Publications

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This paper describes a process for forming a buried field shield in GaN by an etch-and-regrowth process, which is intended to protect the gate dielectric from high fields in the blocking state. GaN trench MOSFETs made at Sandia serve as the baseline to show the limitations in making a trench gated device without a method to protect the gate dielectric. Device data coupled with simulations show device failure at 30% of theoretical breakdown for devices made without a field shield. Implementation of a field shield reduces the simulated electric field in the dielectric to below 4 MV/cm at breakdown, which eliminates the requirement to derate the device in order to protect the dielectric. For realistic lithography tolerances, however, a shield-to-channel distance of 0.4 μm limits the field in the gate dielectric to 5 MV/cm and requires a small margin of device derating to safeguard a long-term reliability and lifetime of the dielectric.

Decarbonization efforts highlight hydrogen as an attractive alternative to fossil fuels, but its tendency to embrittle structural metals demands careful consideration when designing hydrogen infrastructure. Moreover, the mechanisms by which hydrogen degrades these materials are still being elucidated. The current work develops new computational tools to quantify the different contributions of hydrogen to the energy barrier of cross-slip, a key deformation mechanism. Novel features are implemented to a line tension model, which include the use of non-singular dislocation interactions, character-dependent dislocation energies and simulations of the constriction configurations. A new molecular dynamics technique is developed to calculate the interaction energy between the partials of a dissociated dislocation via fixing the centers of mass of the regions below and above the Shockley partials and performing time-averaged calculations. Hydrogen is found to impact the stacking fault width of dislocations in different ways depending on their characters: it decreases for dislocations with a character θ > 30°, remains unchanged for θ = 30° and increases for θ < 30°. The latter regime is a newly identified mechanism by which hydrogen inhibits cross-slip. Moreover, formation of nano-hydrides is predicted to occur around screw dislocations for high hydrogen concentrations, a phenomenon previously identified only in dislocations with an edge component. If nano-hydrides develop, their influence extending the equilibrium stacking fault width and increasing both the constriction and cross-slip energy barriers dominate over all other hydrogen contributions. The theory and tools developed will pave the way towards a comprehensive understanding of hydrogen-dislocation interactions in structural metals.

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This report documents the generation of a mechanism to predict the inclusion of carbon soot particles in a high explosive flow. The mechanism includes gasification and oxidation reactions, formation, sublimation, radiation, and agglomeration. Each part of the mechanism is derived from properties in the literature. The influence of each part of the mechanism is explored using simple, example simulations consisting of a 12 mm diameter 2,4,6-Trinitrotoluene charge detonated in ambient air. The mechanism has not been quantitatively compared to experiments. Additional efforts will be required to tune and validate it, which will require continued advancements in experimental diagnostics and simulation techniques.

This report summarizes FY23 activities to improve mechanistic source term modeling for MSR concepts. Relevant MELCOR capability enhancements made during FY23 are summarized including development of a flexible python-based EOS generator (MELEOS), porous domain modeling capabilities for validation applications, and development of a MELCOR model for the LSTL facility in anticipation of upcoming molten salt experiments.

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This report describes a Late-Start LDRD project on a compact neutron time-of-flight (nTOF) diagnostic, based on the Ultra-Fast Pixel Array Camera (UPAC) platform. By leveraging advancements in microelectronics, the UPAC nTOF is designed to address existing challenges of current nTOFs at the Z-machine that rely on large scintillators and photomultiplier tubes using bulky, discrete digitizing units hindering scalability with signal routing presenting an additional challenge. The report describes the UPAC diagnostic platform, outlines the calibration of the diagnostic and the latest results of fielding the UPAC as a ride-a-long diagnostic on the Magnetized liner inertial fusion (MagLIF) campaigns at the Z-machine supported by the Late-Start LDRD, and finally discusses conclusions and proposed future work.

Superconducting qubits have reached the point where system designers are worried about the heat that control wiring brings into the cryostat. To continue scaling cryogenic quantum systems, control solutions that work inside the cold space must be explored. One possibility is to use control electronics that is native to superconductivity, so called single-flux-quantum (SFQ) circuitry, to form an interface between qubits and whatever other electronics is needed to control eventual quantum systems. To begin exploring the utility of SFQ as control circuitry, we performed modeling and experiments on qubit readout using ballistic fluxons which are SFQ in the limit of ballistic fluxon transport. Our modeling results show that a flavor of qubit, the fluxonium, can be read out using ballistic fluxons. We designed test samples to prove some of the key concepts needed for such a readout but were ultimately unable to getting a working demonstration. The lack of testing success was due to challenges in fabrication and running short of time to perform testing rather than a fundamental problem with our analysis.

