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At least 523 records · Page 29

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DOE OSTI2014

Computation of the halo mass function using physical collapse parameters: application to non-standard cosmologies

In this article we compare the halo mass function predicted by the excursion set theory with a drifting diffusive barrier against the results of N-body simulations for several cosmological models. This includes the standard ΛCDM case for a large range of halo masses, models with different types of primordial non-Gaussianity, and the Ratra-Peebles quintessence model of Dark Energy. We show that in all those cosmological scenarios, the abundance of dark matter halos can be described by a drifting diffusive barrier, where the two parameters describing the barrier have physical content. In the case of the Gaussian ΛCDM, the statistics are precise enough to actually predict those parameters at different redshifts from the initial conditions. Furthermore, we found that the stochasticity in the barrier is non-negligible making the simple deterministic spherical collapse model a bad approximation even at very high halo masses. We also show that using the standard excursion set approach with a barrier inspired by peak patches leads to inconsistent predictions of the halo mass function.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Formation and coarsening of epitaxially-supported metal nanoclusters

This mini-review describes developments over the last ~30 years in characterizing the nucleation & growth of epitaxially-supported metal nanoclusters (NCs) or islands during vapor deposition, as well as their post-deposition coarsening. A beyond-mean-field treatment for homogeneous nucleation & growth corrects the deficiencies of traditional treatments in describing, e.g., the island size distribution, but also necessitates consideration of the spatial distribution of islands and their capture zones. We discuss advances in modeling capabilities, including those based upon on an ab-initio level treatment of periphery diffusion kinetics, for description of the non-equilibrium growth shapes of these NCs, focusing on 2D NCs. For post-deposition coarsening of arrays of NCs, there is generally a competition between Ostwald Ripening (OR) and Smoluchowski Ripening (SR). SR is also known as Particle Migration & Coalescence. For 2D NCs in homoepitaxial systems, conventional OR is observed on pristine fcc(111) surfaces, dramatically enhanced OR in the presence of even trace amounts of chalcogens for Cu(111) and Ag(111), and anomalous OR on anisotropic fcc(110) surfaces. The unexpected discovery of SR for fcc(100) homoepitaxial systems prompted extensive analysis of the underlying diffusivities of 2D NCs as a function of size, as well as of NC coalescence dynamics. A comprehensive understanding of these processes is now available. Self-assembly of 3D NCs during deposition, issues related to heterogeneous nucleation, directed assembly, NC growth structure selection, and coarsening are addressed. Finally, for SR of 3D epitaxial NCs, recent insights into the size-dependence of diffusivity are described.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Ratcheted electrophoresis of Brownian particles

The realization of nanoscale machines requires efficient methods by which to rectify unbiased perturbations to perform useful functions in the presence of significant thermal noise. The performance of such Brownian motors often depends sensitively on their operating conditions—in particular, on the relative rates of diffusive and deterministic motions. In this letter, we present a type of Brownian motor that uses contact charge electrophoresis of a colloidal particle within a ratcheted channel to achieve directed transport or perform useful work against an applied load. We analyze the stochastic dynamics of this model ratchet to show that it functions under any operating condition—even in the limit of strong thermal noise and in contrast to existing ratchets. The theoretical results presented here suggest that ratcheted electrophoresis could provide a basis for electrochemically powered, nanoscale machines capable of transport and actuation of nanoscale components.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1991

Evaluation of an efficient statistical transport model for turbulent droplet dispersion in dilute combusting sprays

Evaluation of an efficient statistical transport model for turbulent droplet dispersion is made for a dilute spray of methanol droplets injected into a turbulent, axisymmnetric methane-fuelled diffusion flame burning in stagnant air. In the dispersion model, a computational parcel representing a group of physical particles (droplets) is considered to have a normal probability density function (pdf) in space. The mean is determined by Lagrangian tracking through a sequence of stochastically generated turbulent eddies and the variance is evaluated from a statistical formulation based on the linearized particle equations of motion. The basic validity of this model is established through comparison with available experimental data and with theoretical predictions using a conventional stochastic direct modeling approach. The conclusion of the evaluation is that the proposed dispersion model compares favorably with experimental data and provides a valid technique for simulating turbulent combusting sprays with significant computational savings over conventional methods.

