Search NASA⌕ Search

SEARCH · Search NASA

Results for “BOLTZMANN EQUATION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

First principles thermal transport modeling in GaN and related materials

Gallium nitride is a wide bandgap material utilized in a variety of technologies, including high-power electronics and light-emitting diodes, partly due to its favorable thermal properties. This chapter describes modern first-principles-based modeling of phonons and lattice thermal conductivity (k) of GaN, III-nitrides and related materials. In particular, we describe the theoretical underpinnings of calculating phonon dispersions, intrinsic phonon interactions, and other lattice dynamical properties from quantum perturbation theory and density functional theory (DFT) methods. Description of how these methods are then coupled with the Peierls-Boltzmann transport (PBT) equation to determine phonon distributions and lifetimes relevant for thermal transport is given. These theoretical and numerical methods have demonstrated quantitative accuracy and predictive power for calculating pristine k and defect-limited k from first principles for a variety of materials. We present a review of the literature utilizing DFT-PBT methods to understand novel k behaviors in III-nitrides and related materials.

Lindsay, Lucas↗
DOE OSTI2022

VPIC-Kokkos

VPIC is a particle-in-cell (PIC) code that solves the Maxwell-Boltzmann system of equations and can be used to simulate a wide variety of plasmas, including those that are fully kinetic and relativistic. Utilizing the Kokkos performance-portable framework, VPIC achieves high performance on multiple CPU and GPU architectures and is adaptable to future platforms with minimal developer effort. VPIC features very powerful input decks, allowing insertion of arbitrary C++ code for custom diagnostics, boundary conditions, and additional physics models.

Luedtke, Scott↗
DOE OSTI2021

Analysis of a New Implicit Solver for a Semiconductor Model

Here, we present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann--Poisson system. The algorithm builds on recent work that incorporated a sweeping algorithm for the Vlasov--Poisson equations as part of nested inner-outer iterative solvers for the Boltzmann--Poisson equations. The new method eliminates the need for nesting and requires only one transport sweep per iteration. It arises as a new fixed-point formulation of the discretized system which we prove to be contractive for a given electric potential. We also derive an accelerator to improve the convergence rate for systems in the drift-diffusion regime. We numerically compare the efficiency of the new solver, with and without acceleration, against a recently developed nested iterative solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Dynamics of heavy quarks in strongly coupled $\mathcal{N}$ = 4 SYM plasma

We calculate the probability distribution P(k) for a heavy quark with velocity v propagating through strongly coupled N = 4 SYM plasma in the ’t Hooft limit (N c → ∞, λ = g 2 N c → ∞) at a temperature T to acquire a momentum k due to interactions with the plasma. This distribution encodes the well-known drag coefficient η D and the transverse and longitudinal momentum diffusion coefficients κ T and κ L . The jet quenching parameter $\hat{q}$ can be extracted from P(k) for v = 1. Going beyond these known Gaussian characteristics of P(k), our calculation determines all of the higher order and mixed moments to leading order in 1/$\sqrt{λ}$ for the first time. These non-Gaussian features of P(k) include qualitatively novel correlations between longitudinal energy loss and transverse momentum broadening at nonzero v. We show that all higher moments scale characteristically with an effective temperature of the boosted plasma in the heavy quark rest frame, and we demonstrate that these non-Gaussian characteristics can be sizable in magnitude and even dominant in physically relevant situations. We use these results to derive a Kolmogorov equation for the evolution of the probability distribution for the total momentum of a heavy quark that propagates through strongly coupled plasma. This evolution equation accounts for all higher order correlations between transverse momentum broadening and longitudinal energy loss, which we have calculated from first principles. It reduces to a Fokker-Planck equation when truncated to only include the effects of η D , κ T and κ L . Remarkably, while heavy quarks do not reach kinetic equilibrium with the plasma if evolved with this Fokker-Planck equation, by showing that the Boltzmann distribution is a static solution of the all-order Kolmogorov equation that we have derived we demonstrate that heavy quarks do reach kinetic equilibrium if evolved with this equation. Our results thus provide a dynamically complete framework for understanding the thermalization of a heavy quark that may be initially far from equilibrium in the strongly coupled N = 4 SYM plasma — as well as new insight into heavy quark transport and equilibration in quark-gluon plasma.

