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Positive geometries and canonical forms

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as “positive geometries”. The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of “positive geometries” and their associated “canonical forms” as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via “triangulation” on the one hand, and “push-forward” maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest “simplex-like” geometries and the richer “polytope-like” ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

97 MATHEMATICS AND COMPUTING↗

Processing of High-Entropy AlCoCr{sub 0.75}Cu{sub 0.5}FeNi Alloy by Spray Forming

Compositionally complex AlCoCrCuFeNi alloy system is one of the extensively studied high-entropy alloys (HEA). Most of these studies have been carried out on as-cast materials that witness slow cooling rate during solidification. In the present investigation, HEA based on AlCoCrCuFeNi system was processed employing spray forming so as to realize its inherent rapid solidification effect and unique microstructural evolution mechanism. The spray formed as well as the as-cast alloys were compared in terms of their microstructural features, phase constitution and hardness. These microstructural features were also compared with that of the overspray powders (< 250 µm) obtained as a by-product of spray forming. Both the as-cast and spray formed alloys showed a mixture of mainly two phases, i.e., face-centered and body-centered cubic (BCC) phases, in contrast to a single BCC phase in overspray powders. However, the spray formed alloy revealed unidentified phases, as against the as-cast material, which disappeared after heat treatment at 1473 K for 3 h. The grain size of the as-cast alloy was around 600-1000 μm compared to a highly refined grain size of 25-30 μm in the as-spray formed alloy. It was found that the hardness of the regions dominated by the constituent phases as well as the bulk of the spray formed material was higher than that of the as-cast alloy. The results validate the efficacy of the process in achieving drastic refinement in grain size, in a single step of large-scale spray forming. The characteristic microstructural features and the phase constitutions have been discussed in light of the prevailing mechanisms of structural evolution and possible solidification phenomena during spray atomization and deposition. This study gives a new direction in processing of these alloys and understanding their solidification behavior under the conditions of layer-by-layer deposition of semi-solid/liquid droplets.

36 MATERIALS SCIENCE↗

Crystallization of Long-Spaced Precision Polyacetals I: Melting and Recrystallization of Rapidly Formed Crystallites

Rapidly melt-crystallized polyethylenes with acetal groups (-O-CH 2 -O-) precisely spaced by 12, 18, 19, or 23 backbone carbons exhibit two reorganizations and three melting endotherms on heating at relatively low heating rates. Real-time WAXD experiments further confirm that these transitions are associated with reorganization to a different crystalline structure. Here, the DSC endotherms are associated with melting of the initially formed disordered phase, followed by melting of Form I and by melting of Form II crystals with increasing temperature. In parallel with these structural changes, the long spacing undergoes a discrete step increase at the polymorphic transitions. Upon the transition from disordered to Form I crystals, the core crystal thickness increases by one repeating unit, whereas the crystal thickness remains basically unchanged during the transition from Form I to Form II crystallites. The effect of even vs. odd CH2 spacer on the observed melting temperatures is prevalent for spacer < 10 CH 2 units. The even or odd number of methylenes between acetals also affects the type and kinetics of packing assembly in layered crystallites. While a disordered mesomorphic-like structure develops under fast cooling in odd-spaced polyacetals (PA-19, PA-23), the formation of Form I crystals cannot be bypassed in PA-12 and PA-18. Furthermore, some differences are also found in the WAXD patterns of Form II between odd and even-spaced polyacetals, denoting that staggering of the acetals in the crystallites is affected by the configuration of consecutive acetals with respect to the methylene sequence.