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The ion velocity distribution functions of thermonuclear plasmas generated by spherical laser direct drive implosions are studied using deuterium-tritium (DT) and deuterium-deuterium (DD) fusion neutron energy spectrum measurements. A hydrodynamic Maxwellian plasma model accurately describes measurements made from lower temperature (<10 keV), hydrodynamiclike plasmas, but is insufficient to describe measurements made from higher temperature more kineticlike plasmas. The high temperature measurements are more consistent with Vlasov-Fokker-Planck (VFP) simulation results which predict the presence of a bimodal plasma ion velocity distribution near peak neutron production. These measurements provide direct experimental evidence of non-Maxwellian ion velocity distributions in spherical shock driven implosions and provide useful data for benchmarking kinetic VFP simulations.

Frontal polymerization involves the propagation of a thermally driven polymerization wave through a monomer solution to rapidly generate high-performance polymeric materials with little energy input. The balance between latent catalyst activation and sufficient reactivity to sustain a front can be difficult to achieve and often results in systems with poor storage lives. This is of particular concern for frontal ring-opening metathesis polymerization (FROMP) where gelation occurs within a single day of resin preparation due to the highly reactive nature of Grubbs-type catalysts. In this report we demonstrate the use of encapsulated catalysts to provide remarkable latency to frontal polymerization systems, specifically using the highly active dicyclopentadiene monomer system. Negligible differences were observed in the frontal velocities or thermomechanical properties of the resulting polymeric materials. FROMP systems with encapsulated catalyst particles are shown with storage lives exceeding 12 months and front rates that increase over a well-characterized 2 month period. Moreover, the modularity of this encapsulation method is demonstrated by encapsulating a platinum catalyst for the frontal polymerization of silicones by using hydrosilylation chemistry.

In polymer-filled granular composites, damage may develop in mechanical loading prior to material failure. Damage mechanisms such as microcracking or plastic deformation in the binder phase can substantially alter the material's mesostructure. For energetic materials, such as solid propellants and plastic bonded explosives, these mesostructural changes can have far reaching effects including degraded mechanical properties, potentially increased sensitivity to further insults, and changes in expected performance. Unfortunately, predicting damage is nontrivial due to the complex nature of these composites and the entangled interactions between inelastic mechanisms. In this work, we assess the current literature of experimental knowledge, focusing on the pressure-dependent shear response, and propose a simple simulation framework of bonded particles to study four limiting-case material formulations at both meso- and macro-scales. To construct the four cases, we systematically vary the relative interfacial strength between the polymer binder and granular filler phase and also vary the polymer's glass transition temperature relative to operating temperature which determines how much the binder can plastically deform. These simulations identify key trends in global mechanical response, such as the emergence of strain hardening or softening regimes with increasing pressure which qualitatively resemble experimental results. By quantifying the activation of different inelastic mechanisms, such as bonds breaking and plastically straining, we identify when each mechanism becomes relevant and provide insight into potential origins for changes in mechanical responses. The locations of broken bonds are also used to define larger, mesoscopic cracks to test various metrics of damage. We primarily focus on triaxial compression, but also test the opposite case of triaxial extension to highlight the impact of Lode angle on mechanical behavior.

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We demonstrate the discrimination of ground-state hyperfine manifolds of a cesium atom in an optical tweezer using a simple probe beam with Formula Presented% detection fidelity and 0.9(2)% detection-driven loss of bright-state atoms. Our detection infidelity of Formula Presented% is an order of magnitude better than previously published low-loss readout results for alkali-metal atoms in optical tweezers. We achieve these results by identifying and mitigating an extra depumping mechanism due to stimulated Raman transitions induced by trap light in the presence of probe light. In this work, complex optical systems and stringent vacuum pressures are not required, enabling straightforward adoption of our techniques on contemporary experiments.

