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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. - Graphical abstract:.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction–diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction–diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth. - Highlights: • A hybrid method for stochastic multi-scale models of cells populations that extends existing hybrid methods for reaction–diffusion system. • Our analysis unveils non-trivial macroscopic effects triggered by noise at the level of structuring variables. • Our hybrid method hugely speeds up age-structured SSA simulations while preserving stochastic effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

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

Confinement and diffusion modulate bistability and stochastic switching in a reaction network with positive feedback

Positive feedback is a common feature in signal transduction networks and can lead to phenomena such as bistability and signal propagation by domain growth. Physical features of the cellular environment, such as spatial confinement and the mobility of proteins, play important but inadequately understood roles in shaping the behavior of signaling networks. Here, we use stochastic, spatially resolved kinetic Monte Carlo simulations to explore a positive feedback network as a function of system size, system shape, and mobility of molecules. We show that these physical properties can markedly alter characteristics of bistability and stochastic switching when compared with well-mixed simulations. Notably, systems of equal volume but different shapes can exhibit qualitatively different behaviors under otherwise identical conditions. We show that stochastic switching to a state maintained by positive feedback occurs by cluster formation and growth. Additionally, the frequency at which switching occurs depends nontrivially on the diffusion coefficient, which can promote or suppress switching relative to the well-mixed limit. Taken together, the results provide a framework for understanding how confinement and protein mobility influence emergent features of the positive feedback network by modulating molecular concentrations, diffusion-influenced rate parameters, and spatiotemporal correlations between molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Can stochastic, dissipative wave fields be treated as random walk generators

A suggestion by Meek et al. (1985) that the gravity wave field be viewed as stochastic, with significant nonlinearities, is applied to calculate diffusivities. The purpose here is to calculate the diffusivity for stochastic wave model and compare it with previous diffusivity estimates. The researchers do this for an idealized case in which the wind velocity changes but slowly, and for which saturation is the principal mechanism by which wave energy is lost. A related calculation was given in a very brief way (Weinstock, 1976), but the approximations were not fully justified, nor were the physical pre-suppositions clearly explained. The observations of Meek et al. (1985) have clarified the pre-suppositions for the researchers and provided a rationalization and improvement of the approximations employed.

Weinstock, J.↗
DOE OSTI2016

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

SOLAR INTERACTING PROTONS VERSUS INTERPLANETARY PROTONS IN THE CORE PLUS HALO MODEL OF DIFFUSIVE SHOCK ACCELERATION AND STOCHASTIC RE-ACCELERATION

With the first observations of solar γ-rays from the decay of pions, the relationship of protons producing ground level enhancements (GLEs) on the Earth to those of similar energies producing the γ-rays on the Sun has been debated. These two populations may be either independent and simply coincident in large flares, or they may be, in fact, the same population stemming from a single accelerating agent and jointly distributed at the Sun and also in space. Assuming the latter, we model a scenario in which particles are accelerated near the Sun in a shock wave with a fraction transported back to the solar surface to radiate, while the remainder is detected at Earth in the form of a GLE. Interplanetary ions versus ions interacting at the Sun are studied for a spherical shock wave propagating in a radial magnetic field through a highly turbulent radial ray (the acceleration core) and surrounding weakly turbulent sector in which the accelerated particles can propagate toward or away from the Sun. The model presented here accounts for both the first-order Fermi acceleration at the shock front and the second-order, stochastic re-acceleration by the turbulence enhanced behind the shock. We find that the re-acceleration is important in generating the γ-radiation and we also find that up to 10% of the particle population can find its way to the Sun as compared to particles escaping to the interplanetary space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

FuseIM: Fusing Probabilistic Traversals for Influence Maximization on Exascale Systems

