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At least 973 records · Page 54

A Tidal Hydrodynamic Model for Cook Inlet, Alaska, to Support Tidal Energy Resource Characterization

Cook Inlet in Alaska has been identified as a prime site in the U.S. for potential tidal energy development, because of its enormous tidal power potential that accounts for nearly one-third of the national total. As one important step to facilitate tidal energy development, a tidal hydrodynamic model based on the unstructured-grid, finite-volume community ocean model (FVCOM) was developed for Cook Inlet to characterize the tidal stream energy resource. The model has a grid resolution that varies from about 1000 m at the open boundary to 100–300 m inside the Inlet. Extensive model validation was achieved by comparing model predictions with field observations for tidal elevation and velocity at various locations in Cook Inlet. The error statistics confirmed the model performs reasonably well in capturing the tidal dynamics in the system, e.g., R2 > 0.98 for tidal elevation and generally > 0.9 for velocity. Model results suggest that tides in Cook Inlet evolve from progressive waves at the entrance to standing waves at the upper Inlet, and that semi-diurnal tidal constituents are amplified more rapidly than diurnal constituents. The model output was used to identify hotspots that have high energy potential and warrant additional velocity and turbulence measurements such as East Foreland, where averaged power density exceeds 5 kw/m2. Lastly, a tidal energy extraction simulation was conducted for a hypothetical turbine farm configuration at the Forelands cross section to evaluate tidal energy extraction and resulting changes in far-field hydrodynamics.

16 TIDAL AND WAVE POWER↗

An Evaluation of Departmental Radiation Oncology Incident Reports: Anticipating a National Reporting System

Purpose: Systems to ensure patient safety are of critical importance. The electronic incident reporting systems (IRS) of 2 large academic radiation oncology departments were evaluated for events that may be suitable for submission to a national reporting system (NRS). Methods and Materials: All events recorded in the combined IRS were evaluated from 2007 through 2010. Incidents were graded for potential severity using the validated French Nuclear Safety Authority (ASN) 5-point scale. These incidents were categorized into 7 groups: (1) human error, (2) software error, (3) hardware error, (4) error in communication between 2 humans, (5) error at the human-software interface, (6) error at the software-hardware interface, and (7) error at the human-hardware interface. Results: Between the 2 systems, 4407 incidents were reported. Of these events, 1507 (34%) were considered to have the potential for clinical consequences. Of these 1507 events, 149 (10%) were rated as having a potential severity of ≥2. Of these 149 events, the committee determined that 79 (53%) of these events would be submittable to a NRS of which the majority was related to human error or to the human-software interface. Conclusions: A significant number of incidents were identified in this analysis. The majority of events in this study were related to human error and to the human-software interface, further supporting the need for a NRS to facilitate field-wide learning and system improvement.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

MO-FG-202-07: Real-Time EPID-Based Detection Metric For VMAT Delivery Errors

Purpose: To create and test an accurate EPID-frame-based VMAT QA metric to detect gross dose errors in real-time and to provide information about the source of error. Methods: A Swiss cheese model was created for an EPID-based real-time QA process. The system compares a treatmentplan- based reference set of EPID images with images acquired over each 2° gantry angle interval. The metric utilizes a sequence of independent consecutively executed error detection Methods: a masking technique that verifies infield radiation delivery and ensures no out-of-field radiation; output normalization checks at two different stages; global image alignment to quantify rotation, scaling and translation; standard gamma evaluation (3%, 3 mm) and pixel intensity deviation checks including and excluding high dose gradient regions. Tolerances for each test were determined. For algorithm testing, twelve different types of errors were selected to modify the original plan. Corresponding predictions for each test case were generated, which included measurement-based noise. Each test case was run multiple times (with different noise per run) to assess the ability to detect introduced errors. Results: Averaged over five test runs, 99.1% of all plan variations that resulted in patient dose errors were detected within 2° and 100% within 4° (∼1% of patient dose delivery). Including cases that led to slightly modified but clinically equivalent plans, 91.5% were detected by the system within 2°. Based on the type of method that detected the error, determination of error sources was achieved. Conclusion: An EPID-based during-treatment error detection system for VMAT deliveries was successfully designed and tested. The system utilizes a sequence of methods to identify and prevent gross treatment delivery errors. The system was inspected for robustness with realistic noise variations, demonstrating that it has the potential to detect a large majority of errors in real-time and indicate the error source. J. V. Siebers receives funding support from Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗

TU-H-BRA-03: Performance of a Clinical Gridded Electron Gun in Magnetic Fields: Implications for MRI-Linac Therapy

