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All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Monte Carlo↗
NASA NTRSDate not supplied

Assessing Risk Due to Small Sample Size in Probability of Detection Analysis Using Tolerance Intervals

Small sample size (e.g.6-30) poses risk in results of probability of detection (POD) analysis using tolerance intervals. This method is also called as the limited sample or LS POD. The analysis is performed either during NDE procedure qualification or for assessment of reliability of an NDE procedure. The risk is primarily due to sampling error. Smaller samples are not likely to be random to the population or representative of the population. The small samples are likely to be biased. Biased samples have smaller standard deviation compared to the population. POD analysis with small biased sample can lead to overestimation of POD. Many sampling schemes are available in statistics to mitigate sampling risk. Primary objective of POD analysis is to determine a decision threshold from signal response measurements of a sample such that it is less than or equal to population decision threshold for 90% POD. Sampling error implies that this NDE reliability condition is violated. One of sampling types is called a representative sample. Representative samples reduce variance in POD estimates but also reduce magnitude of the error. Sampling sensitivity analysis for some sampling types is performed here using repetitive random sampling or Monte Carlo method. Six sampling types are considered for comparison. Some of the sampling types are similar to drawing a representative sample. LS POD model assumes random sampling. Therefore, random sampling is used as a basis for comparison with each sampling type. The sampling types used in the analysis are, A. Nominal and worst-case sampling, B. Worst-case sampling, C. Nominal case sampling, D. Random sampling, E. Random target, and sub-target sampling. F. Nominal target and sub-target sampling. Results of Monte Carlo simulation indicate that type F sampling can mitigate sampling risk and is also more practical to implement. Type A sampling may also mitigate the sampling risk, but it may be less practical to implement.

Ajay M Koshti↗
NASA NTRS2008

The Integrated Medical Model: Statistical Forecasting of Risks to Crew Health and Mission Success

The Integrated Medical Model (IMM) helps capture and use organizational knowledge across the space medicine, training, operations, engineering, and research domains. The IMM uses this domain knowledge in the context of a mission and crew profile to forecast crew health and mission success risks. The IMM is most helpful in comparing the risk of two or more mission profiles, not as a tool for predicting absolute risk. The process of building the IMM adheres to Probability Risk Assessment (PRA) techniques described in NASA Procedural Requirement (NPR) 8705.5, and uses current evidence-based information to establish a defensible position for making decisions that help ensure crew health and mission success. The IMM quantitatively describes the following input parameters: 1) medical conditions and likelihood, 2) mission duration, 3) vehicle environment, 4) crew attributes (e.g. age, sex), 5) crew activities (e.g. EVA's, Lunar excursions), 6) diagnosis and treatment protocols (e.g. medical equipment, consumables pharmaceuticals), and 7) Crew Medical Officer (CMO) training effectiveness. It is worth reiterating that the IMM uses the data sets above as inputs. Many other risk management efforts stop at determining only likelihood. The IMM is unique in that it models not only likelihood, but risk mitigations, as well as subsequent clinical outcomes based on those mitigations. Once the mathematical relationships among the above parameters are established, the IMM uses a Monte Carlo simulation technique (a random sampling of the inputs as described by their statistical distribution) to determine the probable outcomes. Because the IMM is a stochastic model (i.e. the input parameters are represented by various statistical distributions depending on the data type), when the mission is simulated 10-50,000 times with a given set of medical capabilities (risk mitigations), a prediction of the most probable outcomes can be generated. For each mission, the IMM tracks which conditions occurred and decrements the pharmaceuticals and supplies required to diagnose and treat these medical conditions. If supplies are depleted, then the medical condition goes untreated, and crew and mission risk increase. The IMM currently models approximately 30 medical conditions. By the end of FY2008, the IMM will be modeling over 100 medical conditions, approximately 60 of which have been recorded to have occurred during short and long space missions.

