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Results for “Stochastic diffusion”

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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

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

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

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Tuning structure and mobility of solvation shells surrounding tracer additives

Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction, and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordination-shell structure [Carmer et al., Soft Matter 8, 4083–4089 (2012)]. For the latter case, we show that the mobility of surrounding solvent particles is also increased by addition of the soft repulsive interaction, which helps to rationalize the mechanism underlying the tracer’s enhanced diffusivity. However, if multiple tracer surfaces are in closer proximity (as at higher tracer concentrations), similar interactions that disrupt local solvation structure instead suppress the position-dependent solvent dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

An Evaluation of Size-Resolved Cloud Microphysics Scheme Numerics for Use with Radar Observations. Part I: Collision–Coalescence

This study evaluates some available schemes designed to solve the stochastic collection equation (SCE) for collision–coalescence of hydrometeors using a size-resolved (bin) microphysics approach and documents their numerical properties within the framework of a box model. Comparing three widely used SCE schemes, we find that all converge to almost identical solutions at sufficiently fine mass grids. However, one scheme converges far slower than the other two and shows pronounced numerical diffusion at the large-drop tail of the size distribution. One of the remaining two schemes is recommended on the basis that it is well converged on a relatively coarse mass grid, stable for large time steps, strictly mass conservative, and computationally efficient. To examine the effects of SCE scheme choice on simulating clouds and precipitation, two of the three schemes are compared in large-eddy simulations of a drizzling stratocumulus field. A forward simulator that produces Doppler spectra from the large-eddy simulation results is used to compare the model output directly with radar observations. The scheme with pronounced numerical diffusion predicts excessively large mean Doppler velocities and overly broad and negatively skewed spectra compared with observations, consistent with numerical diffusion demonstrated in the box model. Statistics obtained using the recommended scheme are closer to observations, but notable differences remain, indicating that factors other than SCE scheme accuracy are limiting simulation fidelity.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2003

Stochastic Optimal Control via Bellman's Principle

This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.

Crespo, Luis G.↗
NASA NTRS1989

Stochastic acceleration of cometary pickup ions - The classic leaky box model

The acceleration of cometary pickup ions by magnetohydrodynamic waves at P/Giacobini-Zinner is examined in a model where acceleration predominantly occurs downstream of the bow shock throughout the cometosheath where intense magnetic turbulence exists. The mean free path for scattering by the magnetic fluctuations in this region is less than the characteristic dimension of the cometosheath so that pickup ions are rendered isotropic and energized by a modest amount in the process. This principal loss mechanism for the ions is spatial diffusion out of the acceleration region moderated by the self-same accelerating waves. This particular feature constrains the model in a way that the predicted ion spectrum is uniquely determined by the power spectrum of the magnetic turbulence. At both P/Giacobini-Zinner and P/Halley, the turbulence is non-Kolmogoroff with a spectral index of 2 resulting in an ion spectral behavior that is approximately an exponential in ion speed, consistent with a recent analysis of the Giacobini-Zinner data (see Richardson et al.).

Barbosa, D. D.↗
DOE OSTI2016

Population dynamics, information transfer, and spatial organization in a chemical reaction network under spatial confinement and crowding conditions

Here, we investigate, via Brownian dynamics simulations, the reaction dynamics of a generic, nonlinear chemical network under spatial confinement and crowding conditions. In detail, the Willamowski-Rossler chemical reaction system has been “extended” and considered as a prototype reaction-diffusion system. These results are potentially relevant to a number of open problems in biophysics and biochemistry, such as the synthesis of primitive cellular units (protocells) and the definition of their role in the chemical origin of life and the characterization of vesicle-mediated drug delivery processes. More generally, the computational approach presented in this work makes the case for the use of spatial stochastic simulation methods for the study of biochemical networks in vivo where the “well-mixed” approximation is invalid and both thermal and intrinsic fluctuations linked to the possible presence of molecular species in low number copies cannot be averaged out.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

The quasi-periodic oscillations and very low frequency noise of Scorpius X-1 as transient chaos - A dripping handrail?

