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Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

97 MATHEMATICS AND COMPUTING↗

Impact response of US Army and National Football League helmet pad systems

Lawrence Livermore National Laboratory [LLNL] was tasked to compare the impact response of NFL helmet pad systems and U.S. Army pad systems compatible with an Advanced Combat Helmet [ACH] at impact velocities up to 20 ft/s. This was a one-year study funded by the U.S. Army and JIEDDO. The Army/JIEDDO point of contact is COL R. Todd Dombroski, DO, JIEDDO Surgeon. LLNL was chosen by committee to perform the research based on prior published computational studies of the mechanical response of helmets and skulls to blast. Our collaborators include the U.S. Army Aeromedical Research Laboratory [USAARL] (a DoD laboratory responsible for impact testing helmets), Team Wendy and Oregon Aero (current and former ACH pad manufacturers), Riddell and Xenith (NFL pad manufacturers), and d3o (general purpose sports pad manufacturer). The manufacturer-supplied pad systems that were studied are shown in the figure below. The first two are the Army systems, which are bilayer foam pads with both hard and soft foam and a water-resistant airtight wrapper (Team Wendy) or a water-resistant airtight coating (Oregon Aero). The next two are NFL pad systems. The Xenith system consists of a thin foam pad and a hollow air-filled cylinder that elastically buckles under load. The Riddell system is a bilayer foam pad that is encased in an inflatable airbag with relief channels to neighboring pads in the helmet. The inflatable airbag is for comfort and provides no enhancement to impact mitigation. The d3o system consists of a rate-sensitive homogeneous dense foam. LLNL performed experiments to characterize the material properties of the individual foam materials and the response of the complete pad systems, to obtain parameters needed for the simulations. LLNL also performed X-ray CT scans of an ACH helmet shell that were used to construct a geometrically accurate computational model of the helmet. Two complementary sets of simulations were performed. The first set of simulations reproduced the experimental helmet impact certification tests performed by USAARL, who provided data for comparison. The goal of this set of simulations was to demonstrate the overall validity of LLNL's computational analyses and methods and understand the general physics of helmet impacts. In these tests and the corresponding simulations, an inverted ACH containing pads and a head-form are dropped onto a hemispherical anvil, at 10 and 14.14 ft/s impact velocities. The simulations predicted peak accelerations (the metric used by USAARL for comparing the performance of pad systems), rebound velocities, and impact durations consistent with the experimental data, thus demonstrating the validity and relevance of the simulation methods. Because the NFL pad systems are approximately double the thickness of the U.S. Army pads, they do not fit into the ACH. As a result, the NFL pads could not be simply placed into an ACH shell in either a simulation or an experiment without modifying their size and shape. Since impact mitigation depends critically on the available stopping distance and the area over which the stopping force is applied, it is important to consider identically shaped pads in order to compare their performance in a fair and meaningful manner. Consequently, the second set of simulations utilized a simplified simulation geometry consisting of a 5 kg cylindrical impactor (equal in mass to a head) striking equally sized pads from each manufacturer. The simulated bilayer foam pads had the same proportions of hard and soft foam as the actual pad systems, while the Xenith pads were simulated as a bilayer foam pad with material properties adjusted to give the same response as the actual Xenith pads. The effects of trapped air were included in the simulations of the Team Wendy and Oregon Aero pads. All simulations used material properties derived from the experiments conducted at LLNL. The acceleration history of the center of mass of the impactor was used to calculate the Head Injury Criterion (HIC) for each simulation, to assess the pad performance. The HIC is a well-established metric that combines both acceleration and duration of impact to assess the danger of injury, and is a more robust measure than peak acceleration. Our key findings are: (1) The performance of a pad depends on the range of impact velocities. At lower impact velocity, softer pads perform better. At higher impact velocity, harder pads perform better; (2) Thicker pads perform better at all velocities, but especially at high velocities; and (3) For comparable thicknesses, neither the NFL systems nor the Oregon Aero pads outperform the Team Wendy pads currently used in the ACH system in militarily-relevant impact scenarios (impact speeds less than 20 ft/s). The second finding suggests a commercial off-the-shelf solution for mitigating impact-related traumatic brain injury to soldiers.

