Search NASA⌕ Search

SEARCH · Search NASA

Results for “BOLTZMANN DISTRIBUTION”

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 379 records · Page 21

A Monte-Carlo method for Coulomb collisions in moderately coupled plasmas

Here, we introduce a new approach for coupling cumulative and single-scattering distributions, extending Monte Carlo methods for Coulomb collisions in weakly coupled plasmas into the moderately coupled regime. Using time steps typical of cumulative-scattering methods, we show that this approach not only recovers leading-order corrections proportional to the inverse Coulomb logarithm but also solves the full Boltzmann collision integral. A key feature of the method is its simplicity: it can be integrated into cumulative-scattering methods for weakly coupled plasmas with only ~ 10 additional lines of code.

Boltzmann collision integral↗

Interplay of effects of neutron skins in coordinate space and proton skins in momentum space on emission of hard photons in heavy-ion collisions near the Fermi energy

Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck transport model, we investigate the hard photons emission from neutron-proton bremsstrahlung in the reaction system of 208 Pb + 208 Pb around Fermi energy. Effects of neutron skins in coordinate (r) space and proton skins in momentum (k) space on the time evolution, the angular distribution, and the transverse momentum spectra of hard photons with different energies are studied. It is shown that the emission of direct hard photons is sensitive to the neutron skin, which has larger effects for more energetic hard photons. Meanwhile, we find that the proton skins have an important influence on the emission of direct hard photons, and its effect is actually even larger than that of neutron skins. Furthermore, it needs to take the effect of proton skins into account when we determine the size of neutron skins by comparing transport mode predictions of hard photons with the corresponding experimental measurements.

190 ≤ A ≤ 219↗

A multi-dimensional kinetic-based upwind solver for the Euler equations

A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.

Eppard, W. M.↗

Evolution of in-medium baryon-baryon scattering cross sections and stiffness of dense nuclear matter from Bayesian analyses of FOPI proton-flow excitation functions

Within a Bayesian statistical framework using a Gaussian process (GP) emulator for an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions with momentum-independent Skyrme interactions, we infer from the proton directed and elliptical flow in mid-central Au + Au reactions, measured at beam energies from 150 to 1200 MeV/nucleon by the FOPI Collaboration, the posterior probability distribution functions (PDFs) of the in-medium baryon-baryon scattering cross section (BBSCS) modification factor 𝑋 (with respect to their free-space values) and the stiffness parameter 𝐾 of dense nuclear matter. Here, we find that the most probable value of 𝑋 evolves from around 0.7 to 1.0 as the beam energy 𝐸 beam /𝐴 increases. On the other hand, the posterior PDF⁡(𝐾) may have dual peaks having roughly the same height or extended shoulders at high 𝐾 values. More quantitatively, the posterior PDF⁡(𝐾) changes from having a major peak around 220 MeV, characterizing a soft EOS in the reaction at 𝐸 beam /𝐴 = 150 MeV, to one that peaks around 320 MeV, indicating a stiff EOS in the reactions at 𝐸 beam /𝐴 higher than about 600 MeV. The transition from soft to stiff happens in mid-central Au + Au reactions at beam energies around 250 MeV/nucleon in which 𝐾 = 220 MeV and 𝐾 = 320 MeV are approximately equally probable. Altogether, the FOPI proton-flow excitation function data indicate a gradual hardening of hot and dense nuclear matter as its density and temperature increase in reactions with higher beam energies.

nuclear matter↗

Lattice Boltzmann model for conjugate heat transfer across thin walls

A lattice Boltzmann (LB) model with an efficient and accurate interface treatment for conjugate heat transfer across a thin wall between two different media is developed. The proposed interface treatment avoids fine meshing and computation within the thin layer; instead, the energy balance within the thin layer and the conjugate conditions on each interface are utilized to construct explicit updating schemes for the microscopic distribution functions of the LB model at the interior lattice nodes of the two media next to the thin layer. The proposed interface schemes reduce to the standard interface scheme for conjugate conditions in the literature in the limit of zero thickness of the thin layer, and thus it can be considered a more general interface treatment. A simplified version of the interface treatment is also proposed when the heat flux variation along the tangential direction of the thin layer is negligible. Three representative numerical tests are conducted to verify the applicability and accuracy of the proposed interface schemes. The results demonstrate that the intrinsic second-order accuracy of the LB model is preserved with the proposed interface schemes for thin layers with constant tangential fluxes, while for general situations with varying tangential fluxes, first-order accuracy is obtained. Finally, this interface treatment within the LB framework is attractive in conjugate heat transfer modeling involving thin layers for its simplicity, accuracy, and significant reduction in computational resources.

