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The dynamics and control of large flexible space structures X, part 1

The effect of delay in the control system input on the stability of a continuously acting controller which is designed without considering the delay is studied. The stability analysis of a second order plant is studied analytically and verified numerically. For this example it is found that the system becomes unstable for a delay which is equivalent to only 16 percent of its natural period of motion. It is also observed that even a small amount of natural damping in the system can increase the amount of delay that can be tolerated before the onset of instability. The delay problem is formulated in the discrete time domain and an analysis procedure suggested. The maximum principle from optimal control theory is applied to minimize the time required for the slewing of a general rigid spacecraft. The slewing motion need not be restricted to a single axis maneuver. The minimum slewing time is calculated based on a quasi-linearization algorithm for the resulting two point boundary value problem. Numerical examples based on the rigidized in-orbit model of the SCOLE also include the more general reflector line-of-sight slewing maneuvers.

Bainum, Peter M.↗

Panel flutter in a low-density atmosphere

The problem of panel flutter is considered in the case of a free-molecule flow, the effect of the aerodynamic shear stress being incorporated into the structural model through distributed longitudinal and bending moment loads. This kind of analysis is relevant in the case of hypersonic flight vehicles, like the NASP, especially because in these conditions the shear stress can be expected to be considerably larger that the pressure at a given point. The aerodynamic loading is derived assuming a quasi-steady approximation. Two important parameters are given by alpha-m, the 'momentum accommodation coefficient', and Theta, the temperature ratio between the panel temperature and the temperature of the undisturbed flow. For high enough values of Theta the variation of the linear flutter parameter with alpha-m is close to linear. Comparison with continuum theory, given by linear piston theory, depends on the values of Theta and alpha-m considered. Finally, it is shown that buckling with respect to a uniform distributed longitudinal load is stabilizing.

Resende, Hugo B.↗

Arylethynyl Substituted 9,lO-Anthraquinones: Tunable Stokes Shifts by Substitution and Solvent Polarity

2-Arylethynyl- and 2,6- and 2,7-diarylethynyl-substituted 9,lO-anthraquinones were synthesized via Sonogashira coupling reactions of 2-bromo-, 2,6-dibromo-, and 2,7-dibromo-9,10- anthraquinone with para-substituted phenylacetylenes. While the redox properties of those compounds are almost insensitive to substitution, their absorption maxima are linearly related to the Hammett constants with different slopes for electron donors and electron acceptors. ABI compounds are photoluminescent both in solution (quantum yields of emission <= 6 %), and as solids. The emission spectra have the characteristics of charge-transfer bands with large Stokes shifts (100-250 nm). The charge-transfer character of the emitting state is supported by large dipole moment differences between the ground and the excited state as concluded on the basis of molecular modeling and Lippert-Mataga correlations of the Stokes shifts with solvent polarity. Maximum Stokes shifts are attained by both electron-donating and -withdrawing groups. This is explained by a destabilization of the HOMO by electron donors and a stabilization of the LUMO by electron acceptors. X-ray crystallographic analysis of, for example, 2,7-bisphenylethynfl- 9,lO-anthraquinone reveals a monoclinic P21In space group and no indication for pi-overlap that would promote quenching, thus explaining emission from the solid state. Representative reduced forms of the title compounds were isolated as stable acetates of the corresponding dihydrs-9,10- anthraquinones. The emission of these compounds is blue-shifted relative to the parent oxidized forms and is attributed to internal transitions in the dihydro-9,lO-anthraquinone core.