Litchford, Ron J.↗

DOE OSTI2025

Control-Affine Schrödinger Bridge and Generalized Bohm Potential

From a stochastic control perspective, the Schrödinger bridge is a density-valued continuous curve parameterized by time that connects a given pair of initial and terminal probability densities via minimum effort controlled Brownian motion. The control-affine Schrödinger bridge extends this idea to a generic control-affine Itô diffusion, possibly with an additive state cost. Here, in this letter, we recast the necessary conditions of optimality for the control-affine Schrödinger bridge problem as a two point boundary value problem for a quantum mechanical Schrödinger PDE with complex potential. This complex-valued potential is a generalization of the real-valued Bohm potential in quantum mechanics. Our derived potential is akin to the optical potential in nuclear physics where the real part of the potential encodes elastic scattering (transmission of wave function), and the imaginary part encodes inelastic scattering (absorption of wave function). The key takeaway is that the process noise that drives the evolution of probability densities induces an absorbing medium in the evolution of wave function. These results make new connections between control theory and non-equilibrium statistical mechanics through the lens of quantum mechanics.

Markov processes↗

DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

ESR studies of the slow tumbling of vanadyl spin probes in nematic liquid crystals

ESR line shapes that are appropriate for slowly tumbling vanadyl spin probes in viscous nematic liquid crystals were calculated by the stochastic Liouville method. Because of the symmetry possessed by vanadyl, the analysis and interpretation of these line shapes was simplified considerably. Spectral line shapes agreed well with experimental spectra of VOAcAc in the nematic liquid crystal Phase V and BEPC. Deviations from Brownian rotational diffusion were noted. A slowly fluctuating torque analysis yielded good agreement with the experimental spectra.

Eastman, M. P.↗

DOE OSTI2016

Dimension-independent likelihood-informed MCMC

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated low-dimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Two nonlinear inverse problems are used to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces

Here we introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial hydrodynamic coupling, traction coupling with the surrounding bulk fluid, and thermal fluctuations. For fluid-structure interactions, we introduce Immersed Boundary Methods (IBM) and related Stochastic Eulerian-Lagrangian Methods (SELM) for curved surfaces. We use these approaches to investigate the statistics of surface fluctuating hydrodynamics and microstructures. For velocity autocorrelations, we find characteristic power-law scalings $τ^{-1}, τ^{-2}$, and plateaus can emerge. This depends on the physical regime associated with the geometry, surface viscosity, and bulk viscosity. This differs from the characteristic $τ^{-3/2}$ scaling for bulk three dimensional fluids. We develop theory explaining these observed power-laws associated with time-scales for dissipation within the fluid interface and coupling to the surrounding fluid. We then use our introduced methods to investigate a few example systems and roles of hydrodynamic coupling and thermal fluctuations including for the kinetics of passive particles and active microswimmers in curved fluid interfaces.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Ab Initio Thermodynamics and Kinetics for Coalescence of Two-Dimensional Nanoislands and Nanopits on Metal (100) Surfaces

Postdeposition coalescence or sintering of pairs of lowstrain two-dimensional nanoislands and nanopits on unreconstructed metal (100) surfaces is typically mediated by diffusion along step edges, and is highly sensitive to the associated kinetics. Thus, for selected systems, we provide an ab initio density functional theory (DFT) level description of both system thermodynamics and kinetics. Specifically, we assess lateral pair and trio interactions both conventionally with adatoms at 4-fold hollow adsorption sites, and unconventionally with one adatom at the bridge-site transition state for hopping. Rather than use standard cluster expansion algorithms, these interactions are determined subject to the constraint that key step-edge properties are recovered exactly. Together, both classes of interactions determine barriers for edge diffusion processes for any local step configuration, including diffusion along close-packed $\langle$110$\rangle$ edges, kink rounding, meandering processes at kinked $\langle$100$\rangle$ steps, and extraction processes at pit corners. Our formalism applies for homoepitaxial systems, and also for several lattice-matched heteroepitaxial systems. The barriers provide input for stochastic models of nanocluster evolution, which are analyzed by kinetic Monte Carlo simulation. Such modeling with DFT energetics from the PBEsol functional recovers extensive experimental observations of both the time scale and the island-size dependence for sintering of Ag islands on Ag(100). In conclusion, description of pit sintering on Ag(100) is more delicate, being sensitive to specific unconventional trio interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Turbulence-driven anisotropic electron tail generation during magnetic reconnection

