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Two-color, intracavity pump–probe, cavity ringdown spectroscopy

Here, we report a proof-of-principle demonstration of intracavity pump–probe, cavity ringdown (CRD) detection in a three-mirror, traveling-wave cavity. With cavity-enhanced pump power and probe absorption path length, the technique is a generally applicable, high-sensitivity, high-selectivity detection method. In our experiments, the pump radiation is switched off during every other probe ringdown, which allows uncorrelated measurements of analyte and background cavity decay rates. The net, two-color signal from the difference between the pump-on and pump-off decay rates is immune to empty-CRD drifts and spectral overlaps from non-target molecular transitions. The immunity to the ringdown drifts allows longer signal-averaging and, thus, higher detection sensitivity. The ability to compensate for the background absorption enhances the detection selectivity in spectrally congested regions. Our technique is well-suited for trace-detection in the mid-IR region, where pump–probe schemes based on strong rovibrational transitions can be applied. In this work, two-color CRD detection is implemented on a ladder-type, three-level system based on the N 2 O, ν 3 = 1 ← 0, P(19) (pump) and ν 3 = 2 ← 1, R(18) (probe), rovibrational transitions. By frequency-locking two-quantum cascade lasers to the p-polarization (pump, Finesse = 5280) and s-polarization (probe, Finesse = 67 700) cavity modes, we achieve high intracavity pump power (36 W) and high probe ringdown rates (>2 kHz). The observed two-color spectra are simulated by a density-matrix, three-level system model that is solved under the constraints of the cavity resonance conditions. In addition to its background compensation capability, experimental flexibility in the selection of pump–probe schemes and signal insensitivity to intracavity laser power are further features that enhance the utility of our technique for mid-IR trace-detection.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SU-E-T-353: Effects of Time and Temperature On a Potential Reusable 3D Dosimeter

Purpose: Preliminary studies of a novel, optically-clearing PRESAGE 3D dosimeter formulation (Presage-RU) demonstrated potential reusability. This study investigates the effects of time and temperature on the accuracy and reusability of Presage-RU, and reports on progress toward developing a reusable 3D dosimeter. Methods: Presage-RU was cast as small volume samples (1×1×4.5cm). The effect of dose response sensitivity with reirradiation and time was evaluated by irradiating samples from 0–10Gy, measuring change in optical density (ΔOD), clearing at room temperature (RT) (5–7 days to fully clear), and then repeating for a total of 5 irradiations. Effects of heating on clearing rate were investigated by irradiating samples to 8Gy, then tracking measurements with samples held at RT, 35°C, and 45°C. Two cylindrical dosimeters (11cm diameter, 9.5cm length) were evaluated for dosimetric accuracy when stored at RT and −3°C prior to irradiation. Plans delivered were 2 overlapping AP fields (RT) and VMAT (-3°C). Results: Heating the dosimeters reduced the clearing half-life from 16.3h at RT to 5.8h (35°C) and 5.1h (45°C), but also increased background ΔOD by 1.7x (35°C) and 2.3x (45°C). Reductions in dose response were more closely linked to age than reirradiation, and storage at RT showed pronounced desensitization from dosimeter edges. These results suggest desensitization from oxygen diffusion. It should be noted that atmospheric diffusion into the dosimeter is not seen in standard, single-use PRESAGE, and is likely caused by differences in the Presage-RU polyurethane matrix. The dosimeter kept in cold storage, however, showed no evidence of desensitization and exhibited accuracy on par with standard PRESAGE with a 3%/3mm 3D gamma passing rate of 98.1%. Conclusions: Presage-RU is sensitive to storage temperatures and time, both of which affect oxygen diffusion and subsequent desensitization. Development shows promising progress with further formulation optimization as the next step toward achieving a successful reusable 3D dosimeter. This work was supported by NIH R01CA100835. John Adamovics is the president of Heuris Inc., which commercializes PRESAGE.