36 MATERIALS SCIENCE↗

The pesticidal Cry6Aa toxin from Bacillus thuringiensis is structurally similar to HlyE-family alpha pore-forming toxins

Background: The Cry6 family of proteins from Bacillus thuringiensis represents a group of powerful toxins with great potential for use in the control of coleopteran insects and of nematode parasites of importance to agriculture. These proteins are unrelated to other insecticidal toxins at the level of their primary sequences and the structure and function of these proteins has been poorly studied to date. This has inhibited our understanding of these toxins and their mode of action, along with our ability to manipulate the proteins to alter their activity to our advantage. To increase our understanding of their mode of action and to facilitate further development of these proteins we have determined the structure of Cry6Aa in protoxin and trypsin-activated forms and demonstrated a pore-forming mechanism of action. Results: The two forms of the toxin were resolved to 2.7 Å and 2.0 Å respectively and showed very similar structures. We report Cry6Aa shows structural homology to a known class of pore-forming toxins including hemolysin E from Escherichia coli and two Bacillus cereus proteins: the hemolytic toxin HblB and the NheA component of the non-hemolytic toxin (pfam05791). Cry6Aa also shows atypical features compared to other members of this family, including internal repeat sequences and small loop regions within major alpha helices. Trypsin processing was found to result in the loss of some internal sequences while the C-terminal region remains disulfide-linked to the main core of the toxin. Based on the structural similarity of Cry6Aa to other toxins, the mechanism of action of the toxin was probed and its ability to form pores in vivo in Caenorhabditis elegans was demonstrated. A non-toxic mutant was also produced, consistent with the proposed pore-forming mode of action. Conclusions: Cry6 proteins are members of the alpha helical pore-forming toxins – a structural class not previously recognized among the Cry toxins of B. thuringiensis and representing a new paradigm for nematocidal and insecticidal proteins. Elucidation of both the structure and the pore-forming mechanism of action of Cry6Aa now opens the way to more detailed analysis of toxin specificity and the development of new toxin variants with novel activities.

59 BASIC BIOLOGICAL SCIENCES↗

Form and Aging of Plutonium in Savannah River Site Waste Tank 18

Process modeling; injection molding; long-fiber thermoplastic; fiber orientation; fiber lengt This report provides a summary of the effects of aging on and the expected forms of plutonium in Tank 18 waste residues. The findings are based on available information on the operational history of Tank 18, reported analytical results for samples taken from Tank 18, and the available scientific literature for plutonium under alkaline conditions. These findings should apply in general to residues in other waste tanks. However, the operational history of other waste tanks should be evaluated for specific conditions and unique operations (e.g., acid cleaning with oxalic acid) that could alter the form of plutonium in heel residues. Based on the operational history of other tanks, characterization of samples from the heel residues in those tanks would be appropriate to confirm the form of plutonium. During the operational period and continuing with the residual heel removal periods, Pu(IV) is the dominant oxidation state of the plutonium. Small fractions of Pu(V) and Pu(VI) could be present as the result of the presence of water and the result of reactions with oxygen in air and products from the radiolysis of water. However, the presence of Pu(V) would be transitory as it is not stable at the dilute alkaline conditions that currently exists in Tank 18. Most of the plutonium that enters Savannah River Site (SRS) high-level waste (HLW) tanks is freshly precipitated as amorphous plutonium hydroxide, Pu(OH) 4(am) or hydrous plutonium oxide, PuO 2(am,hyd) and coprecipitated within a mixture of hydrous metal oxide phases containing metals such as iron, aluminum, manganese and uranium. The coprecipitated plutonium would include Pu 4+ that has been substituted for other metal ions in crystal lattice sites, Pu 4+ occluded within hydrous metal oxide particles and Pu 4+ adsorbed onto the surface of hydrous metal oxide particles. The adsorbed plutonium could include both inner sphere coordination and outer sphere coordination of the plutonium. PuO 2(am,hyd) is also likely to be present in deposits and scales that have formed on the steel surfaces of the tank. Over the operational period and after closure of Tank 18, Ostwald ripening has and will continue to transform PuO 2(am,hyd) to a more crystalline form of plutonium dioxide, PuO 2(c) . After bulk waste removal and heel retrieval operations, the free hydroxide concentration decreased and the carbonate concentration in the free liquid and solids increased. Consequently, a portion of the PuO 2(am,hyd) has likely been converted to a hydroxy-carbonate complex such as Pu(OH) 2 (CO 3 ) (s) . or PuO(CO 3 ) · xH 2 O (am) . Like PuO 2(am,hyd) , Ostwald ripening of Pu(OH) 2 (CO 3 ) (s) or PuO(CO 3 ) · xH 2 O (am) would be expected to occur to produce a more crystalline form of the plutonium carbonate complex. Due to the high alkalinity and low carbonate concentration in the grout formulation, it is expected that upon interaction with the grout, the plutonium carbonate complexes will transform back into plutonium hydroxide. Although crystalline plutonium dioxide is the more stable thermodynamic state of Pu(IV), the low temperature and high water content of the waste during the operating and heel removal periods in Tank 18 have limited the transformation of the plutonium into crystalline plutonium dioxide. During the tank closure period of thousands of years, transformation of the plutonium into a more crystalline plutonium dioxide form would be expected. However, the continuing presence of water, reaction with water radiolysis products, and low temperatures will limit the transformation, and will likely maintain an amorphous Pu(OH) 4 or PuO 2(am,hyd) form on the surface of any crystalline plutonium dioxide produced after tank closure. X-ray Absorption Spectroscopic (XAS) measurements of Tank 18 residues are recommended to confirm coordination environments of the plutonium. If the presence of PuO(CO 3 ) (am,hyd) is confirmed by XAS, it is recommended that experiments be conducted to determine if plutonium carbonates are transformed back into PuO 2(am,hyd) upon contact with grout.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Updated Liquid Secondary Waste Grout Formulation and Preliminary Waste Form Qualification