Scientific software (SciSoft) is complex, often containing a mixture of production capabilities co-mingled with features under active research and development. Furthermore, SciSoft is often developed over decades by non-computer scientists who may not have a strong background in or prioritize software architecture design, testing, and quality (e.g., test coverage). These conditions lead to difficulty in understanding which software components or functions implement what user-facing features and therefore those features’ software quality pedigree. This lack of understanding poses challenges in assessing readiness and credibility of user features, and often relies on a SciSoft subject matter expert’s (SME) laborious investigation and assertion. This final report of a one-year Computing and Information Sciences Lab Directed Research and Development project presents a general framework for modeling SciSoft architecture as a direct relationship between user features and the software components/functions that implement them. Our approach leverages automated labeling of the SciSoft’s regression test suite and employs machine learning algorithms to construct the architecture model. We demonstrate this framework on the Solid Mechanics component of the SIERRA multi-physics engineering analysis suite developed at Sandia National Laboratories.

Distribution system model calibration is a key enabling task for incipient failure identification within the distribution system. This report summarizes the work and publications by Sandia National Laboratories on the GMLC project titled “Incipient Failure Identification for Common Grid Asset Classes”. This project was a joint effort between Sandia National Laboratories, Lawrence Livermore National Laboratory, National Energy Technology Laboratory, and Oak Ridge National Laboratory. The included work covers distribution system topology identification, transformer groupings, phase identification, regulator and tap position estimation, and the open-source release and implementation of the developed algorithms.

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Computational and mathematical models are essential to understanding complex systems and phenomena. However, when developing such models, limited knowledge and/or resources necessitates the use of simplifying assumptions. It is therefore crucial to quantify the impact of such simplifying assumptions on the reliability and accuracy of resulting model predictions. This work develops a first-of-its-kind approach to quantify the impact of physics modeling assumptions on predictions. Here, we leverage the emerging field of model-form uncertainty (MFU) representations, which are parameterized modifications to modeling assumptions, in combination with grouped Sobol’ indices to quantitatively measure an assumption’s importance. Specifically, we compute the grouped Sobol’ index for the MFU representation’s parameters as a single importance measure of the assumption for which the MFU representation characterizes uncertainty. To ensure this approach is robust to the subjective choice of how to parameterize a MFU representation, we establish bounds for the difference between sensitivity results for two different MFU representations based on differences in model prediction statistics. The capabilities associated with this approach are demonstrated on three exemplar problems: an upscaled subsurface contaminant transport problem, ablation modeling for hypersonic flight, and nuclear waste repository modeling. We found that our grouped approach is able to assess the impact of modeling assumptions on predictions and offers computational advantages over classical Sobol’ index computation while providing more interpretable results.

A critical mission need exists to develop new materials that can withstand extreme environments and multiple sequential threats. High entropy materials, those containing 5 or more metals, exhibit many exciting properties which would potentially be useful in such situations. However, a particularly hard challenge in developing new high entropy materials is determining a priori which compositions will form the desired single phase material. The project outlined here combined several modeling and experimental techniques to explore several structure-property-relationships of high entropy ceramics in an effort to better understand the connection between their compositional components, their observed properties, and stability. We have developed novel machine learning algorithms which rapidly predict stable high entropy ceramic compositions, identified the stability interplay between configurational entropy and cation defects, and tested the mechanical stability of high entropy oxides using the unique capabilities at the Dynamic Compression Sector facility and the Saturn accelerator.

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In this report, we document the process related to developing a regional geologic model of a 605 x 1334 km area centered around Utah and encompassing surrounding states. This model is developed to test the effect that composition of a model has on the generation of synthetic data with the intent of using this information to improve upon full waveform moment tensor inversions. We compare observed data from three seismic events and five stations to the synthetic data generated by a preliminary model derived from a geologic framework model (GFM) developed by the USGS. The synthetic data and observed data comparisons indicate that our preliminary model performs well at smaller offset distances in the northern and central sections of the model. However, the southern stations consistently display synthetic data P- and S-wave arrival times that do not match the observed data arrival times, indicating that the velocity structure of the southern part of the model especially is inaccurate.

