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At least 469 records · Page 26

Galactic cosmic-ray modulation near the heliopause

We investigate the modulation of galactic cosmic rays in the inner and outer heliosheaths using three-dimensional numerical simulations. The model is based on the Parker transport equation integrated using a stochastic phase-space trajectory method. Integration is performed on a plasma background obtained from a global three-dimensional magnetohydrodynamic simulations. Our results predict a negligible amount of modulation in the outer heliosheath because of weak scattering of cosmic ray ions owing to very low levels of magnetic fluctuation power at wavenumbers relevant to the transport of cosmic rays with MeV to GeV energies. This means that the heliopause may be treated as a Dirichlet-type boundary for the purpose of energetic particle modeling. We present models with and without drift velocity to facilitate comparison with papers published earlier. We also attempt to reproduce the sudden step-like increases of cosmic-ray intensity observed by Voyager 1 before its encounter with the heliopause. Our results indicate that very slow cross-field diffusion in the outer heliosheath could produce a large gradient of cosmic rays inside the heliospheric boundary. The resulting large gradient in cosmic-ray intensity near the heliopause qualitatively agrees with recent Voyager 1 observations.

79 ASTRONOMY AND ASTROPHYSICS↗

Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (< 50 eV). Here we have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Interpreting the Strain Tensor During Injection into a Reservoir

A suite of well tests was conducted to evaluate the feasibility of measuring and interpreting the strain tensor during injection. Water was injected at 1 liter/s for a few days to a few weeks into a well completed at a depth of 530 m in the Bartlesville sandstone in the North Avant Field in Oklahoma. The strain tensor was measured using strainmeters at a depth of 30m and a distance of 220m from the well. We used a Gladwin strainmeter, a state-of-the-art geodetic strainmeter, as well as novel borehole strainmeters developed for the project. After processing, the horizontal strains were tensile and the vertical strain was compressive during injection. The radial strain was less than the circumferential strain. Strain magnitudes increased during injection and recovered afterward. The strain rate was as fast as 100 nanostrain/d at the start of injection, and decreased to 10 nanostrain/d after a few days. The normal strain signals were approximately proportional to the log of time during the first few days of injection, and the semi-log slope was 50 to 75 nanostrain. Data from the Gladwin strainmeter were essentially identical to data from a strainmeter we developed using optical fiber sensors. Tilt was measured using two tiltmeters, but the tilts were erratic compared to the normal strain and were of limited value. Strain data were analyzed using a strain type-curve method, an analytical solution to a poroelastic inhomogeneity, and a stochastic inversion method. Poroelastic simulations explain the data well. Results from the interpretation methods are consistent with each other, and with independent information characterizing the area. The hydraulic diffusivity is approximately 0.5 m2/s and the permeability is between 100 and 500 mD, according to analysis of the strain signals. This is consistent with measurements of permeability from cores, and with analyses of pressure transients. The analyses indicate that Young’s modulus of the reservoir is between 2 and 6 GPa. Strain interpretations indicate the well intersects a permeable lens with a maximum dimension of 500 to 1,000 m. An isopach map of coarse-grained sand confirms a feature roughly 1,000 m in lateral extent. The results demonstrate that the strain signal measured at shallow (30m) depth can be used to infer properties and heterogeneities in an underlying reservoir or aquifer.

Murdoch, Larry↗

Stochastic differential equations and turbulent dispersion

Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

Durbin, P. A.↗

Stochastic acceleration of electrons in solar flares

The generation of lower-hybrid waves by cross-field currents is applied to reconnection processes proposed for solar flares. Recent observations on fragmentation of energy release and acceleration, and on hard X-ray (HXR) spectra are taken into account to develop a model for electron acceleration by resonant stochastic interactions with lower-hybrid turbulence. The continuity of the velocity distribution is solved including collisions and escape from the turbulence region. It describes acceleration as a diffusion process in velocity space. The result indicates two regimes that are determined by the energy of the accelerating electrons which may explain the double power-law often observed in HXR spectra. The model further predicts an anticorrelation between HXR flux and spectral index in agreement with observations.

