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NASA NTRS1974

Coherent propagation of charged particle bunches in random magnetic fields

When the distribution function for energetic particles moving in interplanetary space is expressed in terms of eigenfunctions of an operator which describes pitch angle scattering by random magnetic fields, the familiar phenomenon of diffusion is the dominant solution of the transport equations provided that the spectrum of magnetic fluctuations is not too steep. The present paper describes a novel mode of particle transport when the latter condition is not satisfied (i.e., when the exponent for the spectrum of magnetic fluctuations is greater than 2). In this mode, the density inhomogeneities propagate coherently, in wavelike fashion, and with very little dispersion along the guiding field at a characteristic velocity equal to half the particle speed. The most striking manifestation of this phenomenon is the observed scatter-free propagation of solar flare electrons below 1 MeV.-

Earl, J. A.↗

NASA NTRS1976

Frequency of encounter of aircraft in a random horizontal field

Calculations were made of the frequency of encounter as a function of azimuth of encounter of a passing aircraft with the aircraft in a random planar horizontal field. All the field aircraft moved at a constant speed but in random directions. These calculations included the total frequency of encounter with the aircraft of the field and the frequency of encounter with those aircraft of the field which were encountered in the fore quadrant, in the lateral quadrants, and in the rear quadrant; the calculations were made for various speed ratios of the field aircraft and the passing aircraft.

Bird, J. D.↗

DOE OSTI2018

Random Crystal Field in a Mixed Spin S = 1/2 and S = 3/2 Ising Model by Renormalization Group Theory

In this work, we study the Ising model with mixed spins S = 1/2 and S = 3/2 on the hypercubic lattice and the random crystal field at the sublattice with S = 3/2 described by a two peaks law. To achieve this, we use an approximation of position space renormalization group (PSRG) namely Migdal-Kadanoff in which we use both the free energy derivative and the flow in the parameter space of the Hamiltonian. For all values of the random probability, the critical behavior is determined via the critical exponents at the second-order fixed points while at low temperatures; the discontinuities of the of the free energy derivative provide the positions of the first-order transitions. The introduction of a minimal amount of disorder causes a change in the phase diagram showing the relevance of disorder for d = 2 and d = 3. The second-order transition remains always with the same critical exponents as those of the pure model, and a new first-order transition appears at very low temperature. Also, a comparison with other similar works is given.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1985

Probabilistic finite elements for transient analysis in nonlinear continua

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Liu, W. K.↗

NASA NTRS1974

Pitch-angle scattering of charged particles in a random magnetic field

A calculation is presented in terms of the pitch angle that determines the conditions under which a Fokker-Planck equation gives a reasonable approximation of the pitch-angle scattering of low rigidity particles to first order in a random magnetic field. The formulation shows that the correlation scale of the fluctuation of the magnetic field about its mean does not enter directly into the approximation. The calculation is carried out for transverse magnetic fluctuations for which the magnetic field magnitude is constant to the order considered.

Jokipii, J. R.↗

DOE OSTI2021

A modular methodology for time-domain stochastic seismic wave propagation

Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.

58 GEOSCIENCES↗

DOE OSTI2022

Map-based cosmology inference with lognormal cosmic shear maps

ABSTRACT Most cosmic shear analyses to date have relied on summary statistics (e.g. ξ+ and ξ−). These types of analyses are necessarily suboptimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence field of the Universe as a lognormal random field conditioned on the observed shear data. This new map-based inference framework enables us to recover the joint posterior of the cosmological parameters and the convergence field of the Universe. Our analysis properly accounts for the covariance in the mass maps across tomographic bins, which significantly improves the fidelity of the maps relative to single-bin reconstructions. We verify that applying our inference pipeline to Gaussian random fields recovers posteriors that are in excellent agreement with their analytical counterparts. At the resolution of our maps – and to the extent that the convergence field can be described by the lognormal model – our map posteriors allow us to reconstruct all summary statistics (including non-Gaussian statistics). We forecast that a map-based inference analysis of LSST-Y10 data can improve cosmological constraints in the σ8–Ωm plane by $\approx\!{30}{{\ \rm per\ cent}}$ relative to the currently standard cosmic shear analysis. This improvement happens almost entirely along the $S_8=\sigma _8\Omega _{\rm m}^{1/2}$ directions, meaning map-based inference fails to significantly improve constraints on S8.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Study of the Vertical Magnetic Field in Face-on Galaxies Using Faraday Tomography