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The carbon phase diagram is rich with polymorphs which possess very different physical and optical properties ideal for different scientific and engineering applications. An understanding of the dynamically driven phase transitions in carbon is particularly important for applications in inertial confinement fusion, as well as planetary and meteorite impact histories. Experiments on the Z Pulsed Power Facility at Sandia National Laboratories generate dynamically compressed high-pressure states of matter with exceptional uniformity, duration, and size that are ideal for investigations of fundamental material properties. X-ray diffraction (XRD) is an important material physics measurement because it enables direct observation of the strain and compression of the crystal lattice, and it enables the detection and identification of phase transitions. Several unique challenges of dynamic compression experiments on Z prevent using XRD systems typically utilized at other dynamic compression facilities, so novel XRD diagnostics have been designed and implemented. We performed experiments on Z to shock compress carbon (pyrolytic graphite) samples to pressures of 150–320 GPa. The Z-Beamlet Laser generated Mn-Heα (6.2 keV) X-rays to probe the shock-compressed carbon sample, and the new XRD diagnostics measured changes in the diffraction pattern as the carbon transformed into its high-pressure phases. Quantitative analysis of the dynamic XRD patterns in combination with continuum velocimetry information constrained the stability fields and melting of high-pressure carbon polymorphs.

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In this brief report we document algorithmic choices and updates to our code related to the earthquake relocation portion of our tomographic imaging algorithm. We show results of these improvements by relocating over 40,000 events located within 20-30 km of the Rock Valley Direct Comparison (RV/DC) site using both absolute and differential arrival times within the context of two different 3-D Earth models. Accurate hypocentral locations and Earth models are important to the ultimate goals of the RV/DC program, which will co-locate a chemical explosion with a shallow earthquake within Rock Valley, southern Nevada, to investigate differences between the source types and improve our analysis algorithms for both types (Snelson et al., 2022). Our improvements to our relocation algorithms comprise just one step toward achieving these goals

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greater efficiency than fully resolved classical models. In this review article, we first provide a broad overview of fractional-order derivatives with a clear emphasis on the stochastic processes that underlie their use. We then survey three exemplary application areas — subsurface transport, turbulence, and anomalous materials — in which fractional-order differential equations provide accurate and predictive models. For each area, we report on the evidence of anomalous behavior that justifies the use of fractional-order models, and survey both foundational models as well as more expressive state-of-the-art models. We also propose avenues for future research, including more advanced and physically sound models, as well as tools for calibration and discovery of fractional-order models.

The modern global economy relies heavily on carbon-based products that are derived from petroleum, which presents sustainability, resource management, and greenhouse gas exacerbated climate change challenges. Due to these challenges, there is the need for a global industrial transition towards green and sustainable production. Microbial production of valuable chemicals from renewable biomass represents one promising route. However, high-volume low-value products such as commodity chemicals are still difficult to make profitable. One fundamental bottleneck is a waste of more than 1/3 of the feedstock carbon as CO₂ in the fermentation process. Here the project focuses on fundamentally reconfiguring the metabolism to reduce CO₂ loss in central metabolic pathways thereby also improving bioproduct yields. Here we present technologies to prevent CO₂ loss and balance reducing equivalents within the cell to enable complete conversion of glucose from renewable feedstocks into bioproducts.

The wave energy control competition established a benchmark problem which was offered as an open challenge to the wave energy system control community. The competition had two stages: In the first stage, competitors used a standard wave energy simulation platform (WEC-Sim) to evaluate their controllers while, in the second stage, competitors were invited to test their controllers in a real-time implementation on a prototype system in a wave tank. The performance function used was based on converted energy across a range of standard sea states, but also included aspects related to economic performance, such as peak/average power, peak force, etc. This paper compares simulated and experimental results and, in particular, examines if the results obtained in a linear system simulation are borne out in reality. Overall, within the scope of the device tested, the range of sea states employed, and the performance metric used, the conclusion is that high-performance WEC controllers work well in practice, with good carry-over from simulation to experimentation. However, the availability of a good WEC mathematical model is deemed to be crucial.