Probabilistic breadth-first traversals (BPTs) are used in many network science and graph machine learning applications. In this paper, we are motivated by the application of BPTs in stochastic diffusion-based graph problems such as influence maximization. These applications heavily rely on BPTs to implement a Monte-Carlo sampling step for their approximations. Given the large sampling complexity, stochasticity of the diffusion process, and the inherent irregularity in real-world graph topologies, efficiently parallelizing these BPTs remains significantly challenging. In this paper, we present a new algorithm to fuse massive number of concurrently executing BPTs with random starts on the input graph. Our algorithm is designed to fuse BPTs by combining separate traversals into a unified frontier on distributed multi-GPU systems. To show the general applicability of the fused BPT technique, we have incorporated it into two state-of-the-art influence maximization parallel implementations (gIM and Ripples). Our experiments on up to 4K nodes of the OLCF Frontier supercomputer (32,768 GPUs and 196K CPU cores) show strong scaling behavior, and that fused BPTs can improve the performance of these implementations up to 34x (for gIM) and ~360x (for Ripples).

Neff, Reece W.↗
NASA NTRS1994

Stochastic acceleration of energetic ions in Jupiter's magnetosphere

An equation governing the combined radial diffusion and stochastic acceleration of super-Alfvenic ions by magnetohydrodynamic waves in Jupiter's outer magnetosphere is derived. The formulation is based upon a total energy invariant of the adiabatic transport which applies to an isotropic distribution undergoing rapid pitch angle scattering by waves. An analytic solution to the double diffusion equation is obtained and numerical results are presented for two models of ion injection. The first model assumes S(+) and O(+) are injected throughout a broad region of space through photoionization of Jupiter's magnetospheric neutral wind and obtain an initial energy corresponding to the local corotation energy after pickup by the planetary magnetic field. The second model assumes a monoenergetic distribution of energetic protons is implanted in the middle magnetosphere by the action of field-aligned potential drops in Jupiter's auroral ionosphere. For both light and heavy ions the injection process creates a seed population of particles which are further accelerated nonadiabatically by the MHD waves and adiabatically through radial diffusion. A comparison of the theoretical results with a recent data analysis of Voyager low-energy charged particle measurements is made with very good agreement, thus providing a rigorous quantitative account of and definitive explanation for the high-energy ion component of Jupiter's magnetosphere.

Barbosa, D. D.↗
DOE OSTI2016

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

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

Reshaping and sintering of 3D fcc metal nanoclusters: Stochastic atomistic modeling with realistic surface diffusion kinetics

Far-from-equilibrium evolution of metallic nanocluster shapes is highly sensitive to the atomistic-level details of surface diffusion for diverse local surface configurations. A stochastic model was developed incorporating realistic values for the multiple diffusion barriers (contrasting previous unrealistic generic prescriptions) based upon insights from homoepitaxial film growth. Kinetic Monte Carlo simulation then elucidates the conversion of Ag nanocubes to Wulff polyhedra mediated by nucleation of new {100} facets, the pinch-off of sufficiently elongated Ag nanorods, and key aspects of sintering for orientationally aligned Ag and Au nanoclusters. In conclusion, the time scale for sintering of Au nanoclusters observed in high-resolution transmission electron microscopy studies was also recovered.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction–diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Stochastic Analysis of Advection-Diffusion-Reaction Systems with Applications to Reactive Transport in Porous Media (Final Technical Report)

The main objective of this project is to develop new computational tools for uncertainty quantification (UQ) of systems governed by stochastic partial differential equations (SPDEs) with applications to advection-diffusion-reaction systems. We pursue two complementary approaches: (1) generalized polynomial chaos and its extensions and (2) a new theory on deriving PDF equations for systems subject to color noise. The focus of the current work is on high-dimensional systems involving tens or hundreds of uncertain parameters.

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

Hybrid finite element and Brownian dynamics method for charged particles

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures

Here, we present a numerical formulation for the solution of nonisothermal, compressible Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are that it significantly simplifies the discretization of diffusive and stochastic momentum fluxes into a more compact form, and it provides an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously by Balakrishnan et al. [Phys. Rev. E 89, 013017 (2014)1539-375510.1103/PhysRevE.89.013017]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