Purpose: Recent advances towards MRI Linac radiotherapy have motivated a wide range of studies characterizing electromagnetic interactions between the two devices. One of the most sensitive components is the linac electron gun. To data, only non gridded (diode) guns have been investigated however, most linac vendors utilize gridded (triode) guns, which enable efficient and robust beam gating. The purpose of this study was to develop a realistic model of a gridded gun used clinically, and to characterize its performance in magnetic fields. Methods: The gridded electron gun used on Varian high energy machines was measured using 3D laser scanning quoted as accurate to 0.1mm. Based on the scane, a detailed CAD mode was developed. From this, key geometry was extracted and a FEM model was developed (Opera/SCALA). Next, the high voltage (HV), grid voltage, and emission current were read from six dose matched TrueBeam linacs for the 6X, 10X and 15X photon modes (0 B-field). The mean values were used to represent each mode, which was simulated I constant magnetic fields from 0–200G in-line, and 0–35G perpendicular. Results: Experimentally measured HV, grid voltage, and emission current from 6X, 10X and 15X modes were respectively: 15±.03kV, 10±.08kV, 11±.03kV; 93±7V, 41±3V, and 70±6V; 327±27mA, 129±10mA, and 214±19mA. The error in simulated emission current of each mode was 3%,6%, and 3%. For in-line fields, 50% beam loss occurred at 114, 96, and 97G; for perpendicular; at 12, 13 and 14G. Sensitivity for a given geometry is primarily determined by HV setting. Conclusion: Future MRI-Linac systems will almost certainly use gridded guns. We present the first model of a clinical gridded gun, and match the experimental emission current to within 6% across three different operating modes. This clinical gun shows increased sensitivity to magnetic fields than previous work,and different modes show different sensitivity.

60 APPLIED LIFE SCIENCES↗

A Faraday-effect polarimeter for fast magnetic dynamics measurement on DIII-D

A Faraday-effect-based radial-interferometer-polarimeter diagnostic has been developed to explore fast magnetic dynamics in high-performance DIII-D plasmas. The instrument measures radial magnetic field perturbations using three chords positioned near the magnetic axis. Newly developed solid-state sources operating at 650 GHz provide phase noise down to 0.01°/$\sqrt{kHz}$ and tunable bandwidth up to 10 MHz. Various systematic errors which can contaminate the polarimetric measurement have been investigated in detail. Distortion of circular polarization due to non-ideal optical components is calibrated using a rotating quarter wave plate technique. The impact of perpendicular magnetic field, i.e., the Cotton-Mouton effect, is evaluated. The error due to non-collinearity of probe beams is minimized to less than 0.5° for electron density up to 7 × 10 19 m -3 by alignment optimization. Optical feedback, due to multiple reflections induced by the double-pass configuration, is identified and reduced. Lastly, coherent and broadband high-frequency magnetic fluctuations for DIII-D H-mode plasmas are observed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Development of a novel depth of interaction PET detector using highly multiplexed G-APD cross-strip encoding

Purpose: The aim of this study was to develop a prototype PET detector module for a combined small animal positron emission tomography and magnetic resonance imaging (PET/MRI) system. The most important factor for small animal imaging applications is the detection sensitivity of the PET camera, which can be optimized by utilizing longer scintillation crystals. At the same time, small animal PET systems must yield a high spatial resolution. The measured object is very close to the PET detector because the bore diameter of a high field animal MR scanner is limited. When used in combination with long scintillation crystals, these small-bore PET systems generate parallax errors that ultimately lead to a decreased spatial resolution. Thus, we developed a depth of interaction (DoI) encoding PET detector module that has a uniform spatial resolution across the whole field of view (FOV), high detection sensitivity, compactness, and insensitivity to magnetic fields. Methods: The approach was based on Geiger mode avalanche photodiode (G-APD) detectors with cross-strip encoding. The number of readout channels was reduced by a factor of 36 for the chosen block elements. Two 12 × 2 G-APD strip arrays (25μm cells) were placed perpendicular on each face of a 12 × 12 lutetium oxyorthosilicate crystal block with a crystal size of 1.55 × 1.55 × 20 mm. The strip arrays were multiplexed into two channels and used to calculate the x, y coordinates for each array and the deposited energy. The DoI was measured in step sizes of 1.8 mm by a collimated {sup 18}F source. The coincident resolved time (CRT) was analyzed at all DoI positions by acquiring the waveform for each event and applying a digital leading edge discriminator. Results: All 144 crystals were well resolved in the crystal flood map. The average full width half maximum (FWHM) energy resolution of the detector was 12.8% ± 1.5% with a FWHM CRT of 1.14 ± 0.02 ns. The average FWHM DoI resolution over 12 crystals was 2.90 ± 0.15 mm. Conclusions: The novel DoI PET detector, which is based on strip G-APD arrays, yielded a DoI resolution of 2.9 mm and excellent timing and energy resolution. Its high multiplexing factor reduces the number of electronic channels. Thus, this cross-strip approach enables low-cost, high-performance PET detectors for dedicated small animal PET and PET/MRI and potentially clinical PET/MRI systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