Yang, Jinhua↗

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗

Water Start Up Time Model Validation Test

This report is an Oregon Institute of Technology thesis project completed in partial fulfillment for the Masters of Science in Renewable Energy Engineering degree. The testing and research done for this report, investigate the phenomena of water start up time in the spiral case of hydro units. Water start up time is defined as the time it takes for water to accelerate from zero to rated velocity. From analysis of the literature there shows no published article of water start up time being measured and compared to theoretically calculated values. However a multiplier is used to create a buffer in the estimations of water start up time to use in the engineering and selection of governors for hydro units. The multiplier has also been widely used in computer model simulations which causes a dependence of this multiplier. In 2013 an article was published which challenges the hypothesis that water start up time has been over hypothesized and that the multiplier would be of a smaller value than what was hypothesized which would mean that the governing ability is more than what was expected. This proposal of a higher governing ability would mean that the hydro facilities that are currently standing has a higher stability rating than what was initially thought. The higher stability would allow for increased penetration of renewables onto the electrical grid. The lack of actual water start up time measurements as well as the infeasibility of testing on an actual hydro unit meant that a model would need to be designed, built, and tested. The model had two testing parameters that were examined. One of the parameters was flow rate that was controlled by the number of wicket gates that was installed into the system and the other was the reference height from the forebay to tail water. There were one hundred results from the test trials. The data from the trials showed a trend for the multiplier which was not constant as previously hypothesized and instead illustrated a parabolic trend that tapers into a linear digression. This result means that the range of testing was insufficient and the height range in which the trials were taking placed was subjected to higher variability. The results showed that the multiplier used in water start up time is not a constant and is variable based on the water level. The previous hypothesis stating that the water start up time is faster is false. In accordance with the results the trend showed that the actual water start up time is slower than what is hypothesized. This means at lower water levels the hypothesized governing ability is actually less than what is calculated to be using the current method of water start up time calculation for spiral cases. The theoretical analysis showed that with increased water level and flow rate showed that the multiplier has less effect on water start up time. The value of the water start up time tapering off from the experimental data shows that the trend for water start up time for both theoretical and experimental share similarities. An increased testing range of the water level in the trials will hypothetically lower the variability of the multiplier and in turn conform to a linear equation. The linear equation is shown to approach zero with increased head in which a static value can be achieved for a specified range.

13 HYDRO ENERGY↗

Rotating Disk Slurry Au Electrodeposition at Unsupported Carbon Vulcan XC-72 and Ce 3+ Impregnation for Ethanol Oxidation in Alkaline Media

A robust electrodeposition method consisting of the rotating disk slurry electrode (RoDSE) technique to obtain Au nanoparticles highly dispersed on a conductive carbonaceous support, i.e., Vulcan XC-72R, for ethanol electrooxidation reaction in alkaline media was developed. Ceria was used as a cocatalyst using a Ce(III)-EDTA impregnation method in order to enhance the catalytic activity and improve the catalyst’s overall stability. Furthermore, the RoDSE method used to obtain highly dispersed Au nanoparticles does not require the use of a reducing agent or stabilizing agent, and the noble-metal loading was controlled by the addition and tuning of the metal precursor concentration. Inductively coupled plasma and thermogravimetric analysis indicated that the Au loading in the catalyst was 9 %. We determined the particle size and characteristic Au fcc crystal facets by X-ray diffraction. The morphology of the catalyst was also investigated using electron microscopy techniques. In addition, X-ray absorption spectroscopy was used to corroborate the presence and identify the oxidation state of Ce in the system and to observe if there are any electronic interactions within the 8 % Au/CeO x /C system. Cyclic voltammetry of electrodeposited 9 % Au/C and Ce-promoted 8 % Au/C showed a higher catalytic current density for ethanol oxidation when compared with commercially available catalysts (20 % Au/C) of a higher precious metal loading. Additionally, we report a higher stability toward the ethanol electrooxidation process, which was corroborated by 1 mV/s linear sweep voltammetry and chronoamperometric studies.

