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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Olivines in the Kaba carbonaceous chondrite and constraints on their formation

Kaba is unique in containing almost pure fayalitic olivine (Fo(sub 0.1)). Its coexistence with pure forsterite up to Fo(sub 99.6) and normal (Fo(sub 92) to Fo(sub 59)) and reversely (Fo(sub 0.4) to Fo(sub 4.7)) zoned olivines suggest that the Kaba olivines are in thermodynamic disequilibrium and experienced a complicated history. The fayalite is sufficiently pure that it is unlikely that it could have been produced by fractional crystallization. A gas-solid reaction under oxidizing conditions (H2O/H2 ratio approximately 10) is probably responsible for its formation.

Hua, X.↗
NASA NTRS1994

Probabilistic assessment of uncertain adaptive hybrid composites

Adaptive composite structures using actuation materials, such as piezoelectric fibers, were assessed probabilistically utilizing intraply hybrid composite mechanics in conjunction with probabilistic composite structural analysis. Uncertainties associated with the actuation material as well as the uncertainties in the regular (traditional) composite material properties were quantified and considered in the assessment. Static and buckling analyses were performed for rectangular panels with various boundary conditions and different control arrangements. The probability density functions of the structural behavior, such as maximum displacement and critical buckling load, were computationally simulated. The results of the assessment indicate that improved design and reliability can be achieved with actuation material.

Shiao, Michael C.↗
NASA NTRS1998

Sea Ice on the Southern Ocean

Year-round satellite records of sea ice distribution now extend over more than two decades, providing a valuable tool to investigate related characteristics and circulations in the Southern Ocean. We have studied a variety of features indicative of oceanic and atmospheric interactions with Antarctic sea ice. In the Amundsen & Bellingshausen Seas, sea ice extent was found to have decreased by approximately 20% from 1973 through the early 1990's. This change coincided with and probably contributed to recently warmer surface conditions on the west side of the Antarctic Peninsula, where air temperatures have increased by approximately 0.5 C/decade since the mid-1940's. The sea ice decline included multiyear cycles of several years in length superimposed on high interannual variability. The retreat was strongest in summer, and would have lowered the regional mean ice thickness, with attendant impacts upon vertical heat flux and the formation of snow ice and brine. The cause of the regional warming and loss of sea ice is believed to be linked to large-scale circulation changes in the atmosphere and ocean. At the eastern end of the Weddell Gyre, the Cosmonaut Polyna revealed greater activity since 1986, a recurrence pattern during recent winters and two possible modes of formation. Persistence in polynya location was noted off Cape Ann, where the coastal current can interact more strongly with the Antarctic Circumpolar Current. As a result of vorticity conservation, locally enhanced upwelling brings warmer deep water into the mixed layer, causing divergence and melting. In the Ross Sea, ice extent fluctuates over periods of several years, with summer minima and winter maxima roughly in phase. This leads to large interannual cycles of sea ice range, which correlate positively with meridinal winds, regional air temperatures and subsequent shelf water salinities. Deep shelf waters display considerable interannual variability, but have freshened by approximately 0.03/decade since the late 1950's. That could have slowed the thermohaline circulation beneath the Ross Ice Shelf and the properties or volume of local bottom water production.

Jacobs, Stanley S.↗
NASA NTRS1999

Disturbance Dynamics in Transitional and Turbulent Flows

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. First the decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow. Second, homogeneous shear flow, where disturbances can be described by rapid distortion theory (RDT), is studied. The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.

Grosch, Chester E.↗
NASA NTRS2003

Sensor Based Engine Life Calculation: A Probabilistic Perspective

It is generally known that an engine component will accumulate damage (life usage) during its lifetime of use in a harsh operating environment. The commonly used cycle count for engine component usage monitoring has an inherent range of uncertainty which can be overly costly or potentially less safe from an operational standpoint. With the advance of computer technology, engine operation modeling, and the understanding of damage accumulation physics, it is possible (and desirable) to use the available sensor information to make a more accurate assessment of engine component usage. This paper describes a probabilistic approach to quantify the effects of engine operating parameter uncertainties on the thermomechanical fatigue (TMF) life of a selected engine part. A closed-loop engine simulation with a TMF life model is used to calculate the life consumption of different mission cycles. A Monte Carlo simulation approach is used to generate the statistical life usage profile for different operating assumptions. The probabilities of failure of different operating conditions are compared to illustrate the importance of the engine component life calculation using sensor information. The results of this study clearly show that a sensor-based life cycle calculation can greatly reduce the risk of component failure as well as extend on-wing component life by avoiding unnecessary maintenance actions.

