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Development of advanced machine learning models for analysis of plutonium surrogate optical emission spectra

This work investigates and applies machine learning paradigms seldom seen in analytical spectroscopy for quantification of gallium in cerium matrices via processing of laser-plasma spectra. Ensemble regressions, support vector machine regressions, Gaussian kernel regressions, and artificial neural network techniques are trained and tested on cerium-gallium pellet spectra. A thorough hyperparameter optimization experiment is conducted initially to determine the best design features for each model. The optimized models are evaluated for sensitivity and precision using the limit of detection (LoD) and root mean-squared error of prediction (RMSEP) metrics, respectively. Gaussian kernel regression yields the superlative predictive model with an RMSEP of 0.33% and an LoD of 0.015% for quantification of Ga in a Ce matrix. This study concludes that these machine learning methods could yield robust prediction models for rapid quality control analysis of plutonium alloys.

Rao, Ashwin P. (ORCID:0000000319312568)↗

Statistical Hauser-Feshbach model calculation for (α, n) reaction cross section and discrete level population

We calculate the α-particle induced reactions on 17,18 O, 19 F, and 23 Na, in the energy range 0 ≤ E α ≤ 10 MeV, with a particular attention to the branching ratios of populated discrete levels in the (α,n) channels. Since there are too many open channels to employ the R-matrix theory, we apply the statistical Hauser-Feshbach model to calculate these reaction cross sections and branching ratios. The branching ratio is defined as b n = $\frac{σ_n}{Σ_iσ_i + σ_c}$ , where σ n is the n-th level production cross section after the neutron emission, and σ c is the production of the continuum state. In the cases of our target nuclei and the energy range of interest, the residual nuclei of the neutron emission channel are always in their discrete states, so that σ c can be negligible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reflective Fiber Temperature Probe Based on Localized Surface Plasmon Resonance towards Low-Cost and Wireless Interrogation

Reflection fiber temperature sensors functionalized with plasmonic nanocomposite material using intensity-based modulation are demonstrated for the first time. Characteristic temperature optical response of the reflective fiber sensor is experimentally tested using Au-incorporated nanocomposite thin films deposited on the fiber tip, and theoretically validated using a thin-film-optic-based optical waveguide model. By optimizing the Au concentration in a dielectric matrix, Au nanoparticles (NP) exhibit a localized surface plasmon resonance (LSPR) absorption band in a visible wavelength that shows a temperature sensitivity ~0.025%/°C as a result of electron–electron and electron–phonon scattering of Au NP and the surrounding matrix. Detailed optical material properties of the on-fiber sensor film are characterized using scanning electron microscopy (SEM) and focused-ion beam (FIB)-assisted transmission electron microscopy (TEM). Airy’s expression of transmission and reflection using complex optical constants of layered media is used to model the reflective optical waveguide. A low-cost wireless interrogator based on a photodiode transimpedance-amplifier (TIA) circuit with a low-pass filter is designed to integrate with the sensor. The converted analog voltage is wirelessly transmitted via 2.4 GHz Serial Peripheral Interface (SPI) protocols. Feasibility is demonstrated for portable, remotely interrogated next-generation fiber optic temperature sensors with future capability for monitoring additional parameters of interest.