36 MATERIALS SCIENCE↗

A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

In this work, we propose an Exponential DG framework for partial differential equations. We decompose 7 governing equations into linear and nonlinear parts to which we apply the discontinuous Galerkin 8 (DG) spatial discretization. In particular, we construct the linear part using Jacobian that effectively 9 capture stiff characteristics in the system. The former is integrated analytically, whereas the latter 10 is approximated. This approach i) is stable with a large Courant number (Cr > 1); ii) supports 11 high-order solutions both in time and space; iii) is computationally favorable compared to IMEX 12 DG methods with no preconditioner; iv) becomes comparable to explicit RKDG methods on uniform 13 mesh and beneficial on non-uniform grid for Euler equations; v) is scalable in a modern massively 14 parallel computing architecture due to its explicit nature of exponential time integrators and com15 pact communication stencil of DG method. Numerical results demonstrate the performance of our 16 proposed methods through various examples. We also discuss the stability and convergence analysis 17 for our exponential DG scheme in the context of Burgers equation.

42 ENGINEERING↗

Analytical and numerical study of the transverse Kelvin-Helmholtz instability in tokamak edge plasmas

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin- Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared ExB flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at and just outside the separatrix as a result of the distribution of magnetic shear. Lastly implications for reduced edge turbulence modeling codes are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Chain Flexibility and Structure of a Polyimide Copolymer: Revisiting the Freely Rotating Chain Model

Poly(4–4′-oxydiphenylene-pyromellitimide)-based polyimides─trade name Kapton─have wide-ranging engineering applications owing to their thermal and mechanical stability, but little is known about underlying chain-level characteristics. While theoretical models have conceptualized Kapton as inflexible polycyclic rods separated by freely rotating diphenyl ether hinge groups, the model’s core predictions remain untested and subtleties of the relaxation behavior are missed, which atomistic modeling can resolve. To these ends, we examine all-atom Kapton structures in crystalline and glassy amorphous configurations using a DFT-validated class II force field. Constructing amorphous configurations is challenging, as the fused-ring-containing backbone has slow relaxation dynamics and scaling suggestive of entanglements even in oligomers. In conclusion, we find larger backbone rearrangements of the linear polycyclic segments about ether groups that are consistent with the rod-hinge picture on the monomer scale, whereas a ring rotation analysis suggests partially flexible rod-like segments and involves multiple facile rotational relaxation modes.

Liesen, Nicholas T. [Lawrence Livermore National L↗

Model of Wave Driven Flow Oscillation for Solar Cycle

At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These terrestrial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr et al., GRL, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes less than 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock.

Mayr, Hans G.↗

Cs X Si 15 P 21 ( X = Sn or Pb): Polar Noncentrosymmetric Si–P Frameworks Stabilized by Covalent X –P Bonding

Metal silicon phosphides composed of earth-abundant Si and P tend to exhibit semiconducting properties and adopt diverse crystal structures with relatively small additions of structure-directing elements. The potential of silicon phosphide materials in nonlinear optical applications has been hindered by the inability to systematically produce noncentrosymmetric structures with such a flexible framework. Here, in this work, two isostructural compounds with a novel noncentrosymmetric structure were made possible by the inclusion of elements with stereochemically active lone pairs (Sn 2+ and Pb 2+ ). The structures were determined through single-crystal and synchrotron powder X-ray diffraction. Analysis of chemical bonding in real space through the electron localization function revealed stereochemically active Pb 2+ and Sn 2+ species in a trigonal pyramidal coordination with {Pb/Sn}–P bonds. Such covalent bonding between Pb and P is quite uncommon in extended solids and has been reported in a few rare instances. Band structure calculations and linear optical measurements confirm the semiconducting nature of Cs X Si 15 P 21 ( X = Sn or Pb). The synthesis was optimized to yield high-purity polycrystalline samples. The nonlinear optical properties show promising second-harmonic generation (SHG) coefficients from the Kurtz–Perry method. First-principles calculations of the nonlinear optical properties support the experimentally determined SHG values and provide moderate values of birefringence, suggesting Cs X Si 15 P 21 could be phase-matchable and practical nonlinear optical materials in the mid-IR region.

