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Transformation of two and three-dimensional regions by elliptic systems

The research during this period continued to expand the class of numerical algorithms that can be accurately and efficiently implemented on overlapping grids. Whereas previous calculations have been used to solve elliptic equations and to find the steady-state solution of parabolic equations, the present work is aimed towards developing time-accurate solution techniques for parabolic and hyperbolic equations. The primary difficulty here is in the correct treatment of the interior boundary nodes that must be updated at each iteration. The implementation of explicit methods is straightforward. However, the common practice of lagging these values when using an implicit methods leads to inconsistencies in the difference equation. One way to avoid this problem is to alternately calculate with an implicit and an explicit method on each subgrid. With this procedure, the explicit method generates boundary values at the next time level which are then used by the implicit step. It can be shown that when a backward implicit method is combined with a forward explicit method, the composite method is second order accurate and unconditionally stable for linear problems. A second area in which progress can be reported is in the distribution of grid points on curves and surfaces.

Mastin, E. W.↗

Optical Polarization of Light from a Sorghum Canopy Measured Under Both a Clear and an Overcast Sky

Introduction: We tested the hypothesis that the optical polarization of the light reflected by a sorghum canopy is due to a Fresnel-type redirection, by sorghum leaf surfaces, of light from an unpolarized light source, the sun or overcast sky, toward the measuring sensor. If it can be shown that the source of the polarization of the light scattered by the sorghum canopy is a first surface, Fresnel-type reflection, then removing this surface reflected light from measurements of canopy reflectance presumably would allow better insight into the biochemical processes such as photosynthesis and metabolism that occur in the interiors of sorghum canopy leaves. Methods: We constructed a tower 5.9m tall in the center of a homogenous sorghum field. We equipped two Barnes MMR radiometers with polarization analyzers on the number 1, 3 and 7 Landsat TM wavelength bands. Positioning the radiometers atop the tower, we collected radiance data in 44 view directions on two days, one day with an overcast sky and the other, clear and sunlit. From the radiance data we calculated the linear polarization of the reflected light for each radiometer wavelength channel and view direction. Results and Discussion: Our experimental results support our hypothesis, showing that the amplitude of the linearly polarized portion of the light reflected by the sorghum canopy varied dramatically with view azimuth direction under a point source, the sun, but the amplitude varied little with view azimuth direction under the hemispherical source, the overcast sky. Under the clear sky, the angle of polarization depended upon the angle of incidence of the sunlight on the leaf, while under the overcast sky the angle of polarization depended upon the zenith view angle. These results support a polarized radiation transport model of the canopy that is based upon a first surface, Fresnel reflection from leaves in the sorghum canopy.

cloud cover↗

Diffraction by a symmetric material junction simulated with generalized sheet transistion conditions

When diffraction by a material discontinuity in a thick dielectric/ferrite slab is treated for the dual integral equation approach (a variation of the Weiner-Hopf method), the resulting solution displays unknown constants, characteristic of the incompleteness associated with the generalized transition conditions employed in modeling a thick slab. The constants can be shown to depend on the geometry and properties of the discontinuity. Their explicit determination by enforcing field continuity across the slab junction is treated. The field internal to the slab is determined by first expressing the field as an expansion of discrete and continuous eigenmodes valid in the exterior and interior slab region. The expansion or mode coefficients are then identified by recasting the Weiner-Hopf solution in a suitable form, enabling the solution constants to be numerically computed by matching the field expansions to the left and right of the slab discontinuity at a discrete set of points.