Fitts, M. A.↗
NASA NTRS2011

Propulsive Reaction Control System Model

This software models a propulsive reaction control system (RCS) for guidance, navigation, and control simulation purposes. The model includes the drive electronics, the electromechanical valve dynamics, the combustion dynamics, and thrust. This innovation follows the Mars Science Laboratory entry reaction control system design, and has been created to meet the Mars Science Laboratory (MSL) entry, descent, and landing simulation needs. It has been built to be plug-and-play on multiple MSL testbeds [analysis, Monte Carlo, flight software development, hardware-in-the-loop, and ATLO (assembly, test and launch operations) testbeds]. This RCS model is a C language program. It contains two main functions: the RCS electronics model function that models the RCS FPGA (field-programmable-gate-array) processing and commanding of the RCS valve, and the RCS dynamic model function that models the valve and combustion dynamics. In addition, this software provides support functions to initialize the model states, set parameters, access model telemetry, and access calculated thruster forces.

Brugarolas, Paul↗
NASA NTRS2022

Coupling Carbon Oxidation and Surface Recession in Direct-Simulation Monte Carlo Code, SPARTA

Ablative thermal protection system (TPS) materials for spacecraft are composites that are often made out of carbon-based reinforcement and a polymeric matrix. They endure high-temperature oxidation and surface recession when re-entering Earth’s atmosphere. Ablation is the result of many coupled and competing thermal, mechanical, and chemical phenomena, and it is difficult to isolate the role of each on the overall degradation of the TPS. Here we develop an ablation model for material recession coupled explicitly to finite rate carbon oxidation in complex microstructures. In this work, Stochastic PArallel Rarified-gas Time-accurate Analyzer (SPARTA), a direct-simulation Monte Carlo (DSMC) code, is modified to allow oxidation-driven ablation of implicitly defined carbon surfaces. In SPARTA, implicit surfaces are generated from the grid corner point values via a marching cubes algorithm, therefore creating a new set of surface elements every time ablation is performed. The finite-rate oxidation model developed by Gopalan et. al, was adapted to tally surface reactions and other surface data on a per-grid cell basis. The ablation functionality was also adjusted so once the reactions have occurred, the number of reactions leading to CO formation can be converted to corner point reduction values; therefore, carbon removal is directly proportional to surface recession. We also develop robust algorithms which handle the evolution of the flow cells and solid material regions, including split cells (flow cell divided in two by a solid surface). Finally, we demonstrate our implicit chemistry model for 2D and 3D geometries by producing reaction statistics and detailed visualization of oxidation-induced material recession at the microscale.

V Arias↗
NASA NTRS1985

Monte Carlo simulations of electron lateral distributions in the core region of 10(13) - 10(16) eV air showers

This paper contains details of computer models of shower development which have been used to investigate the experimental data on shower cores observed in the Leeds 35 sq m and Sacramento Peak (New Mexico) 20 sq m arrays of current limited spark (discharge) chambers. The simulations include predictions for primaries ranging from protons to iron nuclei (with heavy nuclei treated using both superposition and fragmentation models).

Ash, A. G.↗
NASA NTRS1986

The effect of clulstering of galaxies on the statistics of gravitational lenses

It is examined whether clustering of galaxies can significantly alter the statistical properties of gravitational lenses? Only models of clustering that resemble the observed distribution of galaxies in the properties of the two-point correlation function are considered. Monte-Carlo simulations of the imaging process are described. It is found that the effect of clustering is too small to be significant, unless the mass of the deflectors is so large that gravitational lenses become common occurrences. A special model is described which was concocted to optimize the effect of clustering on gravitational lensing but still resemble the observed distribution of galaxies; even this simulation did not satisfactorily produce large numbers of wide-angle lenses.

Anderson, N.↗
NASA NTRS2017

DNA Repair Domain Modeling Can Predict Cell Death and Mutation Frequency for Wide Range Spectrum of Radiation