60 APPLIED LIFE SCIENCES↗

Tritium Control and Capture in Salt-Cooled Fission and Fusion Reactors: Status, Challenges, and Path Forward

Three advanced nuclear power systems use liquid salt coolants that generate tritium and thus face the common challenges of containing and capturing tritium to prevent its release to the environment. The fluoride salt–cooled high-temperature reactor (FHR) uses clean fluoride salt coolants and the same graphite-matrix coated-particle fuel as high-temperature gas-cooled reactors. Molten salt reactors (MSRs) dissolve the fuel in a fluoride or chloride salt with release of fission product tritium into the salt. In most FHR and MSR systems, the baseline salts contain lithium where isotopically separated 7 Li is proposed to minimize tritium production from neutron interactions with the salt. The Chinese Academy of Sciences plans to start operation of a 2-MW(thermal) molten salt test reactor by 2020. For high-magnetic-field fusion machines, the use of lithium enriched in 6 Li is proposed to maximize tritium generation—the fuel for a fusion machine. Advances in superconductors that enable higher power densities may require the use of molten lithium salts for fusion blankets and as coolants. Recent technical advances in these three reactor classes have resulted in increased government and private interest and the beginning of a coordinated effort to address the tritium control challenges in 700°C liquid salt systems. In this paper, we describe characteristics of salt-cooled fission and fusion machines, the basis for growing interest in these technologies, tritium generation in molten salts, the environment for tritium capture, models for high-temperature tritium transport in salt systems, alternative strategies for tritium control, and ongoing experimental work. Several methods to control tritium appear viable. Finally, limited experimental data are the primary constraint for designing efficient cost-effective methods of tritium control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Trojan horse method as an indirect approach to study resonant reactions in nuclear astrophysics

The primary goal of the Trojan horse method (THM) is to analyze resonant rearrangement reactions when the density of the resonance levels is low and statistical models cannot be applied. The main difficulty of the analysis is related with the facts that in the final state the THM reaction involves three particles and that the intermediate particle, which is transferred from the Trojan horse particle to the target nucleus to form a resonance state, is virtual. Another difficulty is associated with the Coulomb interaction between the particles, especially, taking into account that the goal of the THM is to study resonant rearrangement reactions at very low energies important for nuclear astrophysics. The exact theory of such reactions with three charged particles is very complicated and is not available. This is why different approximations are used to analyze THM reactions. In this review paper we describe a new approach based on a few-body formalism that provides a solid basis for deriving the THM reaction amplitude taking into account rescattering of the particles in the initial, intermediate and final states of the THM reaction. Since the THM uses a two-step reaction in which the first step is the transfer reaction populating a resonance state, we address the theory of the transfer reactions. The theory is based on the surface-integral approach and R-matrix formalism. We also discuss application of the THM to resonant reactions populating both resonances located on the second energy sheet and subthreshold resonances, which are subthreshold bound states located at negative energies close to thresholds. We consider the application of the THM to determine the astrophysical factors of resonant radiative-capture reactions at energies so low that direct measurements can hardly be performed due to the negligibly small penetrability factor in the entry channel of the reaction. Here, we elucidated the main ideas of the THM and outline necessary conditions to perform the THM experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

Method and apparatus for the collection, storage, and real time analysis of blood and other bodily fluids

The present invention provides a simple, portable, relatively inexpensive apparatus for accurately and efficiently collecting, separating, testing, and even storing between about 1-20 ml, preferably about 1-10 ml, of blood or other bodily fluid in situ. The apparatus includes a collection chamber bounded on its sides by an opening in a sheet of material, preferably clear plastic, abutting a filter card. The filter card is made of fibrous material, preferably less than about a millimeter thick, having an average pore size of less than about 3 microns. Preferably, the fibers are glass and the fibrous material has an average pore size of about 1 micron. The fibrous material is treated with a carbohydrate/protein mixture which contains between about 1-40 percent wt/vol carbohydrate and about 0.1-15 percent wt/vol nonspecific protein, preferably between about 10-20 percent carbohydrate and about 5-8 percent protein. A preferred carbohydrate/protein mixture comprises about 10 percent mannitol and about 6 percent albumin. The blood or other fluid moves through the filter card by capillary action aided by an absorbent matrix with a high Klemm factor which abuts the filter card. The absorbent matrix and/or filter card can be treated with a wide spectrum of test reagents. The speed, cleanliness, and efficiency of the separation process can be altered by: (a) changing the absolute concentration of the carbohydrate/protein mixture; (b) applying positive or negative pressure to one side of the filter; and/or (c) varying the relative density and pore size of the filter card and absorbent matrix.

