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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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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal(100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN ~ N -β with β = 3/2. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N < 9; (ii) slow nucleation-mediated diffusion with small β < 1 for “perfect” sizes N = N p = L 2 or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10 2 ); the same also applies for N = N p +3, N p + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and N p + 2 also for moderate sizes 9 ≤ N ≤ O(10 2 ); (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲ β < 3/2, reflecting the quasi-facetted structure of clusters, for larger N = O(10 2 ) to N = O(10 3 ); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where show that diffusivity cycles quasi-periodically from the slowest branch for N p + 3 (not Np) to the fastest branch for Np + 1. Behavior is quantified by Kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back-correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground state and low-lying excited state cluster configurations, and also of kink populations.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology

The main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano- to micrometers. Few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets, such as buffers or active sites. Bridging the small and large spatial scales is achieved by rare events representing Brownian particles finding small targets and characterized by long-time distribution. These rare events are the bottleneck of numerical simulations. A naive stochastic simulation requires running many Brownian particles together, which is computationally greedy and inefficient. Solving the associated partial differential equations is also difficult due to the time dependent boundary conditions, narrow passages and mixed boundary conditions at small windows. We present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains. The first approach is based on a Markov mass-action law equations coupled to a Markov chain. The second is a Gillespie's method based on the narrow escape theory for coarse-graining the geometry of the domain into Poissonian rates. The main application concerns diffusion in cellular biology, where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

EFFECT OF ADIABATIC FOCUSING ON THE DIFFUSION OF ENERGETIC CHARGED PARTICLES

An approximate analytic description of a diffusion coefficient, including the effect of adiabatic focusing, has been developed. This description is formulated with the aid of stochastic differential equations and the steady perturbation solution of the Fokker–Plank transport equation. The analytical formula is based on three important assumptions. First, the pitch-angle diffusion coefficient is set to be separable from the spatial coordinate and the pitch-angle cosine. Second, the spatial dependence of the ratio between the mean-free path and focusing length is assumed to be weak. Third, the pitch-angle distribution relaxes quickly to a steady state. The new analytic formula could be applied to calculate the spatial diffusion coefficient in the interplanetary and interstellar space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SENSITIVITY OF COSMIC-RAY PROTON SPECTRA TO THE LOW-WAVENUMBER BEHAVIOR OF THE 2D TURBULENCE POWER SPECTRUM

In this study, a novel ab initio cosmic ray (CR) modulation code that solves a set of stochastic transport equations equivalent to the Parker transport equation, and that uses output from a turbulence transport code as input for the diffusion tensor, is introduced. This code is benchmarked with a previous approach to ab initio modulation. The sensitivity of computed galactic CR proton spectra at Earth to assumptions made as to the low-wavenumber behavior of the two-dimensional (2D) turbulence power spectrum is investigated using perpendicular mean free path expressions derived from two different scattering theories. Constraints on the low-wavenumber behavior of the 2D power spectrum are inferred from the qualitative comparison of computed CR spectra with spacecraft observations at Earth. Another key difference from previous studies is that observed and inferred CR intensity spectra at 73 AU are used as boundary spectra instead of the usual local interstellar spectrum. Furthermore, the results presented here provide a tentative explanation as to the reason behind the unusually high galactic proton intensity spectra observed in 2009 during the recent unusual solar minimum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. I: spectrum and chemical composition

In this paper we investigate the effect of stochasticity in the spatial and temporal distribution of supernova remnants on the spectrum and chemical composition of cosmic rays observed at Earth. The calculations are carried out for different choices of the diffusion coefficient D(E) experienced by cosmic rays during propagation in the Galaxy. In particular, at high energies we assume that D(E)∝E{sup δ}, with δ = 1/3 and δ = 0.6 being the reference scenarios. The large scale distribution of supernova remnants in the Galaxy is modeled following the distribution of pulsars, with and without accounting for the spiral structure of the Galaxy. We find that the stochastic fluctuations induced by the spatial and temporal distribution of supernovae, together with the effect of spallation of nuclei, lead to mild but sensible violations of the simple, leaky-box-inspired rule that the spectrum observed at Earth is N(E)∝E{sup −α} with α = γ+δ, where γ is the slope of the cosmic ray injection spectrum at the sources. Spallation of nuclei, even with the small rates appropriate for He, may account for small differences in spectral slopes between different nuclei, possibly providing an explanation for the recent CREAM observations. For δ = 1/3 we find that the slope of the proton and helium spectra are ∼ 2.67 and ∼ 2.6 respectively (with fluctuations depending on the realization of source distribution) at energies around ∼ 1 TeV (to be compared with the measured values of 2.66±0.02 and 2.58±0.02). For δ = 0.6 the hardening of the He spectra is not observed. The stochastic effects discussed above cannot be found in ordinary propagation calculations, such as GALPROP, where these effects and the point like nature of the sources are not taken into account. We also comment on the effect of time dependence of the escape of cosmic rays from supernova remnants, and of a possible clustering of the sources in superbubbles. In a second paper we will discuss the implications of these different scenarios for the anisotropy of cosmic rays.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Extending the diffusion approximation to the boundary using an integrated diffusion model

The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.

