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At least 73 records · Page 4

Influence of surface relaxation on solute atoms positioning within atom probe tomography reconstructions

Highlights: • APT measurement of Al/Cu alloy is simulated with a combined electrostatics and molecular dynamics (MD) approach. • Results show segregation of dilute Cu at [111] poles in correspondence to experimental measurements. • No temperature is involved. The effect originates in both disparate evaporation field and bond-energies in the alloy. While thermal or field-induced surface migration has been invoked often in past literature to rationalize the experimental observations of solute and impurity atoms segregation to specific poles and zones lines in atom probe tomography (APT) reconstructions, it does not satisfactorily explain all experimental results. Using a combined finite-element and molecular dynamics simulation approach that models the field evaporation process from mechanically relaxed emitter structures, we show that an additional mechanism, athermal relaxation, can also drive significant solute migration. The mechanism is illustrated for Cu in solid solution in Al, which exhibits segregation of Cu to 111 poles and along [110] zone lines in reconstructed APT data. The higher bonding energy of Cu atoms on the surface, confirmed using density-functional theory calculations, causes longer retention on the surface and preferential evaporation of neighboring Al atoms with subsequent athermal relaxation of Cu into higher-neighbor-count sites left vacant by evaporating Al neighbors. This in turn results in barrier-free long-range migration of the Cu atoms by a series of relaxation events that follow the receding terrace ledges towards high-neighbor count poles and zone lines. This mechanism fundamentally limits spatial resolution in the limit of zero temperature.

36 MATERIALS SCIENCE↗

SCIP: a single-cell image processor toolbox

Abstract Summary Each cell is a phenotypically unique individual that is influenced by internal and external processes, operating in parallel. To characterize the dynamics of cellular processes one needs to observe many individual cells from multiple points of view and over time, so as to identify commonalities and variability. With this aim, we engineered a software, ‘SCIP’, to analyze multi-modal, multi-process, time-lapse microscopy morphological and functional images. SCIP is capable of automatic and/or manually corrected segmentation of cells and lineages, automatic alignment of different microscopy channels, as well as detect, count and characterize fluorescent spots (such as RNA tagged by MS2-GFP), nucleoids, Z rings, Min system, inclusion bodies, undefined structures, etc. The results can be exported into *mat files and all results can be jointly analyzed, to allow studying not only each feature and process individually, but also find potential relationships. While we exemplify its use on Escherichia coli, many of its functionalities are expected to be of use in analyzing other prokaryotes and eukaryotic cells as well. We expect SCIP to facilitate the finding of relationships between cellular processes, from small-scale (e.g. gene expression) to large-scale (e.g. cell division), in single cells and cell lineages. Availability and implementation http://www.ca3-uninova.org/project_scip Supplementary information Supplementary data are available at Bioinformatics online.

Martins, Leonardo (ORCID:0000000333512910)↗

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.

Metzger, Philip T.↗

Space Station Freedom altitude strategy

The Space Station Freedom (SSF) altitude strategy provides guidelines and assumptions to determine an altitude profile for Freedom. The process for determining an altitude profile incorporates several factors such as where the Space Shuttle will rendezvous with the SSF, when reboosts must occur, and what atmospheric conditions exist causing decay. The altitude strategy has an influence on all areas of SSF development and mission planning. The altitude strategy directly affects the micro-gravity environment for experiments, propulsion and control system sizing, and Space Shuttle delivery manifests. Indirectly the altitude strategy influences almost every system and operation within the Space Station Program. Evolution of the SSF altitude strategy has been a very dynamic process over the past few years. Each altitude strategy in turn has emphasized a different consideration. Examples include a constant Space Shuttle rendezvous altitude for mission planning simplicity, or constant micro-gravity levels with its inherent emphasis on payloads, or lifetime altitudes to provide a safety buffer to loss of control conditions. Currently a new altitude strategy is in development. This altitude strategy will emphasize Space Shuttle delivery optimization. Since propellant is counted against Space Shuttle payload-to-orbit capacity, lowering the rendezvous altitude will not always increase the net payload-to-orbit, since more propellant would be required for reboost. This altitude strategy will also consider altitude biases to account for Space Shuttle launch slips and an unexpected worsening of atmospheric conditions. Safety concerns will define a lower operational altitude limit, while radiation levels will define upper altitude constraints. The evolution of past and current SSF altitude strategies and the development of a new altitude strategy which focuses on operational issues as opposed to design are discussed.

