are poised to become a valuable new tool for lunar science and exploration during the next decade. These low-cost ballistic probes can be deployed in large numbers from orbit, or from descending robotic or crewed vehicles, in order to explore and characterize the diversity of extreme lunar shallow subsurface environments. In this paper, we describe the general overview of penetrator objectives, potential instrumentation, and how these would benefit the advancement of lunar science at various extreme environments.

47 OTHER INSTRUMENTATION↗

Nondestructive assessment of penetration of electron-beam welds

Empirical method correlates penetration of an electron-beam weld with external measurements of the weld. Empirical polygon accurately confirms full-penetration welds while a second, larger polygon provides for penetration of welds near the tip.

Harmon, T. J.↗

Phenomena after meteoroid penetration of a bumper plate

The analysis of hypervelocity impact of particles on a detector in space, with flow and shock penetration through fluid, plastic, and elastic zones was studied. The original paper and computer program on this topic is presented. Improvements in the program for the study of the formation of a cone of debris are discussed. The truncated apex of the cone is at the hole formed by the penetration of an initially spherical rock through a thin plate. A solution for the penetration of the thin plate was sought.

Todd, F. C.↗