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DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. Further, the calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Modeling the Charge and Exciton Distributions in Phosphorescent White Organic Light-Emitting Diodes

A comprehensive numerical model is developed to quantitatively analyze the charge and exciton distributions in phosphorescent white organic light emitting diodes (WOLEDs). The model encompasses bipolar charge drift-diffusion transport with doping-dependent charge mobilities, field-dependent charge hopping across multiple interfaces, exciton generation, diffusion, energy transfer, radiative decay, and non-radiative exciton annihilation. The model is validated by direct measurement of the exciton distribution in monochromatic phosphorescent OLEDs. It is then applied to complex, multilayer WOLEDs where it is used to accurately predict their intensity and current-dependent spectral shifts. The magnitudes of different exciton loss channels in WOLEDs are calculated and quantitatively compared. This model provides an alternative for the many experimental iterations commonly used to optimize the color balance of complex OLEDs. In this context, the model inspired the addition of a hole blocking layer in the WOLED to balance the charge conduction and reduce spectral shifts – a design that is verified by experiment.

42 ENGINEERING↗

DOE OSTI2024

Modeling transient edge plasma transport with dynamic recycling

The work presents numerical simulation studies of the role that dynamic plasma recycling on the main wall and divertor target surfaces plays in transient edge plasma transport phenomena, such as edge localized modes (ELMs). The studies are performed by coupling the edge plasma transport code UEDGE [Rognlien et al., J. Nucl. Mater. 196–198, 347 (1992)] and the wall reaction–diffusion transport code FACE [Smirnov et al., Fusion Sci. Technol. 71, 75 (2017)]. The two-dimensional, time-dependent, two-way coupling of the codes, in a realistic tokamak geometry, is accomplished using the Integrated Plasma Simulator framework [Elwasif et al., in 18th Euromicro Conference on Parallel, Distributed and Network-Based Processing (PDP 2010), Pisa, Italy (IEEE, 2010), pp. 419–427] for all modeled material plasma boundaries. The simulations show that dynamic plasma recycling has substantially different characteristics on the main wall and on the divertor plates. It is demonstrated that during an ELM cycle the outer wall can dynamically absorb and release a number of particles comparable to that expelled by the ELM from the core plasma, by far exceeding the dynamic retention capacity of the divertor surfaces. The resulting evolution of the edge and divertor plasma conditions during an ELM cycle is analyzed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Parallel diffusion operator for magnetized plasmas with improved spectral fidelity

Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge for describing non-grid-aligned magnetic structures in Eulerian (grid-based) simulations. Here, the present paper describes and validates a new method for parallel diffusion in magnetized plasmas based on the anti-symmetry representation [Halpern and Waltz, Phys. Plasmas 25, 060703 (2018)]. In the anti-symmetry formalism, diffusion manifests as a flow operator involving the logarithmic derivative of the transported quantity. Qualitative plane wave analysis shows that the new operator naturally yields better discrete spectral resolution compared to its conventional counterpart. Numerical simulations comparing the new method against existing finite difference methods are carried out, showing significant improvement. In particular, we find that combining anti-symmetry with finite differences in diagonally staggered grids essentially eliminates the so-called “artificial numerical diffusion” that affects conventional finite difference and finite volume methods.

Anisotropic diffusion↗

DOE OSTI2025

Challenges and approaches to interpretive modeling of boundary plasma and neutral transport in a closed, pumped divertor