This report describes the results from liquid secondary waste grout (LSWG) formulation and cementitious waste form qualification tests performed by Pacific Northwest National Laboratory (PNNL) for Washington River Protection Solutions, LLC (WRPS). New formulations for preparing a cementitious waste form from a high-sulfate liquid secondary waste stream simulant, developed for Effluent Management Facility (EMF) process condensates merged with low activity waste (LAW) caustic scrubber, and the release of key constituents (e.g. 99 Tc and 129 I) from these monoliths were evaluated. This work supports a technology development program to address the technology needs for Hanford Site Effluent Treatment Facility (ETF) liquid secondary waste (LSW) solidification and supports future Direct Feed Low-Activity Waste (DFLAW) operations. High-priority activities included simulant development, LSWG formulation, and waste form qualification. The work contained within this report relates to waste form development and testing and does not directly support the 2017 integrated disposal facility (IDF) performance assessment (PA). However, this work contains valuable information for use in PA maintenance past FY17, and for future waste form development efforts. The provided data should be used by (i) cementitious waste form scientists to further understanding of cementitious dissolution behavior, (ii) IDF PA modelers who use quantified constituent leachability, effective diffusivity, and partitioning coefficients to advance PA modeling efforts, and (iii) the U.S. Department of Energy (DOE) contractors and decision makers as they assess the IDF PA program. The results obtained help fill existing data gaps, support final selection of a LSWG waste form, and improve the technical defensibility of long-term waste form performance estimates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Effluent Management Facility Evaporator Bottom-Waste Streams Formulation and Waste Form Qualification Testing

This report describes the results from grout formulation and cementitious waste form qualification testing performed by Pacific Northwest National Laboratory (PNNL) for Washington River Protection Solutions, LLC (WRPS). These results are part of a screening test that investigates three grout formulations proposed for wide-range treatment of different waste stream compositions expected for the Hanford Effluent Management Facility (EMF) evaporator bottom waste. This work supports the technical development need for alternative disposition paths for the EMF evaporator bottom wastes and future direct feed low-activity waste (DFLAW) operations at the Hanford Site. High-priority activities included simulant production, grout formulation, and cementitious waste form qualification testing. The work contained within this report relates to waste form development and testing, and does not directly support the 2017 Integrated Disposal Facility (IDF) performance assessment (PA). However, this work contains valuable information for use in PA maintenance past FY 2017 and future waste form development efforts. The provided results and data should be used by (1) cementitious waste form scientists to further the understanding of cementitious leach behavior of contaminants of concern (COCs), (2) decision makers interested in off-site waste form disposal, and (3) the U.S. Department of Energy, their Hanford Site contractors and stakeholders as they assess the IDF PA program at the Hanford Site. The results reported help fill existing data gaps, support final selection of a cementitious waste form for the EMF evaporator bottom waste, and improve the technical defensibility of long-term waste form risk estimates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Effluent Management Facility Evaporator Bottoms: Waste Streams Formulation and Waste Form Qualification Testing