Ricoy, Mark A.↗

Single-pixel interior filling function approach for detecting and correcting errors in particle tracking

We present a general method for detecting and correcting biases in the outputs of particle-tracking experiments. Our approach is based on the histogram of estimated positions within pixels, which we term the single-pixel interior filling function (SPIFF). We use the deviation of the SPIFF from a uniform distribution to test the veracity of tracking analyses from different algorithms. Unbiased SPIFFs correspond to uniform pixel filling, whereas biased ones exhibit pixel locking, in which the estimated particle positions concentrate toward the centers of pixels. Although pixel locking is a well-known phenomenon, we go beyond existing methods to show how the SPIFF can be used to correct errors. Here, the key is that the SPIFF aggregates statistical information from many single-particle images and localizations that are gathered over time or across an ensemble, and this information augments the single-particle data. We explicitly consider two cases that give rise to significant errors in estimated particle locations: undersampling the point spread function due to small emitter size and intensity overlap of proximal objects. In these situations, we show how errors in positions can be corrected essentially completely with little added computational cost. Additional situations and applications to experimental data are explored in SI Appendix. In the presence of experimental-like shot noise, the precision of the SPIFF-based correction achieves (and can even exceed) the unbiased Cramér–Rao lower bound. We expect the SPIFF approach to be useful in a wide range of localization applications, including single-molecule imaging and particle tracking, in fields ranging from biology to materials science to astronomy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND

NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.

WIND↗

Updated constraints on self-interacting dark matter from Supernova 1987A

Here we revisit SN1987A constraints on light, hidden sector gauge bosons (“dark photons”) that are coupled to the standard model through kinetic mixing with the photon. These constraints are realized because excessive bremsstrahlung radiation of the dark photon can lead to rapid cooling of the SN1987A progenitor core, in contradiction to the observed neutrinos from that event. The models we consider are of interest as phenomenological models of strongly self-interacting dark matter. We clarify several possible ambiguities in the literature and identify errors in prior analyses. We find constraints on the dark photon mixing parameter that are in rough agreement with the early estimates of Dent et al. [arXiv:1201.2683.], but only because significant errors in their analyses fortuitously canceled. Our constraints are in good agreement with subsequent analyses by Rrapaj & Reddy [Phys. Rev. C 94, 045805 (2016).] and Hardy & Lasenby [J. High Energy Phys. 02 (2017) 33.]. We estimate the dark photon bremsstrahlung rate using one-pion exchange (OPE), while Rrapaj & Reddy use a soft radiation approximation (SRA) to exploit measured nuclear scattering cross sections. We find that the differences between mixing parameter constraints obtained through the OPE approximation or the SRA approximation are roughly a factor of ~2–3. Hardy & Laseby [J. High Energy Phys. 02 (2017) 33.] include plasma effects in their calculations finding significantly weaker constraints on dark photon mixing for dark photon masses below ~10 MeV. We do not consider plasma effects. Lastly, we point out that the properties of the SN1987A progenitor core remain somewhat uncertain and that this uncertainty alone causes uncertainty of at least a factor of ~2–3 in the excluded values of the dark photon mixing parameter. Further refinement of these estimates is unwarranted until either the interior of the SN1987A progenitor is more well understood or additional, large, and heretofore neglected effects, such as the plasma interactions studied by Hardy & Lasenby [J. High Energy Phys. 02 (2017) 33.], are identified.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A group finder algorithm optimised for the study of local galaxy environments

Context. The majority of galaxy group catalogues available in the literature use the popular friends-of-friends algorithm which links galaxies using a linking length. One potential drawback to this approach is that clusters of points can be linked with thin bridges which may not be desirable. In order to study galaxy groups, it is important to obtain realistic group structures. Aim. Here, in this study, we present a new simple group finder algorithm, TD-ENCLOSER, that finds the group that encloses a target galaxy of interest. Methods. TD-ENCLOSER is based on the kernel density estimation method which treats each galaxy, represented by a zero-dimensional particle, as a two-dimensional circular Gaussian. The algorithm assigns galaxies to peaks in the density field in order of density in descending order (‘top down’) so that galaxy groups ‘grow’ around the density peaks. Outliers in under-dense regions are prevented from joining groups by a specified hard threshold, while outliers at the group edges are clipped below a soft (blurred) interior density level. Results. The group assignments are largely insensitive to all free parameter variations apart from the hard density threshold and the kernel standard deviation, although this is a known feature of density-based group finder algorithms and it operates with a computing speed that increases linearly with the size of the input sample. In preparation for a companion paper, we also present a simple algorithm to select unique representative groups when duplicates occur. Conclusions. TD-ENCLOSER is tested on a mock galaxy catalogue using a smoothing scale of 0.3 Mpc and is found to be able to recover the input group distribution with sufficient accuracy to be applied to observed galaxy distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