Whitson, Peggy A.↗

Operator Relaxation and the Optimal Depth of Classical Shadows

Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via “shallow shadows,” a recently proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth t. Here we show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing (“twirling”) circuit—namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially contiguous Pauli operators of weight k, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth t~log⁡(k), guarantees an exponential gain in sample complexity over the t=0 protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our Letter connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly optimized protocols for learning different properties of quantum states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sintering Behaviors of ZrC, NbC, and TaC Mono-and Binary Carbides

Nuclear Thermal Propulsion (NTP) has undergone development as an alternate in-space propulsion system to traditional chemical propulsion methods since the 1950s. In an NTP system, the energy released from fission in the core is utilized as the heat source to directly heat a propellant for propulsion, rather than chemical combustion in a traditional rocket. NTP has many desirable capabilities including flexible mission launch dates and reduced transit times due to it’s capability for high specific impulse. One of the main challenges with NTP systems is the structural integrity of the fuel. The fuel form required in the reactor core must withstand temperatures above 2700 Kelvin. Ceramic-metallic matrix fuel, ceramic-ceramic matrix fuel, and solid solution carbide fuels are the three strongest candidates for the extreme environments. Solid solution carbides have the potential to exhibit promising behavior as a fuel form in an NTP system. Of the multiple refractory metal carbides of interest, here we focus on zirconium carbide (ZrC), niobium carbide (NbC), and tantalum carbide (TaC). ZrC, NbC, and TaC powders were consolidated in monocarbide (ZrC, NbC, and TaC) and bi-carbide (ZrC-NbC, ZrC-TaC, NbC-TaC) forms using spark plasma sintering (SPS). In addition to the pure endpoint carbides, the examined compositions of the various bi-carbides ranged from 25-75 mol%. The sintering temperatures, pressures, and hold times were varied to determine the ideal sintering conditions. Grain size analysis, Archimedes’ density, scanning electron microscopy (SEM), X-ray diffraction (XRD), and energy dispersion spectroscopy (EDS) were used to determine and characterize the grain size, ideal density, porosity, phase stability, and chemical composition of each sample. The data from each sample was then used to generate a Master Sintering Curve (MSC) unique to each monocarbide or bi-carbide.

nuclear thermal propulsion↗

Low Cost Glass-Ceramic Matrix Composite Heat Exchanger

As part of ARPA-E’s High Intensity Thermal Exchange through Materials and Manufacturing Processes (HITEMMP) program, this project sought to develop novel heat exchanger (HX) capabilities to enable efficient and power dense power generation cycles. This class of HX comes under the category of ceramic/composite materials with the higher temperature goal in the program of ≥1100 °C inlet temperature operation. The enabling capability of this effort is the use of glass-ceramic matrix composite (GCMC) material which provides the high temperature durability of a ceramic, the flaw tolerance of a composite, a significantly faster and lower cost manufacturing process than conventional matrix CMCs and very low porosity levels < 0.5%. For thin-walled HX structures and the need to minimize leakage, the low porosity differentiator is particularly important. RTRC has prior experience with this material system and in the current project advanced the component design and manufacturing methods into new territory to produce features required for effective heat exchange under high pressures. In this approach, silicon carbide fiber is fabricated into a fiber preform using various textile processes. Graphite tooling is used both during the build-up of the fiber preform (interior tooling) and after the fiber preform has been completed (exterior tooling). This tooling assembly is heated to high temperature in an environment that has been evacuated and backfilled with inert gas. A reservoir of specialty glass is present and once the desired temperature has been reached to achieve the desired glass viscosity, an actuator distributes the glass throughout the fiber preform using passageways which are part of the tooling design in a process known as glass transfer molding. After the tooling has been removed, the composite is heat treated to convert the amorphous glass to a crystalline ceramic, providing improved properties. The project was divided into three phases focusing on the following: 1) 10 kW HX design and coupon-level tube sheet fabrication, 2) 10 kW HX fabrication, 3) 50 kW HX fabrication. During Budget Period 1 (BP1), additional risks were encountered and the need for additional funds was agreed upon by ARPA-E program leadership. Due to a variety of factors, the contract modification required nominally 18 months to execute at which time the HITEMMP program was effectively concluding. Because of this and the time that would be required to perform BP2 tasks, it was decided to conclude the project at the end of BP1. During the design of the 10 kW HX, manufacturing constraints were learned and incorporated, leading to a revised configuration for the fiber preform and HX. Heat exchange and pressure drop predictions also played a role in modifying the original design concept to be a higher aspect ratio shell-and-tube HX, simplifying the manufacturing process and improving the heat exchanger performance. Good gravimetric and volumetric thermal power densities of 11.2 kW/kg and 10,200 kW/m3 for the entire HX were projected that involved thermo-structural Finite Element Analysis to determine the structural mass needed for the high operation pressures of 250 bar cold inlet and 80 bar hot inlet. Fiber preforms using textile processes were produced for multiple headered tube sheets. Additional challenges were encountered during the glass transfer molding step for which solutions were identified, but programmatics did not allow them to be implemented in BP1. While complete HX test articles were not fabricated, the benefits of this GCMC material for a variety of high temperature applications remain.