42 ENGINEERING↗

First multi-institutional systematic comparison of the neutron ambient dose equivalent produced by proton therapy systems

Objective. Isochronous cyclotrons, synchrocyclotrons, and synchrotrons are used to accelerate protons for proton therapy. An accurate measurement of neutron doses generated by these accelerators and associated delivery systems and its clinical relevance requires systematic protocols and proper neutron dosimetry for a meaningful assessment. We present the first comprehensive comparison of neutron ambient dose equivalent (H*(10)) produced by clinically operational proton therapy systems. Approach. Treatment plans with 10 cm modulation-depth and ranges of 10 cm (R10M10) and 25 cm (R25M10) were created to cover a 10 × 10 × 10 cm 3 water target. The pencil beam scanning proton therapy machines studied were: two gantry-mounted synchrocyclotrons (Hyperscan, Mevion, half-gantry), two isochronous cyclotrons (ProBeam, Varian, full-gantry), one isochronous cyclotron (Proteus, IBA, full-gantry), and two synchrotrons (PROBEAT, Hitachi, full- and half-gantry). Proton beams were delivered to 30 × 30 × 40 cm 3 plastic water phantoms. WENDI-II and LUPIN-BF3-NP neutron rem-meters were positioned at three angles (0°, 45°, 90°) relative to the beam direction to measure the neutron H*(10) at distances between 50–300 cm from the isocenter. Main results. H*(10) showed dependence on beam energy, machine type, and measurement location. The highest reading was for the gantry-mounted synchrocyclotron, whereas other systems produced approximately comparable neutron doses. In all cases, the H*(10) reduced with distance from the isocenter. The H*(10) drop at 2 m distance compared to that at 0.5 m was a factor of ∼5 for the gantry-mounted synchrocyclotron whereas in other systems the decrease was a factor of 10. The WENDI-II device suffered from dead-time-associated under-estimation of the dose by a factor of ∼2–3 under the synchrocyclotron beam due to its high dose-per-pulse. However, WENDI-II and LUPIN-BF3-NP results were within reasonable agreement in isochronous cyclotron and synchrotron beams, indicating that both devices are suitable for those systems. Significance. Neutron H*(10) is dependent on various parameters including beam energy, measurement location, as well as machine design. Caution must be exercised in choosing the appropriate neutron-dose-measurement device to be used for low-duty-factor, particularly in high-instantaneous-rate proton delivery systems. By delivering the same volumetric proton dose across different machines, this work provides a benchmark for inter-system comparisons and serves as a foundation for future studies.

LUPIN↗

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

Measurement of stray radiation within a scanning proton therapy facility: EURADOS WG9 intercomparison exercise of active dosimetry systems