36 MATERIALS SCIENCE↗
DOE OSTI2012

ANOMALOUS TRANSPORT OF HIGH-ENERGY COSMIC RAYS IN GALACTIC SUPERBUBBLES. I. NUMERICAL SIMULATIONS

We present a simple continuous-time random-walk model for the transport of energetic particles accelerated by a collection of supernova explosions in a galactic superbubble, developed to simulate and highlight signatures of anomalous transport on the particles' evolution and their spectra in a multi-shock context. We assume standard diffusive shock acceleration (DSA) theory for each shock encounter. The superbubble (an OB stars association) is idealized as a heterogeneous region of particle sources and sinks bounded by a random surface. The model is based on two coupled stochastic differential equations and is applied for protons and alpha particles. Using characteristic values for a typical bubble, our simulations suggest that acceleration and transport in the bubble may be sub-diffusive. In addition, a spectral break in the particles' evolution and spectra is evident located at Almost-Equal-To 10{sup 15} eV for protons and Almost-Equal-To 3 Multiplication-Sign 10{sup 15} eV for alphas. Our simulations are consistent with a bubble's mean magnetic field strength of Almost-Equal-To 1 {mu}G and a shock separation distance {approx}0.1 Multiplication-Sign the characteristic radius of the bubble. The simulations imply that the diffusion coefficient (for the elementary shock acceleration process) is {approx}< 10{sup 27} cm{sup 2} s{sup -1} at 1 GeV/c. While the sub-diffusive transport is readily attributed to the stochastic nature of the acceleration time according to DSA theory, the spectral break appears to be an artifact of transport in a finite medium. These simulations point to a new and intriguing phenomenon associated with the statistical nature of collective acceleration of high-energy cosmic rays in galactic superbubbles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Design optimization of a scramjet under uncertainty using probabilistic learning on manifolds

Here, we demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differential equation. The objective function and constraints of the optimization problem are then efficiently framed as non-parametric conditional expectations. Different spatial resolutions of a large-eddy simulation filter are used to explore the robustness of the model to the training dataset and to gain insight into the significance of spatial resolution on optimal design.

42 ENGINEERING↗
DOE OSTI2014

Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes

Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averaged mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Thermal diffusion segregation of an impurity in a driven granular fluid

We study segregation of an impurity in a driven granular fluid under two types of steady states. In the first state, the granular gas is driven by a stochastic volume force field with a Fourier-type profile while in the second state, the granular gas is sheared in such a way that inelastic cooling is balanced by viscous heating. We compare theoretical results derived from a solution of the (inelastic) Boltzmann equation at Navier-Stokes (NS) order with those obtained from the Direct Monte Carlo simulation (DSMC) method and molecular dynamics (MD) simulations. Good agreement is found between theory and simulation, which provides strong evidence of the reliability of NS granular hydrodynamics for these steady states (including the dynamics of the impurity), even at high inelasticity. In addition, preliminary results for thermal diffusion in granular fluids at moderate densities are also presented. As for dilute gases, excellent agreement is also found in this more general case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On the Representation of Hyporheic Exchange in Models for Reactive Transport in Stream and River Corridors

Efforts to include more detailed representations of biogeochemical processes in basin-scale water quality simulation tools face the challenge of how to tractably represent mass exchange between the flowing channels of streams and rivers and biogeochemical hotspots in the hyporheic zones. Multiscale models that use relatively coarse representations of the channel network with subgrid models for mass exchange and reactions in the hyporheic zone have started to emerge to address that challenge. Two such multiscale models are considered here, one based on a stochastic Lagrangian travel time representation of advective pumping and one on multirate diffusive exchange. The two models are formally equivalent to well-established integrodifferential representations for transport of non-reacting tracers in steady stream flow, which have been very successful in reproducing stream tracer tests. Despite that equivalence, the two models are based on very different model structures and produce significantly different results in reactive transport. In a simple denitrification example, denitrification is two to three times greater for the advection-based model because the multirate diffusive model has direct connections between the stream channel and transient storage zones and an assumption of mixing in the transient storage zones that prevent oxygen levels from dropping to the point where denitrification can progress uninhibited. By contrast, the advection-based model produces distinct redox zonation, allowing for denitrification to proceed uninhibited on part of the hyporheic flowpaths. These results demonstrate that conservative tracer tests alone are inadequate for constraining representation of mass transfer in models for reactive transport in streams and rivers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Magnetorheological effect in the magnetic field oriented along the vorticity