Mcdonald, Brian M.↗

Observation of biexciton emission from single semiconductor nanoplatelets

Quasi-two-dimensional semiconductor nanoplatelets (NPLs) are intriguing systems for studying the influence of Auger recombination processes on the multiexciton emission efficiencies in the weak in-plane confinement regime. We investigate CdSe/CdS core/shell NPLs using cryogenic temperature single particle spectroscopy and observe bright biexciton emission at high excitation powers. The average binding energy of the biexcitons is determined to be 16.5 meV. The observed switching between the biexciton and trion states indicates charging-decharging dynamics of the NPLs mediated by the Auger ionization process. These findings are highly relevant for harvesting efficient biexciton emission for energy, lighting, and quantum applications.

36 MATERIALS SCIENCE↗

Counting generations in birth and death processes with competing Erlang and exponential waiting times

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, then each cell can be imagined as sampling from a probability density of times to division and death. The exponential density is the most mathematically and computationally convenient choice. It has the advantage of satisfying the memoryless property, consistent with a Markov process, but it overestimates the probability of short division times. With the aim of preserving the advantages of a Markovian framework while improving the representation of experimentally-observed division times, we consider a multi-stage model of cellular division and death. We use Erlang-distributed (or, more generally, phase-type distributed) times to division, and exponentially distributed times to death. We classify cells into generations, using the rule that the daughters of cells in generation n are in generation n + 1. In some circumstances, our representation is equivalent to established models of lymphocyte dynamics. We find the growth rate of the cell population by calculating the proportions of cells by stage and generation. The exponent describing the late-time cell population growth, and the criterion for extinction of the population, differs from what would be expected if N steps with rate λ were equivalent to a single step of rate λ/N. We link with a published experimental dataset, where cell counts were reported after T cells were transferred to lymphopenic mice, using Approximate Bayesian Computation. In the comparison, the death rate is assumed to be proportional to the generation and the Erlang time to division for generation 0 is allowed to differ from that of subsequent generations. The multi-stage representation is preferred to a simple exponential in posterior distributions, and the mean time to first division is estimated to be longer than the mean time to subsequent divisions.

59 BASIC BIOLOGICAL SCIENCES↗

Reprocessing Microflare Data

The report concerns work on detecting and cataloging solar microflares using an automated. An accompanying figure represents the solar microflare distribution during the period of April 1991 to November 1992, the height of solar activity after the launch of CGRO. It also shows the distribution extending below the distribution obtained at GSFC by manual means. We have implemented significant refinements in the search algorithm. The algorithm in its simplest form searches for transient events and based upon the distribution of the signal among the different BATSE detectors, we can assign it to be of solar origin if the signal distribution conforms to what one expects from a burst or transient from that direction. One of the major problems in an earlier effort was to search for microflares and large flares simultaneously. The requirement for a dynamic range of almost 10(exp 4) resulted in ambiguous identifications at the low side of the distribution. We have since restricted the search to events with peak count rates under 2000/s. Larger events are easily identified in the manual search, so we have chosen not to duplicate that work. The second problem was that missing counts existed below channel 0 in the BATSE Large Area Detector (LAD) data. These have been recovered and are now included in the search process. This provides data below 20 keV, and as we get closer to the thermal part of the spectrum, it provides greater sensitivity. The third problem was that too many BATSE detectors were used in the search. Detectors with pointing directions far from the Sun, although detecting the event, had poorly known responses. Detectors greater than approximately 60 degrees off the Sun are no longer included in the search process. By reducing the systematic errors with the large off-axis detectors we can conduct more rigorous statistical tests of a candidate event to ascertain whether it originated from the solar direction. We have reprocessed the period in the early mission that covers solar maximum and constructed the microflare distribution shown in the figure. The results of the automated search start to deviate from the manual search results below about 1000/s. Not only do we now have this distribution but we have a database of solar microflares that was used to construct the distribution. This database contains the signal at higher energy channels as well as that in channel zero (and below). From this one can, using software at GSFC, construct a photon spectrum for some of the larger microflares. It can also be used in other solar studies, especially those that correlate the X-ray flux with emission at other wavelengths. With some additional effort we hope to integrate this database into the corresponding one residing at the Solar Data Analysis Center at GSFC. The entire CGRO mission's data can now be reprocessed to obtain the microflare distribution at all phases of the solar cycle. This work is in progress. The results of this work will be presented in forthcoming scientific workshops and conferences.

