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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2021

Odd Diffusivity of Chiral Random Motion

Diffusive transport is characterized by a diffusivity tensor which may, in general, contain both a symmetric and an antisymmetric component. Although the latter is often neglected, we derive Green-Kubo relations showing it to be a general characteristic of random motion breaking time-reversal and parity symmetries, as encountered in chiral active matter. In analogy with the odd viscosity appearing in chiral active fluids, we term this component the odd diffusivity. Furthermore, we show how odd diffusivity emerges in a chiral random walk model, and demonstrate the applicability of the Green-Kubo relations through molecular dynamics simulations of a passive tracer particle diffusing in a chiral active bath.

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

Theory of x-ray photon correlation spectroscopy for multiscale flows

Complex multiscale flows associated with instabilities and turbulence are commonly induced under high-energy density (HED) conditions, but accurate measurement of their transport properties has been challenging. X-ray photon correlation spectroscopy (XPCS) with coherent x-ray sources can, in principle, probe material dynamics to infer transport properties using time autocorrelation of density fluctuations. Here we develop a theoretical framework for utilizing XPCS to study material diffusivity in multiscale flows. We extend single-scale shear flow theories to broadband flows using a multiscale analysis that captures shear and diffusion dynamics. Our theory is validated with simulated XPCS for Brownian particles advected in multiscale flows. We demonstrate the versatility of the method over several orders of magnitude in timescale using sequential-pulse XPCS, single-pulse x-ray speckle visibility spectroscopy (XSVS), and double-pulse XSVS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

FORSE+: Simulating non-Gaussian CMB foregrounds at 3 arcmin in a stochastic way based on a generative adversarial network

We present FORSE+, a Python package that produces non-Gaussian diffuse Galactic thermal dust emission maps at arcminute angular scales and that has the capacity to generate random realizations of small scales. This represents an extension of the FORSE (Foreground Scale Extender) package, which was recently proposed to simulate non-Gaussian small scales of thermal dust emission using generative adversarial networks (GANs). With the input of the large-scale polarization maps from observations, FORSE+ has been trained to produce realistic polarized small scales at 3′ following the statistical properties, mainly the non-Gaussianity, of observed intensity small scales, which are evaluated through Minkowski functionals. Furthermore, by adding different realizations of random components to the large-scale foregrounds, we show that FORSE+ is able to generate small scales in a stochastic way. In both cases, the output small scales have a similar level of non-Gaussianity compared with real observations and correct amplitude scaling as a power law. These realistic new maps will be useful, in the future, to understand the impact of non-Gaussian foregrounds on the measurements of the cosmic microwave background (CMB) signal, particularly on the lensing reconstruction, de-lensing, and the detection of cosmological gravitational waves in CMB polarizationB-modes.

Astronomy & Astrophysics↗
DOE OSTI2026

Noise-canceling quantum feedback: Non-Hermitian dynamics with applications to state preparation and magic state distillation

Time-continuous quantum measurement allows for the tracking of a quantum system in real time via sequences of short, and individually weak, measurement intervals. Such measurements are necessarily invasive, imparting backaction to the system, and allowing the observer to update their state estimate based on stochastic measurement outcomes. Feedback control then involves real-time interventions by an observer, conditioned on the time-continuous measurement signal that they receive. Here, we consider here diffusive quantum trajectories and focus on the “noise-canceling” subset of feedback protocols that aim to minimize the degree of stochasticity in the dynamics. We derive such a class of feedback operations, showing that under the idealized assumptions of pure states, unit measurement efficiency, and zero time delay in implementing feedback operations, perfectly noise-canceling feedback always exists. We consider the resulting noise-canceled dynamics generated by an effective non-Hermitian Hamiltonian; while non-Hermitian Hamiltonians from continuous monitoring generally describe rare dynamics (accessible by costly postselection), the use of noise-canceling feedback here leads to non-Hermitian dynamics that occur deterministically. We demonstrate this via examples of entangled state preparation and stabilization. We then illustrate the potential for the application of noise cancellation to boost success rates in magic state distillation protocols. We show that adding feedback based on noise cancellation into a time-continuous five-to-one distillation protocol leads to higher probabilities of successful distillation across a range of input errors and increases the threshold on input errors for which the protocol is effective. Our results highlight the efficacy of noise-canceling feedback-aided protocols for quantum state preparation and stabilization tasks.