We present evidence that the quasi-periodic oscillations (QPO) and very low frequency noise (VLFN) characteristic of many accretion sources are different aspects of the same physical process. We analyzed a long, high time resolution EXOSAT observation of the low-mass X-ray binary (LMXB) Sco X-1. The X-ray luminosity varies stochastically on time scales from milliseconds to hours. The nature of this variability - as quantified with both power spectrum analysis and a new wavelet technique, the scalegram - agrees well with the dripping handrail accretion model, a simple dynamical system which exhibits transient chaos. In this model both the QPO and VLFN are produced by radiation from blobs with a wide size distribution, resulting from accretion and subsequent diffusion of hot gas, the density of which is limited by an unspecified instability to lie below a threshold.

Scargle, Jeffrey D.↗
NASA NTRS1989

The relationship between infrared, optical, and ultraviolet extinction

The parameterized extinction data of Fitzpatrick and Massa (1986, 1988) for the ultraviolet and various sources for the optical and near-infrared are used to derive a meaningful average extinction law over the 3.5 micron to 0.125 wavelength range which is applicable to both diffuse and dense regions of the interstellar medium. The law depends on only one parameter R(V) = A(V)/E(B-V). An analytic formula is given for the mean extinction law which can be used to calculate color excesses or to deredden observations. The validity of the law over a large wavelength interval suggests that the processes which modify the sizes and compositions of grains are stochastic in nature and very efficient.

Cardelli, Jason A.↗
DOE OSTI2023

Stochastic fluctuations in relativistic fluids: Causality, stability, and the information current

We develop a general formalism for introducing stochastic fluctuations around thermodynamic equilibrium which takes into account, for the first time, recent developments in the causality and stability properties of relativistic hydrodynamic theories. The method is valid for any covariantly stable theory of relativistic viscous fluid dynamics derived from a covariant maximum entropy principle. We illustrate the formalism with some applications, showing how it could be used to consistently introduce fluctuations in a model of relativistic heat diffusion and in conformally invariant Israel-Stewart theory in a general hydrodynamic frame. Furthermore, the latter example is used to study the hydrodynamic frame dependence of the symmetric two-point function of fluctuations of the energy-momentum tensor.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Photoinduced correlations in stochastic dynamics of a solid-state ionic conductor

Photoexcitation by ultrashort laser pulses plays a crucial role in controlling reaction pathways, creating nonequilibrium material properties, and probing complex molecular dynamics. The photoresponse following a laser pulse is generally nonidentical between exposures due to spatiotemporal fluctuations or the stochastic nature of dynamical pathways. However, most ultrafast pump-probe experiments struggle to distinguish intrinsic sample fluctuations from extrinsic apparatus noise, often missing deviations from the averaged response. Leveraging the stability and high photon flux of time-resolved X-ray micro-diffraction at a synchrotron, we characterized stochastic photoinduced dynamics in a solid-state ionic conductor. By analyzing temporal evolutions of the lattice parameter of a single grain, we found that shot-to-shot fluctuations are not independent. Instead, correlations exist between nonequilibrium lattice trajectories following adjacent shots, with a characteristic correlation length of approximately 1500 shots, corresponding to an energy barrier of 0.4 ± 0.1 eV, close to the activation energy of lithium-ion diffusion.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Kinetic-energy dissipation and fluctuations in strongly damped heavy-ion collisions within the stochastic mean-field approach

Microscopic mean-field approaches have been successful in describing the most probable reaction outcomes in low-energy heavy-ion reactions. However, those approaches are known to severely underestimate dispersions of observables around the average values that has limited their applicability. Recently it has been shown that a quantal transport approach based on the stochastic mean-field (SMF) theory significantly improves the description, while its application has been limited so far to fragment mass and charge dispersions. In this work, we extend the quantal transport approach based on the SMF theory for relative kinetic energy dissipation and angular momentum transfer in low-energy heavy-ion reactions. Based on the SMF concept, analytical expressions are derived for the radial and tangential friction and associated diffusion coefficients. Those quantal transport coefficients are calculated microscopically in terms of single-particle orbitals within the time-dependent Hartree-Fock (TDHF) approach. As the first application of the proposed formalism, we consider the radial linear momentum dispersion, neglecting the coupling between radial and angular momenta. We analyze the total kinetic energy (TKE) distribution of binary reaction products in the 136 Xe + 208 Pb reaction at E c.m. =526 MeV and compare with experimental data. From time evolution of single-particle orbitals in TDHF, the radial diffusion coefficient is computed on a microscopic basis, while a phenomenological treatment is introduced for the radial friction coefficient. By solving the quantal diffusion equation for the radial linear momentum, the dispersion of the radial linear momentum is obtained, from which one can construct the TKE distribution. We find that the calculations provide a good description of the TKE distribution for strongly damped events with large energy losses, TKEL ≳ 150 MeV. However, the calculations underestimate the TKE distribution for smaller energy losses. Further studies are needed to improve the technical details of calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects

In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

Physics↗
DOE OSTI2018

Adaptive Sampling of Large Deviations

We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting the probability and pathways of rare events in stochastic processes, as well as for understanding the physics of nonequilibrium systems driven in steady states by external forces and reservoirs. The algorithm uses methods from risk-sensitive and feedback control to estimate from a single trajectory a new process, called the driven process, known to be efficient for importance sampling. Its advantages compared to other simulation techniques, such as splitting or cloning, are discussed and illustrated with simple equilibrium and nonequilibrium diffusion models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Probing the PeV region in the astrophysical neutrino spectrum using 𝜈 𝜇 from the Southern sky

IceCube has observed a diffuse astrophysical neutrino flux over the energy region from a few TeV to a few PeV. At PeV energies, the spectral shape is not yet well measured due to the low statistics of the data. This analysis probes the gap between 1 and 10 PeV by using high-energy downgoing muon neutrinos. Here, to reject the large atmospheric muon background, two complementary techniques are combined. The first technique selects events with high stochasticity to reject atmospheric muon bundles whose stochastic energy losses are smoothed due to high muon multiplicity. The second technique vetoes atmospheric muons with the IceTop surface array. Using 9 yrs of data, we found two neutrino candidate events in the signal region, consistent with expectation from background, each with relatively high signal probabilities. A joint maximum likelihood estimation is performed using this sample and an independent 9.5-yr sample of tracks to measure the neutrino spectrum. A likelihood ratio test is done to compare the single power-law (SPL) vs SPL+cutoff hypothesis; the SPL+cutoff model is not significantly better than the SPL. High-energy astrophysical objects from four source catalogs are also checked around the direction of the two events. No significant coincidence was found.

Abbasi, R. [Loyola University Chicago] (ORCID:0000↗
DOE OSTI2022

Space charge limited corrections to the power figure of merit for diamond

An interpretation of the unipolar figure of merit is formulated for wide bandgap (WBG) semiconductors based on the on-state specific resistance (RON,sp) derived from the space charge limited current–voltage relationship (Mott–Gurney square law). The limitations of the traditional Ohmic R ON,sp for WBG semiconductors are discussed, particularly at low doping, while the accuracy of the Mott–Gurney based R ON,sp is confirmed by Silvaco ATLAS drift–diffusion simulations of diamond Schottky pin diodes. The effects of incomplete ionization are considered as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Collisional broadening of nonlinear resonant wave–particle interactions

A general procedure for understanding plasma behaviour when resonant wave–particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principal results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas, narrow collisional boundary layers must be retained for resonant wave–particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear processes.

Physics↗
DOE OSTI2022

Comparison of Lagrangian Superdroplet and Eulerian Double-Moment Spectral Microphysics Schemes in Large-Eddy Simulations of an Isolated Cumulus Congestus Cloud

Abstract Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2014

Cross-Scale Observational Signatures of Magnetic Reconnection

Magnetic reconnection is a significant mechanism for energy release across many astrophysical applications. In the solar atmosphere, reconnection is considered a primary contributor of flare evolution and coronal heating. Directly observing reconnection occurring in the solar atmosphere, however, is not trivial considering that the scale size of the diffusion region is magnitudes smaller than the observational capabilities of current instrumentation, and coronal magnetic field measurements are not currently sufficient to capture the process. Meanwhile, reconnection occurring in the Earth's magnetosphere transfers energy from the solar wind through a comparable process, although on vastly different scales. Magnetospheric measurements are made in situ rather than remotely; ergo, comparison of observations between the two regimes allows for potentially significant insight into reconnection as a stochastic and possibly turbulent process. We will present a set of observations from long-duration solar events and compare them to in situ measurements from the magnetosphere.

Savage, Sabrina↗