Faraday tomography allows astronomers to probe the distribution of the magnetic field along the line of sight (LOS), but that can be achieved only after the Faraday spectrum is interpreted. However, the interpretation is not straightforward, mainly because the Faraday spectrum is complicated due to a turbulent magnetic field; it ruins the one-to-one relation between the Faraday depth and the physical depth, and appears as many small-scale features in the Faraday spectrum. In this paper, by employing “simple toy models” for the magnetic field, we describe numerically as well as analytically the characteristic properties of the Faraday spectrum. We show that the Faraday spectrum along “multiple LOSs” can be used to extract the global properties of the magnetic field. Specifically, considering face-on spiral galaxies and modeling turbulent magnetic field as a random field with a single coherence length, we numerically calculate the Faraday spectrum along a number of LOSs and its shape-characterizing parameters, that is, the moments. When multiple LOSs cover a region of ≳(10 coherence length){sup 2}, the shape of the Faraday spectrum becomes smooth and the shape-characterizing parameters are well specified. With the Faraday spectrum constructed as a sum of Gaussian functions with different means and variances, we analytically show that the parameters are expressed in terms of the regular and turbulent components of the LOS magnetic field and the coherence length. We also consider the turbulent magnetic field modeled with a power-law spectrum, and study how the magnetic field is revealed in the Faraday spectrum. Our work suggests a way to obtain information on the magnetic field from a Faraday tomography study.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Do Epistemic Uncertainties Allow for Replacing Microstructural Experiments with Reconstruction Algorithms?

A novel problem in computational materials modeling is addressed: “Are the computational microstructure reconstruction techniques reliable enough to replace experiments?” Here, “reliable” computations are associated with producing “expected” reconstructions that are adequately close to the experimental data. The output of computational techniques can deviate from the experimental measurements because of the epistemic uncertainties in the algorithms. In this work, an analytical formulation for quantification of epistemic uncertainties in a microstructure reconstruction algorithm based on Markov random field is presented. The method is used to predict the large-scale spatial distribution of a microstructure given an experimental input measured over a small spatial domain. However, small variations are observed on the microstructural features of the synthesized samples due to the Markov random field algorithm. The proposed analytical technique aims to quantify these uncertainties and estimate their propagation to the macroscale material properties to provide a significant understanding on how reliable it is to replace the experiments with the Markov random field model to predict microstructural maps over large spatial domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Random strain induced correlations in materials with intertwined nematic and magnetic orders

Electronic nematicity is rarely observed as an isolated instability of a correlated electron system. Instead, in iron pnictides and in certain cuprates and heavy-fermion materials, nematicity is intertwined with an underlying spin-stripe or charge-stripe state. As a result, random strain, ubiquitous in any real crystal, creates both random-field disorder for the nematic degrees of freedom and random-bond disorder for the spin or charge ones. Here, we put forward an Ashkin-Teller model with random Baxter fields to capture the dual role of random strain in nematic systems for which nematicity is a composite order arising from a stripe state. Using Monte Carlo to simulate this random Baxter-field model, we find not only the expected break-up of the system into nematic domains, but also the emergence of nontrivial disorder-promoted magnetic correlations. Such correlations enhance and tie up the fluctuations associated with the two degenerate magnetic stripe states from which nematicity arises, leaving characteristic signatures in the spatial profile of the magnetic domains, in the configurational space of the spin variables, and in the magnetic noise spectrum. We discuss possible experimental manifestations of these effects in iron-pnictide superconductors. Furthermore, our work establishes the random Baxter-field model as a more complete alternative to the random-field Ising model to describe complex electronic nematic phenomena in the presence of disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2017

Transverse eV Ion Heating by Random Electric Field Fluctuations in the Plasmasphere

Charged particle acceleration in the Earth inner magnetosphere is believed to be mainly due to the local resonant wave-particle interaction or particle transport processes. However, the Van Allen Probes have recently provided interesting evidence of a relatively slow transverse heating of eV ions at distances about 2-3 Earth radii during quiet times. Waves that are able to resonantly interact with such very cold ions are generally rare in this region of space, called the plasmasphere. Thus, non-resonant wave-particle interactions are expected to play an important role in the observed ion heating. We demonstrate that stochastic heating by random transverse electric field fluctuations of whistler (and possibly electromagnetic ion cyclotron) waves could explain this weak and slow transverse heating of H+ and O+ ions in the inner magnetosphere. The essential element of the proposed model of ion heating is the presence of trains of random whistler (hiss) wave packets, with significant amplitude modulations produced by strong wave damping, rapid wave growth, or a superposition of wave packets of different frequencies, phases, and amplitudes. Such characteristics correspond to measured characteristics of hiss waves in this region. Using test particle simulations with typical wave and plasma parameters, we demonstrate that the corresponding stochastic transverse ion heating reaches 0.07-0.2 eV/h for protons and 0.007-0.015 eV/h for O+ ions. This global temperature increase of the Maxwellian ion population from an initial Ti approx. 0.3 eV could potentially explain the observations.

