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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Finite Difference informed Random Walk solver for simulating radiation defect evolution in polycrystalline structures with strongly inhomogeneous diffusivity

Diffusivity of species and defects on grain boundaries is usually several orders of magnitude larger than that inside grains. Such strongly inhomogeneous diffusivity requires prohibitively high computational demands for modeling microstructural evolution. Here, this paper presents a highly-efficient numerical solver, combining the Finite Difference method and Random Walk model, designed for accurately modeling strongly inhomogeneous diffusion within polycrystalline structures. The proposed solver, termed Finite Difference informed Random Walk (FDiRW), integrates a customized Finite Difference (cFD) scheme tailored for fast diffusion along thin grain boundaries represented by a single-layer of nodes. Numerical experiments demonstrate that the FDiRW solver achieves an impressive efficiency gain of 1560x compared to traditional Finite Difference methods while maintaining accuracy, making it feasible for personal computer machines to handle diffusional systems with strongly inhomogeneous diffusivity across static polycrystalline microstructures. The model has been successfully applied to simulate radiation defect evolution, showcasing its scalability to engineering scales in both length and time dimensions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A GPU Accelerated Mixed‐Precision Finite Difference Informed Random Walker (FDiRW) Solver for Strongly Inhomogeneous Diffusion Problems

In nature, many complex multi‐physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU‐accelerated, mixed‐precision configuration for the FDiRW solver to maximize efficiency through GPU multi‐threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU‐accelerated mixed‐precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU‐accelerated mixed‐precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium‐sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Three-dimensional representation of late-arriving photons for detecting inhomogeneities in diffuse optical tomography

A method for rapid detection of absorbing inhomogeneity in a strongly scattering medium having the properties of a biological tissue before the image reconstruction is described based on the principles of diffuse optical tomography. The method is based on preliminary processing of a three-dimensional surface obtained from the set of time-resolved data in the Cartesian coordinate system, followed by its conformal transformation into two surfaces in the cylindrical coordinate system. A specific feature of the method is the use of late-arriving photons, scattered and diffusely transmitted through an optically turbid object. (optical tomography)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2011

Visualisation of structural inhomogeneities in strongly scattering media using the method of spatially-resolved reflectometry: Monte Carlo simulation

Two-dimensional spatial intensity distributions of diffuse scattering of near-infrared laser radiation from a strongly scattering medium, whose optical properties are close to those of skin, are obtained using Monte Carlo simulation. The medium contains a cylindrical inhomogeneity with the optical properties, close to those of blood. It is shown that stronger absorption and scattering of light by blood compared to the surrounding medium leads to the fact that the intensity of radiation diffusely reflected from the surface of the medium under study and registered at its surface has a local minimum directly above the cylindrical inhomogeneity. This specific feature makes the method of spatially-resolved reflectometry potentially applicable for imaging blood vessels and determining their sizes. It is also shown that blurring of the vessel image increases almost linearly with increasing vessel embedment depth. This relation may be used to determine the depth of embedment provided that the optical properties of the scattering media are known. The optimal position of the sources and detectors of radiation, providing the best imaging of the vessel under study, is determined. (biophotonics)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Efficient lasing in mixtures of helium and fluorine in diffuse discharges formed by runaway electrons

The parameters of stimulated lasing in diffuse discharges formed in mixtures of helium and fluorine in a strongly inhomogeneous electric field are investigated. Lasing is obtained in the visible and VUV spectral regions on the transitions of fluorine atoms and molecules. It is shown that lasing in He – F{sub 2} mixtures at a wavelength of 157 nm continues for several half-periods of the discharge current. Due to the homogeneity of the diffuse discharge, the maximum lasing efficiency of the F{sub 2} laser is 0.15 %, which corresponds to the efficiency of this type of lasers pumped by pre-ionised transverse volume discharges. (paper)

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Solute diffusion behavior during heat treatment and its impact in Sc-microalloyed Al-Cu system

Scandium (Sc) is a promising microalloying element that enhances the strength and thermal stability of aluminum (Al) alloys. However, these benefits are not fully realized in aluminum-copper (Al-Cu) systems, and corrosion resistance often declines due to the complex phase evolution and diffusion behavior of Cu and Sc. Here, to clarify this, solute diffusion behavior and Cu-Sc interaction during heat treatment (HT) were investigated using in situ synchrotron-based transmission x-ray microscopy (TXM), wide-angle x-ray scattering (WAXS), and x-ray absorption near-edge structure (XANES) spectroscopy. The results, supported by electron microscopy, reveal strong Cu-Sc bonding that significantly impedes solute diffusion, leading to inhomogeneous solute distribution and non-uniform precipitation. Moreover, the Al-Cu-Sc eutectic phase exhibits high thermal stability, resisting dissolution even near the matrix liquidus. These findings quantitatively elucidate the sluggish diffusion kinetics of Cu and Sc, which can help redesign HT schedules to improve both mechanical properties and corrosion resistance in Sc-microalloyed Al-Cu alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2015