30 DIRECT ENERGY CONVERSION↗

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of oxygen on weld shape and crystallographic orientation of duplex stainless steel weld using advanced A-TIG (AA-TIG) welding method

The double-shielded advanced A-TIG (AA-TIG) welding method was adopted in this study for the welding of the SUS329J4L duplex stainless steel with the shielding gases of different oxygen content levels. The oxygen content in the shielding gas was controlled by altering the oxygen content in the outer layer gas, while the inner layer remained pure argon to suppress oxidation on the tungsten electrode. As a result, a deep weld penetration was obtained due to the dissolution of oxygen into the weld metals. Additionally, the microstructure of the weld metal was changed by the dissolution of oxygen. The austenite phase at the ferrite grain boundary followed a Kurdjumov–Sachs (K–S) orientation relationship with the ferrite matrix phase at any oxide content. On the other hand, the orientation relationship between the intragranular austenite phase and the ferrite matrix phase exhibited different patterns under different oxygen content levels. When there was little oxide in the fusion zone, only a limited part of the intragranular austenite phase and the ferrite matrix phase followed the K–S orientation relationship. With the increase of the oxide, the correspondence of the K–S relationship increased and fit very well in the 2.5% O{sub 2} shielded sample. The investigation of this phenomenon was carried out along with the nucleation mechanisms of the intragranular austenite phases. - Highlights: • Weld penetration increased with the increase of the oxygen content. • Average diameter and number density of oxide were changed by the oxygen content. • K-S relationship of Widmanstätten austenite/ferrite wasn’t varied by oxide. • Orientation relationship of intragranular austenite/ferrite was varied by oxide.

36 MATERIALS SCIENCE↗

Flutter and Divergence Analysis using the Generalized Aeroelastic Analysis Method

The Generalized Aeroelastic Analysis Method (GAAM) is applied to the analysis of three well-studied checkcases: restrained and unrestrained airfoil models, and a wing model. An eigenvalue iteration procedure is used for converging upon roots of the complex stability matrix. For the airfoil models, exact root loci are given which clearly illustrate the nature of the flutter and divergence instabilities. The singularities involved are enumerated, including an additional pole at the origin for the unrestrained airfoil case and the emergence of an additional pole on the positive real axis at the divergence speed for the restrained airfoil case. Inconsistencies and differences among published aeroelastic root loci and the new, exact results are discussed and resolved. The generalization of a Doublet Lattice Method computer code is described and the code is applied to the calculation of root loci for the wing model for incompressible and for subsonic flow conditions. The error introduced in the reduction of the singular integral equation underlying the unsteady lifting surface theory to a linear algebraic equation is discussed. Acknowledging this inherent error, the solutions of the algebraic equation by GAAM are termed 'exact.' The singularities of the problem are discussed and exponential series approximations used in the evaluation of the kernel function shown to introduce a dense collection of poles and zeroes on the negative real axis. Again, inconsistencies and differences among published aeroelastic root loci and the new 'exact' results are discussed and resolved. In all cases, aeroelastic flutter and divergence speeds and frequencies are in good agreement with published results. The GAAM solution procedure allows complete control over Mach number, velocity, density, and complex frequency. Thus all points on the computed root loci can be matched-point, consistent solutions without recourse to complex mode tracking logic or dataset interpolation, as in the k and p-k solution methods.