Karmakar, Tathagata [University of California, Ber↗
DOE OSTI2024

Quasi-mode evolution in a stochastic magnetic field

Abstract We present a multi-scale model of quasi-mode evolution in a stochastic magnetic field. The similarity between a quasi-mode and a ballooning mode enables us to address the challenges arising from the disparate geometries in the theories of ballooning modes in the presence of resonant magnetic perturbations. We obtain useful insights into our understanding of ballooning mode dynamics in a stochastic background. To maintain quasi-neutrality at all scales, the beat between the quasi-mode and the stochastic magnetic field drives microturbulence, which drives the turbulent background that promotes mixing and damps the quasi-mode. As a result of the broad mode structure of the quasi-mode, the turbulent viscosity and the turbulent diffusivity produced by the microturbulence are larger than those in our related study on resistive interchange modes. The stochastic magnetic field can also enhance the effective plasma inertia and reduce the effective drive, thereby slowing the mode growth. A nontrivial correlation between the microturbulence and the magnetic perturbations is shown to develop. This could account for the reduction in the Jensen–Shannon complexity of pedestal turbulence in the Resonant Magnetic Perturbation Edge-Localized Mode suppression phase observed in recent experiments. Directions for future experimental and theoretical studies are suggested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Real-time calibration of a feedback trap

Feedback traps use closed-loop control to trap or manipulate small particles and molecules in solution. They have been applied to the measurement of physical and chemical properties of particles and to explore fundamental questions in the non-equilibrium statistical mechanics of small systems. These applications have been hampered by drifts in the electric forces used to manipulate the particles. Although the drifts are small for measurements on the order of seconds, they dominate on time scales of minutes or slower. Here, we show that a recursive maximum likelihood (RML) algorithm can allow real-time measurement and control of electric and stochastic forces over time scales of hours. Simulations show that the RML algorithm recovers known parameters accurately. Experimental estimates of diffusion coefficients are also consistent with expected physical properties.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Modeling of the Flows of Admixtures in a Random Layered Strip with Probable Arrangement of Inclusions Near the Boundaries of the Body

We study the random flow of admixtures in a two-phase stochastically inhomogeneous strip with the most probable arrangement of inclusions in the vicinity of the surfaces of the body. A mathematical model is formulated for the function of diffusion flow with nonzero constant initial concentration. A random diffusion flow is represented in the form of a Neumann series. The procedure of averaging of the random mass flow over the ensemble of phase configurations with arcsine distribution function is performed. The influence of the characteristics of the medium on the distribution of mass flow is analyzed. It is shown that if the diffusion coefficient of admixtures in the inclusion is higher than for the matrix, then the increase in the characteristic thickness of the layers causes a decrease in the value of the diffusion flow, whereas the mass flow in the entire body increases with the volume fraction of the inclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Tempered fractional calculus

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A NUMERICAL STUDY OF DIFFUSIVE COSMIC-RAY TRANSPORT WITH ADIABATIC FOCUSING

Focused particle transport in a nonuniform large-scale magnetic field is investigated numerically in the case of isotropic pitch-angle scattering. Evolving particle density profiles and distribution moments are computed from solutions of a system of stochastic differential equations, equivalent to the original Fokker-Planck equation for the particle distribution. Conflicting analytical predictions for the transport coefficients in the diffusion limit, independently calculated by Beeck and Wibberenz and Shalchi, are compared with the numerical results. The reasons for the discrepancies among the analytical and numerical treatments, as well as the general limitations of the diffusion model, are discussed. The telegraph equation, derived in a higher-order expansion of the particle distribution function, is shown to describe the particle transport much more accurately than the diffusion model, especially ahead of a moving density pulse.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Stranski-Krastanow islanding initiated on the stochastic rough surfaces of the epitaxially strained thin films

Quantum dots (QD) have discrete energy spectrum, which can be adjusted over a wide range by tuning composition, density, size, lattice strain, and morphology. These features make quantum dots attractive for the design and fabrication of novel electronic, magnetic and photonic devices and other functional materials used in cutting-edge applications. The formation of QD on epitaxially strained thin film surfaces, known as Stranski-Krastanow (SK) islands, has attracted great attention due to their unique electronic properties. Here, we present a systematic dynamical simulation study for the spontaneous evolution of the SK islands on the stochastically rough surfaces (nucleationless growth). During the development of SK islands through the mass accumulation at randomly selected regions of the film via surface drift-diffusion (induced by the capillary and mismatch stresses) with and/or without growth, one also observes the formation of an extremely thin wetting layer having a thickness of a few Angstroms. Above a certain threshold level of the mismatch strain and/or the size of the patch, the formation of multiple islands separated by shallow wetting layers is also observed as metastable states such as doublets even multiplets. These islands are converted into a distinct SK islands after long annealing times by coalescence through the long range surface diffusion. Extensive computer simulation studies demonstrated that after an initial transient regime, there is a strong quadratic relationship between the height of the SK singlet and the intensity of the lattice mismatch strain (in a wide range of stresses up to 8.5 GPa for germanium thin crystalline films), with the exception at those critical points where the morphological (shape change with necking) transition takes place.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