Purpose: To characterize stray radiation around the target volume in scanning proton therapy and study the performance of active neutron monitors. Methods: Working Group 9 of the European Radiation Dosimetry Group (EURADOS WG9—Radiation protection in medicine) carried out a large measurement campaign at the Trento Centro di Protonterapia (Trento, Italy) in order to determine the neutron spectra near the patient using two extended-range Bonner sphere spectrometry (BSS) systems. In addition, the work focused on acknowledging the performance of different commercial active dosimetry systems when measuring neutron ambient dose equivalents, H{sup ∗}(10), at several positions inside (8 positions) and outside (3 positions) the treatment room. Detectors included three TEPCs—tissue equivalent proportional counters (Hawk type from Far West Technology, Inc.) and six rem-counters (WENDI-II, LB 6411, RadEye™ NL, a regular and an extended-range NM2B). Meanwhile, the photon component of stray radiation was deduced from the low-lineal energy transfer part of TEPC spectra or measured using a Thermo Scientific™ FH-40G survey meter. Experiments involved a water tank phantom (60 × 30 × 30 cm{sup 3}) representing the patient that was uniformly irradiated using a 3 mm spot diameter proton pencil beam with 10 cm modulation width, 19.95 cm distal beam range, and 10 × 10 cm{sup 2} field size. Results: Neutron spectrometry around the target volume showed two main components at the thermal and fast energy ranges. The study also revealed the large dependence of the energy distribution of neutrons, and consequently of out-of-field doses, on the primary beam direction (directional emission of intranuclear cascade neutrons) and energy (spectral composition of secondary neutrons). In addition, neutron mapping within the facility was conducted and showed the highest H{sup ∗}(10) value of ∼51 μSv Gy{sup −1}; this was measured at 1.15 m along the beam axis. H{sup ∗}(10) values significantly decreased with distance and angular position with respect to beam axis falling below 2 nSv Gy{sup −1} at the entrance of the maze, at the door outside the room and below detection limit in the gantry control room, and at an adjacent room (<0.1 nSv Gy{sup −1}). Finally, the agreement on H{sup ∗}(10) values between all detectors showed a direct dependence on neutron spectra at the measurement position. While conventional rem-counters (LB 6411, RadEye™ NL, NM2-458) underestimated the H{sup ∗}(10) by up to a factor of 4, Hawk TEPCs and the WENDI-II range-extended detector were found to have good performance (within 20%) even at the highest neutron fluence and energy range. Meanwhile, secondary photon dose equivalents were found to be up to five times lower than neutrons; remaining nonetheless of concern to the patient. Conclusions: Extended-range BSS, TEPCs, and the WENDI-II enable accurate measurements of stray neutrons while other rem-counters are not appropriate considering the high-energy range of neutrons involved in proton therapy.

07 ISOTOPE AND RADIATION SOURCES↗

INL@Work Firefighter

Did you know INL has its own firefighting team? Its members help protect our remote 890-square-mile site from range fires and other incidents. Meet firefighter Wendy Baron, who was recently named Idaho's firefighter of the year.

99 GENERAL AND MISCELLANEOUS↗

Covalent Attachment of Diphosphine Ligands to Glassy Carbon Electrodes via Cu-Catalyzed Alkyne-Azide Cycloaddition. Metallation with Ni(II)

Covalent tethering of PPh2NC6H4C=CH2 ligands (PPh2NC6H4C=CH2 = 1,5-di-(4-ethynylphenyl)-3,7-diphenyl-1,5-diaza-3,7-diphosphacyclooctane) to planar, azide-terminated glassy carbon electrode surfaces has been accomplished using a CuI-catalyzed alkyne-azide cycloaddition (CuAAC) as the coupling reaction, using a BH3?P protection-deprotection strategy. Deprotected, surface-confined ligands were metallated using [NiII(MeCN)6](BF4)2. X-ray photoelectron spectroscopic measurements demonstrate that metallation introduced 1.3 equivalents NiII per diphosphine onto the electrode surface. Exposure of the surface to a second diphosphine ligand, PPh2NPh2, resulted in the removal of Ni from the surface. Protection, coupling, deprotection, and metallation conditions were optimized using solution-phase model systems, with benzyl azide as a model for the azide-terminated carbon surface; these reactions generate a [NiII(diphosphine)2]2+ complex. Acknowledgment. This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. The XPS measurements were performed at the Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the U. S. Department of Energy, Office of Science, Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. The x-ray crystal structure analysis was carried out by S.L., who was supported by a grant to Wendy J. Shaw from the Early Career Research Program through the U.S. Department of Energy, Office of Science. Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy.