Holography and Hydrodynamics↗
DOE OSTI2022

Numerical modeling of ion transport and adsorption in porous media: A pore-scale study for capacitive deionization desalination

In this report a pore-scale model is presented to simulate the dynamic ion transport and adsorption processes in porous electrodes used for capacitive deionization (CDI). The Stokes equation governing water flow is solved using the lattice Boltzmann method and Nernst-Planck equation describing ion transport is solved using the finite volume method. The ion adsorption process is considered at the surface of carbon electrodes. After validation against analytical solutions and published results, the model is used to study the coupled water flow, ion transport and adsorption in both two-dimensional and three-dimensional porous CDI electrodes at the pore scale. The effect of electrode microstructure, electrical potential and flow velocity on the adsorption processes is quantitatively investigated, and the relative importance of various parameters is determined. The presented model can be a powerful numerical tool to quantitatively analyze ion transport and adsorption in porous electrodes, and may provide useful information for the design and optimization of CDI electrodes and operating conditions for desired desalination efficiency, water throughput and cost.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Two-dimensional turbulence in a massless fluid with a relativistic lattice Boltzmann model

We investigate a relativistic adaptation of the lattice Boltzmann method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical lattice Boltzmann method and its extension to relativistic fluid dynamics are described. The numeric formulation is evaluated using a zero-averaged stirring force introduced into the numerics to induce turbulence, and the flow characteristics produced are compared to properties of a classical turbulent hydrodynamic flow. The model can reasonably be expected to offer quantitative simulations of electron fluid flows in graphene or Kagome lattices.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Collisional stopping power of ions in warm dense matter

Here, a model for the collisional stopping of ions on free electrons in warm dense matter is developed and explored. It is based on plasma kinetic theory, but with modifications to address the warm dense matter regime. Specifically, it uses the Boltzmann-Uehling-Uhlenbeck kinetic equation to incorporate effects of Fermi degeneracy of electrons. The cross section is computed from quantum scattering of electrons and ions occurring via the potential of mean force derived from an average atom model, which incorporates effects of strong Coulomb correlations. Predictions from this model show comparable accuracy to results from time-dependent density functional theory calculations for deuterium near solid density and a temperature of several electronvolts, at a fraction of the computational cost. Further, the model captures the transition of a plasma from the classical limit to the degenerate limit, including qualitative behaviors of solid state theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Accelerated computation of lattice thermal conductivity using neural network interatomic potentials

We report with the development of the density functional theory (DFT) and ever-increasing computational capacity, an accurate prediction of lattice thermal conductivity based on the Boltzmann transport theory becomes computationally feasible, contributing to a fundamental understanding of thermal conductivity as well as a choice of the optimal materials for specific applications. However, steep costs in evaluating third-order force constants limit the theoretical investigation to crystals with high symmetry and few atoms in the unit cell. Currently, machine learning potentials are garnering attention as a computationally efficient high-fidelity model of DFT, and several studies have demonstrated that the lattice thermal conductivity could be computed accurately via the machine learning potentials. However, test materials were mostly crystals with high symmetries, and the applicability of machine learning potentials to a wide range of materials has yet to be demonstrated. Furthermore, establishing a standard training set that provides consistent accuracy and computational efficiencies across a wide range of materials would be useful. To address these issues, herein we compute lattice thermal conductivities at 300 K using neural network interatomic potentials. As test materials, we select 25 materials with diverse symmetries and a wide range of lattice thermal conductivities between 10 -1 and 10 3 Wm -1 K -1 . Among various choices of training sets, we find that molecular dynamics trajectories at 50–700 K consistently provide results at par with DFT for the test materials. In contrast to pure DFT approaches, the computational cost in the present approach is uniform over the test materials, yielding a speed gain of 2–10 folds. When a smaller reduced training set is used, the relative efficiency increases by up to ~50 folds without sacrificing accuracy significantly. The current work will broaden the application scope of machine learning potentials by establishing a robust framework for accurately computing lattice thermal conductivity with machine learning potentials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Feasibility of a multigroup Boltzmann–Fokker–Planck solution for electron beam dose calculations