An experimental discharge from the DIII-D tokamak is modeled using the SOLPS-ITER code suite and compared against measurements in the pumped and relatively closed upper divertor. Uncertainties of boundary plasma simulations are identified by attempting to match code inputs to experimental conditions, including iteratively solving transport coefficients to match upstream experimental profiles using varying quantities of core particle flux, different pumping models, and various assumptions of ion thermal transport. Simulated boundary conditions for particle injection at the core interface are shown to be relevant to the plasma solution at the divertor targets, even if upstream transport is modified so that plasma profiles are comparatively similar, although seperatrix density is not held constant. When upstream plasma profiles are matched to experimental measurements by varying diffusive transport coefficients, using either poloidally symmetric or ballooning structure, the model finds a majority of injected energy being transported radially off the computational domain, in conflict with experimental radiated power measurements and heat flux measurements at the divertor target. Imposing a maximum thermal diffusivity or radially shifting the experimental separatrix location of the fitted profiles to increase power conducted to the targets by increasing the upstream electron temperature does not significantly modify this result. Including a thermalizing plenum volume in the simulation domain is shown to maintain the experimental volumetric pumping rate without knowing the neutral energy distribution incident on the pump duct a priori. By modifying transport parameters to match different assumptions for ion temperature, downstream neutral pressure changes by more than a factor of two, suggesting that attention to ion thermal transport may be a critical parameter for simulations to accurately resolve recycling and neutral transport, particularly in a closed divertor geometry. In addition to quantifying various modeling uncertainties, this work motivates both further experimental study and modeling improvements to improve predictive capabilities.

divertor↗

DOE OSTI2022

Structural measurement of electron-phonon coupling and electronic thermal transport across a metal-semiconductor interface

Scattering of energetic charge carriers and their coupling to lattice vibrations (phonons) in dielectric materials and semiconductors are crucial processes that determine the functional limits of optoelectronics, photovoltaics, and photocatalysts. The strength of these energy exchanges is often described by the electron-phonon coupling coefficient, which is difficult to measure due to the microscopic time- and length-scales involved. In the present study, we propose an alternate means to quantify the coupling parameter along with thermal boundary resistance and electron conductivity by performing a high angular-resolution time-resolved X-ray diffraction measurement of propagating lattice deformation following laser excitation of a nanoscale, polycrystalline metal film on a semiconductor substrate. Our data present direct experimental evidence for identifying the ballistic and diffusive transport components occurring at the interface, where only the latter participates in thermal diffusion. This approach provides a robust measurement that can be applied to investigate microscopic energy transport in various solid-state materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Parallel Diffusion Coefficient of Energetic Charged Particles in the Inner Heliosphere from the Turbulent Magnetic Fields Measured by Parker Solar Probe

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ ∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ ∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ ∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ ∥ = (5.16 ± 1.22) × 10 18 r 1.17 ± 0.08 E 0.71 ± 0.02 (cm 2 s -1 ) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Mechanisms of energetic-particle transport in magnetically confined plasmas

Super-thermal ions and electrons occur in both space and fusion plasmas. Because these energetic particles (EP) have large velocities, EP orbits necessarily deviate substantially from magnetic surfaces. Orbits are described by conserved constants of motion that define topological boundaries for different orbit types. Electric and magnetic field perturbations produced by instabilities can disrupt particle orbits, causing the constants of motion to change. The statistics of the “kicks” associated with these perturbations determines the resulting cross field transport. A unifying theme of this tutorial is the importance of the perturbation’s phase at the particle’s position Θ = k • r – ωt, where k and ω are the wavevector and frequency of the perturbation, r is the EP position, and t is the time. A distinction is made between field perturbations that resonate with an aspect of the orbital motion and those that do not. Resonance occurs when the wave phase returns to its initial value in an integer multiple of an orbital period. Convective transport occurs when resonant particles experience an unvarying wave phase. Alternatively, multiple wave-particle resonances usually decorrelate the phase, resulting in diffusive transport. Large orbits increase the number of important resonances and can cause chaotic orbits even for relatively small amplitude waves. In contrast, in the case of non-resonant perturbations, orbital phase averaging reduces transport. Here, large field perturbations introduce additional effects, including nonlinear resonances at fractional values of the orbital motion. In summary, large orbits are a blessing and a curse: For non-resonant modes, orbit-averaging reduces transport but, for resonant transport, large orbits facilitate jumps across topological boundaries and enhance the number of important resonances.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Analytical modeling for redox flow battery design

Deeper market penetration of redox flow batteries requires optimization of the cell performance. Though important for optimization, detailed analytical solutions have not been developed for electrolyte flow, mass and charge transport, and reaction kinetics within redox flow batteries. To this end, here we present analytical solutions to active species concentration and over-potential based on advection-diffusion transport for ions and Bulter-Volmer model for interface reaction kinetics. The solutions were validated with results from a finite element model. These solutions were then applied to investigate the relationship between over-potential and state of charge, current density, reaction rate constant, flow velocity, diffusivity, total active species concentration, and electrode structure. Explicit formulas were identified for minimum activation over-potential and limiting current density as well as their dependence on electrolyte properties, operation conditions, and electrode structure. With our new mathematical formulas, this work provides a theoretical framework for flow battery design.