Edwards, John W.↗

Orientational Dependence of Cofacial Porphyrin–Quinone Electronic Interactions within the Strong Coupling Regime

We examine the relative magnitudes of electronic coupling HDA in two face-to-face rigid and diastereomeric (porphinato)zinc(II)–quinone (PZn–Q) as-semblies, 1β-ZnA and 1β-ZnB, in which the six quinonyl carbon atoms lie in virtually identical arrangements relative to the PZn plane at sub-van der Waals donor–acceptor (D–A) interplanar separations. Steady-state and time-resolved transient optical data and computational studies show that minor differences in relative D–A cofacial orientation give rise to disparate H DA magnitudes for both photoinduced charge separation (CS) and thermal charge recombination (CR). Here, time-dependent density functional theory (TDDFT) computations illuminate the nature of direct charge transfer states and the electronic structural factors that give rise to these differential H DA s. These data show more extensive mixing of locally excited (LE) and CS states in 1β-ZnA relative to 1β-ZnB and that these H DA differences track the magnitudes of electronic coupling matrix elements determined from steady-state electronic spectral data and thermal CR rate constants measured via pump–probe spectroscopy. Collectively, this work shows that electron transfer dynamics may be manipulated in cofacial D–A systems, even at sub-van der Waals contact, provided that conformational rigidity precludes structural fluctuations that modulate D–A interactions on the charge transfer time scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Robust Predictive Control for Modular Solid-State Transformer With Reduced DC Link and Parameter Mismatch

This paper presents the analysis and implementation of a predictive control method for dc-link regulation and voltage balance in a cascaded modular reduced dc-link solid-state transformer (SST). Passive components like bulky dc links limit the power density of power converters, especially medium-voltage (MV) SST. Reduced dc-link or low-inertia converters can dramatically reduce the size, cost, and weight by tolerating larger dc-link ripples and improve the reliability with electrolytic capacitor-less dc link. However, a small dc link leads to tight coupling between the input and the output stages, which is a challenge for control design. In stacked low-inertia converters (SLIC), the low-inertia converter modules are stacked for MV applications, resulting in coupling between the modules and making the control more challenging. A new model predictive control method which can achieve deadbeat regulation on the dc link without weighting factors has been proposed to address this novel problem. This paper focuses on analyzing the condition of the low-inertia dc link up to 80% ripple, the robustness of the control under parameter mismatches, high-order terms, and important implementation issues such as model-based sampling and computation delay compensation. Significantly, the high-order terms are introduced because of the large dc-link ripple. These high-order terms are unique to the SLIC and negligible in conventional high-inertia converters. A discrete-time large-signal model is built to capture the dc-link’s nonlinear dynamics, and the eigenvalues of a small-signal Jacobian matrix are analyzed with Floquet theory to evaluate stability, using the modular soft-switching solid-state transformer (M-S4T) as an example of the SLIC. Simulation and experimental results of an MVDC M-S4T verify the analysis and the predictive control method. Finally, the general application of the predictive control to low-inertia converters is compared against a conventional PI controller using a reduced dc-link active-front-end (AFE) rectifier as an example.

14 SOLAR ENERGY↗

Dynamically weighted multireference perturbation theory: Combining the advantages of multi-state and state-averaged methods

In this paper, we introduce two new approaches to compute near-degenerate electronic states based on the driven similarity renormalization group (DSRG) framework. The first approach is a unitary multi-state formalism based on the DSRG (MS-DSRG), whereby an effective Hamiltonian is built from a set of state-specific solutions. The second approach employs a dynamic weighting parameter to smoothly interpolate between the multi-state and the state-averaged DSRG schemes. The resulting dynamically weighted DSRG (DW-DSRG) theory incorporates the most desirable features of both multi-state approaches (ability to accurately treat many states) and state-averaged methods (correct description of avoided crossings and conical intersections). We formulate second-order perturbation theories (PT2) based on the MS- and DW-DSRG and study the potential energy curves of LiF, the conical intersection of the two lowest singlet states of NH 3 , and several low-lying excited states of benzene, naphthalene, and anthracene. The DW-DSRG-PT2 predicts the correct avoided crossing of LiF and avoids artifacts produced by the corresponding state-specific and multi-state theories. Excitation energies of the acenes computed with the DW-DSRG-PT2 are found to be more accurate than the corresponding state-averaged values, showing a small dependence on the number of states computed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

