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DOE OSTI2010

Progress Report, December 2010: Improved Site Characterization And Storage Prediction Through Stochastic Inversion Of Time-Lapse Geophysical And Geochemical Data

Over the last project six months, our project activities have concentrated on three areas: (1) performing a stochastic inversion of pattern 16 seismic data to deduce reservoir permeability, (2) development of the geochemical inversion strategy and implementation of associated software, and (3) completing the software implementation of TProGS and the geostatistical analysis that provides the information needed when using the software to produce realizations of the Midale reservoir. The report partially the following deliverables: D2: Model development: MCMC tool (synthetic fluid chemistry data); deliverable completed. D4: Model development/verification: MCMC tool (TProGS, field seismic/chemistry data) work product; deliverable requirements partially fulfilled. D5: Field-based single-pattern simulations work product; deliverable requirements partially fulfilled. When completed, our completed stochastic inversion tool will explicitly integrate reactive transport modeling, facies-based geostatistical methods, and a novel stochastic inversion technique to optimize agreement between observed and predicted storage performance. Such optimization will be accomplished through stepwise refinement of: (1) the reservoir model - principally its permeability magnitude and heterogeneity - and (2) geochemical parameters - primarily key mineral volume fractions and kinetic data. We anticipate that these refinements will facilitate significantly improved history matching and forward modeling of CO{sub 2} storage. Our tool uses the Markov Chain Monte Carlo (MCMC) methodology. Deliverable D1, previously submitted as a report titled ''Development of a Stochastic Inversion Tool To Optimize Agreement Between The Observed And Predicted Seismic Response To CO{sub 2} Injection/Migration in the Weyburn-Midale Project'' (Ramirez et al., 2009), described the stochastic inversion approach that will identify reservoir models that optimize agreement between the observed and predicted seismic response. The software that implements this approach has been completed, tested, and used to process seismic data from pattern 16. A previously submitted report titled ''Model verification: synthetic single pattern simulations using seismic reflection data'', Ramirez et al. 2010, partially fulfilled deliverable D3 by summarizing verification activities that evaluate the performance of the seismic software and its ability to recover reservoir model permeabilities using synthetic seismic reflection data. A future progress report will similarly describe summarizing verification activities of the geochemical inversion software, thereby completing deliverable D3. This document includes a chapter that shows and discusses permeability models produced by seismic inversion that used seismic data from pattern 16 in Phase 1A. It partially fulfills deliverable D5: Field-based single-pattern simulations work product. The D5 work product is supposed to summarize the results of applying NUFT/MCMC to refine the reservoir model and geochemical parameters by optimizing observation/prediction agreement for the seismic/geochemical response to CO{sub 2} injection/migration within a single pattern of Phase 1A/1B. A future progress report will show inversion results for the same pattern using geochemical data, thereby completing deliverable D5. This document also contains a chapter that fulfills deliverable D2: Model development: MCMC tool (synthetic fluid chemistry data). The chapter will summarize model development activities required to facilitate application of NUFT/MCMC to optimize agreement between the observed and predicted geochemical response to CO{sub 2} injection/migration. Lastly, this document also contains a chapter that partially fulfills deliverable D4: Model development/verification: MCMC tool (TProGS, field seismic/chemistry data) work product. This work product is supposed to summarize model development activities required for (1) application of TProGS to Weyburn, (2) use of TProGS within the MCMC tool, and (3) application of the MCMC tool to address field seismic and geochemical data. The chapter included here fulfills requirements 1 and 2. Requirement 3 will be addressed in a future progress report.

