Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “high performance and distributed computing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,513 records · Page 84
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

MPI, HPF or OpenMP: A Study with the NAS Benchmarks

Porting applications to new high performance parallel and distributed platforms is a challenging task. Writing parallel code by hand is time consuming and costly, but this task can be simplified by high level languages and would even better be automated by parallelizing tools and compilers. The definition of HPF (High Performance Fortran, based on data parallel model) and OpenMP (based on shared memory parallel model) standards has offered great opportunity in this respect. Both provide simple and clear interfaces to language like FORTRAN and simplify many tedious tasks encountered in writing message passing programs. In our study, we implemented the parallel versions of the NAS Benchmarks with HPF and OpenMP directives. Comparison of their performance with the MPI implementation and pros and cons of different approaches will be discussed along with experience of using computer-aided tools to help parallelize these benchmarks. Based on the study, potentials of applying some of the techniques to realistic aerospace applications will be presented.

Jin, H.↗
NASA NTRS1999

MPI, HPF or OpenMP: A Study with the NAS Benchmarks

Porting applications to new high performance parallel and distributed platforms is a challenging task. Writing parallel code by hand is time consuming and costly, but the task can be simplified by high level languages and would even better be automated by parallelizing tools and compilers. The definition of HPF (High Performance Fortran, based on data parallel model) and OpenMP (based on shared memory parallel model) standards has offered great opportunity in this respect. Both provide simple and clear interfaces to language like FORTRAN and simplify many tedious tasks encountered in writing message passing programs. In our study we implemented the parallel versions of the NAS Benchmarks with HPF and OpenMP directives. Comparison of their performance with the MPI implementation and pros and cons of different approaches will be discussed along with experience of using computer-aided tools to help parallelize these benchmarks. Based on the study,potentials of applying some of the techniques to realistic aerospace applications will be presented

Jin, Hao-Qiang↗
DOE OSTI2015

SU-E-T-150: Brachytherapy QA Employing a High Resolution Liquid Filled Ionisation Chamber Array: Initial Experience and Limitations

Purpose: Verifying a complex 3D brachytherapy dose distribution by measurement is non-trivial. Ideally a photon detector array should be independent of energy and angle, have high spatial resolution and be robust for routine clinical use. Methods: An iridium-192 source was used. A PMMA jig was constructed comprising an outer slab and a central insert with eight milled channels for 1.33mm (outer diameter) steel needles, see figure. All calculations were performed using an empty CT study reconstructing eight virtual needles (QA-CT), using the v2 source model (Elekta AG, Sweden). A high resolution liquid filled ionisation chamber array SRS1000, together with Verisoft software v6.0 (PTW Freiburg, Germany), was used to perform measurements of plans of increasing complexity to evaluate its suitability for device- and patient-specific QA. The dimension of backscatter material was investigated. The patient plan dwell time distribution was entered manually into the QA-CT and the dose distribution was calculated. Results: Our measurements indicate that the array is independent of energy and angle. The resulting measured dose values are linearly interpolated to 2025 values. Shifts of 1mm of the entire needle are readily detectable. Individual dwell position shifts (2.5mm) are also readily measurable. Moreover a dwell time increase of 1 second both in the edge and central region are detectable. Conclusion: The high resolution SRS1000 array is a powerful instrument for brachytherapy QA enabling 977 simultaneous measurements to be performed. Our measurements suggest 60mm of RW3 backscatter material upstream and downstream are sufficient. Local percentage difference analysis is useful for device based QA, normalized relative percentage difference is arguably better for patient specific QA. Automated transfer of patient plan dwell time distribution to the QA plan is required to enable a comprehensive patient QA study to be performed. Moreover the described measurement technique can be used for commissioning new brachytherapy applicators.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

HyMARC Seedling: Optimized Hydrogen Adsorbents via Machine Learning and Crystal Engineering