Limits on Mode Coherence in Pulsating DA White Dwarfs Due to a Nonstatic Convection Zone

The standard theory of pulsations deals with the frequencies and growth rates of infinitesimal perturbations in a stellar model. Modes which are calculated to be linearly driven should increase their amplitudes exponentially with time; the fact that nearly constant amplitudes are usually observed is evidence that nonlinear mechanisms inhibit the growth of finite amplitude pulsations. Models predict that the mass of convection zones in pulsating hydrogen-atmosphere (DAV) white dwarfs is very sensitive to temperature (i.e., M CZ α T –90 eff ), leading to the possibility that even low-amplitude pulsators may experience significant nonlinear effects. In particular, the outer turning point of finite-amplitude g-mode pulsations can vary with the local surface temperature, producing a reflected wave that is out of phase with what is required for a standing wave. This can lead to a lack of coherence of the mode and a reduction in its global amplitude. In this paper we show that: (1) whether a mode is calculated to propagate to the base of the convection zone is an accurate predictor of its width in the Fourier spectrum, (2) the phase shifts produced by reflection from the outer turning point are large enough to produce significant damping, and (3) amplitudes and periods are predicted to increase from the blue edge to the middle of the instability strip, and subsequently decrease as the red edge is approached. Furthermore, this amplitude decrease is in agreement with the observational data while the period decrease has not yet been systematically studied.

79 ASTRONOMY AND ASTROPHYSICS↗

Effect of grain size on the melting point of confined thin aluminum films

The melting of aluminum thin film was studied by a molecular dynamics (MD) simulation technique. The effect of the grain size and type of confinement was investigated for aluminum film with a constant thickness of 4 nm. The results show that coherent intercrystalline interface suppress the transition of solid aluminum into liquid, while free-surface gives melting point depression. The mechanism of melting of polycrystalline aluminum thin film was investigated. It was found that melting starts at grain boundaries and propagates to grain interiors. The melting point was calculated from the Lindemann index criterion, taking into account only atoms near to grain boundaries. This made it possible to extend melting point calculations to bigger grains, which require a long time (in the MD scale) to be fully molten. The results show that 4 nm thick film of aluminum melts at a temperature lower than the melting point of bulk aluminum (933 K) only when the grain size is reduced to 6 nm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Implementation and validation of optimal start control strategy for air conditioners and heat pumps

Commercial buildings are responsible for approximately 20 % of the total energy consumption and greenhouse gas emissions in the United States. Over 85 % of these buildings lack building automation systems, and many are small (<50,000 square feet), underserved, and use rooftop units (RTUs) for heating, ventilation, and air-conditioning needs. Because these buildings lack proper energy management systems, several operational deficiencies lead to excess energy consumption. Studies have shown that managing the RTUs’ heating and cooling set points, schedules, setbacks, and optimal start can result in a 20 % to 25 % reduction in electricity consumption in small commercial buildings. These buildings typically use fixed schedules to start the RTUs 60 to 120 min before occupancy begins, which results in excess energy consumption. This paper presents research that demonstrates and evaluates the performance of four optimal start methods, which utilize data-based modeling as a key element in facilitating adaptive control in response to time-varying inputs while requiring minimal sensor inputs. The evaluation found energy savings in two commercial buildings equipped with RTUs by periodically alternating four different optimal start models during the cooling and heating season. The resulting energy savings are positive for all models and range from 2 to 5 kWh/day/unit. The units on the east side of the building showed higher savings, while interior units showed greater variability in savings due to the differences in capacities and room sizes. Savings were considerably greater during the heating season compared to the cooling season. The performance of all four models on Mondays was poor; models suggested a shorter optimal start time, which resulted in relatively larger errors. Finally, the future work will look at using a different model for the days after weekends and holidays.

