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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Aggregation-fragmentation-diffusion model for trail dynamics

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)~w –γ for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. In conclusion, the exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

An Adaptive Reduced Basis Collocation Method Based on PCM ANOVA Decomposition for Anisotropic Stochastic PDEs

The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. Here, we study the stochastic collocation methods that can be combined with reduced basis methods to solve high-dimensional parameterized stochastic PDEs. We also propose an adaptive algorithm using a probabilistic collocation method (PCM) and ANOVA decomposition. This procedure involves two stages. First, the method employs an ANOVA decomposition to identify the effective dimensions, i.e., subspaces of the parameter space in which the contributions to the solution are larger, and sort the reduced basis solution in a descending order of error.Then, the adaptive search refines the parametric space by increasing the order of polynomials until the algorithm is terminated by a saturation constraint. We demonstrate the effectiveness of the proposed algorithm for solving a stationary stochastic convection-diffusion equation, a benchmark problem chosen because solutions contain steep boundary layers and anisotropic features. Lastly, we show that two stages of adaptivity are critical in a benchmark problem with anisotropic stochasticity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Catalytic conversion in nanoporous materials: Concentration oscillations and spatial correlations due to inhibited transport and intermolecular interactions

We show that steady-state catalytic conversion in nanoporous materials can occur in a quasi-counter-diffusion mode with the reactant (product) concentration strongly decaying (growing) into the pore, but also with oscillations in the total concentration. These oscillations reflect the response of the fluid to the transition from an extended to a confined environment near the pore opening. We focus on the regime of strongly inhibited transport in narrow pores corresponding to single-file diffusion. Here, limited penetration of the reactant into the pores and the associated low reaction yield is impacted by strong spatial correlations induced by both reaction (non-equilibrium correlations) and also by intermolecular interactions (thermodynamic correlations). We develop a generalized hydrodynamic formulation to effectively describe inhibited transport accounting for the effect of these correlations, and incorporate this description of transport into appropriate reaction-diffusion equations. These equations accurately describe both shorter-range concentration oscillations near the pore opening and the longer-range mesoscale variation of concentration profiles in the pore (and thus also describe reaction yield). Success of the analytic theory is validated by comparison with a precise kinetic Monte Carlo simulation of an appropriate molecular-level stochastic reaction-diffusion model. As a result, this work elucidates unconventional chemical kinetics in interacting confined systems.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Density perturbation mode structure of high frequency compressional and global Alfvén eigenmodes in the National Spherical Torus Experiment using a novel reflectometer analysis technique

Reflectometry measurements of compressional (CAE) and global (GAE) Alfvén eigenmodes are analyzed to obtain the amplitude and spatial structure of the density perturbations associated with the modes. A novel analysis technique developed for this purpose is presented. The analysis also naturally yields the amplitude and spatial structure of the density contour radial displacement, which is found to be 2–4 times larger than the value estimated directly from the reflectometer measurements using the much simpler ‘mirror approximation’. The modes were driven by beam ions in a high power (6 MW) neutral beam heated H-mode discharge (#141398) in the National Spherical Torus Experiment. The results of the analysis are used to assess the contribution of the modes to core energy transport and ion heating. The total displacement amplitude of the modes, which is shown to be larger than previously estimated (Crocker et al 2013 Nucl. Fusion 53 43017), is compared to the predicted threshold (Gorelenkov et al 2010 Nucl. Fusion 50 84012) for the anomalously high heat diffusion inferred from transport modeling in similar NSTX discharges. The results of the analysis also have strong implications for the energy transport via coupling of CAEs to kinetic Alfvén waves seen in simulations with the Hybrid MHD code (Belova et al 2015 Phys. Rev. Lett. 115 15001). Finally, the amplitudes of the observed CAEs fall well below the threshold for causing significant ion heating by stochastic velocity space diffusion (Gates et al 2001 Phys. Rev. Lett. 87 205003).