Guo, Ten-Huei↗
NASA NTRS2013

Causes and Predictability of the 2012 Great Plains Drought

Central Great Plains precipitation deficits during May-August 2012 were the most severe since at least 1895, eclipsing the Dust Bowl summers of 1934 and 1936. Drought developed suddenly in May, following near-normal precipitation during winter and early spring. Its proximate causes were a reduction in atmospheric moisture transport into the Great Plains from the Gulf of Mexico. Processes that generally provide air mass lift and condensation were mostly absent, including a lack of frontal cyclones in late spring followed by suppressed deep convection in summer owing to large-scale subsidence and atmospheric stabilization. Seasonal forecasts did not predict the summer 2012 central Great Plains drought development, which therefore arrived without early warning. Climate simulations and empirical analysis suggest that ocean surface temperatures together with changes in greenhouse gases did not induce a substantial reduction in summertime precipitation over the central Great Plains during 2012. Yet, diagnosis of the retrospective climate simulations also reveals a regime shift toward warmer and drier summertime Great Plains conditions during the recent decade, most probably due to natural decadal variability. As a consequence, the probability for severe summer Great Plains drought may have increased in the last decade compared to the 1980s and 1990s, and the so-called tail-risk for severe drought may have been heightened in summer 2012. Such an extreme drought event was nonetheless still found to be a rare occurrence within the spread of 2012 climate model simulations. Implications of this study's findings for U.S. seasonal drought forecasting are discussed.

Forecasts↗
NASA NTRS2020

Modeling the Transport Processes of a Pair of Solar Energetic Particle Events Observed by Parker Solar Probe near Perihelion

We present model calculations of the transport processes of solar energetic particles in the corona and interplanetary medium for two events detected by Parker Solar Probe near its second perihelion on 2019 April 2 and April 4. In the 2019 April 2 event, the <100 keV proton differential intensity measured by the ISOIS EPI-Lo instrument increased by more than a factor of 10 above the pre-event intensity, whereas the ~1 MeV proton differential intensity detected by the EPI-Hi instrument did not show any intensity enhancement. In the 2019 April 4 event, the ~1 MeV proton intensity showed an increase of more than a factor of 100 above the pre-event intensity, but the <100 keV proton intensity enhancement was rather low and gradual. The observational fact that only the 2019 April 4 event displayed a high-energy intensity enhancement indicates that the associated acceleration process in the second event was more energetic than the first event. However, the gradual and low enhancement of the low-energy proton intensity in the second event is at odds with the scenario. In this paper, we investigate the injection and transport processes of protons in the corona and interplanetary magnetic fields with numerical model simulations. Our model calculations suggest that the gradual and low rise of the low-energy protons in the April 4 event was probably due to the different diffusion conditions in these two events and the fact that the spacecraft was moving away from the source region during these two events.

Solar energetic particles↗
NASA NTRS2003

Upward Flammability Testing: A Probabilistic Measurement

Examination of NASA-STD-6001 Test 1 data suggests burn length outcome for a given environment has a large statistical variation from run to run. Large data sets show that burn length data form cumulative probability distribution curves, which describe a material's characteristic to burn in a specific environment, suggesting that the current practice of testing three samples at specific conditions is inadequate. Sufficient testing can establish material characteristics probability curves to provide the probability that a material will sustain a burn length of at least 15.24 cm (6.0 in.) or will sustain burning until all material is consumed. A simple pasdfail criterion may not be possible or practical. Future application of flammability data for some material classes may require the engineer to assess risk based on the probability of an occurrence and the probable outcome with different materials as characterized with cumulative burn length distributions for specific use conditions.

Davis, Samuel E.↗
NASA NTRS1994

A probability distribution model for rain rate

A systematic approach is suggested for modeling the probability distribution of rain rate. Rain rate, conditional on rain and averaged over a region, is modeled as a temporally homogeneous diffusion process with appropiate boundary conditions. The approach requires a drift coefficient-conditional average instantaneous rate of change of rain intensity-as well as a diffusion coefficient-the conditional average magnitude of the rate of growth and decay of rain rate about its drift. Under certain assumptions on the drift and diffusion coefficients compatible with rain rate, a new parametric family-containing the lognormal distribution-is obtained for the continuous part of the stationary limit probability distribution. The family is fitted to tropical rainfall from Darwin and Florida, and it is found that the lognormal distribution provides adequate fits as compared with other members of the family and also with the gamma distribution.