42 ENGINEERING↗

Multimodal Nondestructive Dry Cask Basket Structure and Spent Fuel Evaluation

This NEUP-IRP assembled a team from diverse institutions and a diverse set of expertise to examine the problem of assessing the structural health of dry nuclear fuel storage casks, specifically the TN-32 design. With no physical access designed into these storage casks and the high cost and risk associated with opening casks for direct inspection, the technical difficulty of structural assessment of the basket structure and fuel assemblies is high. In response to this challenge, this IRP brought together experts in both traditional and novel NDE methodologies: active acoustics (University of Mississippi), emissions tomography (University of Florida), muon tomography (Oregon State University), and passive-active ultrasonics (University of South Carolina). Further, our industry partners in the Electric Power Research Institute (EPRI) and AREVA provided invaluable insight into technical design details for the cask, practical knowledge of operating parameters at a storage facility, and key relationships that enabled activities unforeseen at the time of the proposed work but were critical in guiding the path of the research. The team decided early in the project that we had a collective goal of laying the technical ground work for practical solutions that could be implemented in the field with reasonable cost, time, and reliability. A fortunate opportunity arose early in this IRP project to obtain access to a new TN-32 cask at Columbiana High Tech. Both acoustics teams were given access for testing concepts in the first year of the project. This ended up providing critical guidance in the design of subsequent laboratory experiments. Specifically, it became clear that the only reliable acoustic pathways to the interior were through the trunnions, base plate, and top ring of the cask. Based on these field tests and discussions about what would be of practical interest, the team as a whole decided a realistic goal was to detect catastrophic failure of a single fuel assembly, or one that was missing. It is clear from this work that the active acoustics / resonance and muon tomography methodologies would be capable of detecting interior structural integrity problems at this level. The other two areas of investigation (emissions tomography and passive/active ultrasonics) would need more testing to determine a successful implementation, but each may also have other applications such as long term monitoring and monitoring during transportation. This IRP project resulted in technical advances with applications that extend beyond the problem at hand, supported the training of 10 graduate students + 1 post doc, 21 publications, and 13 conference presentations. The remainder of this summary highlights significant activities and achievements in each of the methodologies and a brief discussion on how they can be combined to leverage strengths. Active Acoustics The active acoustics team at UM used both linear and non-linear structural resonance methods to infer information about the internal structure of a cask. Significant activities were a set of four field test measurements on a full scale TN-32 cask at the Columbiana Hi Tech facility in Greensboro, NC and the design and fabrication of a 1/6th scale model TN-32 cask for laboratory measurements. A significant set of acoustic data has been acquired on both the full scale and laboratory scale casks. It was determined early in the project that mechanical resonance techniques were not going to be sensitive to small scale (centimeter) cracks and structural defects in the basket structure or fuel assemblies. We were able to ascertain that both the energy and complexity of the resonance spectra were sensitive to “bulk state” of the fuel assemblies – an intact assembly versus a severely degraded assembly. By developing a novel combination of metrics, we are able to measure a statistically significant shift due to one out of the 32 fuel assemblies being either missing or degraded to a point of complete loss of structural coherence (i.e. “rubble”). We believe this combination of resonance metrics is new to the field and will have applications beyond the fuel storage problem. Emissions Tomography The Emissions Tomography team at the University of Florida explored the concept of using scattering of radiation emissions from the stored fuel as method of evaluating the internal structural health of the cask. Due to the need for emissive fuel assemblies and the difficulties of gaining access to storage facilities, this team primarily relied on simulations to inform feasibility. A key question was the flux estimates of neutrons with a small enough number of scattering events to retain spatial information. Some key conclusions from the transmission component of this work are that the number of scattering events falls rapidly with energy – setting a 11MeV threshold, the average number of scattering events is 8∓4. Rough estimates of scanning times using an ideal detector array would be 1 week. The team also explored the case of significant structural failure resulting in a shift of the source material (fuel). The result is that a +/- 2% mass shift results in a detectable (5.13%) shift in the correlated 2 neutron emission counts and thus may be a candidate as an initial survey. Finally, simulations for predicting the azimuthal dependence of the flux based on specific loading patterns were conducted. Due to self-shielding effects of the assemblies, a periodic pattern results and could potentially be used to identify missing or severely degraded assemblies. This work forms a basis for proper detector placement with the goal of optimizing sensitivity. Muon Tomography Muon tomography (MT) is a relatively novel method of interrogating interior structure on a large scale. One of the advantages of this technique is that the exciting energy source (cosmic muons) is ubiquitous and relatively stable in time. Challenging aspects are relatively low flux rates and appropriate detector technologies. The efforts of the muon group at Oregon State University focused on two areas: (1) simulation of various combinations of muon scattering events and detection schemes to assess sensitivities and time scales for image construction and (2) building a prototype muon detection system applicable to the dry storage cask problem as well as many other similar systems. Significant accomplishments in this area are: (1) demonstration that MT is a viable method for detecting missing or severely degraded rod assemblies, (2) a scintillation based detector with 4 panels and 32 channels of position data each were constructed, tested, and calibrated. Testing of the panels using natural muon background and no scattering objects yielded largely expected results – a straight line path for the muon through the four panels. However some anomalies (paths deviating from a line) were also detected. A redesign of the board improved the signal which greatly improved the muon tracking through the panels. Testing with lead bricks as scattering bodies showed a reduction in the coincidence rate with increasing bricks indicating increased scattering events. A refinement of the scintillator detector design resulted in a spatial image resolution of around 2 cm based on lead brick spacing tests lasting 24 hours. Passive/Active Ultrasonics This team at the University of South Carolina investigated the feasibility of combining passive ultrasonics, in which an elastic pulse is generated by a degradation process (such as a crack extending), and active ultrasonics, in which a known excitation is introduced into the structure and detected by an array of transducers. Significant accomplishments in this area include the development of elastic wave propagation simulation in relevant materials, development of diagnostic algorithms, and laboratory testing and validation using laser doppler vibrometry. This group demonstrated the applicability of various non-contact vibration detection methodologies such as air-coupled ultrasonic transducers and scanning laser doppler vibrometry. While passive acoustic emissions monitoring will likely have a role during the transportation of a fuel storage cask, the level of detailed information about the defect generating the event which can be ascertained from the detections in a complex structure remains for future work. Thermography The EPRI team contributed early in the project a series of thermography measurements in which various levels of water pooled in a mock-up canister were analyzed using commercially available infrared imaging technologies. While large levels of water (100 L, ~10 cm deep) were observable in the thermograms, more realistic levels of pooled water (1 L) were not detectable whether localized or distributed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Reentry Thermal Analysis of a Generic Crew Exploration Vehicle Structure

