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DOE OSTI2018

Stochastic Acceleration of ~0.1–5 keV Pickup Ions in the Heliotail

We seek to understand the quantitative role of the dominant physical processes (charge-exchange, adiabatic heating, stochastic acceleration) governing the proton distribution in the heliotail using observations of hydrogen energetic neutral atoms (ENAs) from the Interstellar Boundary Explorer ( IBEX ). We solve the Parker transport equation for solar wind protons and pickup ions (PUIs) as they propagate from the termination shock (TS) down the heliotail, including charge-exchange between protons and neutral hydrogen atoms as source terms derived from an MHD-fluid and kinetic-neutral simulation of the heliosphere. We compute ENA fluxes at 1 au from the results of the proton transport model and compare them with IBEX observations. We find that, under the assumptions of our model, a stochastic acceleration process is needed to counteract the energy-dependent losses of ~0.1–5 keV PUIs from charge-exchange to reproduce IBEX data. The power-law velocity dependence of the diffusion coefficient (spectral index γ ) is limited to the range 0.67 < γ < 2, and the best fit to IBEX data appears close to γ ~ 1.25. The diffusion rate ~1.1 × 10 -8 km 2 s -3 ( v / v 0 ) 1.25 nearly balances the loss of ~0.1–5 keV PUIs by charge-exchange. Our analysis suggests that cyclotron resonance with two widely known incompressible MHD turbulence: namely, isotropic Kolmogorov and anisotropic Goldreich–Sridhar turbulence, as well as stochastic particle interactions with compressive waves are not by themselves the dominant diffusion mechanisms. However, some intermediate processes may be occurring due to the presence of PUIs.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2022

Toward data assimilation of ship-induced aerosol–cloud interactions

Satellite imagery can detect temporary cloud trails or ship tracks formed from aerosols emitted from large ships traversing our oceans, a phenomenon that global climate models cannot directly reproduce. Ship tracks are observable examples of marine cloud brightening, a potential solar climate intervention that shows promise in helping combat climate change. In this paper, we demonstrate a simulation-based approach in learning the behavior of ship tracks based upon a novel stochastic emulation mechanism. Our method uses wind fields to determine the movement of aerosol–cloud tracks and uses a stochastic partial differential equation (SPDE) to model their persistence behavior. This SPDE incorporates both a drift and diffusion term which describes the movement of aerosol particles via wind and their diffusivity through the atmosphere, respectively. We first present our proposed approach with examples using simulated wind fields and ship paths. We then successfully demonstrate our tool by applying the approximate Bayesian computation method-sequential Monte Carlo for data assimilation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Bifurcation physics of magnetic islands and stochasticity explored by heat pulse propagation studies in toroidal plasmas

Bifurcation physics of the magnetic island was investigated using the heat pulse propagation technique produced by the modulation of electron cyclotron heating. There are two types of bifurcation phenomena observed in LHD and DIII-D. One is a bifurcation of the magnetic topology between nested and stochastic fields. The nested state is characterized by the bi-directional (inward and outward) propagation of the heat pulse with slow propagation speed. The stochastic state is characterized by the fast propagation of the heat pulse with electron temperature flattening. The other bifurcation is between magnetic island with larger thermal diffusivity and that with smaller thermal diffusivity. The damping of toroidal flow is observed at the O-point of the magnetic island both in helical plasmas and in tokamak plasmas during a mode locking phase with strong flow shears at the boundary of the magnetic island. Associated with the stochastization of the magnetic field, the abrupt damping of toroidal flow is observed in LHD. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. Lastly, this observation suggests that this flow damping is due to the change in the non-diffusive term of momentum transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

FERMI BUBBLE γ-RAYS AS A RESULT OF DIFFUSIVE INJECTION OF GALACTIC COSMIC RAYS

Recently, the Fermi Space Telescope discovered two large γ-ray emission regions, the so-called Fermi bubbles, that extend up to ∼50° above and below the Galactic center (GC). The γ-ray emission from the bubbles is found to follow a hard spectrum with no significant spatial variation in intensity and spectral shape. The origin of the emission is still not clearly understood. Suggested explanations include the injection of cosmic-ray (CR) nuclei from the GC by high-speed Galactic winds, electron acceleration by multiple shocks, and stochastic electron acceleration inside the bubbles. In this Letter, it is proposed that the γ-rays may be the result of diffusive injection of Galactic CR protons during their propagation through the Galaxy. Considering that the bubbles are slowly expanding, and CRs undergo much slower diffusion inside the bubbles than in the average Galaxy and at the same time suffer losses due to adiabatic expansion and inelastic collisions with the bubble plasma, this model can explain the observed intensity profile, the emission spectrum and the measured luminosity without invoking any additional particle production processes, unlike other existing models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Influence of pseudopotentials on excitation energies from selected configuration interaction and diffusion Monte Carlo