58 GEOSCIENCES↗

DOE OSTI2015

STOCHASTIC MODEL OF THE SPIN DISTRIBUTION OF DARK MATTER HALOS

We employ a stochastic approach to probing the origin of the log-normal distributions of halo spin in N-body simulations. After analyzing spin evolution in halo merging trees, it was found that a spin change can be characterized by a stochastic random walk of angular momentum. Also, spin distributions generated by random walks are fairly consistent with those directly obtained from N-body simulations. We derived a stochastic differential equation from a widely used spin definition and measured the probability distributions of the derived angular momentum change from a massive set of halo merging trees. The roles of major merging and accretion are also statistically analyzed in evolving spin distributions. Several factors (local environment, halo mass, merging mass ratio, and redshift) are found to influence the angular momentum change. The spin distributions generated in the mean-field or void regions tend to shift slightly to a higher spin value compared with simulated spin distributions, which seems to be caused by the correlated random walks. We verified the assumption of randomness in the angular momentum change observed in the N-body simulation and detected several degrees of correlation between walks, which may provide a clue for the discrepancies between the simulated and generated spin distributions in the voids. However, the generated spin distributions in the group and cluster regions successfully match the simulated spin distribution. We also demonstrated that the log-normality of the spin distribution is a natural consequence of the stochastic differential equation of the halo spin, which is well described by the Geometric Brownian Motion model.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2016

A DSMC Surface Chemistry Model for Carbon-Based Ablators

A detailed molecular surface chemistry model for the DSMC (Direct Simulation Monte Carlo) method is proposed and implemented into the SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) DSMC solver. Molchanova et al. constructed a molecular model for surface recombination in DSMC that includes different surface processes (adsorption, desoprtion, Eley-Rideal and Langmuir-Hinshelwood). All surface processes can be divided into two groups: surface mechanisms, which involve only the particle adsorbed by the surface (desorption and Langmuir-Hinshelwood), and impact mechanisms, which also involve gas-phase particles (adsorption, Eley-Rideal). Using a similar approach, the 14-reaction kinetic model of oxygen-carbon interaction suggested by Zhlukhtov and Abe, as well as more recent models by Alba et al., Poovathinghal et al., and a new model developed in the scope of this work, are implemented in SPARTA. The computational results for the different oxidation models are compared with experimental results from Murray et al. (oxidation of a vitreous carbon surface due to a hyperthermal beam of O and O2), with a particular focus on fluxes, angular and Time-Of-Flight distributions of scattered particles.

oxidation↗

DOE OSTI2022

Time domain probabilistic seismic risk analysis using ground motion prediction equations of Fourier amplitude spectra

Modeling of Fourier amplitude spectra (FAS) of seismic motions has gained much attention in engineering seismology. In the past few years, several ground motion prediction equations (GMPEs) and inter-frequency correlation structure of FAS have been established. Due to many preferable characteristics of FAS, probabilistic seismic hazard/risk analysis is rapidly changing from ergodic, spectrum acceleration Sa(T 0 )-based approach to non-ergodic, site-specific, FAS-based approach. This paper presents time domain intrusive framework for probabilistic seismic risk analysis using GMPE of FAS. Herein, methodology for time domain stochastic ground motion modeling based on GMPEs of FAS is presented in some detail. The simulated uncertain motions are modeled as a random process and represented by polynomial chaos Karhunen-Loève expansion. The random process excitations are further propagated into the uncertain structural system using Galerkin stochastic finite element method (SFEM). Probabilistic evolution of structural response is solved, and such solution is used to develop seismic risk for any damage state. The presented framework is illustrated through seismic risk analysis of a four-story building subjected to possible earthquakes from two strike slip faults. The influences of the epistemic uncertainties in source stress drop Δσ and site attenuation κ0 on seismic risk are investigated. The need for non-ergodic seismic risk analysis with source-specific and site specific characterizations is emphasized.