42 ENGINEERING↗

Radiative transfer in stars by feebly interacting bosons

Starting from first principles, we study radiative transfer by new feebly-interacting bosons (FIBs) such as axions, axion-like particles (ALPs), dark photons, and others. Our key simplification is to include only boson emission or absorption (including decay), but not scattering between different modes of the radiation field. Based on a given distribution of temperature and FIB absorption rate in a star, we derive explicit volume-integral expressions for the boson luminosity, reaching from the free-streaming to the strong-trapping limit. The latter is seen explicitly to correspond to quasi-thermal emission from a “FIB sphere” according to the Stefan-Boltzmann law. Our results supersede expressions and approximations found in the recent literature on FIB emission from a supernova core and, for radiatively unstable FIBs, provide explicit expressions for the nonlocal (“ballistic”) transfer of energy recently discussed in horizontal-branch stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Shock-wave structure in a partially ionized gas

The structure of a steady plane shock in a partially ionized gas has been investigated using the Boltzmann equation with a kinetic model as the governing equation and the discrete ordinate method as a tool. The effects of the electric field induced by the charge separation on the shock structure have also been studied. Although the three species of an ionized gas travel with approximately the same macroscopic velocity, the individual distribution functions are found to be very different. In a strong shock the atom distribution function may have double peaks, while the ion distribution function has only one peak. Electrons are heated up much earlier than ions and atoms in a partially ionized gas. Because the interactions of electrons with atoms and with ions are different, the ion temperature can be different from the atom temperature.

Lu, C. S.↗

Preshock region acceleration of implanted cometary H(+) and O(+)

A self-consistent, three-fluid model of plasma transport and implanted ion acceleration in the unshocked solar wind is presented. The solar wind plasma is depleted by charge exchange with the expanding cometary exosphere, while implanted protons and heavy ions are produced by photoionization and charge transfer and lost by charge exchange. A generalized transport equation describing convection, adiabatic and diffusive velocity change, and the appropriate production terms is used to describe the evolution of the two cometary ion components, while the moments of the Boltzmann equation are used to calculate the solar wind density and pressure. The flow velocity is obtained self-consistently by combining the conservation equations of the three ion species. The results imply that second-order Fermi acceleration can explain the implanted spectra observed in the unshocked solar wind. Comparison of measured and calculated distribution indicates that spatial diffusion of implanted ions probably plays an important role in forming the energetic particle environment in the shock vicinity.

Gombosi, Tamas I.↗

High-speed leading edge problem.

The sharp leading edge problem has been studied for both monatomic and diatomic gases using the Boltzmann equation with the Bhatnagar-Gross-Krook type models as the governing equation and the discrete ordinate method with a closed-boundary value approach as a tool. Plate length relative to the freestream mean free path is taken to be 52. The gas-surface interaction law is assumed to be diffuse reflection. The local distribution functions of molecular velocities and internal energies (for the diatomic gas) for the entire flowfield have been calculated for a freestream Mach number of 6.1. Comparisons are made between the calculated results and experimental data.

Huang, A. B.↗

Rarefied gas dynamics; Proceedings of the Eighth International Symposium, Stanford University, Stanford, Calif., July 10-14, 1972

Recent studies in the theory of rarefied gases (kinetic theory, shock structure, molecular forces and interactions, evaporation and condensation, expansions and jets, flow past bodies, gas-solid interactions) are presented along with descriptions of numerous experiments in these areas. Some of the topics covered include: singular limits of solutions of Boltzmann's equations, the Boltzmann and Klimontovich formalisms with reference to turbulent resolution, higher-order kinetic theory for the Lorentz gas, intermolecular potentials from shock structure experiments, cooling of particles in aerosol beams, hypersonic-subsonic transition in spherically symmetric expanding flows, absolute velocity measurements in a rarefied gas flow by an ion time-of-flight technique, the product distribution of gas-solid reactions from absolute rate theory, and relaxation of a gas with internal degrees of freedom. Individual items are announced in this issue.

Karamcheti, K.↗

Multi-GPU porting of a phase-change cascaded lattice Boltzmann method for three-dimensional pool boiling simulations

The Lattice Boltzmann method (LBM) has proven effective in simulating phase-change phenomena, such as melting, solidification, evaporation, and boiling. In this work, we develop a highly parallelized multi-GPU implementation of LBM for three-dimensional pool boiling simulations. The code is based on the OpenACC programming model, which enables the code to be deployed efficiently on multi-core CPUs, GPUs, and potentially other accelerators, without the need for architecture-specific rewrites. To support large-scale simulations, the domain is decomposed and distributed across multiple compute nodes using MPI. We demonstrate that the code exhibits excellent scaling properties, with ideal strong-scaling running with up to 256 GPUs on the MareNostrum5 cluster.