Benz, A. O.↗

Stochastic reacceleration of cosmic rays in the interstellar medium

The effects of reacceleration on cosmic rays have been studied over a wide charge and energy range using a model of reacceleration by the interstellar turbulence. We take into account only inevitable stochastic reacceleration of cosmic rays by the random hydrodynamic waves, which supposedly exist in the interstellar medium and provide a means for cosmic-ray scattering and spatial diffusion in the Galaxy. Our calculations reproduce not only the B/C ratio but also the H and He data over the entire energy range where the measurements are available. However, the sub-Fe to Fe ratio is not fitted as well as the B/C ratio, and the reacceleration effect does not seem to remove the need for truncation of short path lengths, which is apparently required by the standard leaky box model. This work demonstrates that the cosmic-ray data can be represented at least as well by a reacceleration model with a simple rigidity power-law escape length, which agrees with the Kolmogorov-type spectrum of hydromagnetic turbulence, as they can by the standard leaky box model with its ad hoc escape lengths.

Seo, E. S.↗

Neutrino and cosmic-ray emission and cumulative background from radiatively inefficient accretion flows in low-luminosity active galactic nuclei

We study high-energy neutrino and cosmic-ray (CR) emission from the cores of low-luminosity active galactic nuclei (LLAGN). In LLAGN, the thermalization of particles is expected to be incomplete in radiatively inefficient accretion flows (RIAF), allowing the existence of non-thermal particles. In this work, assuming stochastic particle acceleration due to turbulence in RIAFs, we solve the Fokker–Planck equation and calculate spectra of escaping neutrinos and CRs. The RIAF in LLAGN can emit CR protons with ≳10 PeV energies and TeV–PeV neutrinos generated via pp and/or pγ reactions. We find that, if ∼1% of the accretion luminosity is carried away by non-thermal ions, the diffuse neutrino intensity from the cores of LLAGN may be as high as E{sub ν}{sup 2}Φ{sub ν}∼3×10{sup −8} GeV cm{sup −2} s{sup −1} sr{sup −1}, which can be compatible with the observed IceCube data. This result does not contradict either of the diffuse gamma-ray background observed by Fermi or observed diffuse CR flux. Our model suggests that, although very-high-energy gamma-rays may not escape, radio-quiet active galactic nuclei with RIAFs can emit GeV gamma-rays, which could be used for testing the model. We also calculate the neutron luminosity from RIAFs of LLAGN, and discuss a strong constraint on the model of jet mass loading mediated by neutrons from the diffuse neutrino observation.

79 ASTRONOMY AND ASTROPHYSICS↗

Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise

We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transport of High-energy Charged Particles through Spatially Intermittent Turbulent Magnetic Fields

Identifying the sources of the highest energy cosmic rays requires understanding how they are deflected by the stochastic, spatially intermittent intergalactic magnetic field. Here we report measurements of energetic charged-particle propagation through a laser-produced magnetized plasma with these properties. We characterize the diffusive transport of the particles experimentally. The results show that the transport is diffusive and that, for the regime of interest for the highest-energy cosmic rays, the diffusion coefficient is unaffected by the spatial intermittency of the magnetic field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics.

autonomous↗

A hybrid approach to the neutron transport K-eigenvalue problem using NDA-based algorithms

In order to provide more physically accurate solutions to the neutron transport equation it has become increasingly popular to use Monte Carlo simulation to model nuclear reactor dynamics. These Monte Carlo methods can be extremely expensive, so we turn to a class of methods known as hybrid methods, which combine known deterministic and stochastic techniques to solve the transport equation. In our work, we show that we can simulate the action of a transport sweep using a Monte Carlo simulation in order to solve the k-eigenvalue problem. We'll accelerate the solution using nonlinear diffusion acceleration (NDA) as in [1,2]. Our work extends the results in [1] to use Monte Carlo simulation as the high-order solver. (authors)

97 MATHEMATICS AND COMPUTING↗

A theoretical review of diffusive shock acceleration

We discuss the fundamental ideas of particle acceleration in plasma shocks with emphasis on those features that are required to produce the 'universal' power-law spectrum. We compare shock acceleration with the more familiar second-order or stochastic acceleration and see that they are not too different in many respects. We discuss the features of shock acceleration that make it appealing and some of its problems as well.

