Here, we study orthogonal polynomials with respect to self-similar measures, focusing on the class of infinite Bernoulli convolutions, which are defined by iterated function systems with overlaps, especially those defined by the Pisot, Garsia, and Salem numbers. By using an algorithm of Mantica, we obtain graphs of the coefficients of the 3-term recursion relation defining the orthogonal polynomials. We use these graphs to predict whether the singular infinite Bernoulli convolutions belong to the Nevai class. Based on our numerical results, we conjecture that all infinite Bernoulli convolutions with contraction ratios greater than or equal to 1/2 belong to Nevai’s class, regardless of the probability weights assigned to the self-similar measures.
Sandia's GEMINI-Scout Mine Rescue Robot is an unmanned ground vehicle designed to enter potentially hazardous environments to explore, assess, and evaluate dangerous situations first responders may face when conducting a rescue mission. GEMINI is approximately four feet long and two feet tall, which enables the robot to maneuver through small locations on rough terrains caused by earthquakes, fires, or radiological incidents. GEMINI uses track propulsion to climb stairs, travel through gravel and sand pits, pivot in place, and traverse 45-degree climbs with few problems. Furthermore, the vehicle's dual tracked-chassis design allows it to operate in hostile, dark, muddy, high-temperature, and explosive debris-strewn environments, while maintaining efficient ground mobility. The mobility and modularity of the vehicle allow for easy integration of sensors to conduct gas and temperature sensing and offers pan/tilt, zoom color, and thermal camera video streaming capabilities. The vehicle is also able to carry a payload of about 50 pounds of batteries and can handle an additional 200 pounds of payload, whether for additional diagnostics, supplies, or clothing for those trapped in an effected area. GEMINI is remotely operated through a wireless connection and an onboard computer running a customized embedded control application, which directly communicates to all onboard components except for the audio and video systems. When line of sight is not possible, operators use a shockresistant fiber optic cable to ensure continuous functionality of the vehicle. This allows for direct local control of the vehicle, which streams collected data back to the operator for enhanced situational awareness. In addition, the vehicle incorporates safety features such as explosion proof housing to ensure safe electronic operations in hazardous gas or flooded environments; a four-channel video link and two-way audio to ensure located survivors can communicate with operators; and an MSHA-approved multi-gas sensor to monitor air quality.
Continuing previous efforts to investigate and develop the Unclassified Radioisotope Algorithm, the goal of the FY19-FY20 effort was to develop a prototype detector system which uses the algorithm to confirm warhead attributes related to the presence of either weapons grade plutonium (WGPu) or highly enriched uranium (HEU). The final deliverable is a prototype attribute measurement system built with common, commercially available gamma radiation detector components, capable of confirming the presence of specific, complex radioactive sources of interest, without the collection and storage of gamma energy spectra. This is accomplished by processing each gamma pulse as it is received, applying weight values based on the energy and incrementing or decrementing scalar counters which can be compared with expected values to determine if the measured source is consistent with WGPu or HEU. This report documents the design of the prototype system as well as the development of the algorithm and performance testing results. While the previously conceptualized, simple algorithm resulted in a prohibitive amount of false positives, the goal for a simple attribute measurement system capable of verifying Ba-133 and Ra-226 (weapons grade plutonium and highly enriched uranium surrogate testing sources) at over 95% accuracy with sub 5% false positive rate was demonstrated.
Milestone Description: Enhance Nalu-Wind's actuator disc model through hardening, documenting, stress-testing, verifying, and validating. Existing workflows will be improved by reducing the data output stream, and by making the analysis capabilities more modular and generally better. These model capabilities are needed by other A2e areas, namely Wake Dynamics, AWAKEN, and VV&UQ.
The defect detection capabilities of Power Spectrum Analysis (PSA) [1] have been successfully combined with local laser heating to isolate defective circuitry in a high-speed Si Phase Locked Loop (PLL). The defective operation resulted in missed counts when operating at multi-GHz speeds and elevated temperatures. By monitoring PSA signals at a specific frequency through zero-spanning and scanning the suspect device with a heating laser (1340 nm wavelength), the area(s) causing failure were localized. PSA circumvents the need for a rapid pass/fail detector like that used for Soft Defect Localization (SDL) [2] or Laser-Assisted Defect Analysis (LADA) [3] and converts the at-speed failure to a DC signature. The experimental setup for image acquisition and examples demonstrating utility are described.