This final report is presented in two parts: In Part 1, the H 2 capacities of a diverse set of 918,734 metal-organic frameworks (MOFs) sourced from 19 databases is predicted via machine learning (ML). Using only 7 structural features as input, ML identifies 8,282 MOFs with the potential to exceed the capacities of state-of-the-art materials. The identified MOFs are predominantly hypothetical compounds having low densities (<0.31 g/cm3) in combination with high surface areas (>5,300 m2/g), void fractions ($0.90), and pore volumes (>3.3 cm3/g). The relative importance of the input features are characterized, and dependencies on the ML algorithm and training set size are quantified. The most important features for predicting H 2 uptake are pore volume (for gravimetric capacity) and void fraction (for volumetric capacity). The ML models are available on the web, allowing for rapid and accurate predictions of the hydrogen capacities of MOFs from limited structural data; the simplest models require only a single crystallographic feature. In part 2, ways to improve the poor powder packing density of MOFs is discussed. More specifically, a strategy that improves packing efficiency and volumetric hydrogen gas storage density dramatically through engineered morphologies and controlled-crystal size distributions is presented that holds promise for maximizing storage capacity for a given MOF. The packing density improvement, demonstrated for the benchmark sorbent MOF-5, leads to a significant enhancement of volumetric hydrogen storage performance relative to commercial MOF-5. System model projections demonstrate that engineering of crystal morphology/size or use of a bimodal distribution of cubic crystal sizes in tandem with system optimization can surpass the 25 g/L volumetric capacity of a typical 700 bar compressed storage system and exceed the DOE targets 2020 volumetric capacity (30 g/L). Finally, a critical link between improved powder packing density and reduced damage upon compaction is revealed leading to sorbents with both high surface area and high density.

08 HYDROGEN↗
DOE OSTI2020

Basic factors for acquiring, correcting, and interpreting probe current-voltage characteristic in moderate-collisional plasma for determining electron energy distribution

Methods for inferring the electron distribution function (EDF) from a probe current–voltage trace are reviewed for moderate-collisional plasma. The explicit accounting of particle collisions, modeling sheath depletion, and electron refilling processes are rarely performed when analyzing probe measurements, yet they are critical for regime validity, EDF-profile accuracy, and space potential quantification precision. Furthermore, the advantages, limitations, and utilization of large-area wall probes in moderate-collisional plasma, capable of highly resolved indications of energetic electrons in plasma, are outlined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Multi-Physics Simulations of Molten Chloride Fast Reactor using Nek5000 and PROTEUS-NODAL

This report documents the FY20 work to demonstrate a specific multi-physics capability within NEAMS tools to model molten chloride fast reactors (MCFR). Specifically, the CFD code Nek5000 and the neutronics code PROTEUS-NODAL were coupled off-line to calculate the delayed neutron precursor distribution within the flowing fuel salts in an MCFR core. An MCFR benchmark problem and a 3D test problem based on a conceptual MSR design were successfully solved through the coupled simulation of Nek5000 and PROTEUS-NODAL. In the coupled simulations for these test problems, Nek5000 provided high-quality flow field information, and PROTEUS-NODAL performed the neutron diffusion calculation along with the precursor drift model. The impact of precursor drift on the core status was also investigated. Additionally, the precursor drift model implemented in PROTEUS-NODAL was verified by making use of the reference precursor distribution generated from Nek5000. Results of these test problems suggest that the multi-physics capability of Nek5000 and PROTEUS-NODAL was properly developed for tracking delayed neutron precursor drift.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Cross-code comparison of the impact of the fill tube on high yield implosions on the National Ignition Facility

Fill tubes are used to inject deuterium and tritium fuel into inertial confinement fusion capsules fielded on the National Ignition Facility. These fill tubes have been shown to have a detrimental effect on capsule performance, primarily by introducing a low-density pathway into the central fuel region that enables the jetting of ablation material into the hot spot. Due to the complexity of the highly nonlinear flow associated with the fill tube and the challenge of diagnosing the evolution of the fill tube jet late in the implosion experiments, the uncertainty in how this perturbation source evolves is great. In this work, we report on the results of a detailed code comparison performed to understand uncertainties in computational modeling of the impact of fill tubes on implosion performance. The study employed two radiation-hydrodynamics codes, HYDRA and xRAGE, which employ very different meshing strategies and hydrodynamics solvers, as well as two radiation transport methodologies, discrete ordinates and multi-group diffusion. Our results demonstrate generally good agreement between codes through most of the implosion although they indicate sensitivity to opacity averaging methods. Late in the implosion, differences arise in the distribution and amount of contaminant although these differences have a remarkably small impact on the amount of yield reduction due to the fill tube. While these results demonstrate sensitivity in fill tube modeling to algorithmic choices, the observed differences between codes are small relative to known sensitivities due to expected variations in the fill tube geometry. Finally, we have developed a methodology for performing multi-group diffusion simulations that show good agreement with the more accurate discrete ordinates method