This report describes the results from grout formulation and cementitious waste form testing performed by Pacific Northwest National Laboratory for Washington River Protection Solutions, LLC (WRPS). These results are part of a screening test that investigates grout formulations proposed for encapsulating a wide range of compositions predicted to be present in evaporator bottoms wastes from the Hanford Effluent Management Facility (EMF). This work supports the technical development need for alternative treatment and disposition paths for the EMF evaporator bottoms waste and future direct-feed low-activity waste (DFLAW) operations at the Hanford Site. High-priority activities included simulant production, grout formulation, and cementitious waste form testing. The work contained within this report relates to waste form development and testing, but does not directly support the 2017 Integrated Disposal Facility (IDF) performance assessment (PA). However, this work contains information useful for future PA updates [beyond fiscal year (FY) 2017] and future waste form development efforts. These analytical results can be used by (i) cementitious waste form scientists to further the understanding of cementitious leach behavior of contaminants of concern (COCs), (ii) decision makers interested in off-site waste form disposal, and (iii) the U.S. Department of Energy, their Hanford Site contractors, and stakeholders as they continue to assess the IDF PA program at the Hanford Site. The reported results help fill existing data gaps, support final selection of a cementitious waste form for the EMF evaporator bottoms waste, and improve the technical defensibility of long-term waste form risk estimates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Effluent Management Facility Evaporator Bottoms: Waste Streams Formulation and Waste Form Qualification Testing

This report describes the results from grout formulation and cementitious waste form testing performed by Pacific Northwest National Laboratory for Washington River Protection Solutions, LLC (WRPS). These results are part of a screening test that investigates grout formulations proposed for encapsulating a wide range of compositions predicted to be present in evaporator bottoms wastes from the Hanford Effluent Management Facility (EMF). This work supports the technical development need for alternative treatment and disposition paths for the EMF evaporator bottoms waste and future direct-feed low-activity waste (DFLAW) operations at the Hanford Site. High-priority activities included simulant production, grout formulation, and cementitious waste form testing. The work contained within this report relates to waste form development and testing, but does not directly support the 2017 Integrated Disposal Facility (IDF) performance assessment (PA). However, this work contains information useful for future PA updates [beyond fiscal year (FY) 2017] and future waste form development efforts. These analytical results can be used by (i) cementitious waste form scientists to further the understanding of cementitious leach behavior of contaminants of concern (COCs), (ii) decision makers interested in off-site waste form disposal, and (iii) the U.S. Department of Energy, their Hanford Site contractors, and stakeholders as they continue to assess the IDF PA program at the Hanford Site. The reported results help fill existing data gaps, support final selection of a cementitious waste form for the EMF evaporator bottoms waste, and improve the technical defensibility of long-term waste form risk estimates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Precision Measurement of the Proton Magnetic Form Factor at High Q2