Jones, Frank C.↗

A comparison of two- and three-dimensional neutrino-hydrodynamics simulations of core-collapse supernovae

We present numerical results on two- (2D) and three-dimensional (3D) hydrodynamic core-collapse simulations of an 11.2 M {sub ☉} star. By changing numerical resolutions and seed perturbations systematically, we study how the postbounce dynamics are different in 2D and 3D. The calculations were performed with an energy-dependent treatment of the neutrino transport based on the isotropic diffusion source approximation scheme, which we have updated to achieve a very high computational efficiency. All of the computed models in this work, including nine 3D models and fifteen 2D models, exhibit the revival of the stalled bounce shock, leading to the possibility of explosion. All of them are driven by the neutrino-heating mechanism, which is fostered by neutrino-driven convection and the standing-accretion-shock instability. Reflecting the stochastic nature of multi-dimensional (multi-D) neutrino-driven explosions, the blast morphology changes from model to model. However, we find that the final fate of the multi-D models, whether an explosion is obtained or not, is little affected by the explosion stochasticity. In agreement with some previous studies, higher numerical resolutions lead to slower onset of the shock revival in both 2D and 3D. Based on the self-consistent supernova models leading to the possibility of explosions, our results systematically show that the revived shock expands more energetically in 2D than in 3D.

79 ASTRONOMY AND ASTROPHYSICS↗

Geomechanics-Based Stochastic Analysis of Injection- Induced Seismicity

The production of geothermal energy from dry and low permeability reservoirs is achieved by water circulation in natural and/or man-made fractures, and is referred to as enhanced or engineered geothermal systems (EGS). Often, the permeable zones have to be created by stimulation, a process which involves fracture initiation and/or activation of discontinuities such as faults and joints due to pore pressure and the in-situ stress perturbations. The stimulation of a rock mass is often accompanied by multiple microseismic events. Micro-seismic events associated with rock failure in shear, and shear slip on new or pre-existing fracture planes and possibly their propagations. The microseismic signals contain information about the sources of energy that can be used for understanding the hydraulic fracturing process and the created reservoir properties. Detection and interpretation of microseismic events is useful for estimating the stimulated zone, created reservoir permeability and fracture growth, and geometry of the geological structures and the in-situ stress state. The process commonly is referred to as seismicity-based reservoir characterization (SBRC). Although, progress has been made by scientific & geothermal communities for quantitative and qualitative analysis of reservoir stimulation using SBRC several key questions remain unresolved in the analysis of micro-seismicity namely, variation of seismic activity with injection rate, delayed micro-seismicity, and the relation of stimulated zone to the injected volume and its rate, and the resulting reservoir permeability. In addition, the current approach to SBRC does not consider the full range of relevant poroelastic and thermoelastic phenomena and neglects the uncertainty in rock properties and in-situ stress in the data inversion process. The objective of this research and technology developments was to develop a 3D SBRC model that addresses these shortcomings by taking into account hydro-thermo-poro-mechanical mechanisms associated with injection and utilizing a state-of-the-art stochastic inversion procedure. The approach proposed herein is innovative and significantly improves the existing SBCR technology (e.g., Shapiro et al. 2003) for geothermal reservoirs in several ways. First, the current scope of the SBRC is limited with respect to the physical processes considered and the rock properties used. Usually, the geomechanics analyses within SBRC is limited to the pore pressure diffusion in the rock mass, which is modeled using a time-dependent parabolic equation and solved using a finite element algorithm with either a line or a point source. However, water injection induces both poroelastic and thermoelastic stresses in the rock mass which affect the stress state. In fact, it has been suggested that thermoelastic stresses can play a dominant role in reservoir seismicity (Ghassemi et al., 2007). We include these important effects by using a fully-coupled poro-thermoelastic constitutive equations for the rock mass which will be solved using a 3D finite element model with more realistic injection geometries such as multiple injection/extraction sources (and in fractures), uncertainty in the material parameters and the in-situ stress distribution to better reflect the pore pressure and stress distributions. In addition, we developed a 3D stochastic fracture network model to study MEQ generation in fracture rocks. The model was verified using laboratory experiments, and calibrated and applied to Newberry EGS stimulation. In previous SBRC approaches, the triggering of micro-seismicity is modeled base on the assumption that the prior stochastic criticality model of the rock mass is a valid and adequate description. However, this assumption often does not hold in the field. Thus, we improved upon the current SBRC approach by using the micro-seismic responses to estimate the hydraulic diffusivity as well as the criticality distribution itself within the field. In this way, instead of relying on our a priori knowledge of criticality distribution, we combine an initial probabilistic description of criticality with the information contained in microseismic measurements to arrive at criticality solutions that are conditioned on both field data and our prior knowledge. Previous SBRC have relied upon a deterministic inversion approach to estimate the permeability, and the extent of the stimulated zone, whereas a stochastic inversion algorithm that recognizes and quantifies the uncertainties in the prior model, the time evolution of pore pressure distributions (modeling errors), and the observed seismic events is developed and used herein to realistically assess the quality of the solution. Finally, we developed a technique for processing discrete MEQ data to estimate fracture network properties such as dip and dip directions. The approach was successfully applied to the Fenton Hill HRD experiment and the Newberry EGS with results in good agreement with field observations.