electrocatalysis, surface attachment, XPS↗

NDX: Neutron Dose Rate Meters with Extended Capabilities

Particle accelerators, irradiation facilities, and nuclear power plants would benefit from using neutron dose rate meters featuring improved energy response covering full range of expected neutron energies, improved dynamic range of measured dose rates while providing the real-time data, and improved ability to operate in harsh radiation environments including heavy photon backgrounds and pulsed beams. The novel design of the neutron moderator for the NDX dose rate meter implements a layer of a Beryllium-loaded medium Z material which, similar to the earlier known WENDI detectors, allows the device to detect higher energy neutron flux and convert it to dose. Using Beryllium helps to fill the known dip in the response functions around 5-50 MeV. Optimized design parameter set, obtained using FLUKA Monte Carlo simulations, features the NDX moderator made of polyethylene embedding a layer of BeCu alloy inside, with the dose rate response constant within ±10% in the neutron energy range from about 100 keV to 500 MeV, and ±25% essentially in the full energy range above thermal. A new sensor technique implemented in the NDX is based on using the Ionization Chamber (IC) filled with 3He gas to capture the moderated neutron fluence, and includes a symmetric IC filled with regular 4He to evaluate the contributions due to the non-neutron ionizing radiation. Advantages of the method include large accessible dynamic range, relative insensitivity of the IC probes to photon radiation fields, and the ability to subtract their contribution. Two prototype NDX detectors were built, calibrated, and operated in various conditions at the CEBAF 12 GeV electron accelerator at JLab. The first results showed reliable neutron dose rate measurements in the presence of overwhelming photon radiation fields, and at practical high dose rate levels of up to approximately 10 Sv/h. Detector design, operation, first results, and further development plans are presented.

Degtiarenko, Pavel V.↗

SU-E-T-403: Measurement of the Neutron Ambient Dose Equivalent From the TrueBeam Linac Head and Varian 2100 Clinac

Purpose: High-energy x-ray therapy produces an undesirable source of stray neutron dose to healthy tissues, and thus, poses a risk for second cancer induction years after the primary treatment. Hence, the purpose of this study was to measure the neutron ambient dose equivalent, H*(10), produced from the TrueBeam and Varian 2100 linac heads, respectively. Of particular note is that there is no measured data available in the literature on H*(10) production from the TrueBeam treatment head. Methods: Both linacs were operated in flattening filter mode using a 15 MV x-ray beam on TrueBeam and an 18 MV x-ray beam for the Varian 2100 Clinac with the jaws and multileaf collimators in the fully closed position. A dose delivery rate of 600 MU/min was delivered on the TrueBeam and the Varian 2100 Clinac, respectively and the H*(10) rate was measured in triplicate using the WENDI-2 detector located at multiple positions including isocenter and longitudinal (gun-target) to the isocenter. Results: For each measurement, the H*(10) rate was relatively constant with increasing distance away from the isocenter with standard deviations on the order of a tenth of a mSv/h or less for the given beam energy. In general, fluctuations in the longitudinal H*(10) rate between the anterior-posterior couch directions were approximately a percent for both beam energies. Conclusion: Our preliminary results suggest an H*(10) rate of about 30 mSv/h (40 mSv/h) or less for TrueBeam (Varian Clinac 2100) for all measurements considered in this study indicating a relatively low contribution of produced secondary neutrons to the primary therapeutic beam.

60 APPLIED LIFE SCIENCES↗

WE-D-17A-05: Measurement of Stray Radiation Within An Active Scanning Proton Therapy Facility: EURADOS WG9 Intercomparison Exercise of Active Dosimetry Systems