Deep learning (DL) models have enjoyed increased attention in recent years because of their powerful predictive capabilities. While many successes have been achieved, standard deep learning methods suffer from a lack of uncertainty quantification (UQ). While the development of methods for producing UQ from DL models is an active area of current research, little attention has been given to the quality of the UQ produced by such methods. In order to deploy DL models to high-consequence applications, high-quality UQ is necessary. This report details the research and development conducted as part of a Laboratory Directed Research and Development (LDRD) project at Sandia National Laboratories. The focus of this project is to develop a framework of methods and metrics for the principled assessment of UQ quality in DL models. This report presents an overview of UQ quality assessment in traditional statistical modeling and describes why this approach is difficult to apply in DL contexts. An assessment on relatively simple simulated data is presented to demonstrate that UQ quality can differ greatly between DL models trained on the same data. A method for simulating image data that can then be used for UQ quality assessment is described. A general method for simulating realistic data for the purpose of assessing a model’s UQ quality is also presented. A Bayesian uncertainty framework for understanding uncertainty and existing metrics is described. Research that came out of collaborations with two university partners are discussed along with a software toolkit that is currently being developed to implement the UQ quality assessment framework as well as serve as a general guide to incorporating UQ into DL applications.

Distributed acoustic sensing (DAS) has a demonstrated potential for wide-scale and continuous in situ monitoring of near-surface environmental and anthropogenic processes. DAS is attractive for development as a multi-geophysical observatory due to the prevalence of existing fiber infrastructure in regions with environmental, cultural, or strategic significance. To evaluate the efficacy of this technology for monitoring of polar environmental processes, we collected DAS data from a 37-km long section of seafloor telecommunications fiber located on the continental shelf of the Beaufort Sea, Alaska. This experiment spanned eight, one-week, seasonally-distributed periods across two years. This was the first ever deployment of seafloor DAS beneath sea ice, and the first deployment in any marine environment to span multiple seasons. We recorded a variety of environmental and anthropogenic signals with demonstrable utility for the study of sea ice dynamics and tracking of ocean vessels and ice-traversing vehicles.

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Quantum point contacts (QPC) are the building blocks of quantum dot qubits and semiconducting quantum electrical metrology circuits. QPCs also make highly sensitive electrical amplifiers with the potential to operate in the quantum-limited regime. Though the inherent operational bandwidth of QPCs can eclipse the THz regime, the impedance mismatch with the external circuitry limits the operational frequency to a few kHz. Lumped-element impedance-matching circuits are successful only up to a few hundreds of MHz in frequency. QPCs are characterised by a complex impedance consisting of quantized resistance, capacitance, and inductance elements. Characterising the complex admittance at higher frequencies and understanding the coupling of QPC to other circuit elements and electromagnetic environments will provide valuable insight into its sensing and backaction properties. In this work, we couple a QPC galvanically to a superconducting stub tuner impedance matching circuit realised in a coplanar waveguide architecture to enhance the operation frequency into the GHz regime and investigate the electrical amplification and complex admittance characteristics. The device, operating at ~1.96 $GHz$ exhibits a conductance sensitivity of 2.92 X 10^-5(e²/h)/$\sqrt{Hz}$ with a bandwidth of 13 $MHz$. Besides, the RF reflected power unambiguously reveals the complex admittance characteristics of the QPC, shining more light on the behaviour of quantum tunnel junctions at higher operational frequencies.

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Previous studies have shown that selective laser flash sintering (SLFS) can be initiated in dielectrics that exhibit ionic or electronic conduction at high temperature. These materials required high laser powers to reach the temperatures where electrical conduction is sufficient to initiate SLFS. In this study, SLFS in lanthanum chromite (LC), an intrinsic electronic conductor with high conductivity, and lanthanum strontium chromite (LSC), which is doped to further increase electronic conductivity, were investigated with a focus on understanding the initiation mechanisms. Results show that the initiation of SLFS in LC and LSC occurs when electronic charge carriers are activated and flow to the electrode where the current is measured. A combination of carriers produced at the electrode, temperature-activated intrinsic charge carriers, and extrinsic charge carriers present in LSC due to doping are responsible for the facile initiation of SLFS.

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Crystal plasticity finite element model (CPFEM) is a powerful numerical simulation in the integrated computational materials engineering toolboxes that relates microstructures to homogenized materials properties and establishes the structure–property linkages in computational materials science. However, to establish the predictive capability, one needs to calibrate the underlying constitutive model, verify the solution and validate the model prediction against experimental data. Bayesian optimization (BO) has stood out as a gradient-free efficient global optimization algorithm that is capable of calibrating constitutive models for CPFEM. In this paper, we apply a recently developed asynchronous parallel constrained BO algorithm to calibrate phenomenological constitutive models for stainless steel 304 L, Tantalum, and Cantor high-entropy alloy.