47 OTHER INSTRUMENTATION↗

The Potosi Reservoir Model 2013

As a part of a larger project co-funded by the United States Department of Energy (US DOE) to evaluate the potential of formations within the Cambro-Ordovician strata above the Mt. Simon as potential targets for carbon sequestration in the Illinois and Michigan Basins, the Illinois Clean Coal Institute (ICCI) requested Schlumberger to evaluate the potential injectivity and carbon dioxide (CO2) plume size of the Cambrian Potosi Formation. The evaluation of this formation was accomplished using wireline data, core data, pressure data, and seismic data from the US DOE-funded Illinois Basin–Decatur Project (IBDP) being conducted by the Midwest Geological Sequestration Consortium in Macon County, Illinois. In 2010, technical performance evaluations on the Cambrian Potosi Formation were performed through reservoir modeling. The data included formation tops from mud logs, well logs from the VW1 and the CCS1 wells, structural and stratigraphic formation from three dimensional (3D) seismic data, and field data from several waste water injection wells for Potosi Formation. Intention was for two million tons per annum (MTPA) of CO2 to be injected for 20 years. In the preceding, the 2010 Potosi heterogeneous model (referred to as the "Potosi Dynamic Model 2010" in this topical report) was re-run using a new injection scenario; 3.2 MTPA for 30 years. The extent of the Potosi Dynamic Model 2010, however, appeared too small for the new injection target. It was not sufficiently large enough to accommodate the evolution of the plume. The new model, Potosi Dynamic Model 2013a, was built by extending the Potosi Dynamic Model 2010 grid to 30 miles x 30 miles (48.3km x48.3km), while preserving all property modeling workflows and layering. This model was retained as the base case of Potosi Dynamic Model 2013a. The Potosi reservoir model was updated to take into account the new data from the verification well VW2 which was drilled in 2012. The new porosity and permeability modeling was performed to take into account the log data from the new well. Revisions of the 2010 modeling assumptions were also done on relative permeability, capillary pressures, formation water salinity, and the maximum allowable well bottomhole pressure. Dynamic simulations were run using the injection target of 3.2 MTPA for 30 years. This new dynamic model was named Potosi Dynamic Model 2013b. Due to the major uncertainties on the vugs permeability, two models were built; the Pessimistic and Optimistic Cases. The Optimistic Case assumes vugs permeability of 9,000 mD, which is analog to the vugs permeability identified in the pressure fall off test of a waste water injector in the Tuscola site, approx. 40 miles (64.4km) away from the IBDP area. The Pessimistic Case assumes that the vugs permeability is equal to the log data, which does not take into account the permeability from secondary porosity. The probability of such case is deemed low and could be treated as the worst case scenario, since the contribution of secondary porosity to the permeability is neglected and the loss circulation events might correspond to a much higher permeability. It is considered important, however, to identify the range of possible reservoir performance since there are no rigorous data available for the vugs permeability. The Optimistic Case gives an average CO2 injection rate of 0.8 MTPA and cumulative injection of 26 MT in 30 years, which corresponds to 27% of the injection target. The injection rate is approx. 3.2 MTPA in the first year as the well is injecting into the surrounding vugs, and declines rapidly to 0.8 MTPA in year 4 once the surrounding vugs are full and the CO2 start to reach the matrix. This implies that according to this preliminary model, a minimum of four (4) wells could be required to achieve the injection target. This result is lower than the injectivity estimated in the Potosi Dynamic Model 2013a (43 MT in 30 years), since the permeability model applied in the Potosi Dynamic Model 2013b is more conservative. This revision was deemed necessary to treat the uncertainty in a more appropriate manner. As the CO2 follows the paths where vugs interconnection exists, a reasonably large and irregular plume extent was created. For the Optimistic Case, the plume extends 17 miles (27.4km) in E-W and 14 miles (22.5km) in N-S directions after 30 years. After injection is completed, the plume continues to migrate laterally, mainly driven by the remaining pressure gradient. After 100 years post injection, the plume extends 20 miles (32.2km) in E-W and 15.5 miles (24.9km) in N-S directions. Should the targeted cumulative injection of 96 MT be achieved; a much larger plume extent could be expected. For the Optimistic Case, the increase of reservoir pressure at the end of injection is approximately 1200 psia (8,274 kPa) around the injector and gradually decreases away from the well. The reservoir pressure increase is less than 30 psia (206.8 kPa) beyond 14 miles (22.5km) away from injector. Should the targeted cumulative injection of 96 MT be achieved; a much larger areal pressure increase could be expected. The initial reservoir pressure is nearly restored after approximately 100 years post injection. The presence of matrix slows down the pressure dissipations. The Pessimistic Case gives an average CO2 injection rate of 0.2 MTPA and cumulative injection of 7 MT in 30 years, which corresponds to 7% of the injection target. This implies that in the worst case scenario, a minimum of sixteen (16) wells could be required to achieve the injection target. The present evaluation is mainly associated with uncertainty on the vugs permeability, distribution, and interconnectivity. The different results indicated by the Optimistic and Pessimistic Cases signify the importance of vugs permeability characterization. Therefore, injection test and pressure interference test among the wells could be considered to evaluate the local vugs permeability, extent, and interconnectivity. Porosity mapping derived from the seismic inversion could also be used in the succeeding task to characterize the lateral porosity distribution within the reservoir. With or without seismic inversion porosity mapping, it is worth exploring whether increased lateral heterogeneity plays a significant role in Potosi injectivity. Investigations on vugular, dolomitic outcrops suggest that there may be significantly greater lateral heterogeneity than what has been modeled here. Facies modeling within the Potosi has yet to be thoroughly addressed. The carbonates during the time of deposition are believed to be regionally extensive. However, it may be worth delineating the reservoir with other regional wells or modern day analogues to understand the extent of the Potosi. More specifically, the model could incorporate lateral changes or trends if deemed necessary to represent facies transition. Data acquisitions to characterize the fracture pressure gradient, the formation water properties, the relative permeability, and the capillary pressure could also be considered in order to allow a more rigorous evaluation of the Potosi storage performance. A simulation using several injectors could also be considered to determine the required number of wells to achieve the injection target while taking into account the pressure interference.