nCTEQ15 - Global analysis of nuclear parton distributions with uncertainties

We present the first official release of the nCTEQ nuclear parton distribution functions with errors. The main addition to the previous nCTEQ PDFs is the introduction of PDF uncertainties based on the Hessian method. Another important addition is the inclusion of pion production data from RHIC that give us a handle on constraining the gluon PDF. This contribution summarizes our results from arXiv:1509.00792, and concentrates on the comparison with other groups providing nuclear parton distributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

CAFE: A NEW RELATIVISTIC MHD CODE

We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin–Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin–Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.

79 ASTRONOMY AND ASTROPHYSICS↗

Higher-order adaptive finite-element methods for orbital-free density functional theory

In the present work, we study various numerical aspects of higher-order finite-element discretizations of the non-linear saddle-point formulation of orbital-free density-functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electron-density is a robust solution procedure for higher-order finite-element discretizations. We next study the convergence properties of higher-order finite-element discretizations of orbital-free density functional theory by considering benchmark problems that include calculations involving both pseudopotential as well as Coulomb singular potential fields. Our numerical studies suggest close to optimal rates of convergence on all benchmark problems for various orders of finite-element approximations considered in the present study. We finally investigate the computational efficiency afforded by various higher-order finite-element discretizations, which constitutes the main aspect of the present work, by measuring the CPU time for the solution of discrete equations on benchmark problems that include large Aluminum clusters. In these studies, we use mesh coarse-graining rates that are derived from error estimates and an a priori knowledge of the asymptotic solution of the far-field electronic fields. Our studies reveal a significant 100-1000 fold computational savings afforded by the use of higher-order finite-element discretization, alongside providing the desired chemical accuracy. We consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite-element basis.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tensor networks, p -adic fields, and algebraic curves: arithmetic and the AdS 3 /CFT 2 correspondence

One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which a priori depend on the analytic structure of the spacetime) can be formulated in purely algebraic language. This opens the door to interesting generalizations, obtained by taking another choice of field: for instance, the p-adics. Herein, we generalize the $\mathrm{AdS} / \mathrm{CFT}$ correspondence according to this principle; the result is a formulation of holography in which the bulk geometry is discrete—the Bruhat–Tits tree for $\mathrm{PGL} (2, \mathbb{Q}_p)$—but the group of bulk isometries nonetheless agrees with that of boundary conformal transformations and is not broken by discretization. We anticipate that this forms the natural geometric setting for tensor networks that have been proposed as models of bulk reconstruction via quantum error correcting codes; in certain cases, geodesics in the Bruhat–Tits tree reproduce those constructed using quantum error correction. Other aspects of holography also hold: Standard holographic results for massive free scalar fields in a fixed background carry over to the tree, whose vertical direction can be interpreted as a renormalization-group scale for modes in the boundary $\mathrm{CFT}$. Higher-genus bulk geometries (the $\mathrm{BTZ}$ black hole and its generalizations) can be understood straightforwardly in our setting, and the Ryu–Takayanagi formula for the entanglement entropy appears naturally