Comparative studies were performed on the heat-shielding characteristics of honeycomb-core sandwich panels fabricated with different materials for possible use as wall panels for the proposed crew exploration vehicle. Graphite/epoxy sandwich panel was found to outperform aluminum sandwich panel under the same geometry due to superior heat-shielding qualities and lower material density. Also, representative reentry heat-transfer analysis was performed on the windward wall structures of a generic crew exploration vehicle. The Apollo low Earth orbit reentry trajectory was used to calculate the reentry heating rates. The generic crew exploration vehicle has a graphite/epoxy composite honeycomb sandwich exterior wall and an aluminum honeycomb sandwich interior wall, and is protected with the Apollo thermal protection system ablative material. In the thermal analysis computer program used, the TPS ablation effect was not yet included; however, the results from the nonablation heat-transfer analyses were used to develop a "virtual ablation" method to estimate the ablation heat loads and the thermal protection system recession thicknesses. Depending on the severity of the heating-rate time history, the virtual ablation period was found to last for 87 to 107 seconds and the ablation heat load was estimated to be in the range of 86 to 88 percent of the total heat load for the ablation time period. The thermal protection system recession thickness was estimated to be in the range of 0.08 to 0.11 inches. For the crew exploration vehicle zero-tilt and 18-degree-tilt stagnation points, thermal protection system thicknesses of h = {0.717, 0.733} inches were found to be adequate to keep the substructural composite sandwich temperature below the limit of 300 F.