58 GEOSCIENCES↗

DOE OSTI2017

Precipitation and Release of Solar Energetic Particles from the Solar Coronal Magnetic Field

Most solar energetic particles (SEPs) are produced in the corona. They propagate through complex coronal magnetic fields subject to scattering and diffusion across the averaged field lines by turbulence. We examine the behaviors of particle transport using a stochastic 3D focused transport simulation in a potential field source surface model of coronal magnetic field. The model is applied to an SEP event on 2010 February 7. We study three scenarios of particle injection at (i) the compact solar flare site, (ii) the coronal mass ejection (CME) shock, and (iii) the EUV wave near the surface. The majority of particles injected on open field lines are able to escape the corona. We found that none of our models can explain the observations of wide longitudinal SEP spread without perpendicular diffusion. If the perpendicular diffusion is about 10% of what is derived from the random walk of field lines at the rate of supergranular diffusion, particles injected at the compact solar flare site can spread to a wide range of longitude and latitude, very similar to the behavior of particles injected at a large CME shock. Stronger pitch-angle scattering results in a little more lateral spread by holding the particles in the corona for longer periods of time. Some injected particles eventually end up precipitating onto the solar surface. Even with a very small perpendicular diffusion, the pattern of the particle precipitation can be quite complicated depending on the detailed small-scale coronal magnetic field structures, which could be seen with future sensitive gamma-ray telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Stochastic dynamics of small ensembles of non-processive molecular motors: The parallel cluster model

Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Simulating stochastic and additively manufactured foams at large strains and high strain rates

Understanding the mechanical response of polymer foams is essential in developing system material models and in designing replacements for legacy pads and cushions. Simulations can help elucidate structure-property relationships and compare local stress distributions to understand aging behavior and improve designs. In many applications, these materials experience significant loadings and computations need the capability to reproduce those conditions. We are applying are previously developed material point method (MPM) simulation capability to understand the aging properties of loaded direct ink write (DIW) resins.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Simulating stochastic and additively manufactured foams at large strains and high strain rates

36 MATERIALS SCIENCE↗

NASA NTRS2018

Flood Hazard Assessment from Storm Tides, Rain and Sea Level Rise for a Tidal River Estuary

Cities and towns along the tidal Hudson River are highly vulnerable to flooding through the combination of storm tides and high streamflows, compounded by sea level rise. Here a three-dimensional hydrodynamic model, validated by comparing peak water levels for 76 historical storms, is applied in a probabilistic flood hazard assessment. In simulations, the model merges streamflows and storm tides from tropical cyclones (TCs), offshore extratropical cyclones (ETCs) and inland "wet extratropical" cyclones (WETCs). The climatology of possible ETC and WETC storm events is represented by historical events (1931-2013), and simulations include gauged streamflows and inferred ungauged streamflows (based on watershed area) for the Hudson River and its tributaries. The TC climatology is created using a stochastic statistical model to represent a wider range of storms than is contained in the historical record. TC streamflow hydrographs are simulated for tributaries spaced along the Hudson, modeled as a function of TC attributes (storm track, sea surface temperature, maximum wind speed) using a statistical Bayesian approach. Results show WETCs are important to flood risk in the upper tidal river (e.g., Albany, New York), ETCs are important in the estuary (e.g., New York City) and lower tidal river, and TCs are important at all locations due to their potential for both high surge and extreme rainfall. The raising of floods by sea level rise is shown to be reduced by approximately 30-60 percent at Albany due to the dominance of streamflow for flood risk. This can be explained with simple channel flow dynamics, in which increased depth throughout the river reduces frictional resistance, thereby reducing the water level slope and the upriver water level.

Tidal river↗

DOE OSTI2014

Nonlinear simulations to optimize magnetic nanoparticle hyperthermia

Magnetic nanoparticle hyperthermia is an attractive emerging cancer treatment, but the acting microscopic energy deposition mechanisms are not well understood and optimization suffers. We describe several approximate forms for the characteristic time of Néel rotations with varying properties and external influences. We then present stochastic simulations that show agreement between the approximate expressions and the micromagnetic model. The simulations show nonlinear imaginary responses and associated relaxational hysteresis due to the field and frequency dependencies of the magnetization. This suggests that efficient heating is possible by matching fields to particles instead of resorting to maximizing the power of the applied magnetic fields.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2019