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Modeling dust mineralogical composition: sensitivity to soil mineralogy atlases and their expected climate impacts

Soil dust aerosols are a key component of the climate system, as they interact with short- and long-wave radiation, alter cloud formation processes, affect atmospheric chemistry and play a role in biogeochemical cycles by providing nutrient inputs such as iron and phosphorus. The influence of dust on these processes depends on its physicochemical properties, which, far from being homogeneous, are shaped by its regionally varying mineral composition. The relative amount of minerals in dust depends on the source region and shows a large geographical variability. However, many state-of-the-art Earth system models (ESMs), upon which climate analyses and projections rely, still consider dust mineralogy to be invariant. The explicit representation of minerals in ESMs is more hindered by our limited knowledge of the global soil composition along with the resulting size-resolved airborne mineralogy than by computational constraints. In this work we introduce an explicit mineralogy representation within the state-of-the-art Multiscale Online Nonhydrostatic AtmospheRe CHemistry (MONARCH) model. We review and compare two existing soil mineralogy datasets, which remain a source of uncertainty for dust mineralogy modeling and provide an evaluation of multiannual simulations against available mineralogy observations. Soil mineralogy datasets are based on measurements performed after wet sieving, which breaks the aggregates found in the parent soil. Our model predicts the emitted particle size distribution (PSD) in terms of its constituent minerals based on brittle fragmentation theory (BFT), which reconstructs the emitted mineral aggregates destroyed by wet sieving. Our simulations broadly reproduce the most abundant mineral fractions independently of the soil composition data used. Feldspars and calcite are highly sensitive to the soil mineralogy map, mainly due to the different assumptions made in each soil dataset to extrapolate a handful of soil measurements to arid and semi-arid regions worldwide. For the least abundant or more difficult-to-determine minerals, such as iron oxides, uncertainties in soil mineralogy yield differences in annual mean aerosol mass fractions of up to ~ 100 %. Although BFT restores coarse aggregates including phyllosilicates that usually break during soil analysis, we still identify an overestimation of coarse quartz mass fractions (above 2 µm in diameter). In a dedicated experiment, we estimate the fraction of dust with undetermined composition as given by a soil map, which makes up ~ 10 % of the emitted dust mass at the global scale and can be regionally larger. Changes in the underlying soil mineralogy impact our estimates of climate-relevant variables, particularly affecting the regional variability of the single-scattering albedo at solar wavelengths or the total iron deposited over oceans. All in all, this assessment represents a baseline for future model experiments including new mineralogical maps constrained by high-quality spaceborne hyperspectral measurements, such as those arising from the NASA Earth Surface Mineral Dust Source Investigation (EMIT) mission.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1999

Unstructured Grid Euler Method Assessment for Aerodynamics Performance Prediction of the Complete TCA Configuration at Supersonic Cruise Speed

Unstructured grid Euler computations, performed at supersonic cruise speed, are presented for a proposed high speed civil transport configuration, designated as the Technology Concept Airplane (TCA) within the High Speed Research (HSR) Program. The numerical results are obtained for the complete TCA cruise configuration which includes the wing, fuselage, empennage, diverters, and flow through nacelles at Mach 2.4 for a range of angles-of-attack and sideslip. The computed surface and off-surface flow characteristics are analyzed and the pressure coefficient contours on the wing lower surface are shown to correlate reasonably well with the available pressure sensitive paint results, particularly, for the complex shock wave structures around the nacelles. The predicted longitudinal and lateral/directional performance characteristics are shown to correlate very well with the measured data across the examined range of angles-of-attack and sideslip. The results from the present effort have been documented into a NASA Controlled-Distribution report which is being presently reviewed for publication.