COSMIC RAY TRANSPORT WITH MAGNETIC FOCUSING AND THE “TELEGRAPH” MODEL

Cosmic rays (CR), constrained by scattering on magnetic irregularities, are believed to propagate diffusively. However, a well-known defect of diffusive approximation, whereby some of the particles propagate unrealistically fast, has directed interest toward an alternative CR transport model based on the “telegraph” equation. Though, its derivations often lack rigor and transparency leading to inconsistent results. We apply the classic Chapman–Enskog method to the CR transport problem. We show that no “telegraph” (second order time derivative) term emerges in any order of a proper asymptotic expansion with systematically eliminated short timescales. Nevertheless, this term may formally be converted from the fourth order hyper-diffusive term of the expansion. However, both the telegraph and hyperdiffusive terms may only be important for a short relaxation period associated with either strong pitch-angle anisotropy or spatial inhomogeneity of the initial CR distribution. Beyond this period the system evolves diffusively in both cases. The term conversion, that makes the telegraph and Chapman–Enskog approaches reasonably equivalent, is possible only after this relaxation period. During this period, the telegraph solution is argued to be unphysical. Unlike the hyperdiffusion correction, it is not uniformly valid and introduces implausible singular components to the solution. These dominate the solution during the relaxation period. Because they are shown not to be inherent in the underlying scattering problem, we argue that the telegraph term is involuntarily acquired in an asymptotic reduction of the problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Highly skewed current–phase relation in superconductor–topological insulator–superconductor Josephson junctions

Three-dimensional topological insulators (TIs) in proximity with superconductors are expected to exhibit exotic phenomena, such as topological superconductivity (TSC) and Majorana-bound states (MBS), which may have applications in topological quantum computation. In superconductor–TI–superconductor Josephson junctions, the supercurrent versus the phase difference between the superconductors, referred to as the current–phase relation (CPR), reveals important information including the nature of the superconducting transport. Here, we study the induced superconductivity in gate-tunable Josephson junctions (JJs) made from topological insulator BiSbTeSe 2 with superconducting Nb electrodes. We observe highly skewed (non-sinusoidal) CPR in these junctions. The critical current, or the magnitude of the CPR, increases with decreasing temperature down to the lowest accessible temperature ( T ~ 20 mK), revealing the existence of low-energy modes in our junctions. The gate dependence shows that close to the Dirac point the CPR becomes less skewed, indicating the transport is more diffusive, most likely due to the presence of electron/hole puddles and charge inhomogeneity. Our experiments provide strong evidence that superconductivity is induced in the highly ballistic topological surface states (TSS) in our gate-tunable TI-based JJs. Furthermore, the measured CPR is in good agreement with the prediction of a model which calculates the phase-dependent eigenstate energies in our system, considering the finite width of the electrodes, as well as the TSS wave functions extending over the entire circumference of the TI.

36 MATERIALS SCIENCE↗
DOE OSTI2013

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Holography, Gravity and Condensed Matter

Over the five years of funding from this grant, I produced 26 publications. These include a book-long monograph on "Holographic Quantum Matter" that is currently in press with MIT press. The remainder were mostly published in Physical Review Letters, the Journal of High Energy Physics, Nature Physics, Classical and Quantum Gravity and Physical Review B. Over this period, the field of holography applied to condensed matter physics developed from a promising theoretical approach to a mature conceptual and practical edifice, whose ideas were realized in experiments. My own work played a central role in this development. In particular, in the final year of this grant, I co-authored two experimental papers in which ideas that I had developed in earlier years were shown to usefully describe transport in strongly correlated materials — these papers were published in Science and in the Proceedings of the National Academy of Sciences (obviously my contribution to these papers was theoretical). My theoretical work in this period developed several new directions of research that have proven to be influential. These include (i) The construction of highly inhomogeneous black hole event horizons, realizing disordered fixed points and describing new regimes of classical gravity, (ii) The conjecture of a bound on diffusivities that could underpin transport in strongly interacting media — an idea which may be proven in the near future and has turned out to be intimately connected to studies of quantum chaos in black holes and strongly correlated media, (iii) The characterization of new forms of hydrodynamic transport, e.g. with phase-disordered order parameters. These studies pertain to key open questions in our understanding of how non-quasiparticle, intrinsically strongly interacting systems can behave. In addition to the interface between holography and strongly interacting condensed matter systems, I made several advances on understanding the role of entanglement in quantum gravity. These included the first computation of holographic entanglement beyond the bulk classical limit as well understanding short distance entanglement in the emergent spacetime of the c=1 matrix quantum mechanics. The objective here is ultimately to understanding how a priori non-local degrees of freedom can re-arrange themselves quantum mechanically to support emergent local dynamics. Much of work funded by this grant involved collaboration with postdocs and graduate students, several of which were directly funded by the grant. These students have now successfully graduated to postdoctoral positions and in one case to high tech industry. The ideas developed in this work have directly fed into my current research in which I am aiming to prove fundamental bounds on entropy production and transport from quantum mechanics and statistical physics. As often, as with much of my previous work, black hole physics can be an inspiration for extreme dynamics such as fundamental bounds, but ultimately one hopes to prove them using more general tools of quantum field theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2001