A Stochastic Study of Flow Anisotropy and Channelling in Open Rough Fractures

The quantification of fluid flow in rough fractures is of high interest for reservoir engineering, especially for deep geothermal applications. Herein, rough self-affine fractures are stochastically generated with incremental shear displacement and geometrically described by two aperture definitions, the vertical aperture a vert and the effective aperture a eff . In order to compare their effect on fracture flow, such as anisotropy and channelling, Local Cubic Law (LCL) model-based 2D fluid flow is simulated. The particularity of this approach is the combination of a stochastic generation of self-affine fractures with a statistical analysis (560 individual realizations) of the impact of the LCL’s aperture constraint on fracture flow. The results show that aperture definition affects the quantitative interpretation of flow anisotropy and channeling as well as the aperture distribution of the fractures with shearing. Higher values of mean aperture for a given fracture are found using a vert , whereas the aperture standard deviation is larger with a eff . In addition, flow anisotropy is significantly sensitive to aperture definition for small shear displacements and shows a relative higher dispersion with a eff . Thus, LCL prediction models based on a vert are expected to lead to higher dispersion of anisotropy results with a higher uncertainty (factor ~ 2). Realizations based on avert lead to an enhanced clustering of high flow rates for higher shearing displacements. This channeling development results in higher total flow rates for these simulations. Finally, these findings support the direct calibration of pre-existing LCL anisotropy simulations based on avert towards more representative results using a eff .

58 GEOSCIENCES↗

DOE OSTI2023

Catalyst: Fast and flexible modeling of reaction networks

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst’s broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2011

The Distribution of Chromosomal Aberrations in Human Cells Predicted by a Generalized Time-Dependent Model of Radiation-Induced Formation of Aberrations

New experimental data show how chromosomal aberrations for low- and high-LET radiation are dependent on DSB repair deficiencies in wild-type, AT and NBS cells. We simulated the development of chromosomal aberrations in these cells lines in a stochastic track-structure-dependent model, in which different cells have different kinetics of DSB repair. We updated a previously formulated model of chromosomal aberrations, which was based on a stochastic Monte Carlo approach, to consider the time-dependence of DSB rejoining. The previous version of the model had an assumption that all DSBs would rejoin, and therefore we called it a time-independent model. The chromosomal-aberrations model takes into account the DNA and track structure for low- and high-LET radiations, and provides an explanation and prediction of the statistics of rare and more complex aberrations. We compared the program-simulated kinetics of DSB rejoining to the experimentally-derived bimodal exponential curves of the DSB kinetics. We scored the formation of translocations, dicentrics, acentric and centric rings, deletions, and inversions. The fraction of DSBs participating in aberrations was studied in relation to the rejoining time. Comparisons of simulated dose dependence for simple aberrations to the experimental dose-dependence for HF19, AT and NBS cells will be made.

Ponomarev, Artem L.↗

DOE OSTI2015

Recurrent dynamics in an epidemic model due to stimulated bifurcation crossovers

Epidemics are known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, peaks of activity for infectious diseases like influenza reappear over time. Analysis of a stochastic model is here undertaken to explore a proposed cycle-generating mechanism – the bifurcation crossover. Time series from simulations of the model exhibit oscillations similar to the temporal signature of influenza activity. Power-spectral density indicates a resonant frequency, which corresponds to the annual seasonality of influenza in temperate zones. The study finds that intervention actions influence the extinguishability of epidemic activity. Asymptotic solution to a backward Kolmogorov equation corresponds to a mean extinction time that is a function of both intervention efficacy and population size. Intervention efficacy must be greater than a certain threshold to increase the chances of extinguishing the epidemic. Agreement of the model with several phenomenological features of epidemic cycles lends to it a tractability that may serve as early warning of imminent outbreaks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Stochastic modeling of phosphorus transport in the Three Gorges Reservoir by incorporating variability associated with the phosphorus partition coefficient

