A framework for discrete stochastic simulation on 3D moving boundary domains
Not Available
59 BASIC BIOLOGICAL SCIENCES↗
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.
THE RELATIVE ABUNDANCE OF ISOLATED CLUSTERS AS A PROBE OF DARK ENERGY
Those galaxy clusters that do not belong to superclusters are referred to as isolated clusters. Their relative abundance at a given epoch may be a powerful constraint of the dark energy equation of state since it depends strongly on how fast the structures grow on the largest scale in the universe. We note that the mass function of isolated clusters can be separately evaluated through modification of the recently developed Corasaniti-Achitouv (CA) theory according to which the stochastic collapse barrier is quantified by two coefficients: the drifting average coefficient ({beta}) and the diffusion coefficient (D{sub B} ). Regarding {beta} in the CA formalism as an adjustable parameter and assuming that the formation of isolated clusters corresponds to the case of D{sub B} = 0, we determine the mass function of isolated clusters by fitting the numerical results from the MICE simulations to the modified CA formula. It is found that the best-fit value of {beta} changes with redshift and that the CA mass function with D{sub B} = 0 agrees very well with the numerical results at various redshifts. Defining the relative abundance of isolated clusters, {xi}{sub I}, as the ratio of the cumulative mass function of isolated clusters to that of non-isolated clusters at a given epoch, we finally show how sensitively {xi}{sub I} changes with the dark energy equation of state. It is also discussed how {xi}{sub I} can help break the degeneracy between the dark energy equation of state and the other key cosmological parameters.
79 ASTRONOMY AND ASTROPHYSICS↗
On the spin-axis dynamics of a Moonless Earth
The variation of a planet's obliquity is influenced by the existence of satellites with a high mass ratio. For instance, Earth's obliquity is stabilized by the Moon and would undergo chaotic variations in the Moon's absence. In turn, such variations can lead to large-scale changes in the atmospheric circulation, rendering spin-axis dynamics a central issue for understanding climate. The relevant quantity for dynamically forced climate change is the rate of chaotic diffusion. Accordingly, here we re-examine the spin-axis evolution of a Moonless Earth within the context of a simplified perturbative framework. We present analytical estimates of the characteristic Lyapunov coefficient as well as the chaotic diffusion rate and demonstrate that even in absence of the Moon, the stochastic change in Earth's obliquity is sufficiently slow to not preclude long-term habitability. Our calculations are consistent with published numerical experiments and illustrate the putative system's underlying dynamical structure in a simple and intuitive manner.
79 ASTRONOMY AND ASTROPHYSICS↗
A spectral analysis of the domain decomposed Monte Carlo method for linear systems
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)
97 MATHEMATICS AND COMPUTING↗
Kinetic Monte Carlo simulation of dopant-defect systems under submicrosecond laser thermal processes
An innovative Kinetic Monte Carlo (KMC) code has been developed, which rules the post-implant kinetics of the defects system in the extremely far-from-the equilibrium conditions caused by the laser irradiation close to the liquid-solid interface. It considers defect diffusion, annihilation and clustering. The code properly implements, consistently to the stochastic formalism, the fast varying local event rates related to the thermal field T(r,t) evolution. This feature of our numerical method represents an important advancement with respect to current state of the art KMC codes. The reduction of the implantation damage and its reorganization in defect aggregates are studied as a function of the process conditions. Phosphorus activation efficiency, experimentally determined in similar conditions, has been related to the emerging damage scenario.
36 MATERIALS SCIENCE↗
Entropy-based closure for probabilistic learning on manifolds
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Itˆo stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter ". Currently, " is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of ", based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases.
