Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

The time dependent propensity function for acceleration of spatial stochastic simulation of reaction–diffusion systems

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Low-Rank Solution Methods for Stochastic Eigenvalue Problems

In this report, we study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data, where the underlying operators depend linearly on the random parameters. With the stochastic Galerkin approach, the solutions are represented as generalized polynomial chaos expansions. When these solutions can be approximated well by low-rank objects, we introduce a low-rank variant of the inverse subspace iteration algorithm for computing one or several minimal eigenvalues and corresponding eigenvectors of parameter-dependent matrices. In the algorithm, the iterates are approximated by low-rank matrices, which leads to significant cost savings. Furthermore, the algorithm is tested on two benchmark problems, a stochastic diffusion problem with some poorly separated eigenvalues, and an operator derived from a discrete stochastic Stokes problem whose minimal eigenvalue is related to the inf-sup stability constant. Numerical experiments show that the low-rank algorithm produces accurate solutions compared to the Monte Carlo method, and it uses much less computational time than the original algorithm without low-rank approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗
DOE OSTI2017

Baryon number diffusion with critical fluctuations

The description of dynamical fluctuations near the QCD critical point in heavy-ion collisions is crucial for understanding the existing and upcoming experimental data from the beam energy scan programs. In this talk we discuss the evolution of fluctuations of the net-baryon density as given by a stochastic diffusion equation. In conclusion we study equilibrium as well as dynamical systems for which we can show the impact of nonequilibrium effects on the second-order moment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Dynamics of a reconnection-driven runaway ion tail in a reversed field pinch plasma

While reconnection-driven ion heating is common in laboratory and astrophysical plasmas, the underlying mechanisms for converting magnetic to kinetic energy remain not fully understood. Reversed field pinch discharges are often characterized by rapid ion heating during impulsive reconnection, generating an ion distribution with an enhanced bulk temperature, mainly perpendicular to magnetic field. In the Madison Symmetric Torus, a subset of discharges with the strongest reconnection events develop a very anisotropic, high energy tail parallel to magnetic field in addition to bulk perpendicular heating, which produces a fusion neutron flux orders of magnitude higher than that expected from a Maxwellian distribution. Here, we demonstrate that two factors in addition to a perpendicular bulk heating mechanism must be considered to explain this distribution. First, ion runaway can occur in the strong parallel-to-B electric field induced by a rapid equilibrium change triggered by reconnection-based relaxation; this effect is particularly strong on perpendicularly heated ions which experience a reduced frictional drag relative to bulk ions. Second, the confinement of ions varies dramatically as a function of velocity. Whereas thermal ions are governed by stochastic diffusion along tearing-altered field lines (and radial diffusion increases with parallel speed), sufficiently energetic ions are well confined, only weakly affected by a stochastic magnetic field. High energy ions traveling mainly in the direction of toroidal plasma current are nearly classically confined, while counter-propagating ions experience an intermediate confinement, greater than that of thermal ions but significantly less than classical expectations. The details of ion confinement tend to reinforce the asymmetric drive of the parallel electric field, resulting in a very asymmetric, anisotropic distribution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem

We study a multigrid method for solving large linear systems of equations with tensor product structure here. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the steady-state diffusion problem with random coefficients. When the variance in the problem is not too large, the solution can be well approximated by a low-rank object. In the proposed multigrid algorithm, the matrix iterates are truncated to low rank to reduce memory requirements and computational effort. The technique is proved convergent with an analytic error bound. Numerical experiments show its effectiveness in solving the Galerkin systems compared to the original multigrid solver, especially when the number of degrees of freedom associated with the spatial discretization is large.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Comment on “Hermitian stochastic methodology for x-ray superfluorescence”

This comment critically examines the paper “Hermitian stochastic methodology for x-ray superfluorescence” by Chuchurka, Sukharnikov, and Rohringer [Phys. Rev. A 109, 063705 (2024)]. Here, the paper proposes a Hermitian framework based on the positive-𝑃 stochastic equations (PPSEs), claimed to be derived “from first principles,” through a redefinition of physical variables without a clear rationale. However, because the original PPSEs cannot satisfy Hermiticity under any stochastic-diffusion-gauge transformation, the framework necessarily employs representations beyond this gauge freedom, thereby contradicting the original PPSEs and their ensemble-average predictions. The resulting equations have close structural similarities with the previously established Hermitian formalism of stochastic Maxwell-Bloch equations [arXiv:2305.04653 and Phys. Rev. A 110, 023724 (2024)].