Artemyev, A. V.↗

DOE OSTI2021

Optimal design of acoustic metamaterial cloaks under uncertainty

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Artificial generation of representative single Li-ion electrode particle architectures from microscopy data

Accurately capturing the architecture of single lithium-ion electrode particles is necessary for understanding their performance limitations and degradation mechanisms through multi-physics modeling. Information is drawn from multimodal microscopy techniques to artificially generate LiNi 0.5 Mn 0.3 Co 0.2 O 2 particles with full sub-particle grain detail. Statistical representations of particle architectures are derived from X-ray nano-computed tomography data supporting an ‘outer shell’ model, and sub-particle grain representations are derived from focused-ion beam electron backscatter diffraction data supporting a ‘grain’ model. A random field model used to characterize and generate the outer shells, and a random tessellation model used to characterize and generate grain architectures, are combined to form a multi-scale model for the generation of virtual electrode particles with full-grain detail. This work demonstrates the possibility of generating representative single electrode particle architectures for modeling and characterization that can guide synthesis approaches of particle architectures with enhanced performance.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Optimization, Inference and Learning for Advanced Networks

This piece of software aims at providing an implementation of methods to perform efficient optimization, probabilistic inference and model selection and learning for various type of networked systems. The software contains a suite of methods and functions that: 1) perform probabilistic inference and random sampling on networked models 2) select or learn networked models from data 3) solve optimization tasks with a networked structure Network models that are supported by these features include, but are not limited to, factor graphs and Markov random fields such as Ising models, Potts models, p-spins models, Gaussian random fields and restricted Boltzmann machine.

Hijazi, Hassan↗

NASA NTRS1972

Charged-particle transport in turbulent astrophysical plasmas

The effect of electromagnetic fluctuations, or plasma turbulence, on the motion of the individual particles in a plasma is investigated. Two alternative methods are used to find a general equation governing the time-evolution of a distribution of charged particles subject to both an external force field and the random fields of the fluctuations. It is found that, for the high-temperature, low-density plasmas frequently encountered in the study of astrophysics, the presence of even a small amount of turbulence can have a very important effect on the behavior of the plasma. Two problems in which turbulence plays an important role are treated.

Newman, C. E., Jr.↗

DOE OSTI2017

Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in Pr 2 Zr 2 O 7

Inelastic neutron scattering reveals a broad continuum of excitations in Pr 2 Zr 2 O 7 , the temperature and magnetic field dependence of which indicate a continuous distribution of quenched transverse fields ( Δ ) acting on the non-Kramers Pr 3 + crystal field ground state doublets. Spin-ice correlations are apparent within 0.2 meV of the Zeeman energy. In a random phase approximation an excellent account of the data is provided and contains a transverse field distribution ρ ( Δ ) ∝ ( Δ 2 + Γ 2 ) - 1 , where Γ = 0.27 ( 1 ) meV . Established during high temperature synthesis due to an underlying structural instability, it appears disorder in Pr 2 Zr 2 O 7 actually induces a quantum spin liquid.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

End-to-end learning of multiple sequence alignments with differentiable Smith–Waterman

Abstract Motivation Multiple sequence alignments (MSAs) of homologous sequences contain information on structural and functional constraints and their evolutionary histories. Despite their importance for many downstream tasks, such as structure prediction, MSA generation is often treated as a separate pre-processing step, without any guidance from the application it will be used for. Results Here, we implement a smooth and differentiable version of the Smith–Waterman pairwise alignment algorithm that enables jointly learning an MSA and a downstream machine learning system in an end-to-end fashion. To demonstrate its utility, we introduce SMURF (Smooth Markov Unaligned Random Field), a new method that jointly learns an alignment and the parameters of a Markov Random Field for unsupervised contact prediction. We find that SMURF learns MSAs that mildly improve contact prediction on a diverse set of protein and RNA families. As a proof of concept, we demonstrate that by connecting our differentiable alignment module to AlphaFold2 and maximizing predicted confidence, we can learn MSAs that improve structure predictions over the initial MSAs. Interestingly, the alignments that improve AlphaFold predictions are self-inconsistent and can be viewed as adversarial. This work highlights the potential of differentiable dynamic programming to improve neural network pipelines that rely on an alignment and the potential dangers of optimizing predictions of protein sequences with methods that are not fully understood. Availability and implementation Our code and examples are available at: https://github.com/spetti/SMURF. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Summability of Connected Correlation Functions of Coupled Lattice Fields

We consider two nonindependent random fields ψ and ϕ defined on a countable set Z. For instance, Z=ℤ{sup d} or Z=ℤ{sup d}×I, where I denotes a finite set of possible “internal degrees of freedom” such as spin. We prove that, if the cumulants of ψ and ϕ enjoy a certain decay property, then all joint cumulants between ψ and ϕ are ℓ{sub 2}-summable in the precise sense described in the text. The decay assumption for the cumulants of ψ and ϕ is a restricted ℓ{sub 1} summability condition called ℓ{sub 1}-clustering property. One immediate application of the results is given by a stochastic process ψ{sub t}(x) whose state is ℓ{sub 1}-clustering at any time t: then the above estimates can be applied with ψ=ψ{sub t} and ϕ=ψ{sub 0} and we obtain uniform in t estimates for the summability of time-correlations of the field. The above clustering assumption is obviously satisfied by any ℓ{sub 1}-clustering stationary state of the process, and our original motivation for the control of the summability of time-correlations comes from a quest for a rigorous control of the Green–Kubo correlation function in such a system. A key role in the proof is played by the properties of non-Gaussian Wick polynomials and their connection to cumulants.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