Exploration missions to Mars and other destinations raise many questions about the health of astronauts. The continuous exposure of astronauts to galactic cosmic rays is one of the main concerns for long-term missions. Cosmic ionizing radiations are composed of different ions of various charges and energies notably, highly charged energy (HZE) particles. The HZE particles have been shown to be more carcinogenic than low-LET radiation, suggesting the severity of chromosomal aberrations induced by HZE particles is one possible explanation. However, most mathematical models predicting cell death and mutation frequency are based on directly fitting various HZE dose response and are in essence empirical approaches. In this work, we assume a simple biological mechanism to model DNA repair and use it to simultaneously explain the low- and high-LET response using the exact same fitting parameters. Our work shows that the geometrical position of DNA repair along tracks of heavy ions are sufficient to explain why high-LET particles can induce more death and mutations. Our model is based on assuming DNA double strand breaks (DSBs) are repaired within repair domain, and that any DSBs located within the same repair domain cluster into one repair unit, facilitating chromosomal rearrangements and increasing the probability of cell death. We introduced this model in 2014 using simplified microdosimetry profiles to predict cell death. In this work, we collaborated with NASA Johnson Space Center to generate more accurate microdosimetry profiles derived by Monte Carlo techniques, taking into account track structure of HZE particles and simulating DSBs in realistic cell geometry. We simulated 224 data points (D, A, Z, E) with the BDSTRACKS model, leading to a large coverage of LET from ~10 to 2,400 keV/μm. This model was used to generate theoretical RBE for various particles and energies for both cell death and mutation frequencies. The RBE LET dependence is in agreement with experimental data known in human and murine cells. It suggests that cell shape and its orientation with respect to the HZE particle beam can modify the biological response to radiation. Such discovery will be tested experimentally and, if proven accurate, will be another strong supporting evidence for DNA repair domains and their critical role in interpreting cosmic radiation sensitivity.

Viger, Louise↗
NASA NTRS1997

Predictive Modeling in Plasma Reactor and Process Design

Research continues toward the improvement and increased understanding of high-density plasma tools. Such reactor systems are lauded for their independent control of ion flux and energy enabling high etch rates with low ion damage and for their improved ion velocity anisotropy resulting from thin collisionless sheaths and low neutral pressures. Still, with the transition to 300 mm processing, achieving etch uniformity and high etch rates concurrently may be a formidable task for such large diameter wafers for which computational modeling can play an important role in successful reactor and process design. The inductively coupled plasma (ICP) reactor is the focus of the present investigation. The present work attempts to understand the fundamental physical phenomena of such systems through computational modeling. Simulations will be presented using both computational fluid dynamics (CFD) techniques and the direct simulation Monte Carlo (DSMC) method for argon and chlorine discharges. ICP reactors generally operate at pressures on the order of 1 to 10 mTorr. At such low pressures, rarefaction can be significant to the degree that the constitutive relations used in typical CFD techniques become invalid and a particle simulation must be employed. This work will assess the extent to which CFD can be applied and evaluate the degree to which accuracy is lost in prediction of the phenomenon of interest; i.e., etch rate. If the CFD approach is found reasonably accurate and bench-marked with DSMC and experimental results, it has the potential to serve as a design tool due to the rapid time relative to DSMC. The continuum CFD simulation solves the governing equations for plasma flow using a finite difference technique with an implicit Gauss-Seidel Line Relaxation method for time marching toward a converged solution. The equation set consists of mass conservation for each species, separate energy equations for the electrons and heavy species, and momentum equations for the gas. The sheath is modeled by imposing the Bohm velocity to the ions near the walls. The DSMC method simulates each constituent of the gas as a separate species which would be analogous in CFD to employing separate species mass, momentum, and energy equations. All particles including electrons are moved and allowed to collide with one another with the stipulation that the electrons remain tied to the ions consistent with the concept of ambipolar diffusion. The velocities of the electrons are allowed to be modified during collisions and are not confined to a Maxwellian distribution. These benefits come at a price in terms of computational time and memory. The DSMC and CFD are made as consistent as possible by using similar chemistry and power deposition models. Although the comparison of CFD and DSMC is interesting, the main goal of this work is the increased understanding of high-density plasma flowfields that can then direct improvements in both techniques. This work is unique in the level of the physical models employed in both the DSMC and CFD for high-density plasma reactor applications. For example, the electrons are simulated in the present DSMC work which has not been done before for low temperature plasma processing problems. In the CFD approach, for the first time, the charged particle transport (discharge physics) has been self-consistently coupled to the gas flow and heat transfer.