Farhad Ghaffari↗
NASA NTRS2015

Towards an Open, Distributed Software Architecture for UxS Operations

To address the growing need to evaluate, test, and certify an ever expanding ecosystem of UxS platforms in preparation of cultural integration, NASA Langley Research Center's Autonomy Incubator (AI) has taken on the challenge of developing a software framework in which UxS platforms developed by third parties can be integrated into a single system which provides evaluation and testing, mission planning and operation, and out-of-the-box autonomy and data fusion capabilities. This software framework, named AEON (Autonomous Entity Operations Network), has two main goals. The first goal is the development of a cross-platform, extensible, onboard software system that provides autonomy at the mission execution and course-planning level, a highly configurable data fusion framework sensitive to the platform's available sensor hardware, and plug-and-play compatibility with a wide array of computer systems, sensors, software, and controls hardware. The second goal is the development of a ground control system that acts as a test-bed for integration of the proposed heterogeneous fleet, and allows for complex mission planning, tracking, and debugging capabilities. The ground control system should also be highly extensible and allow plug-and-play interoperability with third party software systems. In order to achieve these goals, this paper proposes an open, distributed software architecture which utilizes at its core the Data Distribution Service (DDS) standards, established by the Object Management Group (OMG), for inter-process communication and data flow. The design decisions proposed herein leverage the advantages of existing robotics software architectures and the DDS standards to develop software that is scalable, high-performance, fault tolerant, modular, and readily interoperable with external platforms and software.

Cross, Charles D.↗
NASA NTRS2023

Modeling Dust Mineralogical Composition: Sensitivity to Soil Mineralogy Atlases and Their Expected Climate Impacts

Soil dust aerosols are a key component of the climate system, as they interact with short- and long-wave radiation, alter cloud formation processes, affect atmospheric chemistry and play a role in biogeochemical cycles by providing nutrient inputs such as iron and phosphorus. The influence of dust on these processes depends on its physicochemical properties, which, far from being homogeneous, are shaped by its regionally varying mineral composition. The relative amount of minerals in dust depends on the source region and shows a large geographical variability. However, many state-of-the-art Earth system models (ESMs), upon which climate analyses and projections rely, still consider dust mineralogy to be invariant. The explicit representation of minerals in ESMs is more hindered by our limited knowledge of the global soil composition along with the resulting size-resolved airborne mineralogy than by computational constraints. In this work we introduce an explicit mineralogy representation within the state-of-the-art Multiscale Online Nonhydrostatic AtmospheRe CHemistry (MONARCH) model. We review and compare two existing soil mineralogy datasets, which remain a source of uncertainty for dust mineralogy modeling and provide an evaluation of multiannual simulations against available mineralogy observations. Soil mineralogy datasets are based on measurements performed after wet sieving, which breaks the aggregates found in the parent soil. Our model predicts the emitted particle size distribution (PSD) in terms of its constituent minerals based on brittle fragmentation theory (BFT), which reconstructs the emitted mineral aggregates destroyed by wet sieving. Our simulations broadly reproduce the most abundant mineral fractions independently of the soil composition data used. Feldspars and calcite are highly sensitive to the soil mineralogy map, mainly due to the different assumptions made in each soil dataset to extrapolate a handful of soil measurements to arid and semi-arid regions worldwide. For the least abundant or more difficult-to-determine minerals, such as iron oxides, uncertainties in soil mineralogy yield differences in annual mean aerosol mass fractions of up to ∼ 100 %. Although BFT restores coarse aggregates including phyllosilicates that usually break during soil analysis, we still identify an overestimation of coarse quartz mass fractions (above 2 µm in diameter). In a dedicated experiment, we estimate the fraction of dust with undetermined composition as given by a soil map, which makes up ∼ 10 % of the emitted dust mass at the global scale and can be regionally larger. Changes in the underlying soil mineralogy impact our estimates of climate-relevant variables, particularly affecting the regional variability of the single-scattering albedo at solar wavelengths or the total iron deposited over oceans. All in all, this assessment represents a baseline for future model experiments including new mineralogical maps constrained by high-quality spaceborne hyperspectral measurements, such as those arising from the NASA Earth Surface Mineral Dust Source Investigation (EMIT) mission.