Purpose: Intercomparison of active dosemeters in the measurement of stray radiation at the Trento active-scanning proton therapy facility. Methods: EURADOS WG9 carried out a large intercomparison exercise to test different dosemeters while measuring secondary neutrons within a 230 MeV scanned proton therapy facility. Detectors included two Bonner Sphere Spectrometers (BSS), three tissue equivalent proportional counters (TEPCHawk) and six rem-counters (Wendi II, Berthold, RadEye, a regular and an extended-range Anderson and Braun NM2B counters). Measurements of neutron ambient dose equivalents, H*(10), were done at several positions inside (8 positions) and outside (3 positions) the treatment room while irradiating a water tank phantom with a 10 × 10 × 10 cc field. Results: A generally good agreement on H*(10) values was observed for the tested detectors. At distance of 2.25 m and angles 45°, 90° and 180° with respect to the beam axis, BSS and proportional counters agreed within 30%. Higher differences (up to 60%) were observed at the closest and farthest distances, i.e. at positions where detectors sensitivity, energy, fluence and angular response are highly dependent on neutron spectra (flux and energy). The highest neutron H*(10) value, ∼60 microSv/Gy, was measured at 1.15 m along the beam axis. H*(10) decreased significantly with the distance from the isocenter dropping to 1.1 microSv/Gy at 4.25 m and 90° from beam axis, ∼2 nanoSv/Gy at the entrance of the maze, 0.2 nanoSv/Gy at the door outside the room and below detection limit in the gantry control room and at an adjacent room. These values remain considerately lower than those of passively scattered proton beams. BSS and Hawk unfolded spectra provide valuable inputs when studying the response of each detector. Conclusion: TEPCs and BSS enable accurate measurements of stray neutrons while other rem-meters also give satisfactory results but require further improvements to reduce uncertainties.

07 ISOTOPE AND RADIATION SOURCES↗

SU-E-T-400: Evaluation of Shielding and Activation at Two Pencil Beam Scanning Proton Facilities

Purpose: To verify acceptably low dose levels around two newly constructed identical pencil beam scanning proton therapy facilities and to evaluate accuracy of pre-construction shielding calculations. Methods: Dose measurements were taken at select points of interest using a WENDI-2 style wide-energy neutron detector. Measurements were compared to pre-construction shielding calculations. Radiation badges with neutron dose measurement capabilities were worn by personnel and also placed at points throughout the facilities. Seven neutron and gamma detectors were permanently installed throughout the facility, continuously logging data. Potential activation hazards have also been investigated. Dose rates near water tanks immediately after prolonged irradiation have been measured. Equipment inside the treatment room and accelerator vault has been surveyed and/or wipe tested. Air filters from air handling units, sticky mats placed outside of the accelerator vault, and water samples from the magnet cooling water loops have also been tested. Results: All radiation badges have been returned with readings below the reporting minimum. Measurements of mats, air filters, cooling water, wipe tests and surveys of equipment that has not been placed in the beam have all come back at background levels. All survey measurements show the analytical shielding calculations to be conservative by at least a factor of 2. No anomalous events have been identified by the building radiation monitoring system. Measurements of dose rates close to scanning water tanks have shown dose rates of approximately 10 mrem/hr with a half-life less than 5 minutes. Measurements around the accelerator show some areas with dose rates slightly higher than 10 mrem/hr. Conclusion: The shielding design is shown to be adequate. Measured dose rates are below those predicted by shielding calculations. Activation hazards are minimal except in certain very well defined areas within the accelerator vault and for objects placed directly in the path of the beam.

60 APPLIED LIFE SCIENCES↗

Phase 1 Development Report for the SESSA Toolkit.