Adushita, Yasmin↗

Rethinking 𝛼−RuCl 3 : Parameters, models, and phase diagram

RuCl 3 was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the 44 Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form 𝛼−RuCl 3 rose to exceptional prominence. This “rediscovery” of 𝛼−RuCl 3 has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of 𝛼−RuCl 3 , and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the nontrivial physical properties of this material. These constraints allow one to focus on the relevant region of the multidimensional phase diagram of the 𝛼−RuCl 3 model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the 𝛼−RuCl 3 parameter space using quasiclassical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization-group methods, demonstrating a remarkably close quantitative accord between them on the general structure and hierarchy of the phases, with the zigzag, ferromagnetic, and incommensurate phases that are proximate to each other. As a result, one of the highlights is the detailed agreement on the nature of the incommensurate phases that realize two distinct counterrotating helical states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Sci—Thur AM: YIS - 06: An EPID-based 3D patient dose verification method for SBRT-VMAT delivery

Purpose: Stereotactic body radiation therapy (SBRT) delivered via volumetric modulated arc therapy (VMAT) can strongly benefit from an in vivo patient dose verification due to the large doses per fraction. Electronic portal imaging devices (EPIDs) can be utilized as a patient dose dosimeter. In this work we present a physics-based model which utilizes on-treatment EPID images to reconstruct the dose delivered to an anthropomorphic phantom during SBRT-VMAT delivery. Methods: An SBRT linac beam was modeled using Monte Carlo methods and verified with measured data. Our dose reconstruction model back-projects EPID measured focal fluence upstream of the patient and adds a predicted extra-focal fluence component. This fluence is forward projected onto the patient's density matrix and convolved with dose kernels to calculate dose. The model was validated for two prostate, three lung, and two spine SBRT-VMAT treatments. Results were compared to the treatment planning system's calculation. Results: 2%/2 mm chi comparison calculations gave pass rates for the whole volume, infield, and high dose region respectively, and no lower than: 98%, 95%, 99% for the prostate plans, 99%, 92%, 85% for the lung plans, and 91%, 85%, 81% for the spine plans. A 3%/3mm calculation gave pass rates no lower than 99%, 94%, and 90% for all dose regions for the prostate, lung, and spine respectively. Conclusions: We have developed a physics-based model which calculates delivered dose to phantom (or patient) for SBRT-VMAT delivery using on treatment EPID images. The accuracy of the results has allowed us to test this model clinically.