Due to their diverse nature, the faithful description of excited states within electronic structure theory methods remains one of the grand challenges of modern theoretical chemistry. Quantum Monte Carlo (QMC) methods have been applied very successfully to ground state properties but still remain generally less effective than other non-stochastic methods for electronically excited states. Nonetheless, we have recently reported accurate excitation energies for small organic molecules at the fixed-node diffusion Monte Carlo (FN-DMC) within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using the selected configuration interaction (sCI) algorithm known as CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively). Albeit highly accurate, these all-electron calculations are computationally expensive due to the presence of core electrons. One very popular approach to remove these chemically-inert electrons from the QMC simulation is to introduce pseudopotentials (also known as effective core potentials). Taking the water molecule as an example, we investigate the influence of Burkatzki-Filippi-Dolg (BFD) pseudopotentials and their associated basis sets on vertical excitation energies obtained with sCI and FN-DMC methods. Although these pseudopotentials are known to be relatively safe for ground state properties, we evidence that special care may be required if one strives for highly accurate vertical transition energies. Indeed, comparing all-electron and valence-only calculations, we show that using pseudopotentials with the associated basis sets can induce differences of the order of 0.05 eV on the excitation energies. Fortunately, a reasonable estimate of this shift can be estimated at the sCI level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling

Self-assembly of supported 2D or 3D nanocrystals (NCs) by vacuum deposition and of 3D NCs by solution-phase synthesis (with possible subsequent transfer to a support) produces intrinsically nonequilibrium systems. Individual NCs can have far-from-equilibrium shapes and composition profiles. The free energy of NC ensembles is lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening are key, e.g., for avoiding catalyst degradation. This review focuses on postsynthesis evolution of metallic NCs. Atomistic-level modeling typically utilizes stochastic lattice-gas models to access appropriate time and length scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution in a vacuum environment. Here, we also discuss modeling of coarsening including diffusion and decay of individual NCs and unconventional coarsening processes. We describe high-level modeling integrated with scanning tunneling microscopy (STM) studies for supported 2D epitaxial nanoclusters and developments in modeling for 3D NCs motivated by in situ transmission electron microscopy (TEM) studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Stochastic inflation in phase space: is slow roll a stochastic attractor?

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

A Generalization of Threshold-Based and Probability-Based Models of Information Diffusion

Diffusion of information through complex networks is of interest in studies such as propagation prediction and influence maximization, both of which have applications in viral marketing and rumor controlling. There are a variety of information diffusion models, all of which simulate the adoption and spread of information over time. However, there is a lack of understanding of whether, despite their conceptual differences, these models represent the same underlying generative structures. For instance, if two different models utilize different conceptual mechanisms, but generate the same results, does the choice of model matter? A classification of diffusion of information models is developed based on the neighbor knowledge of the model infection requirement and the stochasticity of the model. This classification allows for the identification of models that fall into each respective category. The study involves the analysis of the following agent-based models on directed scale-free networks: (1) a linear absolute threshold model (LATM), (2) a linear fractional threshold model (LTFM), (3) the independent cascade model (ICM), (4) Bass-Rand-Rust model (BRRM) (5) a stochastic linear absolute threshold model (SLATM) (6) a stochastic fractional threshold model (SLFTM), and (7) Dodds–Watts model (DWM). Through the execution of simulations and analysis of the experimental results, the distinctive properties of each model are identified. Our analysis reveals that similarity in conceptual design does not imply similarity in behavior concerning speed, final state of nodes and edges, and sensitivity to parameters. Therefore, we highlight the importance of considering the unique behavioral characteristics of each model when selecting a suitable information diffusion model for a particular application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Exploring the stochastic dynamics of correlated movement of receptor proteins in plasma membranes in vivo

Ligand-induced receptor dimerization plays a crucial role in the signaling process of living cells. In this study, we developed a theoretical model and performed single-molecule tracking to explore the correlated diffusion processes of liganded epidermal growth factor receptors prior to dimer formation. We disclosed that both an attractive potential between liganded receptor proteins in proximity and correlated fluctuations in the local environments of the proteins play an important role to produce the observed correlated movement of the receptors. This result can serve as the foundation to shed light on the way in which receptor functions are regulated in plasma membranes in vivo.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

We present a novel approach for solving steady-state stochastic partial differential equations in high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that accurate global solutions can be obtained with significantly reduced computational costs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations

In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2012

Langevin equation with multiplicative white noise: Transformation of diffusion processes into the Wiener process in different prescriptions

A Langevin equation with multiplicative white noise and its corresponding Fokker-Planck equation are considered in this work. From the Fokker-Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: Black-Right-Pointing-Pointer Fokker-Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. Black-Right-Pointing-Pointer Transformation of diffusion processes into the Wiener process in different prescriptions is provided. Black-Right-Pointing-Pointer The prescription parameter is associated with the growth rate for a Gompertz-type model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

Abstract In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

A computational study of turbulent kinetic energy transport in barotropic turbulence on the f-plane