Soil dust↗
DOE OSTI2014

3D and 4D magnetic susceptibility tomography based on complex MR images

Magnetic susceptibility is the physical property for T2*-weighted magnetic resonance imaging (T2*MRI). The invention relates to methods for reconstructing an internal distribution (3D map) of magnetic susceptibility values, .chi. (x,y,z), of an object, from 3D T2*MRI phase images, by using Computed Inverse Magnetic Resonance Imaging (CIMRI) tomography. The CIMRI technique solves the inverse problem of the 3D convolution by executing a 3D Total Variation (TV) regularized iterative convolution scheme, using a split Bregman iteration algorithm. The reconstruction of .chi. (x,y,z) can be designed for low-pass, band-pass, and high-pass features by using a convolution kernel that is modified from the standard dipole kernel. Multiple reconstructions can be implemented in parallel, and averaging the reconstructions can suppress noise. 4D dynamic magnetic susceptibility tomography can be implemented by reconstructing a 3D susceptibility volume from a 3D phase volume by performing 3D CIMRI magnetic susceptibility tomography at each snapshot time.

47 OTHER INSTRUMENTATION↗
NASA NTRS1993

Numerical analysis of base flowfield at high altitude for a four-engine clustered nozzle configuration

The objective of this study is to benchmark a four-engine clustered nozzle base flowfield with a computational fluid dynamics (CFD) model. The CFD model is a pressure based, viscous flow formulation. An adaptive upwind scheme is employed for the spatial discretization. The upwind scheme is based on second and fourth order central differencing with adaptive artificial dissipation. Qualitative base flow features such as the reverse jet, wall jet, recompression shock, and plume-plume impingement have been captured. The computed quantitative flow properties such as the radial base pressure distribution, model centerline Mach number and static pressure variation, and base pressure characteristic curve agreed reasonably well with those of the measurement. Parametric study on the effect of grid resolution, turbulence model, inlet boundary condition and difference scheme on convective terms has been performed. The results showed that grid resolution and turbulence model are two primary factors that influence the accuracy of the base flowfield prediction.

Wang, Ten-See↗
NASA NTRSDate not supplied

Computational investigation on the combined effect of pore attributes on strain concentrators in metal additively manufactured materials

Metal additive manufacturing provides a pathway for creating highly optimized components. However, porosity continues to be a prevalent issue for fatigue performance despite best efforts in optimizing process parameters and postprocessing techniques. This work uses finite element analysis to conduct a parametric study to link various pore attributes (i.e., aspect ratio, orientation, and location) to strain concentration factors (SCF) under elastic/plastic deformation during uniaxial loading. Keyhole and lack-of-fusion pores are idealized by prolate and oblate ellipsoids, respectively. Each simulation of the parametric study assumes a single isolated pore in a Ti-6Al-4V material, modeled with J2-plasticity. A reduced-order model is developed to relate pore attributes to SCF, and then used to quantify the variability in SCF for a given experimentally characterized probability distribution of pore attributes. This reduced-order model can be used in a production environment to provide a first-order evaluation to rapidly screen sub-optimally performing components.

Additive Manufacturing↗
DOE OSTI2020

Automated Integration of Continental-Scale Observations in Near-Real Time for Simulation and Analysis of Biosphere–Atmosphere Interactions

The National Ecological Observatory Network (NEON) is a continental-scale observatory with sites across the US collecting standardized ecological observations that will operate for multiple decades. To maximize the utility of NEON data, we envision edge computing systems that gather, calibrate, aggregate, and ingest measurements in an integrated fashion. Edge systems will employ machine learning methods to cross-calibrate, gap-fill and provision data in near-real time to the NEON Data Portal and to High Performance Computing (HPC) systems, running ensembles of Earth system models (ESMs) that assimilate the data. For the first time gridded EC data products and response functions promise to offset pervasive observational biases through evaluating, benchmarking, optimizing parameters, and training new machine learning parameterizations within ESMs all at the same model-grid scale. Leveraging open-source software for EC data analysis, we are already building software infrastructure for integration of near-real time data streams into the International Land Model Benchmarking (ILAMB) package for use by the wider research community. We will present a perspective on the design and integration of end-to-end infrastructure for data acquisition, edge computing, HPC simulation, analysis, and validation, where Artificial Intelligence (AI) approaches are used throughout the distributed workflow to improve accuracy and computational performance.