Legacy nuclear-reactor Boltzmann solvers start clinical deployment as an alternative to Monte Carlo (MC) codes and Fermi–Eyges semiemprical models in radiation oncology treatment planning. Today’s certified clinical solvers are limited to photon beams. In this paper, ELECTR, a state-of-the-art multigroup electron cross sections generation module in NJOY is presented and validated against Lockwood’s calorimetric measurements, EGS-nrc and GEANT-4 for 1–20 MeV unidirectional electron beams. The nuclear-reactor DRAGON-5 solver is upgraded to access the library and solve the Boltzmann–Fokker–Planck (BFP) equation. A variety of heterogeneous radiotherapy and radiosurgery phantom configurations were used for validation purpose. Case studies include a thorax benchmark, that of a typical breast Intra-Operative Radiotherapy and a high-heterogeneity patient-like benchmark. For all beams, 100% of the water voxels satisfied the American Association of Physicists in Medicine accuracy criterion for a BFP-MC dose error below 2%. At least, 97.0% of adipose, muscle, bone, lung, tumor and breast voxels satisfied the 2% criterion. The average BFP-MC relative error was about 0.56% for all voxels, beams and materials combined. By irradiating homogeneous slabs from Z = 1 (hydrogen) to Z = 99 (einsteinium), we reported performance and defects of the CEPXS mode [US. Sandia National Lab., SAND-89-1685] in ELECTR for the entire periodic table. For all Lockwood’s benchmarks, NJOY-DRAGON dose predictions are within the experimental data precision for 98% of voxels.

42 ENGINEERING↗
DOE OSTI2022

Hybrid-gyrokinetic simulations of low- n toroidal Alfvén eigenmodes using gKPSP

Here, we report a benchmark study of toroidal Alfvén eigenmode (TAE) simulation using the hybrid-gyrokinetic code GyroKinetic Plasma Simulation Program (gKPSP). A simulation capability for energetic particles based on the gyrokinetic δf method has been newly implemented in the gKPSP code. Benchmark simulations have been performed in both circular and realistic tokamak geometries. Good agreement has been found with previously reported results, demonstrating the new capability of the gKPSP code. We have investigated the effects of the distribution function on TAE stability by examining both isotropic and anisotropic slowing-down distributions of energetic particles. The slowing-down distribution produces a higher linear growth rate than a Maxwellian distribution, while a growth rate scan with the anisotropy shows an opposite trend. This can be attributed to competition between Landau damping and the linear drive, which are correlated with the fraction of resonant passing particles and their distribution in phase space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Predicted thermophysical properties of UN, PuN, and (U,Pu)N

Molecular dynamics and density functional theory simulations are used to predict the lattice and electronic contributions of thermophysical properties for UN, PuN, and mixed (U,Pu)N systems. The properties predicted include the lattice parameter, linear thermal expansion, enthalpy, and specific heat capacity, as a function of temperature. The simulation predictions for high temperature specific heat capacity are compared against experimental measurements to understand the behavior, and why differences in the experimental measurements are observed. The influence of adding U vacancies, N interstitials, and Pu to UN is also examined. For this, a new PuN potential parameter set is developed and used with the Kocevski UN potential, enabling the dynamics of mixed (U,Pu)N systems to be studied. How defects impact the thermophysical properties is important for understanding fuel behavior under different reactor conditions, and these mechanistic predictions can be used to support fuel performance codes where data is scarce.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Electron mobility of SnO 2 from first principles

The transparent conducting oxide SnO 2 is a wide bandgap semiconductor that is easily n-type doped and widely used in various electronic and optoelectronic applications. Experimental reports of the electron mobility of this material vary widely depending on the growth conditions and doping concentrations. In this work, we calculate the electron mobility of SnO 2 from first principles to examine the temperature and doping concentration dependence and to elucidate the scattering mechanisms that limit transport. We include both electron–phonon scattering and electron-ionized impurity scattering to accurately model scattering in a doped semiconductor. Furthermore, we find a strongly anisotropic mobility that favors transport in the direction parallel to the c-axis. At room temperature and intrinsic carrier concentrations, the low-energy polar-optical phonon modes dominate scattering, while ionized-impurity scattering dominates above 10 18 cm −3 .