Ko, William L.↗

Aircraft noise control in the 1980's

It is pointed out that a need exists for the orderly development of technology and engineering methods for noise control of all types of aircraft. The nature and scope of aircraft noise problems are reviewed, and a description is provided of noise control progress made to date. The most serious aircraft noise problems confronting communities in the past two decades have been associated with the subsonic air carrier jet transport. Operational trends related to traffic growth and operational constraints are examined, and noise level trends are considered, taking into account engine cycle developments, the role of Federal noise certification, future noise exposures, and multiple noise sources. Advanced source noise reduction technology developments are discussed along with a noise impact assessment, and advanced operating procedures. Attention is also given to engine noise and sonic boom exposures in connection with supersonic air carrier aircraft, and exterior and interior noise control related to propeller/rotor aircraft.

Hubbard, H. H.↗

A Rainbow Coverage Path Planning for a Patrolling Mobile Robot With Circular Sensing Range

In this paper, we proposed a coverage path (CP) planning approach for a mobile robot moving in a dynamically changing environment. Our family of algorithms begins by finding the first path around the center of interior obstacles/disks of a given target region (TR) through the Graham scan algorithm. The first path is then used as a foundational path to generate a collision free, first order differentiable, and observable CP through a complete set of input and output transformation algorithms which together form the rainbow CP planning approach. The last algorithm of the rainbow CP planning approach finds a sufficient number of observation points on the CP needed to observe the TR. The novelty of our rainbow CP planning approach is that it partitions the TR into different shapes with different properties needed to obtain complete coverage while achieving first order path differentiability. The main technical contributions of the proposed approach is to provide a holistic solution that segments any TR, uses triangulation to determine the line of sights and observation points, and computes the collision-free CP within a quadratic runtime. The proposed method can be readily generalized to address problems of higher dimensions, and it is scalable with respect to the size of TR and the number of robots. Computer simulations are used to illustrate the effectiveness and correctness of the proposed approach.

54 ENVIRONMENTAL SCIENCES↗

Exploring strain rate effects upon 3D materials using high speed in situ X-ray tomoscopy

Cellular materials are ubiquitous in our modern society. They may be stochastic gas-blown foams (e.g., polyurethane), foamed starches (e.g., cereals), or, in this case, 3D printed microlattices. Failure in these materials is often driven by surface or sub-surface defects, which may be nucleated at a surface roughness, an interior void, or inclusion interfaces that may not be typically observable. Obfuscating our understanding further, bulk materials are known to exhibit strain-rate-dependent mechanical response, making a subsurface understanding of damage even more critical. For the first time, an in situ uniaxial mechanical loading stage that simultaneously rotates specimens up to 18 Hz was fielded at a synchrotron for 3D tomographic imaging. This capability opens a plethora of materials science opportunities to explore strain rate effects in materials and examining deformation, fracture, and delamination’s (in composites) for a complete 3D picture (movie) of material response. We demonstrate the deformation of 3D printed polymer lattice structures, of three different material types, at 0.25, 1.1, and 2.2 s −1 strain rates. We successfully imaged the 3D deformation of these materials and can directly compare the same printed structure to the three material types at three strain rates, all in 3D. Material point method simulations were applied to one of the materials to better understand the role of voids on the 3D printed structure’s performance.

36 MATERIALS SCIENCE↗

SU-G-201-13: Investigation of Dose Variation Induced by HDR Ir-192 Source Global Shift Within the Varian Ring Applicator Using Monte Carlo Methods