Elastic electromagnetic form factors characterize the distribution of electric charge and magnetization current inside the nucleon and reflect the internal structure determined by Quantum Chromodynamics. Existing data on the proton magnetic form factor at high Q2 (the 4-momentum transfer squared) have large statistical and systematic uncertainties. The GMp experiment E12-07-108 was one of the first set of experiments to run in Hall A at Jefferson Lab after the 12 GeV upgrade with the goal of this experiment to precisely measure the electron-proton elastic cross section for Q2 up to 17 GeV2 with an accuracy of better than 2% - several times better than existing data in this Q2 range. This will allow further tests of form factor scaling predicted by pQCD and, additionally, will be an important benchmark for many other experiments where elastic electron-proton scattering is used for normalization. Since, GMp data were taken at lower ?(virtual photon polarization) than SLAC data, the measured cross sections recieve a smaller contribution from the electric form factor. This dissertation analyzed the GMp experiment data for five different kinematic settings determining the form factor with total uncertainties nearly two times smaller than the existing data at these Q2. This dissertation also presents the results of all Fall 2016 and Spring 2016 GMp experiment data. The proton magnetic form factors were extracted using both the Rosenbluth separation method and a parameterization of the form factor ratio (?pGpE=GpM) obtained from a fit to the existing cross section data. At the end of this thesis, the extracted GMp form factor data is compared to the existing data. The results for ?pGpE=GpM from Rosenbluth separations are found to be consistent with previous extractions, but with significantly reduced uncertainties, further highlighting the discrepancy with the polarization transfer technique. This data set can provide significant additional constraints on contributions from two-photon exchange.

Narayan Gautam, Thir↗

Updated Liquid Secondary Waste Grout Formulation and Preliminary Waste Form Qualification

This report describes the results from liquid secondary waste grout (LSWG) formulation and cementitious waste form qualification tests performed by Pacific Northwest National Laboratory (PNNL) for Washington River Protection Solutions, LLC (WRPS). New formulations for preparing a cementitious waste form from a high-sulfate liquid secondary waste stream simulant, developed for Effluent Management Facility (EMF) process condensates merged with low activity waste (LAW) caustic scrubber, and the release of key constituents (e.g. 99Tc and 129I) from these monoliths were evaluated. This work supports a technology development program to address the technology needs for Hanford Site Effluent Treatment Facility (ETF) liquid secondary waste (LSW) solidification and supports future Direct Feed Low-Activity Waste (DFLAW) operations. High-priority activities included simulant development, LSWG formulation, and waste form qualification. The work contained within this report relates to waste form development and testing and does not directly support the 2017 integrated disposal facility (IDF) performance assessment (PA). However, this work contains valuable information for use in PA maintenance past FY17, and for future waste form development efforts. The provided data should be used by (i) cementitious waste form scientists to further understanding of cementitious dissolution behavior, (ii) IDF PA modelers who use quantified constituent leachability, effective diffusivity, and partitioning coefficients to advance PA modeling efforts, and (iii) the U.S. Department of Energy (DOE) contractors and decision makers as they assess the IDF PA program. The results obtained help fill existing data gaps, support final selection of a LSWG waste form, and improve the technical defensibility of long-term waste form performance estimates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Transcriptome Dynamics of the Inflorescence in Reciprocally Formed Allopolyploid Tragopogon miscellus (Asteraceae)

Polyploidy is an important evolutionary mechanism and is prevalent among land plants. Most polyploid species examined have multiple origins, which provide genetic diversity and may enhance the success of polyploids. In some polyploids, recurrent origins can result from reciprocal crosses between the same diploid progenitors. Although great progress has been made in understanding the genetic consequences of polyploidy, the genetic implications of reciprocal polyploidization remain poorly understood, especially in natural polyploids. Tragopogon (Asteraceae) has become an evolutionary model system for studies of recent and recurrent polyploidy. Allotetraploid T. miscellus has formed reciprocally in nature with resultant distinctive floral and inflorescence morphologies (i.e., short- vs. long-liguled forms). In this study, we performed comparative inflorescence transcriptome analyses of reciprocally formed T. miscellus and its diploid parents, T. dubius and T. pratensis. In both forms of T. miscellus, homeolog expression of ~70% of the loci showed vertical transmission of the parental expression patterns (i.e., parental legacy), and ~20% of the loci showed biased homeolog expression, which was unbalanced toward T. pratensis. However, 17.9% of orthologous pairs showed different homeolog expression patterns between the two forms of T. miscellus. No clear effect of cytonuclear interaction on biased expression of the maternal homeolog was found. In terms of the total expression level of the homeologs studied, 22.6% and 16.2% of the loci displayed non-additive expression in short- and long-liguled T. miscellus, respectively. Unbalanced expression level dominance toward T. pratensis was observed in both forms of T. miscellus. Significantly, genes annotated as being involved in pectin catabolic processes were highly expressed in long-liguled T. miscellus relative to the short-liguled form, and the majority of these differentially expressed genes were transgressively down-regulated in short-liguled T. miscellus. Given the known role of these genes in cell expansion, they may play a role in the differing floral and inflorescence morphologies of the two forms. In summary, the overall inflorescence transcriptome profiles are highly similar between reciprocal origins of T. miscellus. However, the dynamic homeolog-specific expression and non-additive expression patterns observed in T. miscellus emphasize the importance of reciprocal origins in promoting the genetic diversity of polyploids.