Hash, D. B.↗
NASA NTRS2017

Near Real-Time Probabilistic Damage Diagnosis Using Surrogate Modeling and High Performance Computing

This work investigates novel approaches to probabilistic damage diagnosis that utilize surrogate modeling and high performance computing (HPC) to achieve substantial computational speedup. Motivated by Digital Twin, a structural health management (SHM) paradigm that integrates vehicle-specific characteristics with continual in-situ damage diagnosis and prognosis, the methods studied herein yield near real-time damage assessments that could enable monitoring of a vehicle's health while it is operating (i.e. online SHM). High-fidelity modeling and uncertainty quantification (UQ), both critical to Digital Twin, are incorporated using finite element method simulations and Bayesian inference, respectively. The crux of the proposed Bayesian diagnosis methods, however, is the reformulation of the numerical sampling algorithms (e.g. Markov chain Monte Carlo) used to generate the resulting probabilistic damage estimates. To this end, three distinct methods are demonstrated for rapid sampling that utilize surrogate modeling and exploit various degrees of parallelism for leveraging HPC. The accuracy and computational efficiency of the methods are compared on the problem of strain-based crack identification in thin plates. While each approach has inherent problem-specific strengths and weaknesses, all approaches are shown to provide accurate probabilistic damage diagnoses and several orders of magnitude computational speedup relative to a baseline Bayesian diagnosis implementation.

Warner, James E.↗
NASA NTRS2013

Estimated Probability of a Cervical Spine Injury During an ISS Mission

Introduction: The Integrated Medical Model (IMM) utilizes historical data, cohort data, and external simulations as input factors to provide estimates of crew health, resource utilization and mission outcomes. The Cervical Spine Injury Module (CSIM) is an external simulation designed to provide the IMM with parameter estimates for 1) a probability distribution function (PDF) of the incidence rate, 2) the mean incidence rate, and 3) the standard deviation associated with the mean resulting from injury/trauma of the neck. Methods: An injury mechanism based on an idealized low-velocity blunt impact to the superior posterior thorax of an ISS crewmember was used as the simulated mission environment. As a result of this impact, the cervical spine is inertially loaded from the mass of the head producing an extension-flexion motion deforming the soft tissues of the neck. A multibody biomechanical model was developed to estimate the kinematic and dynamic response of the head-neck system from a prescribed acceleration profile. Logistic regression was performed on a dataset containing AIS1 soft tissue neck injuries from rear-end automobile collisions with published Neck Injury Criterion values producing an injury transfer function (ITF). An injury event scenario (IES) was constructed such that crew 1 is moving through a primary or standard translation path transferring large volume equipment impacting stationary crew 2. The incidence rate for this IES was estimated from in-flight data and used to calculate the probability of occurrence. The uncertainty in the model input factors were estimated from representative datasets and expressed in terms of probability distributions. A Monte Carlo Method utilizing simple random sampling was employed to propagate both aleatory and epistemic uncertain factors. Scatterplots and partial correlation coefficients (PCC) were generated to determine input factor sensitivity. CSIM was developed in the SimMechanics/Simulink environment with a Monte Carlo wrapper (MATLAB) used to integrate the components of the module. Results: The probability of generating an AIS1 soft tissue neck injury from the extension/flexion motion induced by a low-velocity blunt impact to the superior posterior thorax was fitted with a lognormal PDF with mean 0.26409, standard deviation 0.11353, standard error of mean 0.00114, and 95% confidence interval [0.26186, 0.26631]. Combining the probability of an AIS1 injury with the probability of IES occurrence was fitted with a Johnson SI PDF with mean 0.02772, standard deviation 0.02012, standard error of mean 0.00020, and 95% confidence interval [0.02733, 0.02812]. The input factor sensitivity analysis in descending order was IES incidence rate, ITF regression coefficient 1, impactor initial velocity, ITF regression coefficient 2, and all others (equipment mass, crew 1 body mass, crew 2 body mass) insignificant. Verification and Validation (V&V): The IMM V&V, based upon NASA STD 7009, was implemented which included an assessment of the data sets used to build CSIM. The documentation maintained includes source code comments and a technical report. The software code and documentation is under Subversion configuration management. Kinematic validation was performed by comparing the biomechanical model output to established corridors.