97 MATHEMATICS AND COMPUTING↗

SU-E-T-584: Optical Tracking Guided Patient-Specific VMAT QA with ArcCHECK

Purpose: To investigate the novel use of an in-house optical tracking system (OTS) to improve the efficacy of VMAT QA with a cylindrical dosimeter (ArcCHECK™). Methods: The translational and rotational setup errors of ArcCHECK are convoluted which makes it challenging to position the device efficiently and accurately. We first aligned the ArcCHECK to the machine cross-hair at three cardinal angles (0°, 90°, and 270°) to establish a reference position. Four infrared reflective markers were attached to the back of the device. An OTS with 0.2mm/0.2° accuracy was used to control its setup uncertainty. Translational uncertainties of 1 mm and 2 mm in three directions (in, right, and up) were applied on the device. Four open beams of various field sizes and six clinical VMAT arcs were delivered and measured for all simulated setup errors. The measurements were compared with Pinnacle™ calculations using Gamma analysis to evaluate the impact of setup uncertainty. This study also evaluated the improvement in setup reproducibility and efficiency with the aid of the OTS. Results: For open beams, with 3%/3mm, the mean passing rates dropped by less than 5% for all shifts; with 2%/2mm, two significant drops(>5%) were observed: 15.38±6.75% for 2 mm lateral shift and 9.35±4.88% for 2 mm longitudinal shift. For VMAT arcs, the mean passing rates using 2%/2mm dropped by 10.47±7.46% and 22.02±11.39% for 1 and 2 mm shift, respectively. With 3%/3mm, significant drop only occurred with 2 mm longitudinal shift (13.73±8.30%). Setup time could be reduced by >15 min with the aid of the OTS. Conclusion: OTS is an effective tool for separating translational and rotational uncertainties. The current VMAT QA solution was not strongly sensitive to translation errors of 2mm with widely accepted criterion (3%/3mm). This finding raises concerns regarding the efficacy of such QA system in detecting errors in the dynamic VMAT delivery.

61 RADIATION PROTECTION AND DOSIMETRY↗

An analytical method to calculate equivalent fields to irregular symmetric and asymmetric photon fields

Equivalent field is frequently used for central axis depth-dose calculations of rectangular- and irregular-shaped photon beams. As most of the proposed models to calculate the equivalent square field are dosimetry based, a simple physical-based method to calculate the equivalent square field size was used as the basis of this study. The table of the sides of the equivalent square or rectangular fields was constructed and then compared with the well-known tables by BJR and Venselaar, et al. with the average relative error percentage of 2.5 ± 2.5% and 1.5 ± 1.5%, respectively. To evaluate the accuracy of this method, the percentage depth doses (PDDs) were measured for some special irregular symmetric and asymmetric treatment fields and their equivalent squares for Siemens Primus Plus linear accelerator for both energies, 6 and 18 MV. The mean relative differences of PDDs measurement for these fields and their equivalent square was approximately 1% or less. As a result, this method can be employed to calculate equivalent field not only for rectangular fields but also for any irregular symmetric or asymmetric field.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-E-T-299: Small Fields Profiles Correction Through Detectors Spatial Response Functions and Field Size Dependence Analysis

Purpose: To calculate the spatial response function of various radiation detectors, to evaluate the dependence on the field size and to analyze the small fields profiles corrections by deconvolution techniques. Methods: Crossline profiles were measured on a Novalis Tx 6MV beam with a HDMLC. The configuration setup was SSD=100cm and depth=5cm. Five fields were studied (200×200mm2,100×100mm2, 20×20mm2, 10×10mm2and 5×5mm2) and measured were made with passive detectors (EBT3 radiochromic films and TLD700 thermoluminescent detectors), ionization chambers (PTW30013, PTW31003, CC04 and PTW31016) and diodes (PTW60012 and IBA SFD). The results of passive detectors were adopted as the actual beam profile. To calculate the detectors kernels, modeled by Gaussian functions, an iterative process based on a least squares criterion was used. The deconvolutions of the measured profiles were calculated with the Richardson-Lucy method. Results: The profiles of the passive detectors corresponded with a difference in the penumbra less than 0.1mm. Both diodes resolve the profiles with an overestimation of the penumbra smaller than 0.2mm. For the other detectors, response functions were calculated and resulted in Gaussian functions with a standard deviation approximate to the radius of the detector in study (with a variation less than 3%). The corrected profiles resolve the penumbra with less than 1% error. Major discrepancies were observed for cases in extreme conditions (PTW31003 and 5×5mm2 field size). Conclusion: This work concludes that the response function of a radiation detector is independent on the field size, even for small radiation beams. The profiles correction, using deconvolution techniques and response functions of standard deviation equal to the radius of the detector, gives penumbra values with less than 1% difference to the real profile. The implementation of this technique allows estimating the real profile, freeing from the effects of the detector used for the acquisition.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Quantifying the Effect of Lidar Turbulence Error on Wind Power Prediction