54 ENVIRONMENTAL SCIENCES↗

The Lifetimes of Phases in High-mass Star-forming Regions

High-mass stars form within star clusters from dense, molecular regions (DMRs), but is the process of cluster formation slow and hydrostatic or quick and dynamic? We link the physical properties of high-mass star-forming regions with their evolutionary stage in a systematic way, using Herschel and Spitzer data. In order to produce a robust estimate of the relative lifetimes of these regions, we compare the fraction of DMRs above a column density associated with high-mass star formation, N(H{sub 2}) > 0.4–2.5 × 10{sup 22} cm{sup −2}, in the “starless” (no signature of stars ≳10 M{sub ⊙} forming) and star-forming phases in a 2° × 2° region of the Galactic Plane centered at ℓ = 30°. Of regions capable of forming high-mass stars on ∼1 pc scales, the starless (or embedded beyond detection) phase occupies about 60%–70% of the DMR lifetime, and the star-forming phase occupies about 30%–40%. These relative lifetimes are robust over a wide range of thresholds. We outline a method by which relative lifetimes can be anchored to absolute lifetimes from large-scale surveys of methanol masers and UCHII regions. A simplistic application of this method estimates the absolute lifetime of the starless phase to be 0.2–1.7 Myr (about 0.6–4.1 fiducial cloud free-fall times) and the star-forming phase to be 0.1–0.7 Myr (about 0.4–2.4 free-fall times), but these are highly uncertain. This work uniquely investigates the star-forming nature of high column density gas pixel by pixel, and our results demonstrate that the majority of high column density gas is in a starless or embedded phase.

79 ASTRONOMY AND ASTROPHYSICS↗

Probability of Forming Gaps in the GD-1 Stream by Close Encounters of Globular Clusters

One of the most intriguing properties of the GD-1 stellar stream is the existence of three gaps. If these gaps were formed by close encounters with dark matter subhalos, the GD-1 stream opens an exciting window through which we can see the size, mass, and velocity distributions of the dark matter subhalos in the Milky Way. However, in order to use the GD-1 stream as a probe of the dark matter substructure, we need to disprove that these gaps are not due to the perturbations from baryonic components of the Milky Way. Here we ran a large number of test-particle simulations to investigate the probability that each of the known globular clusters (GCs) can form a GD-1-like gap, by using the kinematical data of the GD-1 stream and GCs from Gaia early data release 3 and by fully taking the observational uncertainty into account. We found that the probability that all of the three gaps were formed by GCs is as low as 1.7 × 10 -5 , and the expected number of gaps formed by GCs is only 0.057 in our fiducial model. Our result highly disfavors a scenario in which GCs form the gaps. Given that other baryonic perturbers (e.g., giant molecular clouds) are even less likely to form a gap in the retrograde-moving GD-1 stream, we conclude that at least one of the gaps in the GD-1 stream was formed by dark matter subhalos if the gaps were formed by flyby perturbations.