Magnetic reconnection (MR) plays an important role in particle transport, energization, and acceleration in space, astrophysical, and laboratory plasmas. In the Madison Symmetric Torus reversed field pinch, discrete MR events release large amounts of energy from the equilibrium magnetic field, a fraction of which is transferred to electrons and ions. Previous experiments revealed an anisotropic electron tail that favors the perpendicular direction and is symmetric in the parallel. New profile measurements of x-ray emission show that the tail distribution is localized near the magnetic axis, consistent modeling of the bremsstrahlung emission. The tail appears first near the magnetic axis and then spreads radially, and the dynamics in the anisotropy and diffusion are discussed. The data presented imply that the electron tail formation likely results from a turbulent wave-particle interaction and provides evidence that high energy electrons are escaping the core-localized region through pitch angle scattering into the parallel direction, followed by stochastic parallel transport to the plasma edge. Finally, new measurements also show a strong correlation between high energy x-ray measurements and tearing mode dynamics, suggesting that the coupling between core and edge tearing modes is essential for energetic electron tail formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Collaborative Project. 3D Radiative Transfer Parameterization Over Mountains/Snow for High-Resolution Climate Models. Fast physics and Applications

Under the support of the aforementioned DOE Grant, we have made two fundamental contributions to atmospheric and climate sciences: (1) Develop an efficient 3-D radiative transfer parameterization for application to intense and intricate inhomogeneous mountain/snow regions. (2) Innovate a stochastic parameterization for light absorption by internally mixed black carbon and dust particles in snow grains for understanding and physical insight into snow albedo reduction in climate models. With reference to item (1), we divided solar fluxes reaching mountain surfaces into five components: direct and diffuse fluxes, direct- and diffuse-reflected fluxes, and coupled mountain-mountain flux. “Exact” 3D Monte Carlo photon tracing computations can then be performed for these solar flux components to compare with those calculated from the conventional plane-parallel (PP) radiative transfer program readily available in climate models. Subsequently, Parameterizations of the deviations of 3D from PP results for five flux components are carried out by means of the multiple linear regression analysis associated with topographic information, including elevation, solar incident angle, sky view factor, and terrain configuration factor. We derived five regression equations with high statistical correlations for flux deviations and successfully incorporated this efficient parameterization into WRF model, which was used as the testbed in connection with the Fu-Liou-Gu PP radiation scheme that has been included in the WRF physics package. Incorporating this 3D parameterization program, we conducted simulations of WRF and CCSM4 to understand and evaluate the mountain/snow effect on snow albedo reduction during seasonal transition and the interannual variability for snowmelt, cloud cover, and precipitation over the Western United States presented in the final report. With reference to item (2), we developed in our previous research a geometric-optics surface-wave approach (GOS) for the computation of light absorption and scattering by complex and inhomogeneous particles for application to aggregates and snow grains with external and internal mixing structures. We demonstrated that a small black (BC) particle on the order of 1 μm internally mixed with snow grains could effectively reduce visible snow albedo by as much as 5–10%. Following this work and within the context of DOE support, we have made two key accomplishments presented in the attached final report.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Chaotic Dynamics Driven by Particle-Core Interactions

High-intensity beams in modern linacs are frequently encircled by diffuse halos, which drive sustained particle losses and result in gradual degradation of accelerating structures. In large part, the growth of halos is facilitated by internal space-charge forces within the beams, and detailed characterization of this process constitutes an active area of ongoing research. A partial understanding of dynamics that ensue within space-charge dominated beams is presented by the particle-core interaction paradigm – a mathematical model wherein single particle dynamics, subject to the collective potential of the core, are treated as a proxy for the broader behavior of the beam. In this work, we investigate the conditions for the onset of large-scale chaos within the framework of this model, and demonstrate that the propensity towards stochastic evolution is strongly dependent upon the charge distribution of the beam. In particular, we show that while particle motion within a uniformly charged beam is dominantly regular, rapid deterministic chaos readily arises within space-charge dominated Gaussian beams. Importantly, we find that for sufficiently high values of the beam’s space charge and beam pulsation amplitude, enhanced chaotic mixing between the core and the halo can lead to an enhanced radial diffusion of charged particles. We explain our results from analytic grounds by demonstrating that chaotic motion is driven by the intersection of two principal resonances of the system, and derive the relevant overlap conditions. Additionally, our analysis illuminates a close connection between the mathematical formulation of the particle-core interaction model and the Andoyer family of integrable Hamiltonians

43 PARTICLE ACCELERATORS↗

DOE OSTI2016

Deep mixing in stellar variability: improved method, statistics, and applications