97 MATHEMATICS AND COMPUTING↗
Communication: Memory effects and active Brownian diffusion
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer’s diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer’s propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer’s axis. The corresponding swimmer’s diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
TIME-DEPENDENT ELECTRON ACCELERATION IN BLAZAR TRANSIENTS: X-RAY TIME LAGS AND SPECTRAL FORMATION
Electromagnetic radiation from blazar jets often displays strong variability, extending from radio to γ -ray frequencies. In a few cases, this variability has been characterized using Fourier time lags, such as those detected in the X-rays from Mrk 421 using Beppo SAX. The lack of a theoretical framework to interpret the data has motivated us to develop a new model for the formation of the X-ray spectrum and the time lags in blazar jets based on a transport equation including terms describing stochastic Fermi acceleration, synchrotron losses, shock acceleration, adiabatic expansion, and spatial diffusion. We derive the exact solution for the Fourier transform of the electron distribution and use it to compute the Fourier transform of the synchrotron radiation spectrum and the associated X-ray time lags. The same theoretical framework is also used to compute the peak flare X-ray spectrum, assuming that a steady-state electron distribution is achieved during the peak of the flare. The model parameters are constrained by comparing the theoretical predictions with the observational data for Mrk 421. The resulting integrated model yields, for the first time, a complete first-principles physical explanation for both the formation of the observed time lags and the shape of the peak flare X-ray spectrum. It also yields direct estimates of the strength of the shock and the stochastic magnetohydrodynamical wave acceleration components in the Mrk 421 jet.
79 ASTRONOMY AND ASTROPHYSICS↗
Substrate-Mediated Evaporation and Stochastic Evolution of Supported Au Nanoparticles
Here, we use in situ transmission electron microscopy with automated tracking to study supported gold nanoparticles (NPs) during high-temperature vacuum annealing. The average mass loss per NP is governed by a flat, nearly size-independent substrate-mediated evaporation profile. On top of this mean shrinkage, individual NPs show significant fluctuations in apparent growth or shrinkage, and NP volume follows a random-walk-like trajectory. To rationalize both the ensemble-mean behavior and the particle-resolved variability, we develop a self-consistent theory that couples substrate-mediated evaporation to collective 2D Ostwald-type mass exchange through a shared adatom field, described in terms of a renormalized screening length and background concentration. In the experimentally relevant regime, the theory predicts an approximately size-independent mean shrinkage rate and clarifies how net mass loss suppresses classical coarsening. Superimposed on this deterministic drift, we quantify stochastic volume trajectories and capture their fluctuation spectrum with a minimal Langevin description consistent with intermittent adatom attachment and detachment events. In addition, we characterize the lateral diffusive motion of NPs, which is responsible for their coalescence. Altogether, our results highlight that stochasticity is intrinsic at the nanoscale and that predicting the evolution of supported NPs at early and intermediate times requires a unified framework combining substrate-mediated evaporation, collective mass exchange, and stochastic fluctuations.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Thermal Shape Stability of fcc Metal Nanocrystals Synthesized with Faceted Nonequilibrium Shapes
Highly refined capabilities of the shape-controlled solution-phase synthesis of metal nanocrystals (NCs) allow the generation of NCs with faceted nonequilibrium shapes, which optimize properties for target applications such as catalysis and plasmonics. Often, for such applications and also for TEM analysis, the NCs are removed from the solution-phase environment. We explore the postsynthesis evolution of these metastable NCs in a high-vacuum TEM environment. Specifically, here we analyze their reshaping toward the equilibrium Wulff shapes mediated by surface diffusion, where such reshaping degrades the above-mentioned optimized properties. Typical sizes for these NCs range from 5 to 30 nm or 10 3 –10 6 atoms, and reshaping often occurs on the time scale of minutes for temperatures around, say, 400 °C. We discuss the development of predictive stochastic atomistic-level models for NC evolution with a realistic description of surface diffusion. These models, in contrast to Molecular Dynamics, can naturally address the relevant time and length scales for these systems. KMC simulation results for the stochastic models are described, focusing on the reshaping of slightly elongated nanorods and of mildly truncated octahedra and nanocubes. In addition, we review appropriate theoretical formulations for reshaping, which involves the nucleation and growth on 2D islands or layers on outer facets of the NC. We note the limitations of classical nucleation theory in some scenarios and demonstrate the successes of a more fundamental and general master equation-based analysis.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
MODELING FOCUSED ACCELERATION OF COSMIC-RAY PARTICLES BY STOCHASTIC METHODS
Schlickeiser and Shalchi suggested that a first-order Fermi mechanism of focused particle acceleration could be important in several astrophysical applications. In order to investigate focused acceleration, we express the Fokker-Planck equation as an equivalent system of stochastic differential equations. We simplify the system for a set of physically motivated parameters, extend the analytical theory, and determine the evolving particle distribution numerically. While our numerical results agree with the focused acceleration rate of Schlickeiser and Shalchi for a weakly anisotropic particle distribution, we establish significant limitations of the analytical approach. Momentum diffusion is found to be more significant than focused acceleration at early times. Most critically, the particle distribution rapidly becomes anisotropic, leading to a much slower momentum gain rate. We discuss the consequences of our results for the role of focused acceleration in astrophysics.