crystal structure↗

Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks

We consider two types of nonclassical fracture mechanisms, namely, the fracture of cracked bodies with initial (residual) stresses acting along the crack planes and the fracture of solids under compression along parallel cracks. To investigate nonaxisymmetric and axisymmetric problems for infinite solids containing two parallel coaxial cracks or a periodic set of coaxial parallel cracks, we use a combined analytic-numerical method within the framework of the three-dimensional linearized mechanics of solids. The analysis involves the representation of stresses and displacements in the linearized theory via harmonic potential functions. With the use of the integral Fourier–Hankel transformations, the problems are reduced to the solution of Fredholm integral equations of the second kind. This approach allows us to investigate problems in a unified general form for compressible and noncompressible homogeneous isotropic or transversely isotropic elastic bodies with an arbitrary structure of the elastic potential, and the material specification of the model is carried out only in the stage of numerical analysis of the resolving equations obtained in the general form. The effects of initial stresses on the stress intensity factors are analyzed for highly elastic materials and layered composites (modeled as transversely isotropic elastic bodies). The “resonance-like” effects are revealed when compressive initial stresses reach the values corresponding to the local loss of stability of the material in the vicinity of cracks, which, according to the indicated combined method, allows one to determine the critical (limiting) load parameters under the conditions of compression of the body along the cracks. The conclusions concerning the dependences of the stress intensity factors and critical (limiting) parameters of compression on the geometric parameters of the problems are formulated as well as concerning the dependences on physical and mechanical characteristics of the materials.

42 ENGINEERING↗

Structures of honeybee-infecting Lake Sinai virus reveal domain functions and capsid assembly with dynamic motions

Understanding the structural diversity of honeybee-infecting viruses is critical to maintain pollinator health and manage the spread of diseases in ecology and agriculture. We determine cryo-EM structures of $T$ = 4 and $T$ = 3 capsids of virus-like particles (VLPs) of Lake Sinai virus (LSV) 2 and delta-N48 LSV1, belonging to tetraviruses, at resolutions of 2.3–2.6 Å in various pH environments. Structural analysis shows that the LSV2 capsid protein (CP) structural features, particularly the protruding domain and C-arm, differ from those of other tetraviruses. The anchor loop on the central β-barrel domain interacts with the neighboring subunit to stabilize homo-trimeric capsomeres during assembly. Delta-N48 LSV1 CP interacts with ssRNA via the rigid helix α1’, α1’–α1 loop, β-barrel domain, and C-arm. Cryo-EM reconstructions, combined with X-ray crystallographic and small-angle scattering analyses, indicate that pH affects capsid conformations by regulating reversible dynamic particle motions and sizes of LSV2 VLPs. C-arms exist in all LSV2 and delta-N48 LSV1 VLPs across varied pH conditions, indicating that autoproteolysis cleavage is not required for LSV maturation. The observed linear domino-scaffold structures of various lengths, made up of trapezoid-shape capsomeres, provide a basis for icosahedral $T$ = 4 and $T$ = 3 architecture assemblies. These findings advance understanding of honeybee-infecting viruses that can cause Colony Collapse Disorder.

59 BASIC BIOLOGICAL SCIENCES↗

Analysis of double stub tuner control stability in a many element phased array antenna with strong cross-coupling