The preliminary results on deep-mixing manifestations in stellar variability are tested using our improved method and extended data set. We measure the timescales τ {sub m} of the stochastic change in the spectral power of rotational harmonics with numbers m ≤ 3 in the light curves of 1361 main-sequence stars from the Kepler mission archive. We find that the gradient [log(τ{sub 2})−log(τ{sub 1})]/[log(2)−log(1)] has a histogram maximum at −2/3, demonstrating agreement with Kolmogorov’s theory of turbulence and therefore confirming the manifestation of deep mixing. The squared amplitudes of the first and second rotational harmonics, corrected for integral photometry distortion, also show a quasi-Kolmogorov character with spectral index ≈−5/3. Moreover, the reduction of τ {sub 1} and τ {sub 2} to the timescales τ {sub lam1} and τ {sub lam2} of laminar convection in the deep stellar layers reveals the proximity of both τ {sub lam1} and τ {sub lam2} to the turnover time τ {sub MLT} of standard mixing length theory. Considering this result, we use the obtained stellar variability timescales instead of τ {sub MLT} in our analysis of the relation between stellar activity and the Rossby number P/τ {sub MLT}. Comparison of our diagrams with previous results and theoretical expectations shows that best-fit correspondence is achieved for τ {sub lam1}, which can therefore be used as an analog of τ {sub MLT}. This means that the laminar component (giant cells) of stellar turbulent convection indeed plays an important role in the physics of stars. Additionally, we estimate the diffusivity of magnetic elements in stellar photospheres.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Stochastic Simulation of Isotopic Exchange Mechanisms for Fe(II)-Catalyzed Recrystallization of Goethite

Understanding Fe(II)-catalyzed transformations of Fe(III)- (oxyhydr)oxides is critical for correctly interpreting stable isotopic distributions and for predicting the fate of metal ions in the environment. Recent Fe isotopic tracer experiments have shown that goethite undergoes rapid recrystallization without phase change when exposed to aqueous Fe(II). The proposed explanation is oxidation of sorbed Fe(II) and reductive Fe(II) release coupled 1:1 by electron conduction through crystallites. Given the availability of two tracer exchange data sets that explore pH and particle size effects (e.g., Handler et al. Environ. Sci. Technol. 2014, 48, 11302-11311; Joshi and Gorski Environ. Sci. Technol. 2016, 50, 7315-7324), we developed a stochastic simulation that exactly mimics these experiments, while imposing the 1:1 constraint. We find that all data can be represented by this model, and unifying mechanistic information emerges. At pH 7.5 a rapid initial exchange is followed by slower exchange, consistent with mixed surface- and diffusion-limited kinetics arising from prominent particle aggregation. At pH 5.0 where aggregation and net Fe(II) sorption are minimal, that exchange is quantitatively proportional to available particle surface area and the density of sorbed Fe(II) is more readily evident. Our analysis reveals a fundamental atom exchange rate of ~10-5 Fe nm-2 s-1, commensurate with some of the reported reductive dissolution rates of goethite, suggesting Fe(II) release is the rate-limiting step in the conduction mechanism during recrystallization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Dynamic Network Analysis of Nuclear Science Literature for Research Influence Assessment

Analyzing nuclear science literature via data-driven methods is a critical step for assessing research influence and technology advancements. Indicators of scholarly activities may be buried in large volumes of nuclear research publications and collaboration networks over time. Mining for relevant scholarly influence trends in large volumes of text can be computationally challenging; however, open-source information on research collaborations over time can offer opportunities to extract meaningful insights. While network centrality analysis of scholarly research provides topology-based insights, additional emphasis on dynamics associated with the diffusion of information through these networks is important. Here this paper represents a step in that direction through the development of a novel dynamic network analysis framework and computational engine to identify key entities and capabilities over time within global scholarly nuclear science collaboration networks. Network theoretic, stochastic simulation, and optimization methods are leveraged to address variability in scholarly interactions, influence propagation, and collaboration patterns via network connections. A topic-aware influence maximization algorithm is developed to address the goal of identifying key influential authors in diverse research topics over time. Efficient parallelized implementation of the algorithm is applied to reduce computational costs. A proof-of-concept case study using open-source Scopus data with 33,517 published nuclear research papers from 2000-2019 is presented and representative analytic insights are generated. Broad implications of these insights are discussed and future research directions are also identified.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

Calculating fluctuations and self-correlations numerically for causal charge diffusion in relativistic heavy-ion collisions

Here, we study the propagation and diffusion of electric charge fluctuations in the Bjorken hydrodynamic model with both white and Catteneo noise using purely numerical methods. We show that a lattice of noise fluctuations is required to fully calculate the two-point correlators of charge. We introduce a numerical procedure to solve the stochastic differential equations that arise from the charge conservation equation on the lattice event by event. We explicitly identify the self-correlation term in the case of Catteneo noise and provide a physical interpretation. We provide a numerical recipe to remove this contribution from the full two-point correlators. Finally, we calculate the balance functions for charged hadrons. By limiting the speed of signal propagation, we observe the expected narrowing of the balance functions after removing the self-correlations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