Phosphorus (P) fate and transport plays a crucial role in the ecology of rivers and reservoirs in which eutrophication is limited by P. A key uncertainty in models used to help manage P in such systems is the partitioning of P to suspended and bed sediments. By analyzing data from field and laboratory experiments, we stochastically characterize the variability of the partition coefficient (Kd) and derive spatio-temporal solutions for P transport in the Three Gorges Reservoir (TGR). We formulate a set of stochastic partial different equations (SPDEs) to simulate P transport by randomly sampling Kd from the measured distributions, to obtain statistical descriptions of the P concentration and retention in the TGR. The correspondence between predicted and observed P concentrations and P retention in the TGR combined with the ability to effectively characterize uncertainty suggests that a model that incorporates the observed variability can better describe P dynamics and more effectively serve as a tool for P management in the system. This study highlights the importance of considering parametric uncertainty in estimating uncertainty/variability associated with simulated P transport.

Partition coefficient↗

DOE OSTI2016

Emulation of dynamic simulators with application to hydrology

Many simulation-intensive tasks in the applied sciences, such as sensitivity analysis, parameter inference or real time control, are hampered by slow simulators. Emulators provide the opportunity of speeding up simulations at the cost of introducing some inaccuracy. An emulator is a fast approximation to a simulator that interpolates between design input–output pairs of the simulator. Increasing the number of design data sets is a computationally demanding way of improving the accuracy of emulation. We investigate the complementary approach of increasing emulation accuracy by including knowledge about the mechanisms of the simulator into the formulation of the emulator. To approximately reproduce the output of dynamic simulators, we consider emulators that are based on a system of linear, ordinary or partial stochastic differential equations with a noise term formulated as a Gaussian process of the parameters to be emulated. This stochastic model is then conditioned to the design data so that it mimics the behavior of the nonlinear simulator as a function of the parameters. The drift terms of the linear model are designed to provide a simplified description of the simulator as a function of its key parameters so that the required corrections by the conditioned Gaussian process noise are as small as possible. The goal of this paper is to compare the gain in accuracy of these emulators by enlarging the design data set and by varying the degree of simplification of the linear model. We apply this framework to a simulator for the shallow water equations in a channel and compare emulation accuracy for emulators based on different spatial discretization levels of the channel and for a standard non-mechanistic emulator. Our results indicate that we have a large gain in accuracy already when using the simplest mechanistic description by a single linear reservoir to formulate the drift term of the linear model. Adding some more reservoirs does not lead to a significant improvement in accuracy. However, the transition to a spatially continuous linear model leads again to a similarly large gain in accuracy as the transition from the non-mechanistic emulator to that based on one reservoir.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Brownian aggregation rate of colloid particles with several active sites

We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shown to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Catalytic conversion in nanoporous materials: Concentration oscillations and spatial correlations due to inhibited transport and intermolecular interactions

We show that steady-state catalytic conversion in nanoporous materials can occur in a quasi-counter-diffusion mode with the reactant (product) concentration strongly decaying (growing) into the pore, but also with oscillations in the total concentration. These oscillations reflect the response of the fluid to the transition from an extended to a confined environment near the pore opening. We focus on the regime of strongly inhibited transport in narrow pores corresponding to single-file diffusion. Here, limited penetration of the reactant into the pores and the associated low reaction yield is impacted by strong spatial correlations induced by both reaction (non-equilibrium correlations) and also by intermolecular interactions (thermodynamic correlations). We develop a generalized hydrodynamic formulation to effectively describe inhibited transport accounting for the effect of these correlations, and incorporate this description of transport into appropriate reaction-diffusion equations. These equations accurately describe both shorter-range concentration oscillations near the pore opening and the longer-range mesoscale variation of concentration profiles in the pore (and thus also describe reaction yield). Success of the analytic theory is validated by comparison with a precise kinetic Monte Carlo simulation of an appropriate molecular-level stochastic reaction-diffusion model. As a result, this work elucidates unconventional chemical kinetics in interacting confined systems.

36 MATERIALS SCIENCE↗