Energy transport by eddies is diagnosed from a series of simulations of stochastically forced, inhomogeneous two-dimensional turbulence—barotropic dynamics on the f-plane. The divergence of the energy flux is compared to diffusive models, both fractional and harmonic, and the inferred diffusivity κ is compared to a mixing-length model κ ∝ Vℓ where V and ℓ are eddy velocity and length scales, respectively. The flux-divergence is found to be well approximated by Laplacian diffusion with a mixing-length approximation. This study provides some support for diffusive modeling of mesoscale eddy energy transport in ocean model parameterizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Spatiotemporal 4D Whole-cell Modeling of a Minimal Autotroph Reveals Central Carbon Metabolism Regulated Locally by Protein Megacomplexes via Post-translational Modifications under Light Disturbance

Photosynthetic microorganisms rely on multiple pathways in central carbon metabolism to adapt to fluctuating light and energy availability across diel cycles. Mechanistic insight into the regulatory dynamics of this adaptation requires integrating processes spanning disparate timescales, from rapid redox-dependent post-translational modifications (PTMs) to slower changes in protein expression and metabolic pathway usage. To address this complexity beyond genome-based inference and traditional modeling, we develop a whole-cell four-dimensional (3D + time) model of the marine cyanobacterium Prochlorococcus marinus MED4 that explicitly represents the spatial organization of enzymatic and molecular processes in central carbon metabolism under light perturbation. We employ a perturbation-based research design to experimentally generate time-series, multi-omics measurements that provide molecular descriptors and cryo-ET derived 3D segmented volumes as constraints for this dynamic 4D framework. The integration of experiments and modeling across defined light regimes enables quantitative validation of system-level responses and forecasting under distinct light disturbances. We test the hypothesis that light-dependent redox PTMs regulating the structural assembly of a protein megacomplex, the “dark complex,” modulate metabolic flux at a conserved regulatory node of the Calvin–Benson cycle (CBC) in cyanobacteria. Our model shows that subcellular spatial organization buffers rapid light-induced changes in thylakoid reaction rates, which are followed by redox-PTM-mediated sequestration or release of CBC enzymes in the dark complex, ultimately impacting carbon fixation dynamics within carboxysomes. Comparison with an equivalently parameterized well-mixed stochastic model demonstrates that post-translational regulation not only buffers transcriptional noise and diffusion-driven fluctuations but also stabilizes phenotypic outcomes, underscoring the importance of spatial heterogeneity in phenotypic robustness. This ability to probe adaptive, spatiotemporally resolved mechanisms in photosynthetic machinery and central carbon metabolism addresses a critical gap in genotype-to-phenotype inference and expands modeling and design capabilities for understudied or genetically intractable autotrophs such as P. marinus MED4.

Johnson, Connah G.↗

DOE OSTI2020

Quantum Monte Carlo benchmarking of large noncovalent complexes in the L7 benchmark set

We have used diffusion Monte Carlo (DMC) to perform calculations on the L7 benchmark set. DMC is a stochastic numerical integration scheme in real-space and part of a larger set of quantum Monte Carlo methods. The L7 set was designed to test the ability of electronic structure methods to include dispersive interactions. While the agreement between DMC and quantum-chemical state-of-the-art methods is excellent for some of the structures, there are significant differences in others. In contrast to wavefunction-based quantum chemical methods, DMC is a first-principle many-body method with the many-body wavefunction evolving in real space. It includes explicitly all electron–electron interactions and is relatively insensitive to the size of the basis set.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Versatile stochastic model for predictive KMC simulation of fcc metal nanostructure evolution with realistic kinetics

Stochastic lattice-gas models provide the natural framework for analysis of the surface diffusion-mediated evolution of crystalline metal nanostructures on the appropriate time scale (often 10 1 –10 4 s) and length scale. Model behavior can be precisely assessed by kinetic Monte Carlo simulation, typically incorporating a rejection-free algorithm to efficiently handle the broad range of Arrhenius rates for hopping of surface atoms. The model should realistically prescribe these rates, or the associated barriers, for a diversity of local surface environments. However, commonly used generic choices for barriers fail, even qualitatively, to simultaneously describe diffusion for different low-index facets, for terrace vs step edge diffusion, etc. We introduce an alternative Unconventional Interaction–Conventional Interaction formalism to prescribe these barriers, which, even with few parameters, can realistically capture most aspects of behavior. Here, the model is illustrated for single-component fcc metal systems, mainly for the case of Ag. It is quite versatile and can be applied to describe both the post-deposition evolution of 2D nanostructures in homoepitaxial thin films (e.g., reshaping and coalescence of 2D islands) and the post-synthesis evolution of 3D nanocrystals (e.g., reshaping of nanocrystals synthesized with various faceted non-equilibrium shapes back to 3D equilibrium Wulff shapes).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution

Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.

97 MATHEMATICS AND COMPUTING↗