The Site Exploitation System for Situational Awareness ( SESSA ) tool kit , developed by Sandia National Laboratories (SNL) , is a comprehensive de cision support system for crime scene data acquisition and Sensitive Site Exploitation (SSE). SESSA is an outgrowth of another SNL developed decision support system , the Building R estoration Operations Optimization Model (BROOM), a hardware/software solution for data acquisition, data management, and data analysis. SESSA was designed to meet forensic crime scene needs as defined by the DoD's Military Criminal Investigation Organiza tion (MCIO) . SESSA is a very comprehensive toolki t with a considerable amount of database information managed through a Microsoft SQL (Structured Query Language) database engine, a Geographical Information System (GIS) engine that provides comprehensive m apping capabilities, as well as a an intuitive Graphical User Interface (GUI) . An electronic sketch pad module is included. The system also has the ability to efficiently generate necessary forms for forensic crime scene investigations (e.g., evidence submittal, laboratory requests, and scene notes). SESSA allows the user to capture photos on site, and can read and generate ba rcode labels that limit transcription errors. SESSA runs on PC computers running Windows 7, but is optimized for touch - screen tablet computers running Windows for ease of use at crime scenes and on SSE deployments. A prototype system for 3 - dimensional (3 D) mapping and measur e ments was also developed to complement the SESSA software. The mapping system employs a visual/ depth sensor that captures data to create 3D visualizations of an interior space and to make distance measurements with centimeter - level a ccuracy. Output of this 3D Model Builder module provides a virtual 3D %22walk - through%22 of a crime scene. The 3D mapping system is much less expensive and easier to use than competitive systems. This document covers the basic installation and operation of th e SESSA tool kit in order to give the user enough information to start using the tool kit . SESSA is currently a prototype system and this documentation covers the initial release of the tool kit . Funding for SESSA was provided by the Department of Defense (D oD), Assistant Secretary of Defense for Research and Engineering (ASD(R&E)) Rapid Fielding (RF) organization. The project was managed by the Defense Forensic Science Center (DFSC) , formerly known as the U.S. Army Criminal Investigation Laboratory (USACIL) . ACKNOWLEDGEMENTS The authors wish to acknowledge the funding support for the development of the Site Exploitation System for Situational Awareness (SESSA) toolkit from the Department of Defense (DoD), Assistant Secretary of Defense for Research and Engineering (ASD(R&E)) Rapid Fielding (RF) organization. The project was managed by the Defense Forensic Science Center (DFSC) , formerly known as the U.S. Army Criminal Investigation Laboratory (USACIL). Special thanks to Mr. Garold Warner, of DFSC, who served as the Project Manager. Individuals that worked on the design, functional attributes, algorithm development, system arc hitecture, and software programming include: Robert Knowlton, Brad Melton, Robert Anderson, and Wendy Amai.

Knowlton, Robert G.↗

Comparison of the MCNP6 and FLUKA Codes in Shielding Calculation at ProNova Proton Therapy Facility

The Monte Carlo method is a powerful tool to simulate particle transport in materials, and can be effectively used to design radiation shielding. The purpose of this study is to compare the results from two Monte Carlo codes (MCNP6 and FLUKA ) in shielding design. The calculation was also compared with the measured results from the ProNova Superconducting 360 degrees (SC360) installation at the Knoxville Provision Center for Proton Therapy (PCPT) facility. The SC360 230 MeV continue wave (CW) proton beam is produced by an isochronous cyclotron, the Sumitomo P235. The maximum beam that is extracted into the beamline is 300 nA, which is of 60% of the full current generated in cyclotron. The SC360 facility has an energy selection system for adjusting the proton range, one fixed beam and one gantry room for rotating the beam around the stationary patient. At the entrance to each treatment room beamline, a thickness adjustable Beryllium degrader inserted in the beam path is used to achieve the desirable beam energy. When protons interact with beamline components, the secondary neutrons become the dominant source to determine the radiation shielding. In this study, the dose rate outside the lateral wall of the beamline vault was discussed. The calculations from two Monte Carlo codes were compared and they agreed very well. The dose rates measured by a Wendi-II Neutron Detector agreed within a factor of less than seven compared with the calculation results. The difference may be explained by a variety of factors such as the uncertainty in knowing the exact composition of shielding materials, geometry difference, and the measurement uncertainty due to instrumentation. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Summary of the the 11th Symposium of the International Society of Root Research