79 ASTRONOMY AND ASTROPHYSICS↗
THE IMPLICIT CONTRIBUTION OF SLAB MODES TO THE PERPENDICULAR DIFFUSION COEFFICIENT OF PARTICLES INTERACTING WITH TWO-COMPONENT TURBULENCE
We explore the transport of energetic particles in two-component turbulence in which the stochastic magnetic field is assumed to be a superposition of slab and two-dimensional modes. It is known that in magnetostatic slab turbulence, the motion of particles across the mean magnetic field is subdiffusive. If a two-dimensional component is added, diffusion is recovered. It was also shown before that in two-component turbulence, the slab modes do not explicitly contribute to the perpendicular diffusion coefficient. In the current paper, the implicit contribution of slab modes is explored and it is shown that this contribution leads to a reduction of the perpendicular diffusion coefficient. This effect improves the agreement between simulations and analytical theory. Furthermore, the obtained results are relevant for investigations of diffusive shock acceleration.
79 ASTRONOMY AND ASTROPHYSICS↗
On the use of reverse Brownian motion to accelerate hybrid simulations
Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Multiple fields in stochastic inflation
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances
Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes it very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Reshaping of Truncated Pd Nanocubes: Energetic and Kinetic Analysis Integrating Transmission Electron Microscopy with Atomistic-Level and Coarse-Grained Modeling
Stability against reshaping of metallic fcc nanocrystals synthesized with tailored far-from-equilibrium shapes is key to maintaining optimal properties for applications such as catalysis. Yet Arrhenius analysis of experimental reshaping kinetics, and appropriate theory and simulation, is lacking. As such, we use TEM to monitor the reshaping of Pd nanocubes of ~25 nm side length between 410 °C (over ~4.5 h) and 440 °C (over ~0.25 h), extracting a high effective energy barrier of E eff ≈ 4.6 eV. We also provide an analytic determination of the energy variation along the optimal pathway for reshaping that involves transfer of atoms across the nanocube surface from edges or corners to form new layers on side {100} facets. The effective barrier from this analysis is shown to increase strongly with the degree of truncation of edges and corners in the synthesized nanocube. Theory matches experiment for the appropriate degree of truncation. In addition, we perform simulations of a stochastic atomistic-level model incorporating a realistic description of diffusive hopping for undercoordinated surface atoms, thereby providing a visualization of the initial reshaping process.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Diffusive dynamics of critical fluctuations near the QCD critical point
A quantitatively reliable theoretical description of the dynamics of fluctuations in nonequilibrium is indispensable in the experimental search for the QCD critical point by means of ultrarelativistic heavy-ion collisions. Herein we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations.With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudocritical temperature.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
COSMIC-RAY DIFFUSION IN A SECTORED MAGNETIC FIELD IN THE DISTANT HELIOSHEATH
Very high intensities of galactic cosmic rays measured by Voyager 1 in the heliosheath appear to be incompatible with the presence of a modulation 'wall' near the heliopause produced by a pile up of the heliospheric magnetic field. We propose that the modulation wall is a structure permeable to cosmic rays as a result of a sectored magnetic field topology compressed by plasma slowdown on approach to the heliopause and stretched to high latitudes by latitudinal flows in the heliosheath. The tightly folded warped current sheet permits efficient cosmic-ray transport in the radial direction via a drift-like mechanism. We show that when stochastic variations in the sector widths are taken into account, particle transport becomes predominantly diffusive both along and across the magnetic sectors. Using a test-particle model for cosmic rays in the heliosheath we investigate the dependence of the diffusion coefficients on the properties of the sector structure and on particle energy.
79 ASTRONOMY AND ASTROPHYSICS↗