97 MATHEMATICS AND COMPUTING↗

Coupled Boltzmann transport equations of heavy quarks and quarkonia in quark-gluon plasma

We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombination drives the system to equilibrium. We then apply our framework to study bottomonium production in heavy-ion collisions. We include Υ(1S), Υ(2S), Υ(3S), χb (1P) and χb (2P) in the framework and take feed-down contributions during the hadronic gas stage into account. Cold nuclear matter effects are included by using nuclear parton distribution functions for the initial primordial heavy flavor production. A calibrated 2 + 1 dimensional viscous hydrodynamics is used to describe the bulk QCD medium. We calculate both the nuclear modification factor R AA of all bottomonia states and the azimuthal angular anisotropy coefficient v 2 of the Υ(1S) state and find that our results agree reasonably with experimental measurements. Our calculations indicate that correlated cross-talk recombination is an important production mechanism of bottomonium in current heavy-ion experiments. The importance of correlated recombination can be tested experimentally by measuring the ratio of R AA ( χb (1P)) and R AA (Υ(2S)).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗

DED Additively Manufactured HEAs Optimized via Parametric Study of Functionally Graded Materials

Complex concentrated alloys (CCAs) are a system of alloys composition of nearly equiatomic elements, creating a state of high configurational entropy in the material. These alloys are of interest for various industrial applications due to their high strength and hardness, wide operational temperature range, creep and diffusion resistance, and radiation resistance. In the current work CoCrFeNi-base CCAs are synthesize by combining three commonly industrial alloys: IN718, SS316L, and 70Co30Cr (commercially known as Stellite 21), in-situ utilizing directed energy deposition (DED) additive manufacturing (AM). One bulk specimen is fabricated with a 1:1:1 ratio of IN718, SS316L, and 70Co30Cr where IN718 is a source of nickel and chrome, SS316 is a source of iron and chrome, and 70Co30Cr is a source of cobalt and supplemental chrome. Additionally, a functionally graded material (FGM) of the identified CCA system from SS316 was fabricated with 10 layers, where the initial five layers are the base material of SS316L and graded by steps of 20% to transition to the CCA system. Overall build quality, microstructure, compositional distribution, phases analysis, and microhardness were studied by laser optical microscopy, scanning election microscopy (SEM), energy dispersive spectroscopy (EDS), X-ray diffraction analysis (XRD), and Vickers microhardness techniques. Overall build quality showed a successful bulk build with acceptable density, however unmelted particles are observed in the as-built alloy. Compositional results show that the system meets the Boltzmann’s hypothesis definition of an HEA, and that an FCC CCA was produced with increased hardness, small grain size, and superior hardness properties to the SS316L substrate. While initial XRD results show predominately FCC structure, EDS analysis of interdendritic regions show the existence of Laves phases in the material. The fabrication of an FGM CCA allowed for potential screening of additional alloy mixes which may be of interest to explore in future research, and the resulting composition is compared to predicted values. This novel method of CCA fabrication results in substantial cost savings of these CCA systems over traditional methods.

36 MATERIALS SCIENCE↗

Moments of the Boltzmann collision operator for Coulomb interactions

Exact moments of the Boltzmann collision operator are calculated in the irreducible Hermitian moment expansion written in terms of the random-velocity variable of each species. The formulas are presented in closed, algebraic form and can be straightforwardly implemented in computer algebra systems. They are valid for two arbitrary masses, temperatures, and flow velocities, and hence include all other existing results derived for distribution functions expanded with respect to reference states of one temperature and flow velocity. In comparison, the Landau collisional moments are good approximations for large Coulomb logarithm and small relative flow velocity, but they fail to predict the correct behavior of most collisional moments for large relative flow even for weakly coupled plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The Concept of Negative Capacitance in Ionically Conductive Van der Waals Ferroelectrics

Negative capacitance (NC) provides a path to overcome the Boltzmann limit that dictates operating voltages in transistors and, therefore, may open up a path to the challenging proposition of lowering energy consumption and waste heat in nanoelectronic integrated circuits. Typically, NC effects in ferroelectric materials are based on either stabilizing a zero-polarization state or slowing down ferroelectric switching in order to access NC regimes of the free-energy distribution. Here, a fundamentally different mechanism for NC, based on CuInP 2 S 6 , a van der Waals layered ferrielectric, is demonstrated. Using density functional theory and piezo-response force microscopy, it is shown that an unusual combination of high Cu-ion mobility and its crucial role in determining polarization magnitude and orientation (P) leads to a negative slope of the polarization versus the electric field E, dP/dE < 0, which is a requirement for NC. This mechanism for NC is likely to occur in a wide class of materials, offering new possibilities for NC-based devices. Finally, the nanoscale demonstration of this mechanism can be extended to the device-level by increasing the regions of homogeneous polarization and polarization switching, for example, through strain engineering and carefully selected electric field pulses.

36 MATERIALS SCIENCE↗

Optimizing temperature distributions for training neural quantum states using parallel tempering

Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.

Neural network simulations↗

Kinetics of metastable atoms and non-Maxwellian electrons in two-temperature plasmas

Numerical and analytical solutions of the electron Boltzmann equation in two-temperature steady-state helium plasma are studied in a broad range of conditions T(a) = 5,000-20,000 K, T(e) = 10,000-20,000 K; N(a) = 10 to the 10th - 10 to the 18th per cu cm. The WKB analytical solution is found to be satisfactory in most situations. The deviation of the electron distribution from Maxwellian and a possibility of raising of the tail of the distribution in presence of sources of fast electrons is also discussed.

Kunc, J. A.↗