Ryan, James M.↗

Multiple-Event, Single-Photon Counting Imaging Sensor

The single-photon counting imaging sensor is typically an array of silicon Geiger-mode avalanche photodiodes that are monolithically integrated with CMOS (complementary metal oxide semiconductor) readout, signal processing, and addressing circuits located in each pixel and the peripheral area of the chip. The major problem is its single-event method for photon count number registration. A single-event single-photon counting imaging array only allows registration of up to one photon count in each of its pixels during a frame time, i.e., the interval between two successive pixel reset operations. Since the frame time can t be too short, this will lead to very low dynamic range and make the sensor merely useful for very low flux environments. The second problem of the prior technique is a limited fill factor resulting from consumption of chip area by the monolithically integrated CMOS readout in pixels. The resulting low photon collection efficiency will substantially ruin any benefit gained from the very sensitive single-photon counting detection. The single-photon counting imaging sensor developed in this work has a novel multiple-event architecture, which allows each of its pixels to register as more than one million (or more) photon-counting events during a frame time. Because of a consequently boosted dynamic range, the imaging array of the invention is capable of performing single-photon counting under ultra-low light through high-flux environments. On the other hand, since the multiple-event architecture is implemented in a hybrid structure, back-illumination and close-to-unity fill factor can be realized, and maximized quantum efficiency can also be achieved in the detector array.

Zheng, Xinyu↗

A valence balanced rule for discovery of 18-electron half-Heuslers with defects

Using first-principles DFT we systematically investigate the thermodynamic stability and off-stoichiometry in 108 nominal 19-electron half-Heusler (hH) compounds. We demonstrate unambiguously that considering a cation deficiency towards the off-stoichiometric valence balanced, VEC = 18 composition is necessary for explaining the stability of all previously reported nominal VEC = 19 compounds. This is understandable in terms of an energy benefit from valence balance considering the valence of each atom using Zintl chemistry that offsets the energy penalty of forming defects in nearly all cases. Thus, we propose a valence balanced rule to understand the ground state stability of half-Heuslers irrespective of stoichiometry and nominal electron count (8, 18 or 19). Using this generalized rule we (a) predict 16 previously unreported nominal 19-electron XYZ half-Heuslers and (b) rationalize the reports of giant off-stoichiometries in compounds such as Ti (1–x) NiSb which has been known for over 50 years. Of the 16 new compounds predicted here, Ti (1–x) PtSb was synthesized and the half-Heusler phase confirmed through X-ray studies. Here, the flexibility in stoichiometry of the half-Heusler systems to attain a stable valence balanced composition by accommodating large defect concentrations opens up multiple dimensions for discovery of multi-component defective half-Heuslers based on intrinsic and extrinsic defects which compensate for the nominally non-18-electron count of the structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Conservation laws and effective hadronization models

Hadronization models based on local string-breaking dynamics are typically Markovian by construction, yet the physical ensemble of final states is shaped by global constraints that couple the entire fragmentation trajectory. Recasting hadronization as a conditioned stochastic diffusion process provides a precise mathematical resolution to this tension. In particular, this language reveals explicitly that constraints stemming from conservation laws induce non-Markovian correlations between otherwise independent fragmentation steps, and that these correlations can be absorbed exactly into a renormalization of the local dynamics through a Doob $h$-transform. We develop this formalism for a $q\bar{q}$ string in the chiral limit, where the longitudinal-transverse factorization of the Lund kernel becomes exact, enabling systematic power counting and clean ultraviolet (UV)/infrared (IR) separation. The dynamics organize naturally into a tower of effective theories distinguished by the remaining string mass, spanning a UV fixed point with scale-invariant transport coefficients, an intermediate regime where transverse phase space induces controlled running, and an IR boundary layer where non-local effects enter at leading order. The tower exhibits genuine Wilsonian structure, including $β$-functions, anomalous dimensions, and systematic matching conditions. The resulting framework achieves a clean factorization of universal microscopic fragmentation dynamics from infrared constraint effects, and opens new directions for both the theoretical analysis and practical simulation of hadronization.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗

Multichannel response analysis on 2D projection views for detection of clustered microcalcifications in digital breast tomosynthesis

Purpose: To investigate the feasibility of a new two-dimensional (2D) multichannel response (MCR) analysis approach for the detection of clustered microcalcifications (MCs) in digital breast tomosynthesis (DBT). Methods: With IRB approval and informed consent, a data set of two-view DBTs from 42 breasts containing biopsy-proven MC clusters was collected in this study. The authors developed a 2D approach for MC detection using projection view (PV) images rather than the reconstructed three-dimensional (3D) DBT volume. Signal-to-noise ratio (SNR) enhancement processing was first applied to each PV to enhance the potential MCs. The locations of MC candidates were then identified with iterative thresholding. The individual MCs were decomposed with Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) basis functions and the channelized Hotelling model was trained to produce the MCRs for each MC on the 2D images. The MCRs from the PVs were fused in 3D by a coincidence counting method that backprojects the MC candidates on the PVs and traces the coincidence of their ray paths in 3D. The 3D MCR was used to differentiate the true MCs from false positives (FPs). Finally a dynamic clustering method was used to identify the potential MC clusters in the DBT volume based on the fact that true MCs of clinical significance appear in clusters. Using two-fold cross validation, the performance of the 3D MCR for classification of true and false MCs was estimated by the area under the receiver operating characteristic (ROC) curve and the overall performance of the MCR approach for detection of clustered MCs was assessed by free response receiver operating characteristic (FROC) analysis. Results: When the HG basis function was used for MCR analysis, the detection of MC cluster achieved case-based test sensitivities of 80% and 90% at the average FP rates of 0.65 and 1.55 FPs per DBT volume, respectively. With LG basis function, the average FP rates were 0.62 and 1.57 per DBT volume at the same sensitivity levels. The difference in the two sets of basis functions for detection of MCs did not show statistical significance. Conclusions: The authors' experimental results indicate that the MCR approach is promising for the detection of MCs on PV images. The HG or LG basis functions are both effective in characterizing the signal response of MCs using the channelized Hotelling model. The coincidence counting method for fusion of the 2D MCR in 3D is an important step for FP reduction. Further study is underway to improve the MCR approach for microcalcification detection in DBT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Wide Dynamic Range, 10 kHz Framing Detector for 4D-STEM

Hybrid pixel array detectors (PADs) have expanded the fidelity, frame rate and dynamic range for diffractive imaging in electron microscopes. With their high detective quantum efficiencies (DQE), the noise performance limited is by counting statistics. Consequently, improving the precision and quality of high-speed images requires increasing the linear dynamic range and the maximum usable beam current. Here we describe a new prototype hybrid PAD, our next-generation electron microscope pixel array detector (NG-EMPAD) that expands both the framing speed and dynamic range of our earlier EMPAD design. Like the EMPAD, electrons are detected directly in a 500 μm thick silicon sensor bonded pixel-by-pixel to a custom signal processing integrated circuit (IC). Each pixel in the IC integrates charge carriers produced by the high-energy incident electrons. Here, in-pixel circuitry uses a combination of techniques to extend the dynamic range, including adaptive gain switching and the quantitative excess charge dumping similar to the EMPAD. In-pixel buffering of signals during readout allows acquiring a new image while reading out the previously collected image, yielding an image collection duty cycle of nearly 100%.

36 MATERIALS SCIENCE↗

A rare gas optics-free absolute photon flux and energy analyzer to provide absolute photoionization rates of inflowing interstellar neutrals

A prototype spectrometer has been developed for space applications requiring long term absolute EUV photon flux measurements. The energy spectrum of the incoming photons is transformed directly into an electron energy spectrum by taking advantage of the photoelectric effect in one of several rare gases at low pressures. Using an electron energy spectrometer, followed by an electron multiplier detector, pulses due to individual electrons are counted. The overall efficiency of this process can be made essentially independent of gain drifts in the signal path, and the secular degradation of optical components which is often a problem in other techniques is avoided. A very important feature of this approach is its freedom from the problem of overlapping spectral orders that plagues grating EUV spectrometers. An instrument with these features has not been flown before, but is essential to further advances in our understanding of solar EUV flux dynamics, and the coupled dynamics of terrestrial and planetary atmospheres. The detailed characteristics of this optics-free spectrometer are presented in the publications section.