Durden, David J.↗
DOE OSTI2020

Temperature-dependent phonon lifetimes and thermal conductivity of silicon by inelastic neutron scattering and ab initio calculations

In this paper, inelastic neutron scattering on a single crystal of silicon was performed at temperatures from 100 to 1500 K. These experimental data were reduced to obtain phonon spectral intensity at all wave vectors $\overset{→}{Q}$ and frequencies ω in the first Brillouin zone. Thermal broadenings of the phonon peaks were obtained by fitting and by calculating with an iterative ab initio method that uses thermal atom displacements on an ensemble of superlattices. Agreement between the calculated and experimental broadenings was good, with possible discrepancies at the highest temperatures. Distributions of phonon widths versus phonon energy had similar shapes for computation and experiment. These distributions grew with temperature but maintained similar shapes. Parameters from the ab initio calculations were used to obtain the thermal conductivity from the Boltzmann transport equation, which was in good agreement with experimental data. Despite the high group velocities of longitudinal acoustic phonons, their shorter lifetimes reduced their contribution to the thermal conductivity, which was dominated by transverse acoustic modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed

Changes in extreme precipitation events may require revisions of civil engineering standards to prevent water infrastructures from performing below the designated guidelines. Climate change may invalidate the intensity-duration-frequency (IDF) computation that is based on the assumption of data stationarity. Efforts in evaluating non-stationarity in the annual maxima series are inadequate, mostly due to the lack of long data records and convenient methods for detecting trends in the higher moments. In this study, using downscaled high resolution climate simulations of the historical and future periods under different carbon emission scenarios, we tested two solutions to obtain reliable IDFs under non-stationarity: (1) identify quasi-stationary time windows from the time series of interest to compute the IDF curves using data for the corresponding time windows; (2) introduce a parameter representing the trend in the means of the extreme value distributions. Focusing on a mountainous site, the Walker Watershed, the spatial heterogeneity and variability of IDFs or extremes are evaluated, particularly in terms of the terrain and elevation impacts. We compared observations-based IDFs that use the stationarity assumption with the two approaches that consider non-stationarity. The IDFs directly estimated based on the traditional stationarity assumption may underestimate the 100-year 24-h events by 10% to 60% towards the end of the century at most grids, resulting in significant under-designing of the engineering infrastructure at the study site. Strong spatial heterogeneity and variability in the IDF estimates suggest a preference for using high resolution simulation data for the reliable estimation of exceedance probability over data from sparsely distributed weather stations. Discrepancies among the three IDFs analyses due to non-stationarity are comparable to the spatial variability of the IDFs, underscoring a need to use an ensemble of non-stationary approaches to achieve unbiased and comprehensive IDF estimates.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2003

Comparison of mode estimation methods and application in molecular clock analysis

BACKGROUND: Distributions of time estimates in molecular clock studies are sometimes skewed or contain outliers. In those cases, the mode is a better estimator of the overall time of divergence than the mean or median. However, different methods are available for estimating the mode. We compared these methods in simulations to determine their strengths and weaknesses and further assessed their performance when applied to real data sets from a molecular clock study. RESULTS: We found that the half-range mode and robust parametric mode methods have a lower bias than other mode methods under a diversity of conditions. However, the half-range mode suffers from a relatively high variance and the robust parametric mode is more susceptible to bias by outliers. We determined that bootstrapping reduces the variance of both mode estimators. Application of the different methods to real data sets yielded results that were concordant with the simulations. CONCLUSION: Because the half-range mode is a simple and fast method, and produced less bias overall in our simulations, we recommend the bootstrapped version of it as a general-purpose mode estimator and suggest a bootstrap method for obtaining the standard error and 95% confidence interval of the mode.

Evolution, Molecular↗