Kedem, Benjamin↗
NASA NTRSDate not supplied

Impact Real World System Validation

Introduction NASA has developed a new evidence-based data-driven probabilistic risk assessment and tradespace analysis tool as a successor to the Integrated Medical Model. This updated decision support tool is known as IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces). IMPACT estimates the frequency and consequences of medical conditions that might arise during exploration missions. A validation analysis of IMPACT was performed with respect to a set of International Space Station (ISS) and Shuttle Transportation System (STS) real world system (RWS) referent data due to the limited referent data available from exploration missions. Methods Observed mission and crew characteristics from STS and ISS missions were used as model inputs within MEDPRAT (Medical Extensible Dynamic Probabilistic Risk Assessment Tool). For each mission, two hundred thousand simulations were generated. For each mission, model outputs included occurrence counts for each condition, total medical events (TME), and the probability of loss of crew life (LOCL). These simulated model outputs were compared to the RWS referent data. Results The predicted number of total medical events exceeded the total RWS medical events for ISS missions and combined ISS and STS missions and fell within the 90% confidence interval for STS missions. For the 32 ISS missions simulated by IMPACT, the number of total medical events was overpredicted for 19 missions and fell within the 90% confidence interval for 13 missions. For the 21 STS missions, the total number of medical events was overpredicted for 3 missions, fell within the 90% confidence interval for 16 missions, and was underpredicted for 2 missions. Combined, 29 missions were in range, 22 were overpredicted, and 2 were underpredicted. The predicted LOCL probability for the 32 ISS missions, the 21 STS missions, and the combined ISS and STS missions was consistent with the zero LOCL events observed in the RWS referent data. The validation analysis included a comparison of the number of medical events predicted by IMPACT and the number of medical events observed in the RWS data on a condition-by-condition basis. For ISS missions, 50 conditions were in range, 52 conditions were statistically underpowered (not enough observed sample to draw any conclusions on precision), 8 conditions were overpredicted, and 9 conditions were underpredicted. Overall, only 14% (17/119) of conditions were out of range for STS missions, 40 conditions were in range, 59 conditions were statistically underpowered, 10 conditions were overpredicted, and 10 conditions were underpredicted. Overall, only 17% (20/119) of conditions were out of range. For combined ISS and STS missions, 11 conditions were overpredicted, and 11 conditions were underpredicted. Overall, only 18% (22/119) of conditions were out of range. For combined ISS and STS missions, 49 conditions were in range, 46 conditions were statistically underpowered, 18 conditions were overpredicted, and 8 conditions were underpredicted. Overall, 21% (26/121) of conditions were out of range. Conclusion The results of this validation analysis should not be interpreted as a pass/fail test of the validity of IMPACT. Instead, this validation analysis should be used to assess some of the IMPACT outcomes in terms of consistencies and inconsistencies with the ISS and STS RWS referent data.

L. Boley↗
DOE OSTI2020

Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

Uncertain or indirect “soft” data, such as geologic interpretation, driller’s logs, geophysical logs or imaging, offer potential constraints or “soft conditioning” to stochastic models of discrete categorical subsurface variables in hydrogeology such as hydrofacies. Previous bivariate geostatistical simulation algorithms have not fully addressed the impact of data uncertainty in formulation of the (co) kriging equations and the objective function in simulated annealing (or quenching). This paper introduces the geostatistical simulation code tsim-s, which accounts for categorical data uncertainty through a data “hardness” parameter. In generating geostatistical realizations with tsim-s, the uncertainty inherent to soft conditioning is factored into both 1) the data declustering and spatial correlation functions in cokriging and 2) the acceptance probability for change of category in simulated quenching. The degree or sensitivity to which soft data conditions a realization as a function of hardness can be quantified by mapping category probabilities derived from multiple realizations. In addition to point or borehole data, arrays of data (e.g., as derived from a depth-dependency function, probability map, or “prior realization”) can be used as soft conditioning. The tsim-s algorithm provides a theoretically sound and general framework for integrating datasets of variable location, resolution, and uncertainty into geostatistical simulation of categorical variables. A practical example shows how tsim-s is capable of generating a large-scale three-dimensional simulation including curvilinear features.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2021