79 ASTRONOMY AND ASTROPHYSICS↗

Design of fabric preforms for double diaphragm forming

Resin Transfer Molding (RTM) has the potential of becoming one of the most cost effective ways of producing composite structures since the raw materials used, resin and dry fabric, are less costly than prepregs. Unfortunately these low material costs are offset by the high labor costs incurred to layup the dry fabric into 3D shapes. To reduce the layup costs, double diaphragm forming is being investigated as a potential technique for creating a complex 3D preform from a simple flat layup. As part of our effort to develop double diaphragm forming into a production capable process, we have undertaken a series of experiments to investigate the interactions between process parameters, mold geometry, fabric weave, tow size, and the quality of the formed part. The results of these tests will be used to determine the forming geometry limitations of double diaphragm forming and to characterize the formability of fabric configurations. An important part of this work was the development of methods to measure and analyze fiber orientations, deformation angles, tow spreading, and shape conformation of the formed parts. This paper will describe the methods used to mark plies, the double diaphragm forming process, the techniques used to measure the formed parts, and the calculation of the parameters of interest. The results can be displayed as 3D contour plots. These experimental results have also been used to verify and improve a computer model which simulates the draping of fabrics over 3D mold shapes.

Luby, Steven↗

Dynamic Forms and Their Application to Control

The rigid body model plays a basic role in both mod- and control of many systems, including aircraft flight control. The distinctive feature of the rigid body is that its motion evolves on a curved space, Consequently, the designer must take into account the deterioration of chosen coordinations near their singularities. In these regions the control actions and the sensitivity to modeling and sensor errors become unacceptable. Thus, coordinate patches and patching logic should be a part of the overall control law design and implementation. The various dynamic forms, such as scalar forms, vector forms, matrix forms, rotational forms, Euler angle forms, and Euler parameter forms, described in the paper provide an effective means for coordinate patching and control law implementation. The utility of these forms is illustrated by means of several applications to flight control.

Meyer, George↗

Highlights of the ASPE 2004 Winter Topical Meeting on Free-Form Optics: Design, Fabrication, Metrology, Assembly

We present highlights from the American Society for Precision Engineering's 2004 winter topical meeting entitled Free-Form Optics: Design, Fabrication, Metrology, Assembly. We emphasize those papers that are most relevant to astronomical optics. Optical surfaces that transcend the bounds of rotational symmetry have been implemented in novel optical systems with fantastic results since the release of Polaroid's first instant camera. Despite these successes, free-form optics have found only a few niche applications and have yet to enter the mainstream. The purpose of this meeting is to identify the state of the art of free-form optics design, fabrication, metrology and assembly and to identify the technical and logistical challenges that inhibit their widespread use. Issues that will be addressed include: What are free-form optics? How can optical systems be made better with free-form optics? How can designers use free-form optics? How can free-form optics be fabricated? How can they be measured? How are free-form optical systems assembled? Control of multi-axis systems.

Ohl, Raymond G.↗

Antibodies Against Three Forms of Urokinase

Antibodies that bind to preselected regions of the urokinase molecule have been developed. These antibodies can be used to measure small quantities of each of three molecular forms of urokinase that could be contained in microsamples or conditioned media harvested from cultures of mammalian cells. Previously available antibodies and assay techniques do not yield both clear distinctions among, and measurements of, all three forms. Urokinase is a zymogen that is synthesized in a single-chain form, called ScuPA, which is composed of 411 amino acid residues (see figure). ScuPA has very little enzyme activity, but it can be activated in two ways: (1) by cleavage of the peptide bond lysine 158/isoleucine 159 and the loss of lysine 158 to obtain the high molecular-weight (HMW) form of the enzyme or (2) by cleavage of the bond lysine 135/lysine 136 to obtain the low-molecular-weight (LMW) form of the enzyme. The antibodies in question were produced in mice and rabbits by use of peptides as immunogens. The peptides were selected to obtain antibodies that bind to regions of ScuPA that include the lysine 158/isoleucine 159 and the lysine 135/lysine 136 bonds. The antibodies include monoclonal and polyclonal ones that yield indications as to whether either of these bonds is intact. The polyclonal antibodies include ones that preferentially bind to the HMW or LMW forms of the urokinase molecule. The monoclonal antibodies include ones that discriminate between the ScuPA and the HMW form. A combination of these molecular-specific antibodies will enable simultaneous assays of the ScuPA, HMW, and LMW forms in the same specimen of culture medium.

Morrison, Dennis R.↗