New sterically hindered polyvinylamine-containing membranes for CO 2 capture from flue gas

Amine-containing facilitated transport membranes can have both high permeability and selectivity due to the reversible reaction between CO 2 and amino groups for effective carbon capture from flue gas. In this study, we have developed an improved method for the synthesis of high-molecular-weight sterically hindered polyvinylamine (PVAm) as the new fixed-site carrier in thin-film composite membranes for CO 2 capture. Commercially available PVAm was N-monomethylated into poly-N-methyl-N-vinylamine (PVAm-CH 3 ) using the stepwise reductive amination with a highly polar fluorinated alcohol as the solvent to enhance the equilibrium shift to the formation of the imine intermediate. The method prevented over-alkylation, resulting in the increased yield of the target product. PVAm-CH 3 exhibited excellent CO 2 facilitation with a CO 2 permeability of 445.7 Barrer (1 Barrer = 3.349 x 10 –16 mol m m –2 s –1 Pa –1 ) and a CO 2 /N 2 selectivity of 70.3, which are above the Robeson 2008 upper bound. The PVAm-CH 3 solution retained a sufficiently high viscosity after incorporating the aminoacid salt, 2-(1-piperazinyl)ethylamine sarcosinate (PZEA-Sar), as the mobile carrier for the membrane coating on nanoporous polyethersulfone (PES) substrates without any penetration issues. The resultant thin-film composite PVAm-CH3/PZEA-Sar membrane with a thickness of approximately 170 nm exhibited a superior CO 2 performance of 1071 GPU (1 GPU = 3.349 x 10 –10 mol m –2 s –1 Pa –1 ) and a CO 2 /N 2 selectivity of 183 at 57°C and a feed gas pressure of 111.64 kPa (1.5 psig). This PVAm-CH 3 /PZEA-Sar membrane surpassed the latest redefined 2019 CO 2 /N 2 upper bound and outperformed other polymer-based membranes. Density functional theory calculations also demonstrated that PVAm-CH 3 showed a stronger preference, relative to PVAm, toward the more efficient bicarbonate pathway. Thus, the steric hindrance effect of PVAm-CH 3 enhanced the solubility of CO 2 in the polymer matrix and resulted in the higher CO 2 permeance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomistic Simulations of Mass and Thermal Transport in Oxide Nuclear Fuels

In this talk we discuss simulations of the mass and thermal transport in oxide nuclear fuels. Redistribution of fission gases such as Xe is closely coupled to nuclear fuel performance. Most fission gases have low solubility in the fuel matrix, specifically the insolubility is most pronounced for large fission gas atoms such as Xe, and as a result there is a significant driving force for segregation of gas atoms to grain boundaries or dislocations and subsequently for nucleation of gas bubbles at these sinks. The first step of the fission gas redistribution is diffusion of individual gas atoms through the fuel matrix to existing sinks, which is governed by the activation energy for bulk diffusion. Fission gas bubbles are then formed by either separate nucleation events or by filling voids that were nucleated at a prior stage; in both cases their formation and latter growth is coupled to vacancy dynamics and thus linked to the production of vacancies via irradiation or thermal events. In order to better understand bulk Xe behavior (diffusion mechanisms) in UO 2±x we first calculate the relevant activation energies using density functional theory (DFT) techniques. By analyzing a combination of Xe solution thermodynamics, migration barriers and the interaction of dissolved Xe atoms with U, we demonstrate that Xe diffusion predominantly occurs via a vacancy-mediated mechanism, though other alternatives may exist in high irradiation fields. Since Xe transport is closely related to diffusion of U vacancies, we have also studied the activation energy for this process. In order to explain the low value of 2.4 eV found for U migration from independent damage experiments (not thermal equilibrium) the presence of vacancy clusters must be included in the analysis. Next a continuum transport model for Xe and U is formulated based on the diffusion mechanisms established from DFT. After combining this model with descriptions of the interaction between Xe and grain boundaries derived from separate atomistic calculations, we simulate Xe redistribution for a few simple microstructures using finite element methods (FEM), as implemented in the MOOSE framework from Idaho National Laboratory. Thermal transport together with the power distribution determines the temperature distribution in the fuel rod and it is thus one of the most influential properties on nuclear fuel performance. The fuel thermal conductivity changes as function of time due to microstructure evolution (e.g. fission gas redistribution) and compositional changes. Using molecular dynamics simulations we have studied the impact of different types of grain boundaries and fission gas bubbles on UO 2 thermal conductivity.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Characterization of scatter in digital mammography from physical measurements