Reflectometry↗
DOE OSTI2017

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

MOLNs: A Cloud Platform for Interactive, Reproducible, and Scalable Spatial Stochastic Computational Experiments in Systems Biology Using PyURDME

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. In conclusion, MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Effective Stochastic Model For Reactive Transport

We propose an effective stochastic advection-diffusion-reaction (SADR) model. Unlike traditional advection-dispersion-reaction models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, the mechanical mixing is driven by random advective velocity with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a fickian diffusion with the effective diffusion coefficient. Both coefficients are given in terms of Peclet number (Pe) and the coefficient of molecular diffusion. We use the experimental results of \cite{Gramling} to demonstrate that for transport and bimolecular reactions in porous media the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the mass of the reaction product by as much as 25\%.

stochastic equations, mixing controlled reactions,↗
DOE OSTI2017

Computational Modeling of Fluctuations in Energy and Metabolic Pathways of Methanogenic Archaea

The methanogenic archaea, anaerobic microbes that convert CO2 and H2 and/or other small organic fermentation products into methane, play an unusually large role in the global carbon cycle. As they perform the final step in the anaerobic breakdown of biomass, methanogens are a biogenic source of an estimated one billion tons methane each year. Depending on the location, produced methane can be considered as either a greenhouse gas (agricultural byproduct), sequestered carbon storage (methane hydrate deposits), or a potential energy source (organic wastewater treatment). These microbes therefore represent an important target for biotechnology applications. Computational models of methanogens with predictive power are useful aids in the adaptation of methanogenic systems, but need to connect processes of wide-ranging time and length scales. In this project, we developed several computational methodologies for modeling the dynamic behavior of entire cells that connects stochastic reaction-diffusion dynamics of individual biochemical pathways with genome-scale modeling of metabolic networks. While each of these techniques were in the realm of well-defined computational methods, here we integrated them to develop several entirely new approaches to systems biology. The first scientific aim of the project was to model how noise in a biochemical pathway propagates into cellular phenotypes. Genetic circuits have been optimized by evolution to regulate molecular processes despite stochastic noise, but the effect of such noise on a cellular biochemical networks is currently unknown. An integrated stochastic/systems model of Escherichia coli species was created to analyze how noise in protein expression gives—and therefore noise in metabolic fluxes—gives rise to multiple cellular phenotype in isogenic population. After the initial work developing and validating methods that allow characterization of the heterogeneity in the model organism E. coli, the project shifted toward investigations of the methanogen Methanosarcina acetivorans. By integrating an unprecedented transcriptomics dataset for growth of the methanogen on many substrates with an in silico model, heterogeneity in metabolic pathway usage and methane production were examined. This lent insight into the physiological requirements of the organism under different environmental conditions and uncovered the unique regulatory role that mRNA half-life has in shaping metabolic flux distributions in this organism.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Jump rates for surface diffusion of large molecules from first principles

We apply a recently developed stochastic model for the surface diffusion of large molecules to calculate jump rates for 9,10-dithioanthracene on a Cu(111) surface. The necessary input parameters for the stochastic model are calculated from first principles using density functional theory (DFT). We find that the inclusion of van der Waals corrections to the DFT energies is critical to obtain good agreement with experimental results for the adsorption geometry and energy barrier for diffusion. The predictions for jump rates in our model are in excellent agreement with measured values and show a marked improvement over transition state theory (TST). We find that the jump rate prefactor is reduced by an order of magnitude from the TST estimate due to frictional damping resulting from energy exchange with surface phonons, as well as a rotational mode of the diffusing molecule.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

ASYMMETRIC DIFFUSION OF MAGNETIC FIELD LINES

Stochasticity of magnetic field lines is important for particle transport properties. Magnetic field lines separate faster than diffusively in turbulent plasma, which is called superdiffusion. We discovered that this superdiffusion is pronouncedly asymmetric, so that the separation of field lines along the magnetic field direction is different from the separation in the opposite direction. While the symmetry of the flow is broken by the so-called imbalance or cross-helicity, the difference between forward and backward diffusion is not directly due to imbalance, but a non-trivial consequence of both imbalance and non-reversibility of turbulence. The asymmetric diffusion perpendicular to the mean magnetic field entails a variety of new physical phenomena, such as the production of parallel particle streaming in the presence of perpendicular particle gradients. Such streaming and associated instabilities could be significant for particle transport in laboratory, space, and astrophysical plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

The Interplay of Magnetically Dominated Turbulence and Magnetic Reconnection in Producing Nonthermal Particles