Purpose: The Varian tandem and ring applicators are used to deliver HDR Ir-192 brachytherapy for cervical cancer. The source path within the ring is hard to predict due to the larger interior ring lumen. Some studies showed the source could be several millimeters different from planned positions, while other studies demonstrated minimal dosimetric impact. A global shift can be applied to limit the effect of positioning offsets. The purpose of this study was to assess the necessities of implementing a global source shift using Monte Carlo (MC) simulations. Methods: The MCNP5 radiation transport code was used for all MC simulations. To accommodate TG-186 guidelines and eliminate inter-source attenuation, a BrachyVision plan with 10 dwell positions (0.5cm step sizes) was simulated as the summation of 10 individual sources with equal dwell times for simplification. To simplify the study, the tandem was also excluded from the MC model. Global shifts of ±0.1, ±0.3, ±0.5 cm were then simulated as distal and proximal from the reference positions. Dose was scored in water for all MC simulations and was normalized to 100% at the normalization point 0.5 cm from the cap in the ring plane. For dose comparison, Point A was 2 cm caudal from the buildup cap and 2 cm lateral on either side of the ring axis. With seventy simulations, 108 photon histories gave a statistical uncertainties (k=1) <2% for (0.1 cm)3 voxels. Results: Compared to no global shift, average Point A doses were 0.0%, 0.4%, and 2.2% higher for distal global shifts, and 0.4%, 2.8%, and 5.1% higher for proximal global shifts, respectively. The MC Point A doses differed by < 1% when compared to BrachyVision. Conclusion: Dose variations were not substantial for ±0.3 cm global shifts, which is common in clinical practice.

60 APPLIED LIFE SCIENCES↗

Algebraic grid generation using tensor product B-splines

Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.

Saunders, B. V.↗

Coal-based Bricks & Blocks (CBBs): Process Development to Prototype Fabrication Coupled with Techno-Economic Analysis and Market Survey

The decline of coal use for energy production provides an abundance of local feedstock for new innovative uses and value-added products. Expanding the U.S. coal-value chain to manufacture high-value carbon products can strengthen the nation’s energy and mineral security, enhance the U.S. national defense security, increase the United States’ economic prosperity, while achieving U.S. environmental objectives. The primary project goal is a relatively light-weight composite product with superior (or comparable) compressive strength. Both virgin and, where available, post-consumer recycled thermoplastic versions are tested for each thermoplastic species. A useful attribute of thermoplastics as binders is that they can be heated to their melting point, cooled, and reheated again without significant degradation. A key advantage of thermoset CBBs is that they require only mixing and molding. CBB advantages include low cost, availability, binding ability and processability. Coal-based bricks and blocks (CBBs) weigh about 50% less than clay bricks and can be manufactured with an interlocking design to promote ease of use for the novice builder. CBB formulation is evaluated according to a design-of-experiments (DoE) approach. DoE variables are a) relative weight fractions of binder, b) relative proportions of large versus small (milled) anthracite size fractions, and c) additive percentage. Fabrication methods include hot-press molding and extrusion, the later being the most commercially viable. CBBs are tested for compressive strength, modulus of rupture (by flexure test) and water absorption per ASTM C67, with density determined by the Archimedes drainage method. Fractured interfaces are examined by SEM (Scanning Electron Microscopy) to resolve fracture dynamics and interior microstructure uniformity. Differential scanning calorimetry (DSC) is used to compare plastic transition temperatures i.e., glass and melting temperatures to contrast virgin with post-consumer recycled thermoplastics and optimize their usage. These results are used in the DoE analysis to identify the binder and relative weight percentages for optimum strength, density, and porosity. Overall, CBBs possess strength comparable to clay-based bricks but are non-permeable and hydrophobic, and hence resistant to degradation by freeze-fracturing, corrosion, and efflorescence. The strongest composites have been made with the following thermoplastic binders (in order of strength): thermoset, high-density polyethylene crosslink resin, high-density polyethylene, nylon 6/6, and polypropylene. Results from a techno-economic analysis TEA show economy of scale for CBBs by modularization and reveal the binder as the cost driver for material costs. Ideally, the incorporation of post-consumer recycled thermoplastic will decrease material acquisition costs and increase product sustainability. Notably, CBBs do not require the high temperature calcination needed to produce cement, nor do they require firing in the 1600-2400 °F range for three days using natural gas, as do clay brick equivalents. Instead, CBBs are heated to a modest <600 °F according to the melt flow index of the thermoplastic binder. Existing anthracite mines can be expanded to produce CBBs to reduce aggregate transportation costs and emissions that exist for clay bricks. TEA reflects this reduced energy cost while a comparative CO2 emission analysis quantifies the reduced environmental footprint. The market survey identifies several commercialization opportunities, dependent upon the brick classification.

01 COAL, LIGNITE, AND PEAT↗