Purpose: That scattered radiation negatively impacts the quality of medical radiographic imaging is well known. In mammography, even slight amounts of scatter reduce the high contrast required for subtle soft-tissue imaging. In current clinical mammography, image contrast is partially improved by use of an antiscatter grid. This form of scatter rejection comes with a sizeable dose penalty related to the concomitant elimination of valuable primary radiation. Digital mammography allows the use of image processing as a method of scatter correction that might avoid effects that negatively impact primary radiation, while potentially providing more contrast improvement than is currently possible with a grid. For this approach to be feasible, a detailed characterization of the scatter is needed. Previous research has modeled scatter as a constant background that serves as a DC bias across the imaging surface. The goal of this study was to provide a more substantive data set for characterizing the spatially-variant features of scatter radiation at the image detector of modern mammography units. Methods: This data set was acquired from a model of the radiation beam as a matrix of very narrow rays or pencil beams. As each pencil beam penetrates tissue, the pencil widens in a predictable manner due to the production of scatter. The resultant spreading of the pencil beam at the detector surface can be characterized by two parameters: mean radial extent (MRE) and scatter fraction (SF). The SF and MRE were calculated from measurements obtained using the beam stop method. Two digital mammography units were utilized, and the SF and MRE were found as functions of target, filter, tube potential, phantom thickness, and presence or absence of a grid. These values were then used to generate general equations allowing the SF and MRE to be calculated for any combination of the above parameters. Results: With a grid, the SF ranged from a minimum of about 0.05 to a maximum of about 0.16, and the MRE ranged from about 3 to 13 mm. Without a grid, the SF ranged from a minimum of 0.25 to a maximum of 0.52, and the MRE ranged from about 20 to 45 mm. The SF with a grid demonstrated a mild dependence on target/filter combination and kV, whereas the SF without a grid was independent of these factors. The MRE demonstrated a complex relationship as a function of kV, with notable difference among target/filter combinations. The primary source of change in both the SF and MRE was phantom thickness. Conclusions: Because breast tissue varies spatially in physical density and elemental content, the effective thickness of breast tissue varies spatially across the imaging field, resulting in a spatially-variant scatter distribution in the imaging field. The data generated in this study can be used to characterize the scatter contribution on a point-by-point basis, for a variety of different techniques.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Large N expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs

In this paper we explain the relation between the free energy of the SYK model for N Majorana fermions with a random q-body interaction and the moments of its spectral density. The high temperature expansion of the free energy gives the cumulants of the spectral density. Using that the cumulants are extensive we find the p dependence of the 1/N 2 correction of the 2p-th moments obtained in [1]. Conversely, the 1/N 2 corrections to the moments give the correction (even q) to the β 6 coefficient of the high temperature expansion of the free energy for arbitrary q. Our result agrees with the 1/q 3 correction obtained by Tarnopolsky using a mean field expansion. These considerations also lead to a more powerful method for solving the moment problem and intersection-graph enumeration problems. We take advantage of this and push the moment calculation to 1/N 3 order and find surprisingly simple enumeration identities for intersection graphs. The 1/N 3 corrections to the moments, give corrections to the β 8 coefficient (for even q) of the high temperature expansion of the free energy which have not been calculated before. Results for odd q, where the SYK “Hamiltonian” is the supercharge of a supersymmetric theory are discussed as well.

1/N Expansion↗