Judge, Darrell L.↗

A rare gas optics-free absolute photon flux and energy analyzer for solar and planetary observations

We have developed a prototype spectrometer for space applications requiring long term absolute EUV photon flux measurements. In this recently developed spectrometer, the energy spectrum of the incoming photons is transformed directly into an electron energy spectrum by taking advantage of the photoelectric effect in one of several rare gases at low pressures. Using an electron energy spectrometer, followed by an electron multiplier detector, pulses due to individual electrons are counted. The overall efficiency of this process can be made essentially independent of gain drifts in the signal path, and the secular degradation of optical components which is often a problem in other techniques is avoided. A very important feature of this approach is its freedom from the problem of overlapping spectral orders that plagues grating EUV spectrometers. An instrument with these features has not been flown before, but is essential to further advances in our understanding of solar EUV flux dynamics, and the coupled dynamics of terrestrial and planetary atmospheres. The detailed characteristics of this optics-free spectrometer are presented in the publications section.

Judge, Darrell L.↗

Feedback-Based, System-Level Properties of Vertebrate-Microbial Interactions

Improved characterization of infectious disease dynamics is required. To that end, three-dimensional (3D) data analysis of feedback-like processes may be considered. To detect infectious disease data patterns, a systems biology (SB) and evolutionary biology (EB) approach was evaluated, which utilizes leukocyte data structures designed to diminish data variability and enhance discrimination. Using data collected from one avian and two mammalian (human and bovine) species infected with viral, parasite, or bacterial agents (both sensitive and resistant to antimicrobials), four data structures were explored: (i) counts or percentages of a single leukocyte type, such as lymphocytes, neutrophils, or macrophages (the classic approach), and three levels of the SB/ EB approach, which assessed (ii) 2D, (iii) 3D, and (iv) multi-dimensional (rotating 3D) host-microbial interactions. In all studies, no classic data structure discriminated disease-positive (D+, or observations in which a microbe was isolated) from disease-negative (D–, or microbial-negative) groups: D+ and D– data distributions overlapped. In contrast, multi-dimensional analysis of indicators designed to possess desirable features, such as a single line of observations, displayed a continuous, circular data structure, whose abrupt inflections facilitated partitioning into subsets statistically significantly different from one another. In all studies, the 3D, SB/EB approach distinguished three (steady, positive, and negative) feedback phases, in which D– data characterized the steady state phase, and D+ data were found in the positive and negative phases. In humans, spatial patterns revealed false-negative observations and three malaria-positive data classes. In both humans and bovines, methicillin-resistant Staphylococcus aureus (MRSA) infections were discriminated from non-MRSA infections. More information can be extracted, from the same data, provided that data are structured, their 3D relationships are considered, and well-conserved (feedback-like) functions are estimated. Patterns emerging from such structures may distinguish well-conserved from recently developed host-microbial interactions. Applications include diagnosis, error detection, and modeling.