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Li, Jian-Zhong↗
DOE OSTI2012

Symmetry breaking effects of density gradient on parallel momentum transport: A new {rho}{sub s}{sup *} effect

Symmetry breaking effects of density gradient on parallel momentum transport is studied via quasilinear theory. It is shown that finite {rho}{sub s}*({identical_to}{rho}{sub s}/L{sub n}), where {rho}{sub s} is ion sound radius and L{sub n} is density scale length, leads to symmetry breaking of the ion temperature gradient (ITG) eigenfunction. This broken symmetry persists even in the absence of mean poloidal (from radial electric field shear) and toroidal flows. This effect, as explained in the text, originates from the divergence of polarization particle current in the ion continuity equation. The form of the eigenfunction allows the microturbulence to generate parallel residual stress via symmetry breaking. Comparison with the E-vector x B-vector shear driven parallel residual stress, parallel polarization stress and turbulence intensity gradient driven parallel residual stress are discussed. It is shown that this {rho}{sub s}* driven parallel residual stress may become comparable to E-vector x B-vector shear driven parallel residual stress in small L{sub n} region. In the regular drift wave ordering, where {rho}{sub s}*<<1, this effect is found to be of the same order as the parallel polarization stress. This {rho}{sub s}* driven parallel residual stress can also overtake the turbulence intensity gradient driven parallel residual stress in strong density gradient region whereas the later one is dominant in the strong profile curvature region. The parallel momentum diffusivity is found to remain undisturbed by this {rho}{sub s}* effect as long as the turbulence intensity inhomogenity is not important.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Phase-field modeling of diffusional phase behaviors of solid surfaces: A case study of phase-separating Li X FePO 4 electrode particles

In this paper, we present a comprehensive phase-field model for simulating diffusion-mediated kinetic phase behaviors near the surface of a solid particle. The model incorporates elastic inhomogeneity and anisotropy, diffusion mobility anisotropy, interfacial energy anisotropy, and Cahn–Hilliard diffusion kinetics. The free energy density function is formulated based on the regular solution model taking into account the possible solute-surface interaction near the surface. The coherency strain energy is computed using the Fourier-spectral iterative-perturbation method due to the strong elastic inhomogeneity with a zero surface traction boundary condition. Employing a phase-separating Li X FePO 4 electrode particle for Li-ion batteries as a model system, we perform parametric three-dimensional computer simulations. The model permits the observation of surface phase behaviors that are different from the bulk counterpart. For instance, it reproduces the theoretically well-established surface modes of spinodal decomposition of an unstable solid solution: the surface mode of coherent spinodal decomposition and the surface-directed spinodal decomposition mode. We systematically investigate the influences of major factors on the kinetic surface phase behaviors during the diffusional process. Finally, our simulation study provides insights for tailoring the internal phase microstructure of a particle by controlling the surface phase morphology.

25 ENERGY STORAGE↗
DOE OSTI2014

How gravitational lensing helps γ-ray photons avoid γ – γ absorption

We investigate potential γ – γ absorption of γ-ray emission from blazars arising from inhomogeneities along the line of sight, beyond the diffuse Extragalactic Background Light (EBL). As plausible sources of excess γ – γ opacity, we consider (1) foreground galaxies, including cases in which this configuration leads to strong gravitational lensing, (2) individual stars within these foreground galaxies, and (3) individual stars within our own galaxy, which may act as lenses for microlensing events. We found that intervening galaxies close to the line of sight are unlikely to lead to significant excess γ – γ absorption. This opens up the prospect of detecting lensed gamma-ray blazars at energies above 10 GeV with their gamma-ray spectra effectively only affected by the EBL. The most luminous stars located either in intervening galaxies or in our galaxy provide an environment in which these gamma-rays could, in principle, be significantly absorbed. However, despite a large microlensing probability due to stars located in intervening galaxies, γ-rays avoid absorption by being deflected by the gravitational potentials of such intervening stars to projected distances ({sup i}mpact parameters{sup )} where the resulting γ – γ opacities are negligible. Thus, neither of the intervening excess photon fields considered here, provide a substantial source of excess γ – γ opacity beyond the EBL, even in the case of very close alignments between the background blazar and a foreground star or galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Substrate-Dependent Exciton Diffusion and Annihilation in Chemically Treated MoS 2 and WS 2