25 ENERGY STORAGE↗

DOE OSTI2023

Initial overview, description, and assessment of the DELFIC atmospheric transport model

We present an overview and description of the atmospheric transport model (ATM) component of the Defense Land Fallout Interpretative Code (DELFIC) and its revision history. In particular, we discuss the hybrid Eulerian-Lagrangian model of the DELFIC diffusive transport module (DTM), its assumptions and constraints, and assess its capability for modeling the transport, dispersion, and deposition of nuclear fallout debris. This hybrid model is an efficient transport model for the wide range of particle sizes found in nuclear fallout debris. Furthermore, we validate the 1979 version of DELFIC using the 1979 test case input and output presented in its documentation. Except for some rounding differences and exposure rate differences from the OPM, the DTM output is in very good agreement with the 1979 results. Overall, the DELFIC DTM provides a reasonable and rapid approximation to the transport and deposition of local nuclear fallout debris.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders

Superdiffusive transport with dynamical exponent z=3/2 has been firmly established at finite temperature for a class of integrable systems with a non-Abelian global symmetry G. On the inclusion of integrability-breaking perturbations, diffusive transport with z=2 is generically expected to hold in the limit of late time. Recent studies of the classical Haldane-Ishimori-Skylanin model have found that perturbations that preserve the global symmetry lead to a much slower time scale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength λ, the characteristic timescale for diffusion goes as t*∼λ−α for some α. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the canonical quantum model showing superdiffusion: the S=1/2 quantum Heisenberg chain. We consider a ladder configuration and look at various perturbations that either break or preserve the SU(2) symmetry, leading to scaling exponents consistent with those observed in one classical study [McCarthy , Phys. Rev. B 110, L180301 (2024)2469-995010.1103/PhysRevB.110.L180301]: α=2 for symmetry-breaking terms and α=6 for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with G=SU(4) and find consistent results. Finally, we consider a generalization to an SU(3) ladder and find that the α=6 scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-Abelian symmetry G.

Wang, Kevin↗

DOE OSTI2023

Integrability Breaking from Backscattering

Herein we analyze the onset of diffusive hydrodynamics in the one-dimensional hard-rod gas subject to stochastic backscattering. While this perturbation breaks integrability and leads to a crossover from ballistic to diffusive transport, it preserves infinitely many conserved quantities corresponding to even moments of the velocity distribution of the gas. In the limit of small noise, we derive the exact expressions for the diffusion and structure factor matrices, and show that they generically have off diagonal components. We find that the particle density structure factor is non-Gaussian and singular near the origin, with a return probability showing logarithmic deviations from diffusion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Diffusive hydrodynamics from integrability breaking

We describe here the crossover from generalized to conventional hydrodynamics in nearly integrable systems. Integrable systems have infinitely many conserved quantities, which spread ballistically, in general. When integrability is broken, only a few of these conserved quantities survive. The remaining conserved quantities are generically transported diffusively; we further derive a compact and general diffusion equation for these. The diffusion constant depends on the matrix elements of the integrability-breaking perturbation; for a certain class of integrability-breaking perturbations, including long-range interactions, the diffusion constant can be expressed entirely in terms of generalized hydrodynamic data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Onset of kinetic effects on Rayleigh–Taylor instability: Advective–diffusive asymmetry