60 APPLIED LIFE SCIENCES↗

Application of BISON to UO 2 MiniFuel fission gas release analysis

There has been a recent push to accelerate fuel qualification by developing revolutionary capabilities to reduce irradiation periods, and thereby, reduce the time required to qualify a new fuel system. One such capability is the MiniFuel irradiation capsule designed to miniaturize fuel samples and irradiate “mini” fuel samples under isothermal temperature conditions. MiniFuel allows steady-state irradiations to decouple the traditionally coupled fission rate (i.e., power) and temperature parameters to understand and generate microstructures observed in fuel operated in a commercial reactor. Furthermore, this process offers the possibility to gather in situ data as well as postirradiation or transient data such as thermal conductivity, specific heat, fission gas diffusion and release, etc. However, accelerating fuel qualification is not solely reliant on generating large amounts of data but also on developing an informed test matrix designed to rapidly generate impactful data. Additionally, this process is reliant on fuel performance codes, such as BISON, to evaluate MiniFuel irradiations using existing material models. This process pinpoints model/data gaps, identifies desired irradiation conditions, and subsequently supports model validation and development. This work describes the use of BISON to perform a number of sensitivity studies designed to understand conditions that lead to fission gas release (FGR) under steady-state isothermal irradiation conditions and temperature transient conditions. The model is applied to a UO 2 MiniFuel example and shows an overall good qualitative agreement with experimental FGR annealing tests under different temperature conditions. It also accounts well for microstructural effects on FGR. When quantitatively compared with FGR data from previously irradiated 103 MWd/kgU UO 2 discs under thermal annealing, the model shows a less satisfactory agreement with the experimental data. Finally, a UO 2 MiniFuel test matrix is proposed to help to extend the model's operational range and validate the new FGR model capabilities to higher burnups and transient conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Singlet, triplet, and pair density wave superconductivity in the doped triangular-lattice moiré system

Recent experimental progress has established the twisted bilayer transition metal dichalcogenide (TMD) as a highly tunable platform for studying many-body physics. Particularly, the homobilayer TMDs under displacement field are believed to be described by a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase θ. To explore the effects of θ on the system, we perform density matrix renormalization group calculations for the relevant triangular lattice t-J model. By changing θ at small hole doping, we obtain a region of quasi-long-range superconducting order coexisting with charge and spin density wave within 0 < θ < π/3. The superconductivity is composed of a dominant spin singlet d-wave and a subdominant triplet p-wave pairing. Intriguingly, the S z = ±1 triplet pairing components feature pair-density waves. In addition, we find a region of triplet superconductivity coexisting with charge-density wave and ferromagnetism within π/3 < θ < 2π/3, which is related to the former phase at smaller θ by a combined operation of spin-flip and gauge transformation. Furthermore, our findings provide insights and directions for experimental search for exotic superconductivity in twisted TMD systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering

A novel fast scalable parallel algorithm is proposed for the solution of large 3-D scattering problems based on: 1) the double (geometrical and current-approximation) higher order (DHO) method of moments (MoM) in the surface integral equation (SIE) formulation and 2) a direct solver for dense linear systems utilizing hierarchically semiseparable (HSS) structures. Namely, an HSS matrix representation is used for compression, factorization, and solution of the system matrix. In addition, a rank-revealing QR decomposition for memory compression is used, with a stopping criterion in terms of the relative rank tolerance value. One method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the HSS algorithm accuracy and parallelization. Numerical examples show how the accuracy of the DHO HSS-MoM-SIE method is easily controllable by using the relative tolerance for the matrix compression. Furthermore, the examples demonstrate low memory consumption, as well as much faster simulation time, when compared to the direct LU decomposition. The method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low-order discretizations. Finally, great scalability of the algorithm is demonstrated on more than one thousand processes.