Brooker, John E.↗
NASA NTRS2011

New Modeling Approaches to Investigate Cell Signaling in Radiation Response

Ionizing radiation damages individual cells and tissues leading to harmful biological effects. Among many radiation-induced lesions, DNA double-strand breaks (DSB) are considered the key precursors of most early and late effects [1] leading to direct mutation or aberrant signal transduction processes. In response to damage, a flow of information is communicated to cells not directly hit by the radiation through signal transduction pathways [2]. Non-targeted effects (NTE), which includes bystander effects and genomic instability in the progeny of irradiated cells and tissues, may be particularly important for space radiation risk assessment [1], because astronauts are exposed to a low fluence of heavy ions and only a small fraction of cells are traversed by an ion. NTE may also have important consequences clinical radiotherapy [3]. In the recent years, new simulation tools and modeling approaches have become available to study the tissue response to radiation. The simulation of signal transduction pathways require many elements such as detailed track structure calculations, a tissue or cell culture model, knowledge of biochemical pathways and Brownian Dynamics (BD) propagators of the signaling molecules in their micro-environment. Recently, the Monte-Carlo simulation code of radiation track structure RITRACKS was used for micro and nano-dosimetry calculations [4]. RITRACKS will be used to calculate the fraction of cells traversed by an ion and delta-rays and the energy deposited in cells in a tissue model. RITRACKS also simulates the formation of chemical species by the radiolysis of water [5], notably the .OH radical. This molecule is implicated in DNA damage and in the activation of the transforming growth factor beta (TGF), a signaling molecule involved in NTE. BD algorithms for a particle near a membrane comprising receptors were also developed and will be used to simulate trajectories of signaling molecules in the micro-environment and characterize autocrine and paracrine cell communication and signal transduction.

Plante, Ianik↗
NASA NTRS2009

DSN Simulator

The DSN Simulator (wherein DSN signifies NASA's Deep Space Network) is an updated version of the software described in DSN Array Simulator (NPO-44506), Software Tech Briefs (Special supplement to NASA Tech Briefs), Vol. 32, No. 9 (September 2008), page 26. To recapitulate: This software is used for computational modeling of proposed DSN facilities comprising arrays of antennas and transmitting and receiving equipment for microwave communication with spacecraft on interplanetary missions. Such modeling is performed to estimate facility performance, evaluate requirements that govern facility design, and evaluate proposed improvements in hardware and/or software. The software includes a Monte Carlo simulation component that enables rapid generation of key mission-set metrics (e.g., numbers of links, data rates, and data volumes), and statistical distributions thereof as functions of time. The prior version of the software could model only one DSN facility at a time and included hard-coded, unconfigurable metrics. The present updated version is capable of modeling the entire DSN and provides for configurable metrics, making it possible to perform loading analyses for alternative future DSN architectures and mission-set scenarios. The present version also features an improved user interface and interfaces for exchange of data with other DSN software and with a DSN mission model database.

Fijany, Amir↗
NASA NTRSDate not supplied

Dragonfly Entry and Descent Flight Mechanics Modeling and Analysis for Mission PDR

Dragonfly is a New Frontiers Program mission led by Johns Hopkins Applied Physics Laboratory (APL) which will deliver a rotorcraft lander to Saturn’s moon, Titan [1]. Relative to previous studies presented, Dragonfly recently passed its mission Preliminary Design Review (PDR) [2]. This study presents the updated design and analysis performed for the Dragonfly mission PDR. The entry vehicle analysis includes the phases of entry and descent prior to cruise stage separation until lander separation. These results discuss the robustness of the overall entry sequence as assessed through a Monte Carlo uncertainty analysis as well as sensitivity analysis.

Modeling↗
NASA NTRS1994

Independent pixel and Monte Carlo estimates of stratocumulus albedo

Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.

Cahalan, Robert F.↗
NASA NTRS1974

A Monte Carlo investigation of experimental data requirements for fitting polynomial functions

This report examines the extent to which sample size affects the accuracy of a low order polynomial approximation of an experimentally observed quantity and establishes a trend toward improvement in the accuracy of the approximation as a function of sample size. The task is made possible through a simulated analysis carried out by the Monte Carlo method, in which data are generated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to linear quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sample sizes and diminishes drastically for moderate and large amounts of experimental data.

Canavos, G. C.↗
NASA NTRS1974

An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials

A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.

Canavos, G. C.↗
NASA NTRS1976

Effects of multiple scattering on light pulses reflected by turbid atmospheres

Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).

Weinman, J. A.↗