Global Soil Water Estimates as Landslide Predictor: The Effectiveness of SMOS, SMAP, and GRACE Observations, Land Surface Simulations, and Data Assimilation

This global feasibility study assesses the potential of coarse-scale, gridded soil water estimates for the probabilistic modeling of hydrologically-triggered landslides, using Soil Moisture Ocean Salinity (SMOS), Soil Moisture Active Passive (SMAP) and Gravity Recovery and Climate Experiment (GRACE) remote sensing data, Catchment Land Surface Model (CLSM) simulations and six data products based on the assimilation of SMOS, SMAP, and/or GRACE observations into CLSM. SMOS or SMAP observations (~40-km resolution) are only available for less than 20% of the globally reported landslide events, because they are intermittent and uncertain in regions with complex terrain. GRACE terrestrial water storage estimates include 75% of the reported landslides but have coarse spatial and temporal resolutions (monthly, ~300-km). CLSM soil water simulations have the added advantage of complete spatial and temporal coverage, and are found to be able to distinguish between “stable slope” (no landslide) conditions and landslide-inducing conditions in a probabilistic way. Assimilating SMOS and/or GRACE data increases the landslide probability estimates based on soil water percentiles for the reported landslides, relative to model-only estimates at 36-km resolution for the period 2011-2016, unless the CLSM model-only soil water content is already high (≥ 50th percentile). The SMAP Level 4 data assimilation product (at 9-km resolution, period 2015-2019) more generally updates the soil water conditions towards higher landslide probabilities for the reported landslides, but is similar to model-only estimates for the majority of landslides where SMAP data cannot easily be converted to soil moisture owing to complex terrain.

Anne Felsberg↗
NASA NTRS1994

REE chemistry and Sm-Nd systematics of late Archean weathering profiles in the Fortescue Group, Western Australia

Two weathering profiles, each consisting of an upper, sericite-rich zone and a lower, chlorite-rich zone, are preserved between flows of the Mt. Roe Basalt in the Fortescue Group, Hamersley Basin, Western Australia. REE concentrations in samples from these two profiles, which originally developed ca 2,760 Ma, show large variations depending on stratigraphic position. LREE abundances and (La/Yb)N are greatest at depths of 3-6 m below the paleosurface of the Mt. Roe #1 profile and are somewhat lower in samples above this level. The LREEs reach concentrations 6-9 times greater than in the underlying basalt, and thus appear to have been mobilized downward in the paleosol and concentrated in its middle part. LREE concentrations in the #2 profile show a similar distribution but with a sharp increase in all REE concentrations within 50 cm of the paleosurface. The distinction between the REE profiles in the two paleosols may be related to the difference in the overlying material. The #1 paleosol is overlain by a few meters of sediments and then by basalt, whereas the #2 paleosol is directly overlain by basalt. The LREEs appear to have been mobilized both during chemical weathering of the parental basalt and during later lower-greenschist-facies metamorphism and metasomatism of the paleosols. Remobilization of the REEs during the regional metamorphism of the Fortescue Group is confirmed by a whole-rock Sm-Nd reference isochron of Mt. Roe #1 samples with an age of 2,151 +/- 360 Ma. Variable initial 143Nd/144Nd values of unweathered basalt samples which may represent the paleosol protolith prevents a confident determination of the magnitude of LREE mobility. Both the initial mobilization of the REEs during weathering and the metasomatic remobilization appear to have taken place under redox conditions where Ce was present dominantly as Ce3+, because Ce anomalies are not developed within the sericite zone samples regardless of concentration. Europium anomalies in the paleoweathering profile are somewhat variable and were probably modified by mobilization of Eu2+ at metamorphic conditions. In all samples, the HREEs appear to have been relatively immobile and correlate with Al, Ti, Cr, V, Zr, and Nb. Sm-Nd systematics and REE patterns of four unweathered basalt samples indicate derivation of the Mt. Roe Basalts from a heterogeneous and enriched source having epsilon Nd between -4.0 and -7.4. Initial 143Nd/144Nd values of these basalts are even lower than those reported by NELSON et al. (1992) for Fortescue Group basalts and indicate a substantial crustal component in the generation of Mt. Roe Basalts.