97 MATHEMATICS AND COMPUTING↗

Microstructural characterization of Mg-based bulk metallic glass and nanocomposite

New magnesium-based bulk metallic glasses Mg{sub 60}Cu{sub 30}Y{sub 10} have been prepared by pressure casting. Glassy alloys were successfully annealed to become nanocomposite containing 200 nm crystallites in an amorphous matrix. The microstructure of bulk glassy alloy and nanocomposite obtained during heat treatment was examined by X-ray diffraction and scanning and high-resolution electron microscopy. Metallic glass has been also studied to explain the structural characteristics by the reverse Monte Carlo (RMC) modeling based on the diffraction data. The HRTEM images allow to indicate some medium-range order (MRO) regions about 2–3 nm in size and formation of local atomic clusters. The RMC modeling results confirmed some kinds of short range order (SRO) structures. It was found that the structure of bulk metallic glass formed by the pressure casting is homogeneous. The composite material contained very small particles in the amorphous matrix. Homogeneous glassy alloy had better corrosion resistance than a composite containing nanocrystalline particles in a glassy matrix. - Highlights: • RMC modeling demonstrates some kinds of SRO structures in Mg-based BMGs. • HRTEM indicated MRO regions about 2–3 nm and SRO regions about 0.5 nm in size. • Mg-based glassy alloys were successfully annealed to become nanocomposite material. • Crystalline particles have spherical morphology with an average diameter of 200 nm. • Glassy alloy had higher corrosion resistance than a nanocomposite sample.

36 MATERIALS SCIENCE↗

A Micro-Mechanical Constitutive Model to Predict Hygrothermal Aging of Cross-Linked Polymers

Abstract A multi-physics material model is presented to describe the effects of temperature, oxygen, and humidity on the constitutive response of cross-linked polymers. The effect of hygrothermal damage on the mechanical integrity of the polymer matrix can be considered as the result of damage accumulation of two independent aging mechanism namely, i) thermo-oxidative, and ii) hydrolytic aging. In order to capture the mutual effects of thermo-oxidative and hydrolytic aging, an assumption has been made that each of the aging phenomenon can be superposed to each other. In fact, each of them works independently and as a result, they can compete with each other. Utilizing the theory of network decomposition, all phenomena and their correlation were modeled and thus, the strain energy function of the polymer matrix is written with respect to four independent mechanisms, i) the shrinking original matrix that has neither been attacked by water nor oxygen, ii) conversion of the first network to two new network due to the reduction and formation of cross-links, and iii) energy loss from network degradation due to attack of the water molecules to polymer active agents. Moreover, the proposed model is micro-mechanically based and is mainly relevant on thin samples due to our underlying assumption of homogeneous diffusion of oxygen and water throughout the matrix. The model has been validated against extensive data-sets obtained from experiments we specifically designed for concept validation.

Bahrololoumi, Amir↗

Primary transcripts: From the discovery of RNA processing to current concepts of gene expression ‐ Review