Park, Jeong-Wan [Argonne National Laboratory (ANL)↗
DOE OSTI2021

Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling

The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Lastly, potential applications and caveats to the usage of LD are included as a summary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Role of the edge stochastic layer in density pump-out by resonant magnetic perturbations

The role of the edge stochastic layer on particle transport is addressed in DIII-D plasmas with applied resonant magnetic perturbations (RMPs) causing density pump-out (a term used to denote the density reduction at the top of the pedestal due to the applied RMPs). Using an analytical model that adds the stochastic parallel transport of electrons (Harvey et al 1981 Phys. Rev. Lett. 47 102) to the fluid equations, the ambipolar radial electric field and particle flux are calculated simultaneously. In this model the nonambipolar electron particle flux, driven by the stochastic magnetic field, is predominantly balanced by the nonambipolar perpendicular ion flux, driven by toroidal viscosity, across a narrow stochastic layer of order two percent of the plasma radius (0.98 < ψn < 1). The model reproduces the level of density pump-out and its dependence on RMP amplitude near the separatrix for three plasma discharges for which the pedestal foot is at medium to high collisionality $(2\leqslant {\nu }_{\text{sep}}^{\ast }\leqslant 30)$. In this work, the experimentally observed and numerically tested inverse density dependence of density pump-out (Hu et al 2020 Nucl. Fusion 60 076001) is accurately captured by the model: an increase in collisionality with density in the pedestal foot results in a decrease in stochastic diffusivity, and hence a decrease in the level of pump-out.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Quasielastic neutron scattering in biology: Theory and applications

Neutrons scatter quasielastically from stochastic, diffusive processes, such as overdamped vibrations, localized diffusion and transitions between energy minima. In biological systems, such as proteins and membranes, these relaxation processes are of considerable physical interest. We review here recent methodological advances and applications of quasielastic neutron scattering (QENS) in biology, concentrating on the role of molecular dynamics simulation in generating data with which neutron profiles can be unambiguously interpreted. We examine the use of massively-parallel computers in calculating scattering functions, and the application of Markov state modeling. The decomposition of MD-derived neutron dynamic susceptibilities is described, and the use of this in combination with NMR spectroscopy. We discuss dynamics at very long times, including approximations to the infinite time mean-square displacement and nonequilibrium aspects of single-protein dynamics. Lastly, we examine how neutron scattering and MD can be combined to provide information on lipid nanodomains.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Theory and observation of the onset of nonlinear structures due to eigenmode destabilization by fast ions in tokamaks

Alfvén waves can induce the ejection of fast ions in different forms in tokamaks. In order to develop predictive capabilities to anticipate the nature of fast ion transport, a methodology is proposed to differentiate the likelihood of energetic-particle-driven instabilities to produce frequency chirping or fixed-frequency oscillations. Furthermore, the proposed method employs numerically calculated eigenstructures and multiple resonance surfaces of a given mode in the presence of energetic ion drag and stochasticity (due to collisions and micro-turbulence). Toroidicity-induced, reversed-shear and beta-induced Alfvén-acoustic eigenmodes are used as examples. Waves measured in experiments are characterized, and compatibility is found between the proposed criterion predictions and the experimental observation or lack of observation of chirping behavior of Alfvénic modes in different tokamaks. It is found that the stochastic diffusion due to micro-turbulence can be the dominant energetic particle detuning mechanism near the resonances in many plasma experiments, and its strength is the key as to whether chirping solutions are likely to arise. We proposed a criterion that constitutes a useful predictive tool in assessing whether the nature of the transport for fast ion losses in fusion devices will be dominated by convective or diffusive processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Calculation of prompt loss and toroidal field ripple loss under neutral beam injection on EAST

Here, neutral beam injection is a major auxiliary heating method in the EAST experimental campaign. This paper gives detailed calculations of beam loss with different plasma equilibria using the guiding center code ORBIT and NUBEAM/TRANSP. Increasing plasma current can dramatically lower the beam ion prompt loss and ripple loss. Countercurrent beam injection gives a much larger prompt loss fraction than co-injection, and ripple-induced collisionless stochastic diffusion is the dominant loss channel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Energetic particle loss mechanisms in reactor-scale equilibria close to quasisymmetry

Abstract Collisionless physics primarily determines the transport of fusion-born alpha particles in 3D equilibria. Several transport mechanisms have been implicated in stellarator configurations, including stochastic diffusion due to class transitions, ripple trapping, and banana drift-convective orbits. Given the guiding center dynamics in a set of six quasihelical and quasiaxisymmetric equilibria, we perform a classification of trapping states and transport mechanisms. In addition to banana drift convection and ripple transport, we observe substantial non-conservation of the parallel adiabatic invariant which can cause losses through diffusive banana tip motion. Furthermore, many lost trajectories undergo transitions between trapping classes on longer time scales, either with periodic or irregular behavior. We discuss possible optimization strategies for each of the relevant transport mechanisms. We perform a comparison between fast ion losses and metrics for the prevalence of mechanisms such as banana-drift convection (Velasco et al 2021 Nucl. Fusion 61 116059), transitioning orbits, and wide orbit widths. Quasihelical configurations are found to have natural protection against ripple-trapping and diffusive banana tip motion leading to a reduction in prompt losses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Dynamic scaling of order parameter fluctuations in model B