Magnetized turbulence and magnetic reconnection are often invoked to explain the nonthermal emission observed from a wide variety of astrophysical sources. By means of fully kinetic 2D and 3D particle-in-cell simulations, we investigate the interplay between turbulence and reconnection in generating nonthermal particles in magnetically dominated (or, equivalently, “relativistic”) pair plasmas. A generic by-product of the turbulence evolution is the generation of a nonthermal particle spectrum with a power-law energy range. The power-law slope p is harder for larger magnetizations and stronger turbulence fluctuations, and it can be as hard as p ≲ 2. The Larmor radius of particles at the high-energy cutoff is comparable to the size l of the largest turbulent eddies. Plasmoid-mediated reconnection, which self-consistently occurs in the turbulent plasma, controls the physics of particle injection. Then, particles are further accelerated by stochastic scattering off turbulent fluctuations. The work done by parallel electric fields—naturally expected in reconnection layers—is responsible for most of the initial energy increase and is proportional to the magnetization σ of the system, while the subsequent energy gain, which dominates the overall energization of high-energy particles, is powered by the perpendicular electric fields of turbulent fluctuations. The two-stage acceleration process leaves an imprint in the particle pitch-angle distribution: lowenergy particles are aligned with the field, while the highest-energy particles move preferentially orthogonal to it. The energy diffusion coefficient of stochastic acceleration scales as Dγ ~ 0.1σ( c/l ) γ 2 , where γ is the particle Lorentz factor. This results in fast cceleration timescales t acc ~ (3 /σ)l/c . Our findings have important implications for understanding the generation of nonthermal particles in high-energy astrophysical sources.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A Kinetic Model for Predicting Trace Gas Uptake and Reaction

A model is developed to describe trace gas uptake and reaction with applications to aerosols and microdroplets. Gas uptake by the liquid is formulated as a coupled equilibria that links gas, surface, and bulk regions of the droplet or solution. Previously, this framework was used in explicit stochastic reaction-diffusion simulations to predict the reactive uptake kinetics of ozone with droplets containing aqueous aconitic acid, maleic acid, and sodium nitrite. With the use of prior data and simulation results, a new equation for the uptake coefficient is derived, which accounts for both surface and bulk reactions. Lambert W functions are used to obtain closed form solutions to the integrated rate laws for the multiphase kinetics; similar to previous expressions that describe Michaelis-Menten enzyme kinetics. Together these equations couple interface and bulk processes over a wide range of conditions and do not require many of the limiting assumptions needed to apply resistor model formulations to explain trace gas uptake and reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Initial Stage of Nanoscale Imaging in Positive Tone Extreme UV Photoresists: The Influence of the Polymer Sequence

Photolithographic patterning using extreme ultraviolet (EUV, 92.5 eV) light is a radiolytic process that initially forms electrons, radical cations, anions, and neutral radicals in the polymeric photoresist matrix. These species may participate in the chemical reactions that define the ultimate resolution of the printed image, and their concentrations and nanometer-scale stochastic variations in their formation influence printed image quality. Proposals have been made that polymer chain uniformity may be advantageous in reducing stochastics due to spatial inhomogeneities, and this aspect of radiolysis is examined in this work. We have simulated the initial subpicosecond stages of the imaging process for a series of photoresist films that are identical in composition but vary in their polymer chain structures. We use detailed, physically accurate stochastic reaction-diffusion calculations to evaluate the influence of defined sequence and random copolymer structures on radiolytic spur formation, i.e., a cluster of species formed by electron-polymer interactions that defines the initial spatial characteristic of the imaging process. Predictions of electron thermalization in the present work are shown to be consistent with the literature, indicating that our overall computational approach for ultrafast nanoscale processes is sound. The computational results show that the polymer sequence has no significant effect on the spur composition. This suggests that any potential imaging improvements to be gained by sequence control must originate from postimaging lithographic process steps.

Absorption↗
DOE OSTI2026

The Cascade Effectiveness of 3-Terminal Tandem Photocathode Architectures as Applied to CO 2 Reduction

Cascade catalysis for photoelectrochemical CO 2 reduction (CO 2 R) decouples the overall reaction into sequential steps occurring on separately optimized catalysts (for example, Ag and Cu) between which an intermediate species such as CO is transferred. A 3-terminal tandem (3TT) photovoltaic architecture advantageously holds two different catalytic regions at different potentials under a single illumination source, but its overall efficiency is low. Using a stochastic reaction-diffusion model, we have examined 3TT photocathode design principles, focusing on the coupling of surface chemistry and transport of CO both inside the boundary layer and outward, into the bulk electrolyte. We find that ensuring that the lateral diffusion distance within the boundary layer is short compared to the boundary layer thickness and controlling bulk flow are key, with interdigitated designs showing an overall conversion efficiency improvement by 2 orders of magnitude compared to the side-by-side case without flow. These findings can be adapted for other cascaded architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