Currently, cup anemometers on meteorological towers are used to measure wind speeds and turbulence intensity to make decisions about wind turbine class and site suitability; however, as modern turbine hub heights increase and wind energy expands to complex and remote sites, it becomes more difficult and costly to install meteorological towers at potential sites. As a result, remote-sensing devices (e.g., lidars) are now commonly used by wind farm managers and researchers to estimate the flow field at heights spanned by a turbine. Although lidars can accurately estimate mean wind speeds and wind directions, there is still a large amount of uncertainty surrounding the measurement of turbulence using these devices. Errors in lidar turbulence estimates are caused by a variety of factors, including instrument noise, volume averaging, and variance contamination, in which the magnitude of these factors is highly dependent on measurement height and atmospheric stability. As turbulence has a large impact on wind power production, errors in turbulence measurements will translate into errors in wind power prediction. The impact of using lidars rather than cup anemometers for wind power prediction must be understood if lidars are to be considered a viable alternative to cup anemometers.In this poster, the sensitivity of power prediction error to typical lidar turbulence measurement errors is assessed. Turbulence estimates from a vertically profiling WINDCUBE v2 lidar are compared to high-resolution sonic anemometer measurements at field sites in Oklahoma and Colorado to determine the degree of lidar turbulence error that can be expected under different atmospheric conditions. These errors are then incorporated into a power prediction model to estimate the sensitivity of power prediction error to turbulence measurement error. Power prediction models, including the standard binning method and a random forest method, were developed using data from the aeroelastic simulator FAST for a 1.5 MW turbine. The impact of lidar turbulence error on the predicted power from these different models is examined to determine the degree of turbulence measurement accuracy needed for accurate power prediction.

17 WIND ENERGY↗

Code verification for practically singular equations

We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.

97 MATHEMATICS AND COMPUTING↗

DPSK based low cost radio over fiber system for communication

The field of radio communication always demands high data rate, large bandwidth, low Bit Error Rate and flexible adaptability to different technologies. The Radio Over Fiber (ROF) technology in which the modulated radio frequency signals are optically modulated and transported through the optical fibers, largely reduce the installation costs and complexity. The present work describes a low-cost DPSK based full duplex two channel ROF communication system between a central station and two base stations in which the optical carrier frequency in the downlink is recovered and reused in the uplink communication.

42 ENGINEERING↗

Automated Reaction Kinetics of Gas-Phase Organic Species over Multiwell Potential Energy Surfaces

Automation of rate-coefficient calculations for gas-phase organic species became possible in recent years and has transformed how we explore these complicated systems computationally. Kinetics workflow tools bring rigor and speed and eliminate a large fraction of manual labor and related error sources. In this paper we give an overview of this quickly evolving field and illustrate, through five detailed examples, the capabilities of our own automated tool, KinBot. Here we bring examples from combustion and atmospheric chemistry of C-, H-, O-, and N-atom-containing species that are relevant to molecular weight growth and autoxidation processes. The examples shed light on the capabilities of automation and also highlight particular challenges associated with the various chemical systems that need to be addressed in future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Intrinsic selectivity and structure sensitivity of Rhodium catalysts for C 2+ oxygenate production [On the intrinsic selectivity and structure sensitivity of Rhodium catalysts for C 2+ oxygenate production]

Synthesis gas (CO + H 2 ) conversion is a promising route to converting coal, natural gas, or biomass into synthetic liquid fuels. Rhodium has long been studied as it is the only elemental catalyst that has demonstrated selectivity to ethanol and other C 2+ oxygenates. However, the fundamentals of syngas conversion over rhodium are still debated. In this work a microkinetic model is developed for conversion of CO and H 2 into methane, ethanol, and acetaldehyde on the Rh (211) and (111) surfaces, chosen to describe steps and close-packed facets on catalyst particles. The model is based on DFT calculations using the BEEF-vdW functional. The mean-field kinetic model includes lateral adsorbate–adsorbate interactions, and the BEEF-vdW error estimation ensemble is used to propagate error from the DFT calculations to the predicted rates. The model shows the Rh(211) surface to be ~6 orders of magnitude more active than the Rh(111) surface, but highly selective toward methane, while the Rh(111) surface is intrinsically selective toward acetaldehyde. A variety of Rh/SiO 2 catalysts are synthesized, tested for catalytic oxygenate production, and characterized using TEM. The experimental results indicate that the Rh(111) surface is intrinsically selective toward acetaldehyde, and a strong inverse correlation between catalytic activity and oxygenate selectivity is observed. Furthermore, iron impurities are shown to play a key role in modulating the selectivity of Rh/SiO 2 catalysts toward ethanol. The experimental observations are consistent with the structure-sensitivity predicted from theory. As a result, this work provides an improved atomic-scale understanding and new insight into the mechanism, active site, and intrinsic selectivity of syngas conversion over rhodium catalysts and may also guide rational design of alloy catalysts made from more abundant elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