In nature and engineering applications, the Rayleigh–Taylor instability (RTI) occurs over a wide range of Atwood, Reynolds, Mach, and Knudsen numbers. At low Atwood, Mach, and Knudsen numbers, the classic advective instability causes quasi-symmetric bubble and spike growth on the two sides of the interface. However, recent findings suggest that at high degrees of rarefaction, advective effects are suppressed and molecular diffusion leads to planar growth of the density fronts on either side of the interface. This study aims to investigate the flow physics of the transition from advective to diffusive behavior, focusing on the onset of the kinetic effects. Using the gas kinetic methodology, RTI is simulated over a range of Knudsen and Mach numbers in the transition regime. The simulation results reveal the various stages of transformation from advective instability to diffusive transport. For the first time, the study demonstrates the existence of a Knudsen–Mach parameter regime where the bubble side exhibits advective instability, while the other side shows a planar density front due to molecular diffusion, rather than the canonical advective spike shape. The dominance of different mechanisms on the two sides of the interface leads to the advective–diffusive asymmetry. In conclusion, the findings of this study can lead to a more comprehensive understanding of RTI over a wide range of Mach and Knudsen numbers.

42 ENGINEERING↗

DOE OSTI2025

Harnessing emergent multiple scattering resonances in a photonic glass structure for photoelectrochemical energy conversion

Light trapping nanostructures are often necessary to improve carrier collection yields in semiconductor photoelectrodes with intrinsically poor electron transport. Photonic crystal templates can generate tailorable light trapping via periodic and precise nanostructure, though this is not a scalable strategy for photoelectrochemical (PEC) applications. It is therefore critical to identify alternative mechanisms for light trapping that tolerate disorder. Light trapping in disordered media is generated by the diffusive transport caused by multiple scattering. In some cases, multiple scattering can generate resonances that resemble those observed in photonic crystals. While resonant multiple scattering is a disorder tolerant light trapping mechanism, it is unclear if the effect is sufficiently adaptable, or even useful, for PEC applications. Here, we describe a photonic omission glass, a nanostructure that can controllably induce resonances in multiple scattering transport. We characterized the emergence of these resonances after coating a disordered SiO 2 colloidal structure with a layer of TiO 2 , which functions both as dielectric contrast and as a light absorbing semiconductor. We show in finite element simulations and spectroscopic characterization that the resonant multiple scattering effect improves light trapping near the interface between the structure and the bulk electrolyte. This effect, coupled with the increased electrochemically active surface area, results in a hierarchically structured TiO 2 photoanode with orders of magnitude higher photocurrents compared to an equivalent planar photoanode for PEC reactions such as alkaline water oxidation. We show that controlling this resonant multiple scattering effect can be advantageous for improving PEC energy conversion in disordered photoelectrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Zonal magnetic fields regulate nonlinear edge-localized-mode dynamics via self-consistent force balance

Edge-localized modes (ELMs) eject intense bursts of heat and particles that threaten plasma-facing components in fusion reactors. Nonlinear full-torus BOUT++ simulations show that turbulence-driven zonal magnetic fields (ZMFs) play an essential role in nonlinear ELM evolution by maintaining self-consistent force balance. Zonal flows mitigate the initial crash through shear but do not prevent continued radial transport. When ZMFs are self-consistently included, turbulence-driven zonal currents modify the parallel current distribution and magnetic tension and are associated with a reduction of the axisymmetric (𝑛 = 0) perturbed radial force imbalance. This coincides with a transition from convective, bursty propagation to more localized, diffusive transport. Similar behavior is observed across the regimes considered, including both resistive-ballooning and peeling-ballooning cases. Finally, associated signatures, including radial electric field shear and parallel current redistribution, provide experimentally accessible diagnostics for present devices and ITER-relevant conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Cosmic ray transport in mixed magnetic fields and their role on the observed anisotropies

ABSTRACT There is a growing set of observational data demonstrating that cosmic rays exhibit small-scale anisotropies (5°–30°) with amplitude deviations lying between 0.01–0.1 per cent that of the average cosmic ray flux. A broad range of models have been proposed to explain these anisotropies ranging from finite-scale magnetic field structures to dark matter annihilation. The standard diffusion transport methods used in cosmic ray propagation do not capture the transport physics in a medium with finite-scale or coherent magnetic field structures. Here, we present a Monte Carlo transport method, applying it to a series of finite-scale magnetic field structures to determine the requirements of such fields in explaining the observed cosmic ray, small-scale anisotropies.

79 ASTRONOMY AND ASTROPHYSICS↗