Atomically thin semiconductors such as monolayer MoS 2 and WS 2 exhibit nonlinear exciton–exciton annihilation at notably low excitation densities (below ~10 excitons/μm 2 in exfoliated MoS 2 ). In this work, we show that the density threshold at which annihilation occurs can be tuned by changing the underlying substrate. When the supporting substrate is changed from SiO 2 to Al 2 O 3 or SrTiO 3 , the rate constant for second-order exciton–exciton annihilation, k XX [cm 2 /s], is reduced by 1 or 2 orders of magnitude, respectively. Using transient photoluminescence microscopy, we measure the effective room-temperature exciton diffusion coefficient in bis(trifluoromethane)sulfonimide-treated MoS 2 to be in the range D = 0.03–0.06 cm 2 /s, corresponding to a diffusion length of L D = 350 nm for an exciton lifetime of τ = 18 ns, which does not depend strongly on the substrate. We discuss possible mechanisms for the observed behavior, including substrate permittivity, long-range exciton–exciton or exciton–charge interactions, defect-mediated Auger recombination, and spatially inhomogeneous exciton populations arising from substrate-induced disorder. Exciton annihilation limits the overall efficiency of 2D semiconductor devices operating at high exciton densities; the ability to tune these interactions via the underlying substrate is an important step toward more efficient optoelectronic technologies featuring atomically thin materials.

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

Probing exciton diffusion dynamics in photosynthetic supercomplexes via exciton–exciton annihilation

Photosynthesis converts solar energy into chemical energy through coordinated energy transfer between light-harvesting complexes and reaction centers (RCs). Understanding exciton motion, particularly the exciton diffusion length, is essential for optimizing energy efficiency in photosystems. In this work, we combine intensity-cycling transient absorption spectroscopy with kinetic Monte Carlo (kMC) simulation to investigate exciton motion in the C2S2 photosystem II supercomplex of spinach. Using exciton–exciton annihilation, revealed in the fifth-order response, we experimentally estimate an exciton diffusion length of 10.9 nm based on a 3D normal diffusion model, suggesting the ability of excitons to traverse the supercomplex. However, kMC simulations reveal that exciton motion is sub-diffusive because of spatial constraints and the strong RC traps. An anomalous diffusion model analysis of the experimental data yields a diffusion length of 9.7 nm, while the simulated diffusion length is 7.4 nm. The variable exciton residence time across subunits, partly influenced by their connectivity to the trap, indicates inhomogeneous annihilation probability and suggests how plants balance efficient light harvesting with photoprotection. We also explore the influence of specific assumptions in the annihilation simulation, which are challenging to access in more complex environments, such as the thylakoid membrane. Our study provides a framework for studying exciton dynamics using exciton–exciton annihilation, which can be extended to understand the light-harvesting efficiencies of larger, more complex photosynthetic assemblies.

Zhang, Kunyan (ORCID:000000026830409X)↗
NASA NTRS2004

Magnetohydrodynamic and Paramagnetic Phenomena in Electrochemistry with Diamagnetic and Ferromagnetic Millielectrodes

There are three kinds of body forces operating in electrolytic solutions in the magnetic field: the magnetohydrodynamic force F(sub B) (=i x B), the F(sub delB) force (approximately B(raised dot)gradB) and the F(sub delC) force (approximately |B|(sup 2)gradC). These three forces manifest themselves differently, depending on the experimental conditions. Thus, diamagnetic disc millielectrodes (e.g., Au) with their plane parallel to the flux density of the homogeneous magnetic field of an electromagnet yield convective behavior analogous to that observed with rotating electrodes; that response is controlled by F(sub B). The same electrodes placed in the inhomogeneous field of a strong permanent magnet yield also convective behavior that is controlled by both F(sub B) and F(sub delB). Finally, similarly sized millielectrodes made of permanent magnets (e.g., Au-coated Nd-Fe-B discs) yield diffusion-controlled behavior at conditions where a gold disc electrode shows behavior dominated by density gradient driven natural convection; in this case the predominant forces are both F(sub delB) and F(sub delC). Under open circuit conditions, ferromagnetic (i.e., magnetizable) millielectrodes (Co, Fe, Ni) dipped in corrosive solutions and placed in homogeneous magnetic fields yield mass-transfer phenomena that seem to be controlled by magnetophoresis.

Leventis, Nicholas↗