15 GEOTHERMAL ENERGY↗

Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation

Here, we present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

97 MATHEMATICS AND COMPUTING↗

PARTICLE ACCELERATION AND HEATING BY TURBULENT RECONNECTION

Turbulent flows in the solar wind, large-scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains “turbulent reconnection.” We constructed a 2D grid on which a number of randomly chosen grid points are acting as scatterers (i.e., magnetic clouds or current sheets). Our goal is to examine how test particles respond inside this large-scale collection of scatterers. We study the energy gain of individual particles, the evolution of their energy distribution, and their escape time distribution. We have developed a new method to estimate the transport coefficients from the dynamics of the interaction of the particles with the scatterers. Replacing the “magnetic clouds” with current sheets, we have proven that the energization processes can be more efficient depending on the strength of the effective electric fields inside the current sheets and their statistical properties. Using the estimated transport coefficients and solving the Fokker–Planck (FP) equation, we can recover the energy distribution of the particles only for the stochastic Fermi process. We have shown that the evolution of the particles inside a turbulent reconnecting volume is not a solution of the FP equation, since the interaction of the particles with the current sheets is “anomalous,” in contrast to the case of the second-order Fermi process.

79 ASTRONOMY AND ASTROPHYSICS↗

DYNAMICAL FIELD LINE CONNECTIVITY IN MAGNETIC TURBULENCE

Point-to-point magnetic connectivity has a stochastic character whenever magnetic fluctuations cause a field line random walk, but this can also change due to dynamical activity. Comparing the instantaneous magnetic connectivity from the same point at two different times, we provide a nonperturbative analytic theory for the ensemble average perpendicular displacement of the magnetic field line, given the power spectrum of magnetic fluctuations. For simplicity, the theory is developed in the context of transverse turbulence, and is numerically evaluated for the noisy reduced MHD model. Our formalism accounts for the dynamical decorrelation of magnetic fluctuations due to wave propagation, local nonlinear distortion, random sweeping, and convection by a bulk wind flow relative to the observer. The diffusion coefficient D{sub X} of the time-differenced displacement becomes twice the usual field line diffusion coefficient D{sub x} at large time displacement t or large distance z along the mean field (corresponding to a pair of uncorrelated random walks), though for a low Kubo number (in the quasilinear regime) it can oscillate at intermediate values of t and z. At high Kubo number the dynamical decorrelation decays mainly from the nonlinear term and D{sub X} tends monotonically toward 2D{sub x} with increasing t and z. The formalism and results presented here are relevant to a variety of astrophysical processes, such as electron transport and heating patterns in coronal loops and the solar transition region, changing magnetic connection to particle sources near the Sun or at a planetary bow shock, and thickening of coronal hole boundaries.

79 ASTRONOMY AND ASTROPHYSICS↗