The main purpose of this review is to recall for investigators - and in particular students -, some of the early data and concepts in molecular genetics and biology that are rarely cited in the current literature and are thus invariably overlooked. There is a growing tendency among editors and reviewers to consider that only data produced in the last 10–20 years or so are pertinent. However this is not the case. In exact science, sound data and lucid interpretation never become obsolete, and even if forgotten, will resurface sooner or later. In the field of gene expression, covered in the present review, recent post-genomic data have indeed confirmed many of the earlier results and concepts developed in the mid-seventies, well before the start of the recombinant DNA revolution. Human brains and even the most powerful computers, have difficulty in handling and making sense of the overwhelming flow of data generated by recent high-throughput technologies. This was easier when low throughput, more integrative methods based on biochemistry and microscopy dominated biological research. Nowadays, the need for organising concepts is ever more important, otherwise the mass of available data can generate only {sup b}uilding ruins{sup }- the bricks without an architect. Concepts such as pervasive transcription of genomes, large genomic domains, full domain transcripts (FDTs) up to 100 kb long, the prevalence of post-transcriptional events in regulating eukaryotic gene expression, and the 3D-genome architecture, were all developed and discussed before 1990, and are only now coming back into vogue. Thus, to review the impact of earlier concepts on later developments in the field, I will confront former and current data and ideas, including a discussion of old and new methods. Whenever useful, I shall first briefly report post-genomic developments before addressing former results and interpretations. Equally important, some of the terms often used sloppily in scientific discussions will be clearly defined. As a basis for the ensuing discussion, some of the issues and facts related to eukaryotic gene expression will first be introduced. In chapter 2 the evolution in perception of biology over the last 60 years and the impact of the recombinant DNA revolution will be considered. Then, in chapter 3 data and theory concerning the genome, gene expression and genetics will be reviewed. The experimental and theoretical definition of the gene will be discussed before considering the 3 different types of genetic information - the {sup T}riad{sup }- and the importance of post-transcriptional regulation of gene expression in the light of the recent finding that 90% of genomic DNA seems to be transcribed. Some previous attempts to provide a conceptual framework for these observations will be recalled, in particular the {sup C}ascade Regulation Hypothesis{sup }(CRH) developed in 1967–85, and the {sup G}ene and Genon{sup }concept proposed in 2007. A knowledge of the size of primary transcripts is of prime importance, both for experimental and theoretical reasons, since these molecules represent the primary units of the {sup R}NA genome{sup }on which most of the post-transcriptional regulation of gene expression occurs. In chapter 4, I will first discuss some current post-genomic topics before summarising the discovery of the high Mr-RNA transcripts, and the investigation of their processing spanning the last 50 years. Since even today, a consensus concerning the real form of primary transcripts in eukaryotic cells has not yet been reached, I will refer to the viral and specialized cellular models which helped early on to understand the mechanisms of RNA processing and differential splicing which operate in cells and tissues. As a well-studied example of expression and regulation of a specific cellular gene in relation to differentiation and pathology, I will discuss the early and recent work on expression of the globin genes in nucleated avian erythroblasts. An important concept is that the primary transcript not only embodies protein-coding information and regulation of its expression, but also the 3D-structure of the genomic DNA from which it was derived. The wealth of recent post-genomic data published in this field emphasises the importance of a fundamental principle of genome organisation and expression that has been overlooked for years even though it was already discussed in the 1970–80ties. These issues are addressed in chapter 5 which focuses on the involvement of the nuclear matrix and nuclear architecture in DNA and RNA biology. This section will make reference to the Unified Matrix Hypothesis (UMH), which was the first molecular model of the 3D organisation of DNA and RNA. The chapter on the {sup R}NA-genome and peripheral memories{sup }discusses experimental data on the ribonucleoprotein complexes containing pre-mRNA (pre-mRNPs) and mRNA (mRNPs) which are organised in nuclear and cytoplasmic spaces respectively. Finally, {sup O}utlook {sup }will enumerate currently unresolved questions in the field, and will propose some ideas that may encourage further investigation, and comprehension of available experimental data still in need of interpretation. In chapter 8, some propositions and paradigms basic to the authors own analysis are discussed. {sup I}n conclusion{sup }the raison d'être of this review is recalled and positioned within the overall framework of scientific endeavour.

60 APPLIED LIFE SCIENCES↗

Constraints on scattering amplitudes in multistate Landau-Zener theory

Here, we derive a set of constraints, which we will call hierarchy constraints, on scattering amplitudes of an arbitrary multistate Landau-Zener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Transient dynamics of terrestrial carbon storage: Mathematical foundation and its applications

Terrestrial ecosystems have absorbed roughly 30% of anthropogenic CO 2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Altogether, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.