The Mobile Radiation Detection and Identification System (MRDIS) is a large mobile scanner that inspects containers in transit from cargo ships for radiological materials. The MRDIS platform operates as a two-part system with one MRDIS using a plastic Polyvinyl Toleune (synthetic polymer) for primary detection and another MRDIS that uses spectroscopic detectors for secondary isotopic identification. MRDIS can operate either independently or as part of a team, depending on the needs of the port. MRDIS is controlled by a human operator, who searches the computer monitor for any traces of radiological materials when the containers pass through the center of the system. Each MRDIS can also feed data into a central system or collect data on its own for additional material analysis. The system integrates radiation detection, radioisotope identification, an optical character recognition system, occupancy/speed sensors, wireless communications, and data processing capabilities to discern what specific radiological materials are of particular interest. In addition, Sandia engineers created a detailed set of requirements for subsequent models, allowing for faster implementation of additional detection systems.
Multi-shaker vibration testing is gaining interest from structural dynamics test engineers as it can provide a much more accurate match to complicated field vibration responses than traditional single-axis shaker tests. However, the force capabilities of the small modal shakers typically used in multi-shaker vibration tests has limited the achievable response levels. To date, most multi-shaker vibration tests have been performed using a variety of standard, commercially-available control systems. While these control systems are adequate for a wide range of multiple-input/multiple-output tests, their control algorithms have not been tailored for the specific problem of multi-shaker vibration tests: efficiently coordinating the various shakers to work together to achieve a desired response. Here, a new input estimation algorithm is developed and demonstrated using simulations and actual test data. This algorithm, dubbed shape-constrained input estimation, is shown to effectively coordinate multiple shakers using a set of constraint vectors based on the deflection shapes of the test structure. This is accomplished by using the singular vector shapes of the system frequency response matrix, which allows the constraint vectors to automatically change as a function of frequency. Simulation and test results indicate a significant reduction in the input forces required to achieve a desired response. Finally, the results indicate that shape-constrained input estimation is an effective method to achieve higher response levels from limited shaker forces which will enable higher level multi-shaker vibration tests to be performed.
The quality of a sonar array's localization capabilities, often expressed as directivity, is limited by the sonar's aperture, that is, the length of the sonar array. Previous attempts to improve directivity, without increasing array size, have been moderately successful. Wave scattering within a nontraditional array, such as an array fabricated from a non-homogeneous material, could provide additional information to the localization calculations and improve array directivity without increasing the size of the array. An investigation of array directivity improvement through wave scattering is performed. This paper modifies existing localization and directivity calculations to consider the scattered waves and uses the derived equations to explain why previous proposed scattering was incapable of increasing directivity. Finally, a scattering relationship capable of enhancing array localization without increasing array size is proposed, and the directivity improvement claims are verified with beamform plot comparisons and directivity index calculations.
With the elimination of underground nuclear testing and declining defense budgets, science-based stockpile stewardship requires increased reliance on high performance modeling and simulation of weapon systems. Today's weapon systems are comprised of various electrical components and systems. As a result, there is a need for tools that will allow the use of massively parallel modeling and simulation techniques on high performance computers in existing and future weapons' electrical systems models. The Xyce Parallel Electronic Simulator is a SPICE (Simulation Program with Integrated Circuit Emphasis)- compatible circuit simulator designed to run on large-scale parallel computing platforms, though it can also execute efficiently on a variety of architectures including single processor workstations. As a mature platform for large-scale parallel circuit simulation, Xyce supports standard capabilities available in commercial simulators, in addition to various devices and models specific to Sandia's needs. Specifically, Xyce aids in the design and verification of electrical and electronic circuits and systems prior to weapons' manufacturing and deployment.