In this work, we have studied the magnetorheological (MR) fluid rheology in the magnetic field parallel to the fluid vorticity. Experimentally, the MR fluid flow was realized in the Couette coaxial cylinder geometry with the magnetic field parallel to the symmetry axis. The rheological measurements were compared to those obtained in the cone-plate geometry with the magnetic field perpendicular to the lower rheometer plate. Experiments revealed a quasi-Bingham behavior in both geometries with the stress level being just a few dozens of percent smaller in the Couette cylindrical geometry at the same internal magnetic field. The unexpectedly high MR response in the magnetic field parallel to the fluid vorticity is explained by stochastic fluctuations of positions and orientations of the particle aggregates. These fluctuations are induced by magnetic interactions between them. Once misaligned from the vorticity direction, the aggregates generate a high stress independent of the shear rate, and thus assimilated to the suspension apparent (dynamic) yield stress. Quantitatively, the fluctuations of the aggregate orientation are modeled as a rotary diffusion process with a diffusion constant proportional to the mean square interaction torque. The model gives a satisfactory agreement with the experimental field dependency of the apparent yield stress and confirms the nearly quadratic concentration dependency σ{sub Y}∝Φ{sup 2.2}, revealed in experiments. The practical interest of this study lies in the development of MR smart devices with the magnetic field nonperpendicular to the channel walls.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Proton imaging of stochastic magnetic fields

Recent laser-plasma experiments report the existence of dynamically significant magnetic fields, whose statistical characterization is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a proton-imaging diagnostic can be used to determine a range of relevant magnetic-field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. This ‘Kugland image-flux relation’ was previously derived under simplifying assumptions typically valid in actual proton-imaging set-ups. We conclude that, as with regular electromagnetic fields, features of the beam’s final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter – the contrast parameter $\unicode[STIX]{x1D707}\equiv d_{s}/{\mathcal{M}}l_{B}$ – which quantifies the relative size of the correlation length $l_{B}$ of the stochastic field, proton displacements $d_{s}$ due to magnetic deflections and the image magnification ${\mathcal{M}}$ . For stochastic magnetic fields, we establish the existence of four contrast regimes, under which proton-flux images relate to their parent fields in a qualitatively distinct manner. These are linear, nonlinear injective, caustic and diffusive. The diffusive regime is newly identified and characterized. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the path-integrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magnetic-energy spectrum can be obtained under a further statistical assumption of isotropy. This is not the case in the caustic or diffusive regimes. We discuss complications to the contrast-regime characterization arising for inhomogeneous, multi-scale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one’s ability to extract magnetic-field statistics. Furthermore, the results presented in this paper are of consequence in providing a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of proton-flux images.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Quantum diffusion during inflation and primordial black holes

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ∼ 1 e -fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Learning effective SDEs from Brownian dynamic simulations of colloidal particles

We construct a reduced, data-driven, parameter dependent effective stochastic differential equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian dynamics simulations. We use diffusion maps (a manifold learning algorithm) to identify a set of useful latent observables. In this latent space we identify an eSDE using a deep learning architecture inspired by numerical stochastic integrators and compare it with the traditional Kramers–Moyal expansion estimation. We show that the obtained variables and the learned dynamics accurately encode the physics of the Brownian dynamic simulations. We further illustrate that our reduced model captures the dynamics of corresponding experimental data. Further, our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Oscillation-like diffusion of two-dimensional liquid dusty plasmas on one-dimensional periodic substrates with varied widths

The long-time diffusion of two-dimensional dusty plasmas on a one-dimensional periodic substrate with varying widths is investigated using Langevin dynamical simulations. When the substrate is narrow and the dust particles form a single row, the diffusion is the smallest in both directions. In this study, we find that as the substrate width gradually increases to twice its initial value, the long-time diffusion of the two-dimensional dusty plasmas first increases, then decreases, and finally increases again, giving an oscillation-like diffusion with varying substrate widths. When the width increases to a specific value, the dust particles within each potential well arrange themselves in a stable zigzag pattern, greatly reducing the diffusion and leading to the observed oscillation in the diffusion with the increase in the width. In addition, the long-time oscillation-like diffusion is consistent with the number of dust particles that are hopping across the potential wells of the substrate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