54 ENVIRONMENTAL SCIENCES↗

ZPPR-15 Criticality Measurements

A reference critical configuration was established for each phase of the ZPPR-15 experimental program. The reference critical configuration for each phase corresponds to a configuration in which the measured excess reactivity was adjusted to a standard set of reporting conditions with an average reactor temperature of 293 K, a zero interface gap and all operational control rods parked 30 inches from the axial centerline of the core. The ZPPR staff published the measured excess reactivity and the statistical uncertainty in the measurement. In reality, the published uncertainty for each reference critical configuration is only a small component of the total uncertainty for that configuration. Additional uncertainties related measurement technique, configuration geometry and material compositions exist. The geometry and material composition uncertainties are the dominant uncertainties for ZPPR-15. A full uncertainty analysis was performed for each ZPPR-15 reference critical configuration. The significant uncertainties related to measurement technique, configuration geometry and material compositions were quantified, and a total uncertainty was derived for each reference critical configuration. The ZPPR-15 experimental records were used to create detailed as-built Monte Carlo models for the reference critical configurations established in ZPPR-15A loading 15, ZPPR-15B loading 88, ZPPR-15C loading 166 and ZPPR-15D loading 185. The as-built models neglect the small, non-uniform gap between matrix halves at full closure, any structures outside the matrix tubes and minor components, e.g., impurities, in some materials. The biases associated with the neglected items were quantified. The experimental value of keff and its associated uncertainty for each reference critical configuration were adjusted to account for biases introduced by items that are neglected in the as-built model for that configuration.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Stripe order from the perspective of the Hubbard model

A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we investigate emergence of stripes in the Hubbard model, a minimal model believed to be relevant to the cuprate superconductors, using determinant quantum Monte Carlo (DQMC) simulations at finite temperatures and density matrix renormalization group (DMRG) ground state calculations. By varying temperature, doping, and model parameters, we characterize the extent of stripes throughout the phase diagram of the Hubbard model. Our results show that including the often neglected next-nearest-neighbor hopping leads to the absence of spin incommensurability upon electron-doping and nearly half-filled stripes upon hole-doping. The similarities of these findings to experimental results on both electron and hole-doped cuprate families support a unified description across a large portion of the cuprate phase diagram.

36 MATERIALS SCIENCE↗

Motion-map constrained image reconstruction (MCIR): Application to four-dimensional cone-beam computed tomography

Purpose: Utilization of respiratory correlated four-dimensional cone-beam computed tomography (4DCBCT) has enabled verification of internal target motion and volume immediately prior to treatment. However, with current standard CBCT scan, 4DCBCT poses challenge for reconstruction due to the fact that multiple phase binning leads to insufficient number of projection data to reconstruct and thus cause streaking artifacts. The purpose of this study is to develop a novel 4DCBCT reconstruction algorithm framework called motion-map constrained image reconstruction (MCIR), that allows reconstruction of high quality and high phase resolution 4DCBCT images with no more than the imaging dose as well as projections used in a standard free breathing 3DCBCT (FB-3DCBCT) scan.Methods: The unknown 4DCBCT volume at each phase was mathematically modeled as a combination of FB-3DCBCT and phase-specific update vector which has an associated motion-map matrix. The motion-map matrix, which is the key innovation of the MCIR algorithm, was defined as the matrix that distinguishes voxels that are moving from stationary ones. This 4DCBCT model was then reconstructed with compressed sensing (CS) reconstruction framework such that the voxels with high motion would be aggressively updated by the phase-wise sorted projections and the voxels with less motion would be minimally updated to preserve the FB-3DCBCT. To evaluate the performance of our proposed MCIR algorithm, we evaluated both numerical phantoms and a lung cancer patient. The results were then compared with the (1) clinical FB-3DCBCT reconstructed using the FDK, (2) 4DCBCT reconstructed using the FDK, and (3) 4DCBCT reconstructed using the well-known prior image constrained compressed sensing (PICCS).Results: Examination of the MCIR algorithm showed that high phase-resolved 4DCBCT with sets of up to 20 phases using a typical FB-3DCBCT scan could be reconstructed without compromising the image quality. Moreover, in comparison with other published algorithms, the image quality of the MCIR algorithm is shown to be excellent.Conclusions: This work demonstrates the potential for providing high-quality 4DCBCT during on-line image-guided radiation therapy (IGRT), without increasing the imaging dose. The results showed that (at least) 20 phase images could be reconstructed using the same projections data, used to reconstruct a single FB-3DCBCT, without streak artifacts that are caused by insufficient projections.

62 RADIOLOGY AND NUCLEAR MEDICINE↗