This report summarizes the measurement and analysis results of initial performance demonstrator wafers patterned at LumArray in January 2023 in accordance with the project Statement of Work.

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The understanding of power flow plasmas is important as we look towards next generation pulsed power (NGPP) as current losses could prohibit the goals of that facility. Therefore, it is important to have accurate diagnostics of the plasma parameters on the current machines, which can be used to help inform and improve simulations. Having these plasma parameters will help validate models and simulations to provide confidence when they are expanded to conditions relevant to NGPP. One important plasma parameter that can be measured is the electron density, which can be measured by photonic Doppler velocimetry (PDV). A PDV system has several key advantages over other interferometers by measuring relatively low densities (> 1 × 10¹⁵ cm^-2) with both spatial and temporal resolution. Experiments were performed on the Mykonos pulsed power machine, which is a 1 MA sub scale machine in which recent platforms have been developed to explore current densities relevant to the inner magnetically insulated transmission line (MITL) on the Z machine. Experiments were performed on two different platforms, the thin foil platform and the Mykonos parallel plate platform (MP3). In addition, a combination of both single-point and multi-point measurements were used. The single-point measurements proved to be very promising, providing a clear increase in density at about 70 ns into the current rise on thin foil experiments up to about 5 × 10¹⁷ cm^-3 before the probe stopped providing signal. While we did also see returns from multi-point measurements on both platforms, the signals were not as easy to interpret due to strong background effects. However, they do show initial promise for this diagnostic to measure density at several points across a 1 mm gap. These measurements provide insights in how to improve the diagnostic so that it can provide useful information on power flow relevant experiments.

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In this project, we experimented the focused ion beam (FIB) based fabrications of semiconductor quantum dots (QDs) by using metal nano particles (NPs) (e.g., Al) on semiconductor as a template and by means of the FIB induced direct metal-to-QD conversion. We have examined effect of the experimental conditions, including Ga⁺ ion energy and dose as well as substrate temperature. The results of experiments have shown AlGaSb QD formation on GaSb substrate can be achieved under certain conditions but there are many challenges about the techniques, including compositional nonuniformity of the QDs formed, partial conversion of the metal NP to QD, and high defect concentration in the QDs.

In this work, thermogravimetric analysis (TGA) was performed on samples of a carbon fiber epoxy composite, a glass fiber epoxy composite, and a mixed carbon fiber/glass fiber epoxy composite, as well on each constituent material (polymer epoxy, carbon fibers and glass fibers). TGA was conducted for heating rates from 1-20 C/min with purified purge gases of nitrogen and dry air. For the fiberglass composite, we find that ~70% of the material remains after heating in air to 1200 C. For the carbon fiber epoxy composite, we observe greater mass loss as the carbon fibers can oxidize, leaving little material by the end of the test. The mixed composite, which has a 2:1 ratio of glass fibers to carbon fibers, experienced a total mass loss between the two other composites. By determining the relationship between the thermal decomposition of a composite material and its constituent materials, we can predict the fire behavior of novel composites during the material design phase.

Developed in 2018, PathTrace is a software package built with the intention of making path analysis simple and intuitive. PathTrace is a top-down pathway analysis software where a user is able to explore vulnerable pathways into a facility. The intention of utilizing a software tool like PathTrace is to characterize an existing physical protection system (PPS) and to upgrade the system to achieve a high level of response interruption, or probability of interruption (P_I) of the adversary. There are four steps for conducting path analysis using PathTrace. The first step is to identify an image to use to build the model and scale the model within PathTrace using a section of known distance (wall or fence perimeter, for example). The scaling process will produce a grid of cells through which the user is able to build a model. The second step is to fill out the grid of cells with four categories of materials: Barriers, Detection Areas, Jumps, and Targets. These materials apply associated delay and detection values to the cells in which they are applied. The third step is to represent the adversary and response forces. The adversaries are represented by their capabilities in interacting with the materials identified in step two, and the response is represented by how quickly they will be able to respond to an adversary attack. Finally, the user is able to take all of the information from the previous three steps and perform a Most Vulnerable Path (MVP) analysis. In this stage, the user is able to visualize vulnerable adversary pathways and reason about how to upgrade these pathways to provide a high level of P_I.