NASA Discipline Exobiology↗
NASA NTRS1993

Comparative measurement of visual stability in Earth and cosmic space (L-4)

The frequency and the intensity of space motion sickness was reviewed and investigated. Unusual induced-gravity situations, such as rotation, linear acceleration, parallel swinging etc. were investigated as well. Visually-induced motion sensation or distorted perception were evaluated with respect to visual stability by many investigators. These studies are all concerned with the effect of gravity and the induction of motion sickness through human visual perception. Direct investigation under the microgravity situation, such as parabolic flight, Skylab, and Spacelab, was carried out. These studies focused on how human visual stability is established through various sensory afferents in specific gravity conditions. Results from these investigations indicate that sensory mismatch probably plays an important role in space motion sickness. The interaction of visual, vestibular, and somatosensory perception is smoothly coordinated under normal gravitational conditions on the Earth in our daily life. When the cooperation is destroyed or a mismatch occurs among them, motion sickness may develop not only on the Earth but also in microgravity. The latter case may be the cause of space motion sickness or space adaption syndrome. How human beings obtain visual stability even with posture changes on the ground was investigated. Visual stability can be categorized as static or dynamic. Static visual stability is concerned with orientation and dynamic stability is concerned with object motion perception. The perception of visual stability is modified by many other sensations, such as somatosensory, vestibular, and muscle tension. We will mainly focus on modifications by vestibular inputs to visual perception produced by eye movements in microgravity. The Vestibular-Oscular Reflex (VOR) is a well-known characteristic which results from the relationship between eye mobility and vestibular afferent inputs. Eye movements also modify dynamic visual perception, such as perceived object motion velocity. The VOR is constantly simulated under 1-g conditions on Earth. In fact, human beings have been habituated and 'programmed' for orientation (visual stability) in their everyday, 1-g environment. When humans are exposed to a different gravity situation, this programmed behavior must change; that is, it is reprogrammed. This is called habituation or familiarization. We hope to examine how object motion perception is perturbed and subsequently adapted in the microgravity environment. This experiment is focused on the cooperation of visual, vestibular, and somatosensory perception coordination and how it is changed or reduced in space compared to 1-g environment. We will obtain information on the coordination between eye movement and neck muscle activity by using EOG and EMG. We will also collect data from Payload Specialists using a self-diagnostic questionnaire concerned with perceptual abnormality. When each sensory input function and its integration in the higher nervous system are well-characterized, then more effective techniques to control SAS may be developed.

Koga, Kazugo↗
NASA NTRS2000

Simulation of X-38 Landing Scenarios With Landing Gear Failures

Abnormal landing scenarios of the X-38 prototype Crew Rescue Vehicle (CRV) were modeled for three different cases involving non-deployment of landing gear with an explicit dynamic nonlinear finite element code, MSC/DYTRAN. The goal of this research was to develop models to predict the probability of crew injuries. The initial velocity conditions for the X-38 with chute deployed were 10 ft/s vertical and 57 ft/s longitudinal velocity. An MSC/NASTRAN structural model was supplied by JSC and was converted to a dynamic MSC/DYTRAN model. The MSC/NASTRAN model did not include seats or floor structure; thus, the acceleration of a lumped-mass attached to the bulkhead near each assumed occupant location was used to determine injury risk for each occupant. The worst case for injury was nondeployment of all gears. The mildest case was nondeployment of one main gear. Although a probability for minor injury was predicted for all cases, it is expected that the addition of energy-absorbing floor structure and seats would greatly diminish the probability of injury.

Fasanella, Edwin L.↗
DOE OSTI2021

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1977

Iron - Whence it came, where it went

Determinations of the abundances of iron and related elements in the photosphere, chromosphere, and corona of the sun as well as in solar and galactic cosmic rays are reviewed and compared with abundances derived from meteoritic data. Observed solar system abundances are found to be in accord with predictions of nucleosynthesis under either hydrostatic or explosive conditions but cannot yet be used to define these processes uniquely. The distribution of iron among planets and meteorites can probably be adequately modelled by condensation and fragmentation under equilibrium conditions above about 700 K, but below that temperature it is likely that inhibited solid-state diffusion perturbed attainment of equilibrium. Pertinent factors which are presently unknown include the mechanism responsible for metal-silicate fractionation, the grain size achieved by metallic iron in the nebula, and whether iron-bearing silicate formed prior to accretion.

Kerridge, J. F.↗
DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