36 MATERIALS SCIENCE↗
DOE OSTI2025

Defect-induced phonon-resonant scattering and its influence on thermal transport of irradiated thorium-dioxide

Thermal transport in proton irradiated thorium-dioxide (ThO 2 ) is investigated. Using a combination of experiments and first-principles computational framework, the role of lattice defects on thermal conductivity is analyzed. A resonant-phonon scattering mechanism beyond the traditionally considered Rayleigh scattering is found to significantly influence low-temperature thermal transport in the presence of irradiation-induced point defects. The existence of localized phonon modes associated with irradiation-induced defects is suggested by the inability of the first-principles based thermal conductivity model—which considers only three-phonon interactions and phonon-defects scattering using the Tamura formalism—to predict the experimental results, unless a resonant scattering mechanism is included. The emergence of additional peaks in the Raman spectra in the proximity of phonon-resonant frequency provides further evidence for the existence of localized modes. Coupled with a microstructure evolution model, this analysis enables more accurate analysis for contrasting the contributions of different phonon scattering mechanisms across all irradiation doses and temperatures.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Light transport with weak angular dependence in fog

Random scattering and absorption of light by tiny particles in aerosols, like fog, reduce situational awareness and cause unacceptable down-time for critical systems or operations. Computationally efficient light transport models are desired for computational imaging to improve remote sensing capabilities in degraded optical environments. To this end, we have developed a model based on a weak angular dependence approximation to the Boltzmann or radiative transfer equation that appears to be applicable in both the moderate and highly scattering regimes, thereby covering the applicability domain of both the small angle and diffusion approximations. An analytic solution was derived and validated using experimental data acquired at the Sandia National Laboratory Fog Chamber facility. The evolution of the fog particle density and size distribution were measured and used to determine macroscopic absorption and scattering properties using Mie theory. A three-band (0.532, 1.55, and 9.68 µ m) transmissometer with lock-in amplifiers enabled changes in fog density of over an order of magnitude to be measured due to the increased transmission at higher wavelengths, covering both the moderate and highly scattering regimes. The meteorological optical range parameter is shown to be about 0.6 times the transport mean free path length, suggesting an improved physical interpretation of this parameter.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Computational Imaging for Intelligence in Highly Scattering Aerosols (Final Report)