A NUMERICAL SIMULATION OF COSMIC RAY MODULATION NEAR THE HELIOPAUSE. II. SOME PHYSICAL INSIGHTS

Cosmic ray (CR) transport near the heliopause (HP) is studied using a hybrid transport model, with the parameters constrained by observations from the Voyager 1 spacecraft. We simulate the CR radial flux along different directions in the heliosphere. There is no well-defined thin layer between the solar wind region and the interstellar region along the tail and polar directions of the heliosphere. By analyzing the radial flux curve along the direction of Voyager 2 , together with its trajectory information, the crossing time of the HP by Voyager 2 is predicted to be in 2017.14. We simulate the CR radial flux for different energy values along the direction of Voyager 1 . We find that there is only a modest modulation region of about 10 au wide beyond the HP, so that Voyager 1 observing the Local Interstellar Spectra is justified in numerical modeling. We analyze the heliospheric exit information of pseudo-particles in our stochastic numerical (time-backward) method, conjecturing that they represent the behavior of CR particles, and we find that pseudo-particles that have been traced from the nose region exit in the tail region. This implies that many CR particles diffuse directly from the heliospheric tail region to the nose region near the HP. In addition, when pseudo-particles were traced from the Local Interstellar Medium (LISM), it is found that their exit location (entrance for real particles) from the simulation domain is along the prescribed Interstellar Magnetic Field direction. This indicates that parallel diffusion dominates CR particle transport in the LISM.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greater efficiency than fully-resolved classical models. In this review article, we first provide a broad overview of fractional-order derivatives with a clear emphasis on the stochastic processes that underlie their use. We then survey three exemplary application areas – subsurface transport, turbulence, and anomalous materials – in which fractional-order differential equations provide accurate and predictive models. For each area, we report on the evidence of anomalous behavior that justifies the use of fractional-order models, and survey both foundational models as well as more expressive state-of-the-art models. We also propose avenues for future research, including more advanced and physically sound models, as well as tools for calibration and discovery of fractional-order models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integration of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Simulating the mechanisms of serrated flow in interstitial alloys with atomic resolution over diffusive timescales

Abstract The Portevin-Le Chatelier (PLC) effect is a phenomenon by which plastic slip in metallic materials becomes unstable, resulting in jerky flow and the onset of inhomogeneous deformation. The PLC effect is thought to be fundamentally caused by the dynamic interplay between dislocations and solute atoms. However, this interplay is almost always inaccessible experimentally due to the extremely fine length and time scales over which it occurs. In this paper, simulations of jerky flow in W-O interstitial solid solutions reveal three dynamic regimes emerging from the simulated strain rate-temperature space: one resembling standard solid solution strengthening, another one mimicking solute cloud formation, and a third one where dislocation/solute coevolution leads to jerky flow as a precursor of dynamic strain aging. The simulations are carried out in a stochastic framework that naturally captures rare events in a rigorous manner, providing atomistic resolution over diffusive time scales using no adjustable parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2025

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗
DOE OSTI2015

Energy in density gradient

Inhomogeneous plasmas and fluids contain energy stored in inhomogeneity and they naturally tend to relax into lower energy states by developing instabilities or by diffusion. But the actual amount of energy in such inhomogeneities has remained unknown. In the present work, the amount of energy stored in a density gradient is calculated for several specific density profiles in a cylindrical configuration. This is of practical importance for drift wave instability in various plasmas, and, in particular, in its application in models dealing with the heating of solar corona because the instability is accompanied with stochastic heating, so the energy contained in inhomogeneity is effectively transformed into heat. It is shown that even for a rather moderate increase of the density at the axis in magnetic structures in the corona by a factor 1.5 or 3, the amount of excess energy per unit volume stored in such a density gradient becomes several orders of magnitude greater than the amount of total energy losses per unit volume (per second) in quiet regions in the corona. Consequently, within the life-time of a magnetic structure such energy losses can easily be compensated by the stochastic drift wave heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Spatial dependence of the growth of polycyclic aromatic compounds in an ethylene counterflow flame

The complex environments that characterize combustion systems can influence the distribution of gas-phase species, the relative importance of various growth mechanisms and the chemical and physical characteristics of the soot precursors generated. In order to provide molecular insights on the effect of combustion environments on the formation of gas-phase species, in this paper, we study the temporal and spatial dependence of soot precursors growth mechanisms in an ethylene/oxygen/argon counterflow diffusion flame. As computational tools of investigation, we included fluid dynamics simulations and stochastic discrete modeling. Results show the relative importance of various reaction pathways in flame, with the hydrogen-abstraction-acetylene-addition mechanism contributing to the formation of pure hydrocarbons near the stagnation plane, and oxygen chemistry prevailing near the maximum temperature region, where the concentration of atomic oxygen reaches its peak and phenols, ethers and furan-embedded species are formed. The computational results show excellent agreement with measurements obtained using aerosol mass spectrometry coupled with vacuum-ultraviolet photoionization. Knowledge acquired in this study can be used to predict the type of compounds formed in various locations of the flame and eventually provide insights on the environmental parameters that influence the growth of soot precursors. In addition, the results reported in this paper highlight the importance of modeling counterflow flames in two or three dimensions to capture the spatial dependence of growth mechanisms of soot precursors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