Active stub tuning with a fast ferrite tuner (FFT) allows for the system to respond dynamically to changes in the plasma impedance such as during the L-H transition or edge localized modes (ELMs), and has greatly increased the effectiveness of fusion ion cyclotron range of frequency systems. A high power waveguide double-stub tuner is under development for use with the Alcator C-Mod lower hybrid current drive (LHCD) system. Exact impedance matching with a double-stub is possible for a single radiating element under most load conditions, with the reflection coefficient reduced from Γ to Γ{sup 2} in the “forbidden region.” The relative phase shift between adjacent columns of a LHCD antenna is critical for control of the launched n{sub ∥} spectrum. Adding a double-stub tuning network will perturb the phase of the forward wave particularly if the unmatched reflection coefficient is high. This effect can be compensated by adjusting the phase of the low power microwave drive for each klystron amplifier. Cross-coupling of the reflected power between columns of the launcher must also be considered. The problem is simulated by cascading a scattering matrix for the plasma provided by a linear coupling model with the measured launcher scattering matrix and that of the FFTs. The solution is advanced in an iterative manner similar to the time-dependent behavior of the real system. System performance is presented under a range of edge density conditions from under-dense to over-dense and a range of launched n{sub ∥}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effects of temperature and time on supercritical methanol Co-Liquefaction of rice straw and linear low-density polyethylene wastes

We report that biofuels are particularly attractive and play an increasingly important role in sustainable energy. However, biofuels originating from lignocellulosic biomass (LCB) are extremely challenging because of their low carbon content, low stability, and high oxygen content. This work evaluates the supercritical methanol (scMeOH) co-liquefaction of rice straw and linear low-density polyethylene (LLDPE) at temperature range of 240-340 °C for 0-2 h, to obtain hydrocarbons (HCs)-rich oil and carbon-rich solid product. Results show that reaction temperature dominated the yield and properties of products, but not the holding time. Among parameters tested, 30.07 wt% oil yield with 75.79% HCs content and 33.05 wt% oil yield with 70.91% HCs content were obtained at 300 °C for 1 h and 1.5 h, respectively. Simultaneously, the remaining solid products were still as high as 53.85 wt% with a carbon content of 79.59% and 48.28 wt% with carbon content of 81.34% under 300 °C for 1 h and 1.5 h, respectively. Ultimate analysis, FT-IR, TGA, and SEM show that solid products could be used as sustainable carbon resources, and solid fuel rather than soil amendment because of risk of micro plastic or adsorbent due to smooth surface without pores.

09 BIOMASS FUELS↗

SU-E-E-15: Design of a Water Calorimeter for Dual Use in An Integrated MRI-Linac and Gamma-Knife

Purpose: To design a water calorimeter for dual use in an integrated MRI-linac and Gamma-Knife. In calorimetry, dose to water is measured based on the assumption that energy absorbed in a sensitive volume is completely converted to temperature rise {sub (}ΔΤ{sub )} according to the specific heat capacity of the medium c: D=c*ΔT*k, where k is heat transfer correction factor and compensates for heat gain or loss at point of measurement due to conductive effects. Methods: A commercial finite element method software package was used to model four different water calorimeter designs. The long term (48 h) thermal stability of each design was accurately modeled, and the optimization of the final design was based on evaluation of the standard deviation of k for ten consecutive irradiation runs (lower standard deviation translates to greater thermal stability). Several insulator materials of varying thicknesses were investigated, and a sensitivity study of thermal stability to variations in ambient temperature fluctuations was undertaken. Specifically, we evaluated the effect of possible variations in coolant temperature circulating around the calorimeter tank in several scenarios (constant, slowly increasing, or fluctuating). Results: Due to MRI-compatibility requirements, the calorimeter is to be built entirely out of plastic. Among all insulation materials tested, solid state aerogel-based insulation resulted in least heat loss and thermal stability. The final design is cylindrical on top (to be used upright in MRI-linac) and semi-spherical at bottom (for use in GammaKnife). The range of k was found to be 1.002 ± 0.013 (k = 1), comparable with a k of 1.002 ± 0.014 for typical water calorimeters used in high energy beams. A long term stability of 0.36 µK/hr was evaluated. Conclusion: Optimization of a water calorimeter design for dual use in MRI-linac and Gamma-Knife has been completed and the device is currently in production. Supported by NSERC RGPIN 435608.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time marching Full Potential cascade solver are developed and verified. In the first method, the Influence Coefficient, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier Transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers.

Bakhle, Milind A.↗