Natural and man-made degraded visual environments pose major threats to national security. The random scattering and absorption of light by tiny particles suspended in the air reduces situational awareness and causes unacceptable down-time for critical systems and operations. To improve the situation, we have developed several approaches to interpret the information contained within scattered light to enhance sensing and imaging in scattering media. These approaches were tested at the Sandia National Laboratory Fog Chamber facility and with tabletop fog chambers. Computationally efficient light transport models were developed and leveraged for computational sensing. The models are based on a weak angular dependence approximation to the Boltzmann or radiative transfer equation that appears to be applicable in both the moderate and highly scattering regimes. After the new model was experimentally validated, statistical approaches for detection, localization, and imaging of objects hidden in fog were developed and demonstrated. A binary hypothesis test and the Neyman-Pearson lemma provided the highest theoretically possible probability of detection for a specified false alarm rate and signal-to-noise ratio. Maximum likelihood estimation allowed estimation of the fog optical properties as well as the position, size, and reflection coefficient of an object in fog. A computational dehazing approach was implemented to reduce the effects of scatter on images, making object features more readily discernible. We have developed, characterized, and deployed a new Tabletop Fog Chamber capable of repeatably generating multiple unique fog-analogues for optical testing in degraded visual environments. We characterized this chamber using both optical and microphysical techniques. In doing so we have explored the ability of droplet nucleation theory to describe the aerosols generated within the chamber, as well as Mie scattering theory to describe the attenuation of light by said aerosols, and correlated the aerosol microphysics to optical properties such as transmission and meteorological optical range (MOR). This chamber has proved highly valuable and has supported multiple efforts inclusive to and exclusive of this LDRD project to test optics in degraded visual environments. Circularly polarized light has been found to maintain its polarization state better than linearly polarized light when propagating through fog. This was demonstrated experimentally in both the visible and short-wave infrared (SWIR) by imaging targets made of different commercially available retroreflective films. It was found that active circularly polarized imaging can increase contrast and range compared to linearly polarized imaging. We have completed an initial investigation of the capability for machine learning methods to reduce the effects of light scattering when imaging through fog. Previously acquired experimental long-wave images were used to train an autoencoder denoising architecture. Overfitting was found to be a problem because of lack of variability in the object type in this data set. The lessons learned were used to collect a well labeled dataset with much more variability using the Tabletop Fog Chamber that will be available for future studies. We have developed several new sensing methods using speckle intensity correlations. First, the ability to image moving objects in fog was shown, establishing that our unique speckle imaging method can be implemented in dynamic scattering media. Second, the speckle decorrelation over time was found to be sensitive to fog composition, implying extensions to fog characterization. Third, the ability to distinguish macroscopically identical objects on a far-subwavelength scale was demonstrated, suggesting numerous applications ranging from nanoscale defect detection to security. Fourth, we have shown the capability to simultaneously image and localize hidden objects, allowing the speckle imaging method to be effective without prior object positional information. Finally, an interferometric effect was presented that illustrates a new approach for analyzing speckle intensity correlations that may lead to more effective ways to localize and image moving objects. All of these results represent significant developments that challenge the limits of the application of speckle imaging and open important application spaces. A theory was developed and simulations were performed to assess the potential transverse resolution benefit of relative motion in structured illumination for radar systems. Results for a simplified radar system model indicate that significant resolution benefits are possible using data from scanning a structured beam over the target, with the use of appropriate signal processing.

58 GEOSCIENCES↗
DOE OSTI2025

Baryon fraction from the BAO amplitude: a consistent approach to parameterizing perturbation growth

Galaxy clustering constrains the baryon fraction Omega_b/Omega_m through the amplitude of baryon acoustic oscillations and the suppression of perturbations entering the horizon before recombination. This produces a different pre-recombination distribution of baryons and dark matter. After recombination, the gravitational potential responds to both components in proportion to their mass, allowing robust measurement of the baryon fraction. This is independent of new-physics scenarios altering the recombination background (e.g. Early Dark Energy). The accuracy of such measurements does, however, depend on how baryons and CDM are modeled in the power spectrum. Previous template-based splitting relied on approximate transfer functions that neglected part of information. We present a new method that embeds an extra parameter controlling the balance between baryons and dark matter in the growth terms of the perturbation equations in the CAMB Boltzmann solver. This approach captures the baryonic suppression of CDM prior to recombination, avoids inconsistencies, and yields a clean parametrization of the baryon fraction in the linear power spectrum, separating out the simple physics of growth due to the combined matter potential. We implement this framework in an analysis pipeline using Effective Field Theory of Large-Scale Structure with HOD-informed priors and validate it against noiseless LCDM and EDE cosmologies with DESI-like errors. The new scheme achieves comparable precision to previous splitting while reducing systematic biases, providing a more robust way to baryon-fraction measurements. In combination with BBN constraints on the baryon density and Alcock-Paczynski estimates of the matter density, these results strengthen the use of baryon fraction measurements to derive a Hubble constant from energy densities, with future DESI and Euclid data expected to deliver competitive constraints.

Crespi, Andrea [U. Waterloo (main); Waterloo U., I↗