59 BASIC BIOLOGICAL SCIENCES↗

Very-Low-Cost, Rugged Vacuum System

NASA, DoD, DHS, and commercial industry have a need for miniaturized, rugged, low-cost vacuum systems. Recent advances in sensor technology have led to the development of very small mass spectrometer detectors as well as other miniature analytical instruments. However, the vacuum systems to support these sensors remain large, heavy, and power-hungry. To meet this need, a miniaturized vacuum system was created based on a very small, rugged, and inexpensive- to-manufacture molecular drag pump (MDP). The MDP is enabled by the development of a miniature, veryhigh- speed, rugged, low-power, brushless DC motor optimized for wide temperature operation and long life. Such a pump represents an order-of-magnitude reduction in mass, volume, and cost over current, commercially available, state-ofthe- art vacuum pumps. The vacuum system consists of the MDP coupled to a ruggedized rough pump (for terrestrial applications or for planets with substantial atmospheres). The rotor in the MDP consists of a simple smooth cylinder of aluminum spinning at approximately 200,000 RPM inside an outer stator housing. The pump stator comprises a cylindrical aluminum housing with one or more specially designed grooves that serve as flow channels. To minimize the length of the pump, the gas is forced down the flow channels of the outer stator to the base of the pump. The gas is then turned and pulled toward the top through a second set of channels cut into an inner stator housing that surrounds the motor. The compressed gas then flows down channels in the motor housing to the exhaust port of the pump. The exhaust port of the pump is connected to a diaphragm or scroll pump. This pump delivers very high performance in a very small envelope. The design was simplified so that a smaller compression ratio, easier manufacturing process, and enhanced ruggedness can be achieved at the lowest possible cost. The machining of the rotor and stators is very simple compared to that necessary to fabricate TMP (turbo molecular pump) rotor and stator blades. Also, the symmetry of the rotor is such that dynamic balancing of the rotor is greatly simplified. Finally, because of the simplified design, the number of parts in the unit is cut by nearly a factor of three. In fact, there are only five parts, not counting the motor and off-the-shelf screws and O-rings. This reduces the amount of machining and also makes fit-up much simpler while allowing the maintenance of close tolerances.

Kline-Schoder, Robert↗

Building a machine learning surrogate model for wildfire activities within a global Earth system model

Abstract. Wildfire is an important ecosystem process, influencing land biogeophysical and biogeochemical dynamics and atmospheric composition. Fire-driven loss of vegetation cover, for example, directly modifies the surface energy budget as a consequence of changing albedo, surface roughness, and partitioning of sensible and latent heat fluxes. Carbon dioxide and methane emitted by fires contribute to a positive atmospheric forcing, whereas emissions of carbonaceous aerosols may contribute to surface cooling. Process-based modeling of wildfires in Earth system land models is challenging due to limited understanding of human, climate, and ecosystem controls on fire counts, fire size, and burned area. Integration of mechanistic wildfire models within Earth system models requires careful parameter calibration, which is computationally expensive and subject to equifinality. To explore alternative approaches, we present a deep neural network (DNN) scheme that surrogates the process-based wildfire model with the Energy Exascale Earth System Model (E3SM) interface. The DNN wildfire model accurately simulates observed burned area with over 90 % higher accuracy with a large reduction in parameterization time compared with the current process-based wildfire model. The surrogate wildfire model successfully captured the observed monthly regional burned area during validation period 2011 to 2015 (coefficient of determination, R2=0.93). Since the DNN wildfire model has the same input and output requirements as the E3SM process-based wildfire model, our results demonstrate the applicability of machine learning for high accuracy and efficient large-scale land model development and predictions.

58 GEOSCIENCES↗

Efficient GPU Implementation of Automatic Differentiation for Computational Fluid Dynamics

Many scientific and engineering applications require repeated calculations of derivatives of output functions with respect to input parameters. Automatic Differentiation (AD) is a method that automates derivative calculations and can significantly speed up code development. In Computational Fluid Dynamics (CFD), derivatives of flux functions with respect to state variables (Jacobian) are needed for efficient solutions of the nonlinear governing equations. AD of flux functions on graphics processing units (GPUs) is challenging as flux computations involve many intermediate variables that create high register pressure and require significant memory traffic because of the need to store the derivatives. This paper presents a forward-mode AD method based on multivariate dual numbers that addresses these challenges and simultaneously reduces the floating-point operation count. The dimension of the multivariate dual numbers is optimized for performance. The flux computations are restructured to minimize the number of temporary variables and reduce register pressure. For effective utilization of memory bandwidth, shared memory is used to store the local flux Jacobian. This AD implementation is compared with several other Jacobian implementations on an NVIDIA V100 GPU (V100). For three-dimensional perfect-gas compressible-flow equations implemented in a practical CFD code, the AD implementation of a flux Jacobian based on multivariate dual numbers of dimension 5 outperforms all other GPU AD implementations on V100. Its performance is comparable with the optimized hand-differentiated version. Finally, the implementation achieves 75% of the peak floating-point throughput and 61 % of the peak global device memory bandwidth usage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