Brookhaven National Laboratory has performed a dedicated set of experiments, called the Beam Energy Scan (BES), with the goal of location a possible critical point in the phase diagram of nuclear matter, This point is analogous to the endpoint of the liquid-gas phase transition in water, where the liquid phase corresponds to a phase of hadrons, and the gas phase to a plasma of quarks and gluons. In order to describe the data generated by these experiments we have studied numerical simulations of the stochastic diffusion equation with a conserved charge. Here, we focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent z ≃ 3.972(2), which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Mercury’s Chaotic Secular Evolution as a Subdiffusive Process

Abstract Mercury’s orbit can destabilize, generally resulting in a collision with either Venus or the Sun. Chaotic evolution can causeg 1 to decrease to the approximately constant value ofg 5 and create a resonance. Previous work has approximated the variation ing 1 as stochastic diffusion, which leads to a phenomological model that can reproduce the Mercury instability statistics of secular andN-body models on timescales longer than 10 Gyr. Here we show that the diffusive model significantly underpredicts the Mercury instability probability on timescales less than 5 Gyr, the remaining lifespan of the solar system. This is becauseg 1 exhibits larger variations on short timescales than the diffusive model would suggest. To better model the variations on short timescales, we build a new subdiffusive phenomological model forg 1 . Subdiffusion is similar to diffusion but exhibits larger displacements on short timescales and smaller displacements on long timescales. We choose model parameters based on the behavior of theg 1 trajectories in theN-body simulations, leading to a tuned model that can reproduce Mercury instability statistics from 1–40 Gyr. This work motivates fundamental questions in solar system dynamics: why does subdiffusion better approximate the variation ing 1 than standard diffusion? Why is there an upper bound ong 1 , but not a lower bound that would prevent it from reachingg 5 ?

Astronomy & Astrophysics↗
NASA NTRS1975

Mathematical formulation of scatter-free propagation of solar cosmic rays

The observations of strong persistent velocity anisotropies in solar flare events demand a mathematical theory closer to the extreme of scatter-free (deterministic) propagation rather than diffusive (stochastic) transport, since the latter breaks down as inferred mean-free-paths exceed 0.1 AU. Equations are derived for the time-dependent phase-space density, and Laplace transform techniques are used to obtain solutions under rather general conditions. The case of an Archimedean spiral field has been solved numerically, and the results compared with observations from Mariner and Explorer spacecraft of nearly 0.4 MeV proton intensity and anisotropy histories. These can both be replicated if the inner boundary of the modulation region is placed beyond 2 AU.

Nolte, J. T.↗
NASA NTRS1977

Observations of large transient magnetospheric electric fields

Transient electric field events were observed with the long, double probe instrumentation carried by the IMP-6 satellite. Nine, clearly defined, exceptionally large amplitude events are presented here. The events are observed in the midnight sector at geocentric distances 3.5 to .5.5 R sub e at middle latitudes within a magnetic L-shell range of 4.8 to 7.5. They usually have a total duration of one to several minutes, with peak power spectra amplitudes occurring at a frequency of about 0.3 Hz. The events occur under magnetically disturbed conditions, and in most cases they can be associated with negative dH/dt excursions at magnetic observatories located near the foot of the magnetic field line intersecting IMP-6. The magnetospheric motions calculated for these electric fields indicated a quasi-stochastical diffusive process rather than the general inward magnetospheric collapsing motion expected during the expansive phases of auroral substorm activity.

Aggson, T. L.↗
NASA NTRS1977

Observations of large transient magnetospheric electric fields

Transient electric field events were studied by means of the long double-probe instrumentation carried by the Imp 6 satellite, and nine clearly defined exceptionally large amplitude events are described. The events were observed in the midnight sector at geocentric distances of 3.5 to 5.5 earth radii at middle latitudes within a magnetic L shell range of 4.8 to 7.5; the duration is from one to several minutes with peak power spectra amplitudes occurring at a frequency of about 0.3 Hz. The events occur under magnetically disturbed conditions and are often associated with negative dH/dt excursions. The magnetospheric motions calculated for these electric fields indicate a quasi-stochastical diffusive process rather than the general inward magnetospheric collapsing motion expected during the expansive phases of auroral substorm activity. It is likely that the transient electric fields are responsible for the impulsive acceleration and injection of plasma to populate the outer radiation belt.

Aggson, T. L.↗