11th Symposium of the International Society of Root Research (ISRR11) and the 9th International Symposium on Root Development (Rooting2021) - Root Biology Never Sleeps virtual meeting May 24 - 28. These meetings are generally held in separate years. However, because of travel restrictions imposed by the COVID-19 pandemic, the organizing committees of both symposia decided to host the two meetings as a fully-joint and virtual-only conference. Various time zones were considered when developing the schedule, as live interactions was an important focus. Scientific sessions were held from 3 a.m. to 10 p.m. US Central Daylight Time (CDT) to meet the international demand. More than 700 participants from 52 countries virtually attend both events which featured 74 talks in 16 sessions including: 10 plenary lectures, 16 keynote speakers and 48 selected talks. Additionally, nearly 300 posters were presented in nine poster sessions. The meeting also featured an Ambassador Program with 21 ambassadors from 10 countries. These ambassadors organized a half-day pre-symposium workshop and produced a review of the meeting for “New Phytologist”. The meeting also awarded a Lifetime Award to Dr. Wendy Silk (Prof. Emerita University of California, Davis). Committee Members: • Bob Sharp (Chair) – University of Missouri • Felix Fritschi (Chair, Int’l Program Committee) – University of Missouri • David Braun – University of Missouri • Vicki Bryan – University of Missouri • Rich Ferrieri – University of Missouri • Laura Greeley – University of Missouri (postdoctoral representative) • Ali Housh – University of Missouri (graduate student representative) • Allison Miller – Donald Danforth Plant Science Center and St Louis University • Mel Oliver – University of Missouri • Jonathan Stemmle – University of Missouri • Gus Thies – University of Missouri & Donald Danforth Plant Science Center (graduate student representative) • Chris Topp - Donald Danforth Plant Science Center

Root Biology↗

Comprehensive study of carbon dioxide adsorption in the metal–organic frameworks M 2 (dobdc) (M = Mg, Mn, Fe, Co, Ni, Cu, Zn)

Analysis of the CO 2 adsorption properties of a well-known series of metal–organic frameworks M 2 (dobdc) (dobdc 4– = 2,5-dioxido-1,4-benzenedicarboxylate; M = Mg, Mn, Fe, Co, Ni, Cu, and Zn) is carried out in tandem with in situ structural studies to identify the host–guest interactions that lead to significant differences in isosteric heats of CO 2 adsorption. Neutron and X-ray powder diffraction and single crystal X-ray diffraction experiments are used to unveil the site-specific binding properties of CO 2 within many of these materials while systematically varying both the amount of CO 2 and the temperature. Unlike previous studies, we show that CO 2 adsorbed at the metal cations exhibits intramolecular angles with minimal deviations from 180°, a finding that indicates a strongly electrostatic and physisorptive interaction with the framework surface and sheds more light on the ongoing discussion regarding whether CO 2 adsorbs in a linear or nonlinear geometry. This has important implications for proposals that have been made to utilize these materials for the activation and chemical conversion of CO 2 . For the weaker CO 2 adsorbents, significant elongation of the metal–O(CO 2 ) distances are observed and diffraction experiments additionally reveal that secondary CO 2 adsorption sites, while likely stabilized by the population of the primary adsorption sites, significantly contribute to adsorption behavior at ambient temperature. In conclusion, density functional theory calculations including van der Waals dispersion quantitatively corroborate and rationalize observations regarding intramolecular CO 2 angles and trends in relative geometric properties and heats of adsorption in the M 2 (dobdc)–CO 2 adducts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Amorphous Diamond: A High-Pressure Superhard Carbon Allotrope

Compressing glassy carbon above 40 GPa, we have observed a new carbon allotrope with a fully sp{sup 3}-bonded amorphous structure and diamondlike strength. Synchrotron x-ray Raman spectroscopy revealed a continuous pressure-induced sp{sup 2}-to-sp{sup 3} bonding change, while x-ray diffraction confirmed the perseverance of noncrystallinity. The transition was reversible upon releasing pressure. Used as an indenter, the glassy carbon ball demonstrated exceptional strength by reaching 130 GPa with a confining pressure of 60 GPa. Such an extremely large stress difference of >70 GPa has never been observed in any material besides diamond, indicating the high hardness of this high-pressure carbon allotrope.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